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Prediction of Calcite Cement Distribution in Shallow Marine Sandstone Reservoirs using Seismic Data
Nils Erik Bakke
August 1996
A Dissertation for the Partial Fulfillment of Requirements for the Degree of Doktor Ingeniqr
Department of Petroleum Engineering and Applied Geophysics Norwegian University of Science and Technology
wmmm of iwe document is u Acknowledgments
I am grateful to my advisers Bj0rn Ursin and Alister MacDonald for their continuous support and guidance during my study. I would like to thank Dr. E. Roaldset, Dr. M. Tygel, and Dr. P.A. Bjprkum for serving on my graduate committee. Financial support from Mobil Exploration Norway Inc. is acknowledged. Thanks to Eivind Berg, Terje Dahl, and Alister MacDonald for arranging my stay at Statoil Research Center. I am grateful to many people in the Reservoir, Geophysical, Geological Departments, and I will specially mention Arve Naess, John Inge Berg, Bjorn Olav Ekren, and Donatella Mellere. At the Norwegian University of Science and Technology I would like to thank my good friend Egil Tjaland, and the former students Huasheng Zhao and Eilif Tom Ertresvag, together with my fellow graduate students. The partners in the Troll license group: Statoil, Norsk Hydro as, Saga Petroleum as, A/S Norske Shell, and Total Norge A.S., have been so kind to let me use and publish data from the Troll Field. British Petroleum, Jason Geosystems B.V., and 0degaard & Danneskiold- Samspe have given me valuable insight in their software packages and assis tance in the use of them. Most of all I am indebted to Marian and Eivind along with the rest of my family for their patience, love and encouragement.
Trondheim, August 1996 /0s Nils Erik Bakke
1 ii DISCLAIMER
Portions of tins document may be illegible in electronic image products. Images are produced from the best available original document. Contents
1 Presentation of the thesis 1 1.1 Introduction ...... 1 1.2 Organization and summary of the thesis...... 2 1.3 Concluding remarks ...... 8
2 Calcite cementation in shallow marine sandstones 9 2.1 Reservoir technical aspects ...... 9 2.2 The conceptual model ...... 12 2.2.1 Possible sources of calcite cement ...... 12 2.2.2 Stable isotopic analyses...... 14 2.2.3 Formation of calcite cemented layers - a growth model 16 2.2.4 Calcite cemented zones in a sequence stratigraphic context ...... 20 2.3 Conclusions ...... 22
3 The Troll Field: geology and petrophysics 25 3.1 Introduction ...... 25 3.2 The reservoir in the TOGI area...... 28 3.2.1 Sequence stratigraphic zonation of the Troll East ... 28 3.3 Seismic parameters...... 29 3.4 Conclusions ...... 31
4 Analyses of tuning amplitudes from stacks of thin calcite cemented layers 35 4.1 Introduction ...... 35 4.2 Seismic modelling ...... 37 4.3 Seismic processing ...... 39
iii 4.4 Results...... 43 4.5 Analyses...... 48 4.6 Discussion ...... 52
5 Prediction of lateral variation in calcite cementation using zero-offset tuning amplitudes 53 5.1 Introduction ...... 53 5.2 Seismic modelling ...... 53 5.3 Regression analyses ...... 57 5.4 Synthetic data example ...... 60 5.4.1 Prediction of calcite cementation ...... 61 5.4.2 Complicating factors ...... 66 5.5 Real data example...... 73 5.5.1 The 2D seismic dataset ...... 73 5.5.2 Prediction of calcite cementation ...... 76 5.6 Conclusions ...... 80
6 Application of seismic data for constraining a stochastic model of calcite cementation - synthetic Test 83 6.1 Introduction ...... 83 6.2 Stochastic model for calcite cementation ...... 84 6.3 Stochastic modelling constrained bysequence stratigraphy . . 85 6.4 The synthetic “true earth model ”...... 88 6.5 Seismic modelling ...... 91 6.6 Inversion of synthetic seismic data ...... 94 6.7 Stochastic modelling constrained byseismic data ...... 99 6.8 Conclusions ...... 105
7 Application of seismic data for constraining a stochastic model of calcite cementation - real test 109 7.1 Introduction ...... 109 7.2 The 3D seismic dataset ...... 109 7.3 Well calibration ...... Ill 7.4 Sparse spike inversion ...... 119 7.5 Depth conversion ...... 123 7.6 Constrained modelling of calcite cemented barriers...... 125 7.7 Conclusions ...... 132
IV A Thin-layer AVO effects 133 A.l Abstract...... 133 A.2 Introduction ...... 133 A.3 Seismic response from a thin layer ...... 135 A.4 Synthetic data examples...... 137 A.4.1 Seismic modelling ...... 137 A.4.2 Data processing for AVO analysis...... 138 A.4.3 High contrast layer...... 139 A.4.4 Low contrast layer...... 146 A.5 Real data ...... 148 A.6 Conclusions ...... 149 Appendix A-l: Geometrical spreading correction ...... 151 Appendix A-2: Travel-time difference ...... 151 Appendix A-3: Comparison with previous work ...... 152
References 155 vi Chapter 1
Presentation of the thesis
1.1 Introduction
Characterization of reservoir heterogeneities is important to optimize well locations and production from any hydrocarbon or ground-water reservoir. Different kinds of reservoir heterogeneities may be important depending on the fluid type, the origin of the reservoir rocks, and their diagenetic and tectonic history. In recent years, a number of new methods have been increasingly applied to subsurface reservoir description. Amongst these methods are:
• stochastic heterogeneity modelling;
• sequence stratigraphy; and
• seismic lithology prediction.
Stochastic modelling has gained popularity because underlying statistical models can generate more realistic reservoir descriptions than those achieved by conventional (smooth) interpolation of zonal averages. The application of high resolution sequence stratigraphy is becoming standard as it provides a more robust methodology for well correlation and reservoir zonation. Al though seismic lithology prediction at a scale relevant for reservoir manage ment is still in its infancy, initial results are promising and seismic lithology prediction has an enormous potential as it, in contrast to other methods, provides data from direct measurement of the inter-well volume.
1 2 Chapter 1. Presentation of the thesis
Although there is little doubt that the three methods outlined have con tribution to improved reservoir description, a recurring problem is that the methods are often used in parallel. It is not uncommon that three parallel studies (stochastic modelling, sequence stratigraphy and seismic lithology) are initiated. Each study produces a reservoir description which may often be in conflict with the results from other studies. I believe that the most significant advances in reservoir description will be achieved through integra tion rather than trough advances in one particular method. In addition to capturing realistic geometries, the use of stochastic models is central to the issue of integration, as genuine integration cannot easily be achieved using deterministic methods. Calcite cemented zones are one type of heterogeneities which are impor tant flow barriers in a large number of hydrocarbon reservoirs. In this thesis I will exclusively consider calcite cementation in reservoirs deposited in a shallow marine environment. The methods derived in this work, however, may be applicable to characterize other reservoir heterogeneities. The cal cite cemented layers occur as small nodules and field-wide barriers. They are generally impermeable and the degree of lateral continuity of these zones has important implications for the production from these fields. The goal of my dr.ing thesis was first to find out whether calcite ce mented layers can be detected by reflection seismic data and secondly, to find methods for how seismic data in combination with other methods can be used to predict lateral variation in calcite cementation in shallow marine sandstone reservoirs. To achieve these goals I have used the three methods for reservoir description mentioned earlier. Focus is on the geophysical as pects, and sequence stratigraphy and stochastic modelling aspects are only covered superficially.
1.2 Organization and summary of the thesis
This work is organized in six chapters and one appendix in addition to this introductory chapter. The chapters are to some degree self-contained, but do also depend on each others. Cross-references to earlier and coming chapters occur. The chapters should therefore be read sequentially. During the course of my study, I have been to several conferences where portions of my thesis have been presented and can be found in published abstracts. Organization and summary of the thesis 3
Summary of Chapter 2
Chapter 2 is devoted to reservoir technical and geological aspects of calcite cementation in shallow marine sandstones. This is mainly a literature study, but important theoretical assumptions for the occurrence of calcite cemented zones are drawn from earlier published work. Depending on the origin of the constituents of the calcite cement, in ternal and external sources relative to the presently cemented rock, may be distinguished. For internal sources transportation of the ions may take place by diffusion, whereas for external sources some sort of fluid flow has to be involved. Stable isotopic and trace element analyses may be used to identify and distinguish between different sources of calcite cements. Bjprkum and Walderhaug (1990b) presented a growth model for the for mation of calcite cementation in shallow marine sandstones. In this model calcite cementation is sourced by dissolution of carbonate fossils within the sandstone. Calcite concretions form by nucleation and diffusion controlled growth of calcite cement. If sufficient carbonate source material is available continuous calcite layers may form by merging of strata-bound concretions. This implies that the geometry of calcite cemented layers is dependent on the geometry of the shell lag layers and that sequence stratigraphic concepts may be used to predict the lateral extent of the cemented layers. The most continuous cemented horizons occur as networks above and around flood ing surfaces and sequence boundaries. Sequence stratigraphic interpretation of wells in the Troll Field which form part of the database for this work, coincides with these observations.
Summary of Chapter 3
In this thesis well data and seismic data from a small part of the Troll Field, known as TOGI (Troll Oseberg Gas Injection) have been analysed. Closely spaced wells and good quality seismic data makes this area well suited for an integrated study like this. Chapter 3 gives an overview of the geology of the field and a sequence stratigraphic zonation of the TOGI area is presented. The reservoir in the Troll Field consists of two types of sandstones: mica ceous and clean quartz sandstones. These are interpreted to be transgressive and highstand systems tracts respectively, deposited in a shoreline-attached tidally-influenced shelf environment. Although these sandstones are of dif ferent reservoir qualities, the thin calcite cemented zones are thought to be 4 Chapter 1. Presentation of the thesis the most important reservoir heterogeneity in the Troll Field. Calcite ce mented intervals account for 6.5% of the reservoir succession in the area of the Troll Field analysed in this work. For seismic modelling purposes realistic velocity and density for the sub surface are crucial. Correcting wire-line log measurements for layer-thickness effects reveal thatconstant velocities and densities for the cemented zones in the Troll Field may be assumed. Clear vertical velocity and density trends were also found in the non-cemented sandstones in the field. To understand the seismic reflections from the reservoir succession in the Troll Field it is important to consider both non-cemented and calcite cemented sandstone intervals.
Summary of Chapter 4 • Presentation at conference: Bakke, N.E. and Ertresvag, E.T. (1995). Analyses of tuning ampli tudes from ID calcite geometries, 2nd Lofoten Seminar, Nyvagar, Nor way, August 17-18. Expanded Abstracts.
Calcite cemented beds are commonly very thin (0.1 m to 2 m in the Troll Field) compared with the wavelengths in the pulse used in the reflec tion seismology. These beds are however associated with very high velocities and densities and in the Troll Field, their acoustic impedance values are al most four times as high as the acoustic impedance of the gas-saturated sand stones. Due to the high contrasts in elastic properties, the calcite cemented beds may be detected even if their thicknesses are below vertical seismic res olution. For instance the amplitude of the composite seismic reflection from a 2 m thick calcite cemented bed will be 25-30% of the reflected amplitude from one single interface between gas-saturated sandstone and calcite ce mented sandstone. The stacking of calcite cemented beds which often occur in association with sequence stratigraphic bounding surfaces, may produce significant seismic reflections. Analyses of zero-offset synthetic seismic data show that the tuning am plitude caused by closely spaced high impedance layers are related to the vertical thickness of the stack of layers and how much high impedance ma terial there is in the stack. Depending on the layer thickness, differential moveout may cause an amplitude increase or decrease with offset. For stack sizes and layer thicknesses investigated in this work, offset dependent tuning Organization and summary of the thesis 5
curves show only slight variation with increasing offset. For the purpose of using seismic amplitudes to predict lateral variation in calcite cementation in the reservoir zero-offset (or stack) seismic data are best suited.
Summary of Chapter 5 • Presentation at conference: Bakke, N.E., Ertresvag, E.T. and Ursin B. (1996). Analysis of the seismic response from thin calcite cemented layers, 58th Conference and Technical Exhibition of the EAGE, Amsterdam, the Netherlands, June 3-7, Expanded Abstract C051.
In Chapter 4 the zero-offset tuning amplitude was shown to be dependent on calcite content in the stack and vertical stack size. In Chapter 5 these relationships are quantified using a regression analysis based on extensive seismic modelling. To get a second independent measurement which may be related to the same two variables, the length of the composite reflected pulse has also been analysed. The empirical relationships have been applied on synthetic seismic data based on a model with realistic geometries of calcite cemented beds as well as real seismic data from the TOGI area. The results are promising, but the work has revealed several complicating factors for this prediction method. Interference from closely spaced stacks of calcite cemented layers makes the use of pulse length measurements specially problematic. This can be overcome by assuming constant stack sizes. For small stack sizes and low calcite content this is a good assumption. In Chapter 6 and 7 seismic in version has been applied to reduce the problem of this kind of interference. Vertical distribution of calcite cemented beds will also affect the seismic response from stacks of these layers. Depending on the spacing between cemented layers these effects can lead to higher or lower calcite content pre diction results. Vertical and lateral variation in velocities and densities for non-cemented sandstones will cause seismic amplitude variations which are of the same order of the variations caused by calcite cemented beds. The work presented in this chapter has revealed that the description of calcite cemented beds is not a deterministic problem. Seismic data contain valuable information which can say something about the probability of ce mentation. In Chapters 6 and 7 seismic inversion and sequence stratigraphy 6 Chapter 1. Presentation of the thesis interpretation of well data have been combined in a stochastic modelling framework to produce models of calcite cemented barriers.
Summary of Chapter 6 and 7 • Presentation at conference: Bakke, N.E., Ertresvag, E.T., Ncess, A., MacDonald, A.C., and Fait, L.M. (1996). Application of seismic data and sequence stratigraphy for constraining a stochastic model of calcite cementation, NPF/SPE European 3-D Reservoir Modelling Conference, Stavanger, Norway, April 16-17, Proceedings SPE35487.
In Chapters 6 and 7 a probabilistic approach to the description of ge ometrical distribution of calcite cemented beds is presented. Geometrical data from outcrop analogue studies, sequence stratigraphy, and seismic data are integrated within a stochastic modelling framework. Analogue studies of field outcrops are used to define the a priori geometry of calcite cemented beds. Sequence stratigraphy interpretation along with well data are used to define a prori vertical trends in the distribution of calcite cement, and to guide seismic inversion. Seismic data are used to define lateral variations in cementation around sequence stratigraphic bounding surfaces. The inte gration of the three techniques produces models which are constrained by a maximum amount of information. Chapter 6 describes a test on a synthetic seismic data-set based on a model with realistic acoustic impedance variations in thenon-cemented sand stones and realistic geometries of calcite cemented sandstones. Working with synthetic data has made it possible to test procedures for extracting informa tion from seismic data and for using seismic data to condition the stochastic model. Interpreted seismic horizons are used to constrain the seismic inver sion. Due to interference of reflections from stacks of calcite cemented beds and from the non-cemented background lithologies, intra-reservoir seismic interpretation is difficult. Conditional probability functions for facies (ce mented or non-cemented sandstones) given the inverted acoustic impedance, reveal that seismic data can be used in a probabilistic framework for predict ing distributions of calcite cemented beds within the Troll Field reservoir. Using stochastic simulation constrained by both sequence stratigraphy and seismic data, very similar geometries to the initial model have been repro duced. Organization and summary of the thesis 7
In Chapter 7 this probabilistic approach has been tested on real seismic data from the Troll Field. To obtain good well calibration of the seismic data, velocities and densities of the calcite cemented beds have to be cor rected for layer-thickness effects. A good estimate of the seismic wavelet is important to obtain good well calibrations and good seismic inversion results. For depth conversion purposes a velocity field has been obtained integrat ing well information with the inverted acoustic impedance field. Stochastic realisations of geometries of calcite cemented beds in the TOGI area in the Troll Field constrained by a maximum amount of information are produced. These may be used to assist reservoir management in the development of the Troll Field.
Summary of Appendix A: Thin-layer AVO effects • Presentation at conference: Bakke, N.E. and Ursin, B. (1995). Thin-bed AVO effects, 57th Con ference and Technical Exhibition of the EAEG, Glasgow, Scotland, May 29 - June 2, Expanded Abstract D010. This chapter has also been submitted for review to the European Association of Geoscien tists & Engineers.
Thin-layer AVO effects have been analysed for a medium consisting of two closely spaced interfaces. Analyses of tuning amplitudes in Chapter 4 revealed there is little to gain from working in the offset domain for the purpose of predicting geometries of calcite cemented beds. The work on thin-layer AVO effects has therefore been included as an appendix. As the layer-thickness decreases the shape of the zero-offset composite reflected pulse from a thin bed approaches the derivative of the incident pulse. For layers thinner than half of the tuning thickness, the zero-offset amplitude is scaled with a factor equal to twice the time-thickness of the thin layer. Offset dependent tuning correction formulas have been derived and tested on synthetic and real seismic data. These correction factors may be applied before conventional AVO analysis is performed. Chapter 1. Presentation of the thesis
1.3 Concluding remarks
The work presented in this thesis has shown that it is possible to utilize seismic data in the description of the geometrical distribution of calcite ce mented beds, but that this has to be done in a probabilistic framework. Although calcite cemented barriers within shallow marine sandstones are generally very thin, they have very high velocities and densities compared to the gas saturated sandstones. In this context it is important to distin guish between what is resolvable and what is detectable by the seismic tool. A 2 m thick calcite cemented layer is in thickness far below the vertical limit of seismic resolution, but the amplitude of the composite seismic re sponse may be as high as 30% of the reflected amplitude from an interface between non-cemented and cemented sandstone. Applying knowledge from field outcrop analogues, and sequence stratigraphic concepts in interpreta tion of well data important assumptions which relate calcite cemented layers to bounding surfaces have been made. In particular, the concentration of several, thin calcite cemented beds around sequence stratigraphic bounding surfaces can be expected to produce a measurable seismic response under re alistic conditions. Different distributions and thickness of beds within stacks can produce identical seismic responses. This non-uniqueness implies that a stochastic modelling approach should be followed. At subcritical angles, offset dependent tuning effects are small and con ventional seismic stacked data are suitable for prediction of calcite cement distribution. Where stacks of cemented beds are well separated and non interfering, it is possible to use amplitude information directly to predict lateral variation in the degree of cementation. Where stacks are more closely spaced interference complicates the prediction problem. In such cases seis mic inversion, tightly constrained by sequence stratigraphic and seismic in terpretations, is required to extract meaningful information on distribution of calcite cemented layers. Closely spaced wells and good quality seismic data makes the TOGI area of the Troll Field well suited to test the integration of different methods for predicting geometries of cemented beds. Analogue outcrop studies, sequence stratigraphic interpretation of well data, and seismic inversion are combined in a stochastic modelling framework to generate realisations of calcite ce mented barriers constrained by a maximum amount of information. The integrated modelling procedure can be used to assist the reservoir manage ment of shallow marine reservoir containing calcite cemented barriers. Chapter 2
Calcite cementation in shallow marine sandstones
2.1 Reservoir technical aspects
Calcite cemented sandstone layers are common heterogeneities in shallow marine sandstone reservoirs. The cemented layers occur as small nodules, as laterally discontinuous baffles, and as field-wide barriers. They are generally impermeable and the degree of lateral continuity of these zones has impor tant implications for the production from these fields. Their effect depends on the reservoir fluid type, cement geometry, their orientation, and the field development program. Regardless of fluid type, concretions probably have only local influence on fluid flow, whereas continuous calcite cemented layers can act as permeability barriers. Since gas viscosity is orders of magnitude lower than the oil viscosity, discontinuous layers will probably have a less severe effect on gas drainage than on production from an oil reservoir. Even small holes in the cemented layers or offsets by small faults, are thought to increase effective permeability for gas drainage considerably. Kantorowicz et al. (1987) evaluated the effect of calcite cemented hori zons on production from vertical wells in an oil reservoir, as shown in Fig ure 2.1. They found that dividing the reservoir into compartments may be beneficial or detrimental to the production. The impermeable zones may reduce the possibility for water influx and gas-coning, but may on the other hand, make drainage difficult. Gibbons et al. (1993) analysed production and injection from horizontal
9 10 Chapter 2. Calcite cementation
Injector Producer
Injector Producer
(b)
Figure 2.1: The effect of calcite cemented horizons on production from ver tical wells, (a) Cemented sand hindering development by isolating 20% of the oil zone in a separate accumulation. Accelerated water-coning is also likely as a result of the orientation of the tight streak, (b) Cemented sand aiding development by reducing possibility of bottom-water coning into the larger upper oil accumulation. However, note reduced communication be tween the oil- and water-saturated parts of the reservoir. From Kantorowicz et al. (1987). Reservoir technical aspects 11 wells in shallow marine reservoirs with extensive calcite cemented zones. They found that three dimensional fluid flow into such wells is determined to a large degree by the vertical permeability of the reservoir rock and by the lateral extent and continuity of reservoir heterogeneities such as calcite cemented horizons. Further, they showed how different well locations relative to calcite cemented horizons, may influence hydrocarbon production. They concluded that even discontinuous calcite cemented layers may affect oil production from a horizontal well and that the total effect of calcite cemented horizons on oil production from horizontal wells is a balance between lateral extension and placement of the barriers, the rate at which oil is produced, and where the horizontal well is perforated. Figure 2.2 shows the relationship between cemented horizons and oil production from horizontal wells.
Figure 2.2: Relationship between cemented horizons and oil production from horizontal wells: (a) reduced gas coning due to a laterally continuous ce mented layer above GOC; (b) reduced water influx due to cemented layer below the OWC; and (c) discontinuous cemented layers reduce vertical per meability and thus reduce productivity from the oil zone. From Gibbons et al. (1993). 12 Chapter 2. Calcite cementation
In some shallow marine sandstone reservoirs calcite cement may also be important for the net-to-gross ratio and in-place hydrocarbon volumes. Walderhaug and Bjprkum (1992) reported that in parts of the Veslefrikk Field in the North Sea more than half of the total reservoir thickness was made up of calcite cemented zones.
2.2 The conceptual model
2.2.1 Possible sources of calcite cement Possible sources of calcite can be grouped into two categories: internal and external. Internal sources are those that are within the sandstone where diagenetic calcite precipitates. Transportation of dissolved calcite is short and may take place by diffusion. If fluid flow is involved the source may be outside the the presently cemented sandstone. Bjprkum and Walderhaug (1990a) estimated transport by diffusion to be limited to centimetres or a few metres and transport by fluid flow to 100 metres to kilometres.
Internal sources Biogenic carbonate has been recognized by several authors to be a common internal source for calcite cement in shallow marine sandstones (Fiirsich, 1982; Kantorowicz et al., 1987; Saigal and Bjprlykke, 1987; Hudson and An drews, 1987; Bryant et al., 1988; Bjprkum and Walderhaug, 1990b). The car bonate might be deposited as scattered fossils in the sandstone or as channel lag deposits (coquinas). The origination of calcite can also be from detrital limestone fragments as described from Wyoming by Dickinson (1988). Further, calcite cement might result from the reaction of Ca2+ and CO3- supplied from different sources. CO2 can be supplied externally and trans ported into the sandstone where it reacts with Ca2+ from dissolved plagio- clase. Preserved and dissolved plagioclase is, however, reported to be rare in North Sea sandstones with abundant calcite cemented intervals, and pla gioclase has therefore been regarded as only of secondary importance here (Saigal and Bjprlykke, 1987; Walderhaug and Bjprkum, 1989; Bjprkum and Walderhaug, 1990a). Another internal source for calcite cement is precipitation of calcite (high- Mg calcite or aragonite) directly from sea water on the sea floor. This type of early marine cementation, known as hardgrounds, can occur during periods The conceptual model 13 of otherwise slow sedimentation, but is reported to account only for a small number of the calcite cemented zones in sandstones from the Norwegian continental shelf (Saigal and Bjbrlykke, 1987; Walderhaug and Bjprkum, 1989; Bjprkum and Walderhaug, 1990a; Bjprkum and Walderhaug, 1990b).
External sources External sources for calcite are those that are outside the presently calcite cemented sandstone. Due to possibly large distances, transportation mech anism must include some sort of fluid flow from the source. Very large volumes of fluid are necessary to supply calcite cement from the external source. Bjprkum and Walderhaug, (1990a) calculated that the amount of calcite cement supplied by fluid flow is insignificant unless the number of pore volume exchanges is close to 105. This requires meteoric water flush ing. Walderhaug and Bjprkum (1992) interpreted the calcite cementation of the Middle Jurassic Oseberg Formation in the Veslefrikk Field, to be partly due to such water flow. They suggested that the pore water was moving at a rate of 1 — 7 metres per year during calcite precipitation. Another ex ample of calcite cement derived from meteoric water flushing was given by Wilkinson (1993a) from the Valtos Sandstone Formation of Skye. Compaction water is probably not available in sufficient quantities to carry enough dissolved calcite from underlying sediments. Bjprkum and Walderhaug (1990a) calculated that half of the water available from com paction of all the sediments in the Norwegian sector of the North Sea would be necessary to support the calcite cement in the Brage Field. It has been suggested by several authors, e.g. Irwin and Hurst (1983), that CO2 from decomposition of organic matter may dissolve in the pore- water and provide a source for authigenic carbonates. They suggested several different depth-related reactions that may produce CO2 from organic mat ter: Bacterial sulphate reduction, bacterial fermentation and abiotic thermal decarboxylation. According to Mom per (1978) the CO2 may be transported into the sandstone dissolved in oil or water or as a gas phase. Saigal and Bjprlykke (1987), however, pointed out that even if CO2 is released from organic matter, the amount of carbonate that can precipitate is limited by the availability of cations such as Ca2+, Mg 2+, and Fe2+. Unless significant amounts of calcium are released from non-carbonate minerals, very little new calcite will precipitate. Saigal and Bjprlykke (1987) pointed out that transport of CO2 into a sandstone simultaneously with calcite precipitation, 14 Chapter 2. Calcite cementation however, could change the carbon isotopic composition of the calcite cement significantly. If CO2 is released at the sea-floor, calcium might be supplied directly from sea-water and calcite precipitation can occur. Bacterial sulphate re duction is one such process that may release CO2 close to the sea floor and generate bicarbonate (a salt containing a cation and the radical HCO3, e.g. NaHCOs). This process relies on a supply of sulphate from sea-water and biogenic or thermogenic methane from thesubsurface, and it may take place at depths down to approximately 10 m below sea floor (Irwin and Hurst, 1983; Lpnpy et al., 1986; Kantorowicz et ah, 1987; Wilkinson, 1991).
2.2.2 Stable isotopic analyses Stable isotopic analyses, often combined with trace element analyses, is usu ally done to identify and distinguish between different sources of carbonate; both depositional and diagenetic. Measurements of the stable isotopic ele ments 18 0 and 13C are compared to those of leO and 12C. Isotopic compo sitions are expressed in terms of the magnitude of the ratios compared to a standard sample. Results for carbonates are usually given as <$ 18 0%0 and 513C%0 PDB values, where the zero PDB (Pee Dee Belemnite) standard is a Cretaceous Belemnite. For other materials than carbonates, the convention is to use Standard Mean Ocean Water, or SMOW, as the measurement unit, where 0%0 PDB = +30.9%o SMOW. The <518 0 value of the cement depends on the isotopic composition (the Source ~Wo Trace element Other [%o PDB1 [%o PDB] [ppm] characteristics Biogenic Low negative Low positive Sr > 1000 Can dissolve and carbonate (ref 1) (ref 1) (ref 7) reprecipitate as mosaic calcite Detrital Varies Varies Varies Minor importance limestone (ref 5) Ca^+ from Varies Depends on Minor importance plagioclase CO2 source (ref 3, 5, 6) Hardgrounds Low negative Low positive Low Fe Fringe texture (ref 1) (ref 1) content (ref 2) Minor importance ref (2,5) Meteoric water —5 to —10 Varies Sr < 500 Locally of great (ref 7) (ref?) importance (ref 7) ■Compaction water Negative(?) Varies 5 Minor importance (ref 6) CO2 from organic (ref 2, 4) matter: -bacterial -close to zero —5 to —50 -generate sulphate reduction (ref 2) bicarbonate -bacterial fermentation -10M 0 to +10 -thermal decarbox -8 to -13W —5 to —13 Table 2.1: Typical 518 0 values, S13C values, important trace element con centrations, and possible other important characteristics for different calcite cement sources. References: 1, 2, 3, 4, 5, 6, 7 = Reading (1986), Kantorowicz et al. (1987), Saigal and Bjprlykke (1987), Irwin and Hurst (1983), Walder- haug and Bjprkum (1989), Bjprkum and Walderhaug (1990b), Walderhaug and Bjprkum (1992). Numbers marked with a M, were reported by Irwin and Hurst (1983) to be due to calcite cement precipitated when CO2 dis solves in the porewater. They, however, may also reflect the precipitation of dissolved biogenic carbonate under the influence of CO2 at increased burial depth. 2.2.3 Formation of calcite cemented layers - a growth model Bjprkum and Walderhaug (1990b) presented a model for the formation of calcite cemented strata-bound concretions in shallow marine sandstones. In the model they explained how calcite cementation can form in shallow ma rine sandstones (deposited between fair weather and storm wave base). The model may therefore not be applicable in other depositional environments The conceptual model 17 such as where calcite cemented layers form directly at the seafloor, nor within thin, vertically confined zones characterized by specific microbiological re actions, or where fluid flow or evaporation effects may be important for the cementation. Based on their geometrical arrangement, calcite cementation in shallow marine sandstones may be grouped into three: continuously cemented lay ers, layers of concretions (stratabound concretions) , or scattered concretions throughout the sandstone. The authors suggested how these three types of calcite cementation may be controlled by thelocal diagenetic redistribution of biogenic carbonate. Calcite should supposedly be sourced by the disso lution of carbonate fossils within the sandstone. The dissolving phases are thought to be aragonite and high-Mg calcite, and the precipitating phase low-Mg (often ferroan) calcite. Concretions should then form by a nucle- ation and diffusion controlled growth of calcite cement. Continuously calcite cemented layers would form by merging of stratabound concretions. Bjprkum and Walderhaug (1990b) propose that the location of individual concretions is controlled by the nucleation process. Nucleation of calcite should be controlled by the degree of super-saturation in the pore-water. Critical supersaturation is supposedly first achieved within carbonate fossil- rich layers, since biogenic carbonates are thought to be the source for calcite. Nucleation points should therefore be confined to these layers. Wilkinson (1993b), however, argued that concretion nucleation within sandstones is generally substrate-controlled. He concluded that both early cement patches and shell material within a shell bed can be the substrates upon which nucleation takes place. According to Walderhaug and Bjprkum (1993), also in these cases their model will function. They claim that this model only requires that nucleation takes place within the biogenic carbonate-rich layers. The concentration of dissolved calcite in the pore-water is thought to be lowered close to the calcite nucleus. The volume affected by the con centration lowering has a radius called the range of influence. This range is a function of time, mineralogy of the carbonate, concentration of clastic carbonate within the system, specific surface area, and dissolution rate of clastic carbonate. After nucleation the range first increases rapidly, but soon slower as a semi-steady state is reached where the amount of carbonate dis solved per unit time equals the amount of calcite precipitated per unit time. It is unlikely that new nuclei form within the range of influence. Since the semi-steady state is quickly established this may lead to a semi-regular distri 18 Chapter 2. Calcite cementation bution of concretions separated by between one and two ranges of influence (in the semi steady state). Nucieation points are thought to be (whether shell fragments or early calcite cement) controlled by supersaturation in the pore-water probably confined to the biogenic carbonate rich beds. The primary distribution of carbonate fossil controls therefore the distribution of calcite cement. The carbonate fossils are often concentrated in beds within the sandstone and may have thicknesses up to a few metres and lateral extents from less than a meter, up to several kilometres (Brenner and Davies, 1973; Fursich, 1982; Walderhaug and Bjprkum, 1989). Such beds may turn into discon- tinuously cemented layers consisting of calcite cemented (often flattened) concretions and intervening areas of non-cemented sandstones. If supply of carbonate is not exhausted, concretions may eventually merge and a con tinuously cemented layer forms. The geometry of the calcite cemented layer will be similar to that of the original fossil-rich bed. This was by Fursich (1982) termed the diagenetic reprint model. Figure 2.3 shows how calcite concretions may form from a fossil-rich layer and merge into a continuously calcite cemented layer. Whether a biogenic carbonate-rich layer will turn into a continuously or discontinuously cemented layer also depends on a number of other factors such as number of nucieation point, concentration of carbonate fossils, and thickness of the carbonate-rich sand unit (Bjprkum and Walderhaug, 1990a). If clastic carbonate is distributed more evenly throughout the sandstone, scattered spherical concretions may form within the sandstone. Bjorkum and Walderhaug (1990a) predicted that since carbonate fossil- rich layers show little lateral variation, the spacing between concretion- centers will be fairly constant within a given layer. In different layers the spacing is however expected to vary systematically as one or more of the factors controlling the range of influence vary. Based on the diagenetic reprint model one can conclude that biogenic carbonate is the most important source for calcite cement in shallow marine sandstones. This conclusion brings up important assumptions which can be used to predict the lateral extension of the calcite cemented layers. The most important implication is that the geometry of cemented layers is dependent on the geometry of the shell lag layers. For the stable isotopic compositions, the model implies that the original compositions are generally altered by two processes: (i) dissolution, reprecipitation and recrystallisation shift the The conceptual model 19 0 TQOTOTCDL Figure 2.3: Formation of a continuously cemented layer from a layer of carbonate fossil-rich sand. Original nucleation points grow into concretions as the clastic carbonate in the layer dissolve, and eventually merge and form a continuously cemented layer. From Bjprkum and Walderhaug (1990b). 518 0 values in a negative trend and (ii) the transport of CO2 from decom position of organic matter into sandstones shifts the <513C values generally in a negative direction. The lateral extent of fossil-rich layers and possible ways to recognize them in cores where classified by Bjprkum and Walderhaug (1990b) based on depositional regime: • During periods of low clastic input. These layers may experience short term in situ reworking and winnowing and can have large lateral ex tent (> 6km) (Davies, 1967; Fiirsich, 1982; Walderhaug and Bjprkum, 1989). They can be recognized in cores by extensive bioturbation, by absence of a coarse siliclastic lag, by absence of fossils transported from other environments, and by not being located above an erosion surface. • As lags at the base of storm-deposited layers. These lags may have lateral extents ranging from 1 m to a few hundred metres. This type 20 Chapter 2. Calcite cementation may be recognized in cores by their location at the base of storm- deposited layers, by containing a coarse siliclastic lag and sometimes by containing fossils transported from other environments. • As lags located at the base of submarine channels. These lags can have lateral extent of more than 1 km and are recognized in core located above erosion surfaces and are coarser grained than underlying sedi ments. • Above submarine erosion surfaces (transgression lags). These layers are of uncertain lateral extent, but can be recognized in cores located above erosion surfaces. Scattered concretions within the sandstone can generally be recognized in cores by not being associated with surfaces of erosion or non-deposition. Similarly for non-biogenic calcite: Hardgrounds are related to periods of non-deposition and may therefore have great lateral extents. 2.2.4 Calcite cemented zones in a sequence stratigraphic con text Several authors (e.g Bryant et al., 1988; Gibbons et al., 1993) have pointed out the relative vertical position of the calcite cemented horizons in repeated sequential arrangements of shallow marine sediments. The cyclicity of the successions may be partly explained by relative sea level fluctuations and indicate that sequence stratigraphic concepts provide a framework for the prediction of lateral extent of calcite cemented horizons. Both the genetic units and surfaces are used in this thesis in such a manner that they con form to the terminologies of sequence stratigraphy (sensu Exxon, e.g. Van Wagoner et al., 1988). Gibbons et al. (1993) studied carbonate cemented horizons in the Troll Field based on well logs and cores. They interpreted 70-75% of the flooding surfaces and 60-65% of the sequence boundaries to be calcite cemented. The lack of calcite cement of 25-30% of the maximum flooding surfaces were ascribed to several factors: the flooding surfaces were erroneously detected or that the time or conditions for development of early cementation had been unfavorable or later dissolution of carbonate had taken place. They estimated that flooding surfaces and sequence boundaries (and the cemented horizons associated with these) to be laterally extensive and probably continuous for several kilometres or more. The conceptual model 21 Extensive work has been carried out by a group of Norwegian oil com panies (Norsk Hydro as, Saga Petroleum as, and Statoil) in order to get an understanding of the extent and origin of calcite cemented beds in the Troll Field by collecting data from outcrop analogues. This work has not yet been published, but some general conclusions are summarized here (pers. comm. Lars Magnus Fait, Statoil) as they have important implications for the work presented in this thesis. Four different formations deposited in shallow ma rine environment were studied: The Eocene Ametlla Formation in Spain, the Liassic Luxembourg in Luxembourg and Belgium, the Cretaceous Al mond Formation in Wyoming, and the Jurassic Sundance Formation also in Wyoming in the United States. Several formations were studied to filter out local effects which are irrelevant to the Troll Field reservoir. The field analogues studies seemed to confirm the work by Bjprkum and Walderhaug (1990b) that calcite cementation is controlled by the primary distribution of calcareous bioclastic material. In a sequence stratigraphic context, calcite cemented surfaces were found to be controlled by the depo sition al bounding surfaces (i.e. sequence boundaries and flooding surfaces). The most continuous cemented layers were associated with these bounding surfaces. Extensive networks of calcite cemented layers often situated in the basal parts of transgressive systems tracts could be followed up to 100 km in lateral distance. The networks were often composed of a number of dif ferent component layers, generated by erosion and bedform migration and abandonment. Continuity of calcite cementation at minor channel scours and reactivation surfaces was found to be low variable. Summary of conceptual model Based on earlier work summarized in this chapter a conceptual model for calcite cementation in shallow marine sandstones can be illustrated by Fig ure 2.4 and summarized by the following items: • Fossil shell fragments provide the main source of calcite cement and calcite cementation is the result of a diffusion process. The proportion of calcite cement in a shallow marine sandstone is therefore directly related to the original quantity of fossil shell fragments in the newly deposited sediment. • A reduction of clastic input during transgressions can provide concen trations of fossil shell fragments around flooding surfaces. 22 Chapter 2. Calcite cementation Figure 2.4: Conceptual model for calcite cementation in shallow marine sandstones. The light grey regions overlying the sequence boundaries (SB 1 and SB 2) are lowstand and transgressive systems tracts. The medium grey regions overlying flooding surfaces (FS 1) are highstand systems tracts. Calcite cementation is in dark grey. Dimensions are metres to tens of metres vertically, and hundreds of metres to kilometres horizontally. • The washing out of finer grained sediment by various erosive processes can also produce beds with high concentrations of shell fragments. High degree of cementation around sequence boundaries can be at tributed to this process. • Rather than occuring directly on the surface, cementation often occurs as a network in a zone directly above or around flooding surfaces and sequence boundaries. 2.3 Conclusions Calcite cemented sandstones act as flow barriers in a large number of North Sea reservoirs. Even though the cemented beds are commonly only up to a few metres in thickness, their lateral extent may large and they can have important implications for hydrocarbon production from these fields. De pending on the orientation and lateral extent the cemented zones may be detrimental or beneficial for production. Conclusions 23 Possible sources for the calcite cement can be grouped into external and internal sources depending on their location relative to the presently ce mented rock. Biogenic carbonate is thought to be the most important source of calcite cement in shallow marine sandstones. Based on the growth model of Bjprkum and Walderhaug (1990b) calcite cemented zones form by the merging of stratabound calcite concretion. Evenly spaced nucleation points or limited calcite source material may result in scattered concretions. Nu cleation points are thought to be shell-fragments or early calcite cement. Biogenic carbonate is often concentrated in fossil-rich layers and this will also be the most likely place where the nucleation and diffusion controlled growth of calcite cement takes place. As a consequence, the geometry of the calcite cemented bed will mimic the geometry of the fossil-rich bed. This is an important result as it implies that the geometry of calcite cemented layers is controlled by sedimentary processes. Shell lag layers may be formed during periods of low clastic input or in association with some sort of erosive or reworking processes. In sequence stratigraphic terms these may be flooding surfaces or sequence boundaries. Outcrop and core studies of shallow marine sandstones confirm that calcite cementation often occur as networks in a zone directly above or around sequence stratigraphic bounding surfaces. 24 Chapter 2. Calcite cementation Chapter 3 The Troll Field: geology and petrophysics 3.1 Introduction In this thesis well data and seismic data from the Troll Field in the Norwegian North Sea have been analysed. Troll is a giant oil and gas field located at the Horda Platform at the eastern margin of the Viking Graben, 250 km NW of Stavanger (Figure 3.1a). The hydrocarbons are trapped in a series of north-easterly and south-westerly tilted fault-blocks. These divide the accumulations into three communicating hydrocarbon-bearing structures (Figure 3.1b): An eastern gas province with a gas-cap of 230 m (maximum) vertical thickness and a 3 m thick oil rim, a western gas province with a gas-cap of 200 m (maximum) thickness and an oil column of 12 m, and a western oil province with an oil column of 22 - 28 m and only a small gas-cap (Hellem et ah, 1986). Total hydrocarbon volumes in place are approximately 1788-10 9 Sm3 of dry gas and 970-10 6 Sm3 of oil (Gray, 1987). The gas-fluid contact is at a depth approximately 1545 m below mean sea-level and can be clearly seen on seismic data as a well defined flat-spot (Figure 3.2). The water-depth in the area varies from 290 to 350 m. The work presented in this thesis has been carried out on data from a region of the field known as TOGI (Troll Oseberg Gas Injection, Figure 3.1b), wheregas is produced for use in a gas injection project in the nearby Oseberg Field. In this area five wells are located on a circle of 330 m in radius (Figure 3.1c). The main gas production from Troll East started in June 1996. 25 26 Chapter 3. The Troll Field NORWAY Itroll IZZI Troll (DENMARK Km\ti (a) (b) 3 1/5-B-5H 3V5-: 1-6H 31/5 MH H /5-B-3H u 31/5-1 I-2H 5000 5500 6000 6500 7000 Scale [m] (c) Figure 3.1: Location maps: (a) location of the Troll Field in the Norwegian sector of the North Sea; (b) location of the TOGI (Troll Oseberg Gas Injec tion) area within the Troll Field; and (c) well locations in the TOGI area. 10 km South North 1.38 1.38 1.44 1.44 1.50 1.50 ® 1.56 1.56 1.62 1.62 1.68 1.68 1.74 1.74 Figure 3.2: North-south seismic stack section located at the crest of the Troll East structure. The location of the line is indicated by the stippled line in Figure 3.1b. In red and yellow are the top and base of the main reservoir (the Sognefjord Formation), and in green is the gas-fluid contact. The arrow on the top indicates the horizontal scale. 28 Chapter 3. The Troll Field 3.2 The reservoir in the TOGI area During the Jurassic the Herd a Platform received a steady supply of coarse clastic sediments which has left an almost complete stratigraphic record of cyclical shoreline transgression and regression. This contrasts other parts of the North Sea Basin where the record of shoreline oscillations is either less clear or less complete. Within the TOGI area there is an approximately 110 m thick gas col umn in sandstones of the Upper Jurassic Sognefjord Formation. This for mation has been interpreted as a shoreline-attached, tidally-influenced shelf complex, deposited during an overall rise in sea-level from late Callovian to early Volgian (Gibbons et ah, 1993). The sandstones of the Sognefjord Formation in the Troll Field are poorly consolidated with calcite cemented sandstones in all reservoir units. The reservoir comprises a large-scale inter stratification (5 - 20 m) of clean, coarse-grained, and finer-grained micaceous sandstones. Although the finer-grained micaceous intervals are of signifi cantly poorer reservoir quality than the clean sandstones they do not form significant heterogeneities for gas production. The most important reservoir heterogeneities are believed to be thin (10 cm -2 m) calcite cemented beds which account for approximately 6.5% of the Sognefjord Formation in the TOGI area. 3.2.1 Sequence stratigraphic zonation of the Troll East A sequence stratigraphic interpretation and reservoir zonation between the five closely spaced TOGI wells has been established (Figure 3.3). This inter pretation coincides with the transgressive model for the Sognefjord Formation in the Troll Field area proposed by Stewart et al. (1993). The micaceous in tervals are interpreted as highstands systems tracts with a maximum flood ing surface at their base. The clean, coarse-grained sandstones are either associated with a sequence boundary at their base or a sequence boundary somewhere in the middle (Figure 3.3). The clean sandstones overlying se quence boundaries are interpreted as transgressive systems tracts, whereas some sandstones at the base of the clean zones are thought to be the upper parts of highstand systems tracts (Gibbons et al., 1993). Lateral thickness variations within the TOGI area are small and there is relatively little topog raphy on the various sequence boundaries and flooding surfaces. The calcite cemented beds occur throughout the reservoir but are typically concentrated Seismic parameters 29 Well 31/5-B-6H Well 31/5-B-2H Calcite proportion Sonic [psfft] Sonic [psfft] curve [%] Figure 3.3: Reservoir stratigraphy of the TOGI area illustrating zonation and calcite distribution in the 6H and 2H wells. The calcite proportion curve has been generated by smoothing the combined proportions observed in the five TOGI wells. around bounding surfaces (Figure 3.3) and their spatial distribution is con sistent with the conceptual model (Figure 2.4). 3.3 Seismic parameters Much of the work in this thesis has been to understand the seismic reflections which can be seen in the reservoir section in the Troll Field (Figure 3.2). To achieve this, seismic modelling of idealized and realistic models of the reservoir in the TOGI area of the Troll Field has been performed. The five TOGI wells have therefore been analysed to obtain realistic velocities and densities for the reservoir sands and the thin calcite cemented layers. 30 Chapter 3. The Troll Field The calcite layers in TOGI are so thin that conventional sonic and density wire-line logs do not measure correct physical values due to log resolution constraints and shoulder effects. Plots of calcite bed thickness versus log measurements for all five TOGI wells reveal a trend of increasing maximum density and velocity values with increasing bed thickness (Figure 3.4). The thicknesses of the calcite cemented layers have been decided based on resis tivity logs and checked on core photos when available. Very high impedance values of 17474 ^3™ appear to be typical for the calcite cemented beds if the maximum (plateau) values for velocity (6520 ™) and density 2.68 ^3) are assumed to be representative (Figure 3.4). These values for velocities and densities have been assigned to all calcite cemented zones in seismic modelling performed in this work, except partly in Chapter 3 and Appendix A which are based on work done before the influence of log resolution and bed thickness became apparent. In addition to the calcite cemented zones, variations in seismic param eters within the non-cemented sandstones are important. Impedance his tograms reveal similar average values of 4625 ^5” and 4775 ^3 ™ for the Vp = 6520 » <2. 3.0 0.0 Calcite bed thickness [m] Figure 3.4: Density and compressional velocity versus calcite cemented bed thickness based on wire-line log measurements in the five TOGI wells. The plateau values associated with the thicker beds are assumed to be represen tative for the calcite cemented zones. Conclusions 31 I______I Clean sand Mcaceaous sand Acoustic impedance [g/cm m/s] Figure 3.5: Acoustic impedance histograms for clean (1650) values and mi caceous (650 values) sandstones based on wire-line log measurements in the five TOGI wells. clean and micaceous sandstones respectively (Figure 3.5). These values are much lower than the 17474 associated with the calcite beds. Even though the average impedance values in the two sandstone types are similar, there are both vertical and lateral variations which are illustrated in Fig ure 3.6. The contribution to the total reflected seismic response from calcite cemented zones and the background sandstones are analysed in Chapter 4 and 5. 3.4 Conclusions The Sogneford Formation of the Troll Field is interpreted as a shoreline- attached, tidally-influenced shelf complex. The formation is generally sandy with two types of sandstones: micaceous and clean quartz sandstones. The 32 Chapter 3. The Troll Field Figure 3.6: Vertical and lateral trends in the non-cemented sandstones in the TOGI area. Wire-line logs (density, velocity, and acoustic impedance) in all five TOGI wells have been depth shifted and merged, after intervals interpreted as calcite cemented have been removed. Lateral variation is seen as the width of each curve. The top of the Sognefjord Formation is at approximately 1425 m and the gas-fluid contact at 1545 m. Conclusions 33 micaceous sandstones are interpreted as highstands systems tracts and the clean quartz sandstones as transgressive systems tracts, deposited during an overall rise in sea-level. Calcite cemented sandstone layers occur in all reser voir units and are believed to the most important reservoir heterogeneities. A reservoir zonation has been established based on sequence stratigraphic interpretation of well data. The calcite cemented beds are typically concen trated around sequence stratigraphic bounding surfaces. Correcting for bed-thickness effects, the calcite cemented beds have ve locities and densities which may be assumed constant. The non-cemented sandstones have clear vertical trends, which are important to capture in seismic modelling. Even in the small TOGI area there are also some lateral velocity and density variations in the non-cemented sandstones. 34 Chapter 3. The Troll Field Chapter 4 Analyses of tuning amplitudes from stacks of thin calcite cemented layers 4.1 Introduction Tuning effects are constructive or destructive interference of pulses resulting from two or more closely spaced reflectors (Sheriff, 1991). At zero-offset such interference is a function of the length of the seismic pulse, often 20- 100 msec, and spacing of the acoustic impedance boundaries in time. The latter is again a function of interval velocity. Widess (1973) showed how the zero-offset composite reflection ampli tude from one thin layer varies as a function of layer thickness. For a thin layer inter-bedded in homogeneous background of lower acoustic impedance Widess found that the maximum constructive interference for a zero-phase wavelet occured when the bed thickness was equal to one quarter of the dominant wavelength in the wavelet. This is also called the tuning thickness. When the layer thickness is one-eighth of the dominant wavelength, the com posite response approximated the derivative of the original signal. Widess called this thickness the theoretical threshold of resolution. For even thinner layers, the shape of the composite response stayed the same but decreased in amplitude. Other criteria for vertical resolution of seismic reflection data have been proposed. The criterion established by Rayleigh (Jenkins and White, 1957) defines the resolution limit to be equal to the tuning thickness 35 36 Chapter 4. A nalyses of tuning amplitudes or half of the dominant wavelength in the pulse. Ricker (1953) chose the separation where the composite reflected waveform has a curvature of zero at its central maximum to be the limit of resolution. The latter limit falls between the two other limits mentioned. Meckel and Nath (1977) and Mahradi (1983) analysed situations at zero- offset where several thin beds were inter-bedded in a homogeneous back ground. They found that if multiple reflectors were closer than a quarter wavelength their contributions add within the first half-cycle of the wavelet and the net thickness of the thin layer medium is roughly proportional with the amplitude of the composite reflected signal. The shape of the wavelet did not change as the number of reflectors changed and the distribution of the individual reflecting horizons could therefore not be determined. If the reflectors were further apart than a quarter wavelength, different half-cycles of the wavelet would interfere. In the offset domain, bed-tuning also becomes a function of differential move-out. For a single thin layer offset dependent tuning can cause an am plitude increase or decrease with offset. Swan (1988) described AVO analysis in a finely layered medium and found that AVO distortions due to differen tial tuning may be larger than the underlying lithologic AVO effect. Tuning caused by NMO convergence may be considered to be noise for some meth ods, like AVO analysis, while it provides additional information for other methods. For example Ball (1988) used the additional information from the offset domain to extend the conventional zero-offset tuning analysis which relates layer thickness to impedance of the thin bed. Different approaches to correct for offset dependent tuning before conventional AVO analysis, have been established. In Appendix A alternative correction factors for offset dependent tuning are presented. Individual calcite cemented beds in shallow marine sandstones are nor mally so thin (10 cm - 2 m; see Chapter 3) that one layer cannot be resolved by the seismic signal. Based on outcrop observations the most continuous calcite cemented layers occur as networks or stacks around or above flooding surfaces and sequence boundaries. The intention of this chapter is to quan tify the seismic response from thin calcite cemented layers and stacks of such layers, and to identify which parts of the offset domain contain information which can be used to predict calcite distribution in the reservoir. Seismic modelling 37 4.2 Seismic modelling ID stacks of alternating calcite cemented and non-cemented sandstone beds have been used as input to seismic modelling to quantify the tuning ampli tude as a function of offset. The models were built varying the configuration of the calcite cemented layers. The geometric description parameters per taining to the calcite cemented layers were varied between models. The following parameters were used: • thickness of calcite cemented, 0.5 m or 1 m, • spacing between calcite cemented layers, and • number of calcite cemented layers. The different ID models are given in Table 4.1. The seismic response from one calcite cemented layer ranging in thickness from 0.5 m to 20 m was also modelled (model A). They were placed in a homogeneous background of non- cemented sandstones and may be regarded as wedges of calcite cemented and non-cemented sandstones as illustrated in Figure 4.1. Two different sets of seismic parameters (velocities and densities) have been used for the calcite cemented and the non-cemented sandstones (Ta ble 4.2). The first set (used for models A to M, Table 4.1) is based on wire-line log measurements of density and velocity without correcting for bed-thickness effects (as described in Chapter 3) and the seismic modelling was initially based on these relatively low contrasts. After the influence of log resolution and bed-thickness on the log measurements became apparent a second set of simulations using higher contrasts was carried out (models N* and O*, Table 4.1). This second set of parameters is more correct for the calcite cemented sands in TOGI. Most of the work in this chapter has however been based on the first set of experiments. As will be demonstrated, the results using the second set of parameters, however, are consistent with the conclusions based on the low contrast experiments, and it is assumed that these conclusions are generally applicable. There are little data in the literature for shear-wave velocities for calcite cemented beds. Shear-wave velocities have not been measured in the Troll East wells. The closest wells with shear-wave logs are located in the Troll West area, approximately 20 km northwest of the TOGI area. Based on these wells, constant Vv/Vs ratios of 1.7 for the calcite cemented sands and 1.5 for the non-cemented sands have been used. 38 Chapter 4. A nalyses of tuning amplitudes The seismic response to the models described, were simulated with a full waveform reflectivity modelling software from 0degaard & Danneskiold- Samspe. The algorithm in OSIRIS is based on the direct global matrix method developed among others by Schmidt and Glattetre (1985) and Schmidt and Tango (1986). It is derived from an approach using continuous wave systems in the frequency domain and is a general method for solving elastic wave propagation problems in a layered media. This method yields an exact solution to the wave equation for a horizontally stratified media. The top of the stacks were placed at constant depths of 1500 m, with an overburden having the same seismic properties as the sands in the stacks. Elastic seismic modelling was performed without a free surface to avoid source and receiver ghosts, and a normal polarity zero-phase Ricker wavelet with three lobes and a center frequency of 40 Hz was used. Offsets from Model Calcite cemented Sandstone bed Number of calcite bed thickness [m] thickness [m] cemented beds A 0.5-20.0 0 1 B 0.5 0.5 1,2,4,6,8 C 1.0 0.5 1,2,4,6,8 D 0.5 1.0 1,2,4,6,8 E 1.0 1.0 1,2,4,6,8,10,12 F 0.5 2.5 1,2,4,6,8 G 1.0 2.5 1,2,4,6,8 H 0.5 5.0 1,2,3,4,5,10 I 1.0 5.0 1,2,3,4,5,10 J 0.5 7.0 1,2,3,4,8 K 1.0 7.0 1,2,3,4,8 L 0.5 10.0 1,2,3,4,6 M 1.0 10.0 1,2,3,4,6 N* 1.0-18.0 0 1 0* 1.0 1.0 1,2,3,4,6,8,10 Table 4.1: ID models with systematically increasing number of calcite ce mented beds and increasing vertical distance between calcite cemented beds. Seismic processing 39 Sand bed thickness [m] 0 1 23456789 10 1 i i i i i i I i I i 1D models: A/N* B/C D/E/O* F/G H/l J/K LVM I I I i 1 1 I Calcite [ s I Sand L 1.195 3 1 .215 g 1.235 1.255 1.275 01 23456789 10 Sand bed thickness [m] Figure 4.1: Schematic illustration of the ID models in Table 4.1. At the top is illustrated a wedge where the thickness of calcite cemented sand, y, is 0.5 m or 1 m. The ID experiments (models A to 0*) are indicated for increasing sand thicknesses. Below are the zero-offset reflected signals for experiments including four calcite cemented beds each 1 m thick for increasing sandstone thicknesses (belonging to model A to M). Also shown is the reflected signal (marked Ref) from a thick calcite cemented layer where no interference occurs. 0 to 2000 m with receiver spacing 50 m were modelled. 4.3 Seismic processing The composite of the reflected primary pulses from a stack of thin alternat ing high and low velocity layers (Figure 4.2) may be given as (Ursin and Dahl, 1992): 40 Chapter 4. A nalyses of tuning amplitudes mp(t -TM)~j§p(t -n(p>)+ - 3/) (4.1) +W)p(t" T”(!,))' ^Mp(t - Tn+l(y>> where t denotes time and y offset. R{y) is reflection coefficient, g(y) is geometrical spreading, T(y) is two-way travel-time. Index 1 denotes reflec tion from the top of the uppermost thin layer in the stack, index 2 from the bottom of the uppermost thin layer, and so on. In equation (4.1) the offset-dependent effects of the source and receiver directivity, visco-elastic attenuation, and transmission through the overburden as well as within the stack have been neglected. p(t) represents the incident wavelet. In order to simplify the analyses the low velocity layers in the stack are assumed to have the same elastic properties as the half-spaces above and below the stack. Also the high velocity layers are assumed to have identical elastic properties. It is further assumed that the total stack thickness is thin compared to the depth (distance to source and receivers). This means that Ri+i(y) = —R%(y) and gi(y) « gn+1 (y). Correcting for offset-dependent geometrical spreading and normal moveout corresponding to the top of the stack of thin layers results in the corrected data-set: 4W = #i(3/M(:/)Pm(t), (4.2) Lithology P-velocity 5-velocity Density [m/sec] [m/sec] [g/cm 3] Set 1 Cemented sand 3810 2241 2.70 Low contrasts Non-Cemented sand 2465 1643 2.12 Set 2 Cemented sand 6520 3835 2.70 High contrasts Non-Cemented sand 2343 1562 2.00 Table 4.2: Seismic parameters for calcite cemented and non-cemented sands used in the models. Two sets of parameters have been used: one with low contrasts between cemented and non-cemented sandstones and one with high contrasts. Seismic processing 41 where A(y) is the offset dependent tuning amplitude and p m(t) is the com posite reflected wavelet assumed to be constant with offsets. A(y) and pm (t) are both functions of layer thickness. In the case where all events can be separated, there is no tuning and A(y) equals unity for all offsets and the pulse pm (t) is simply equal to the incident pulse p(t). In Appendix A it is shown that for one layer embedded in a homogeneous back ground the shape of the composite reflected pulse approaches the derivative of the incident pulse as the layer thickness decreases. For layers thinner than half the tuning thickness, the zero-offset amplitude is changed from P(0) to P(0)AT(0), where P(0) is the reflection coefficient at zero-offset and AT(0) is the two-way time-thickness of the thin layer. To analyze the offset dependent tuning amplitude, A(y), for stacks of thin layers the synthetic data were corrected for offset dependent PP-reflection coefficient (Cerveny et al., 1977), at the top of the uppermost layer in the stack and geometrical spreading given by g\{y) = r, where r is the travel- Layern+1 Figure 4.2: Thin layer model with reflected primary pulses. Light grey color indicates low velocity and dark grey color high velocity layers. 42 Chapter 4. A nalyses of tuning amplitudes path from shot-point via the uppermost reflector in the stack to receiver. The normal moveout corrections and amplitude analyses of the synthetic data were done with a robust AVO analysis technique (Ursin and Ekren, 1993). This technique aligns a time window horizontally for each zero offset sample in a CMP-gather using static time shifts in the NMO correction to avoid NMO stretch. Inaccuracies in this alignment are reduced by a residual NMO correction. The length of the time window is approximately equal to the composite pulse duration. The travel-time corrected data are modelled as a constant pulse multiplied by an amplitude function that is approximated by a polynomial in the offset coordinate: d(t, y)corr « [1 + a[y2 + a2y4]w(t) (4.3) The polynomial coefficients al and a2 and the estimated pulse w(t) are found by a separable least-squares algorithm. The coefficient ao is equal to the value of the estimate w(t) in the middle of the time window. Then the other estimates are given by cq = a(jal and = ao«2- The polynomial in equation (4.3) has been shown to be a good approximation for the Rpp reflection coefficient (Ursin and Dahl, 1992). Using the same polynomial in the robust AVO analysis technique for the analyses of offset dependent tuning amplitudes gave only small differences between the estimated data (equation 4.3) and the reflectivity modelled data. The seismic response from the ID models (Table 4.1) were all processed as described and normalized with respect to the response from a very thick calcite cemented layer. Figure 4.3 shows the reflection coefficients for an interface between non-cemented sandstone and calcite cemented sandstone for the two seismic parameter sets (Table 4.2). For sub-critical offsets the reflection coefficients show only slight decrease with increasing offsets, before they increase towards critical reflection. In Figure 4.1 are shown the zero-offset seismic responses for ID models including four calcite cemented beds each 1 m thick for increasing sandstone thicknesses (belonging to model A to M in Table 4.1). Figure 4.4 shows the finally processed offset dependent seismic response and the correspond ing tuning curve (measured along the first peak in the composite reflected response) for a ID model consisting of four calcite cemented beds each 1 m thick separated by 1 m thick non-cemented sandstones (belonging to model E in Table 4.1). Results 43 = 6520 m/s 0.6 - 0.4- Vc = 3810 m/s 0.2- 1000 1500 2000 2500 Offset [m] Figure 4.3: Reflection coefficients for an interface between non-cemented sandstone and calcite cemented sandstone, as functions of offset for low (Vc = 3810 m/s) and high contrast (Vc = 6520 m/s) seismic parameter sets. 4.4 Results Set 1: Low contrast seismic parameters The normalized offset dependent tuning curves (Figure 4.5) for one calcite cemented bed ranging in thickness from 0.5 m to 20 m (model A in Table 4.1) show generally little variation with offset, but the variation increases with increasing layer thickness. Notice that even a 2 m thick calcite cemented bed gives a seismic response which is almost 30% of the response from the top of a very thick layer. The tuning amplitude increases with increasing layer thickness from 0.5 m to 20 m. Maximum constructive interference, which occurs at the tuning thickness, was not reached for this model. For this model and wavelet, the tuning thickness should be close to 24 m. In Figures 4.6 and 4.7 the tuning curves for increasing number of 0.5 m and 1 m calcite cemented beds with increasing separation (model B to M in Table 4.1) are plotted. For all tuning curves there is generally only a slight decrease in tuning amplitude with offset. Note thatfor the same sand thick- 44 Chapter 4. A nalyses of tuning amplitudes (a) Offset [m] 0 250 500 750 1000 1250 1500 1750 2000 1.195 1.205 — 1.215 pE 1.225 1.235 1.245 E 0.4 Offset [m] Figure 4.4: (a) Seismic response with offset from a stack of four calcite ce mented beds each 1 m thick separated by 1 m thick non-cemented sandstones (belonging to model E in Table 4.1), and (b) offset dependent tuning curve measured along the first peak in the composite reflected seismic response. ness separating 0.5 m and 1 m calcite cemented beds, the tuning amplitude for 1 m calcite cemented bed is approximately twice that of the 0.5 m cal cite cemented bed. For the models with closely separated calcite cemented beds (model B, C, and D in Figure 4.6a-c), the tuning amplitude increases as more calcite cemented beds are added to the stack. Note also that the tuning amplitude increases as the distance between the calcite cemented beds decreases (Figure 4.6a and c). For models E-K (Figure 4.6d-f and Fig ure 4.7a-d) the tuning amplitude first increases as more beds are added and then decreases again as even more beds are added. Maximum constructive interference occurs for different number of beds in the different models, but the general trend is that it occurs for smaller numbers of calcite cemented beds as the sand thickness between them increases. For model L and M (Figure 4.7e and f) where 10 m sands separate the calcite cemented beds the Results 45 1.4 —: Model A Calcite bed: 0.5-20 m Sand bed: 0 m 20.0 m 16.0 m 14.0 m 12.0 m 10.0 m 8.0 m 6.0 m 0.4- 4.0 m 3.0 m 0.2 - 2.0 m -----1.0 m ------6.5 m 1000 1500 2000 Offset [m] Figure 4.5: Tuning curves for one calcite cemented bed ranging in thickness from 0.5 m to 20 m (model A in Table 4.1). The stippled curve is the tuning curve for a very thick calcite cemented bed where no interference occurs. tuning amplitude decreases as the number of calcite cemented beds increase. Set 2: High contrast seismic parameters Figure 4.8 shows the tuning curves for (a) one calcite cemented layer of increasing thickness (velocity of 6520 m/s) and (b) increasing number of 1 m calcite cemented beds separated by 1 m sands. Critical reflection occurs at 1155 m offset (Figure 4.3). In the method used for analysing AVO behavior the pulse shape is assumed constant for all offsets. Due to phase changes and refracted waves, the pulse cannot be assumed constant beyond 1155 m. The analysis is therefore done only up to this offset. All the tuning curves show very little variation with offset. Comparing the tuning curves for these high velocity calcite cemented layer models (Figure 4.8) with the corresponding lower velocity models (Figure 4.5 and 4.6b), the normalized amplitudes are lower for the high velocity calcite cemented layer models. This is because the time thickness for corresponding layer thicknesses is lower for the high velocity models. Multiplying by each zero-offset reflection coefficient for 46 Chapter 4. A nalyses of tuning amplitudes (a) (b) Model C Sand bed: 0.5 -g 0.8 E 0.6- ~ 0.4- Z 0.2- 1000 1500 2000 Offset [m] Offset [m] (c) (d) Model D Model E 0.2- 1000 1500 2000 1500 2000 Offset [m] Offset [m] (e) (f) Model F Model G Calcite bed: 0.5 m Calcite bed: 1.0 m Sand bed: 2.5 m 5 0.3- V O 0.1 - © 0.1 - z 1OOO 1500 1000 1500 2000 Offset [m] Offset [m] Figure 4.6: Tuning curves for increasing number of calcite cemented beds 0.5 m to 2.5 m apart in a homogeneous sand background (models B-G in Table 4.1). (a) 0.5 m calcite cemented beds 0.5 m apart, (b) 1 m calcite cemented beds 0.5 m apart, (c) 0.5 m calcite cemented beds 1 m apart, (d) 1 m calcite cemented beds 1 m apart, (e) 0.5 m calcite cemented beds 2.5 m apart, and (f) 1 m calcite cemented beds 2.5 m apart. The numbers to the right of the curves indicate number of calcite cemented beds in the stack. Results 47 (a) (b) Model H Model Sand bed: S.O m 5 0.15- 5 0.15- o 0.05- © 0.05 2000 Offset [m] Offset [m] (C) (d) 0.15 Model J Model K 1000 2000 1000 Offset [m] Offset [m] (e) (f) 0.15 Model L Model M =S. 0.1- 1000 1500 2000 1000 1500 Offset [m] Figure 4.7: Tuning curves for increasing number of calcite cemented beds 5 m to 10 m apart in a homogeneous background of sand (Models H to M in Table 4.1). (g) 0.5 m thick calcite cemented beds 5 m apart, (h) 1 m calcite cemented beds 5 m apart, (i) 0.5 m calcite cemented beds 7 m apart, (j) 1 m calcite cemented beds 7 m apart, (k) 0.5 m calcite cemented beds 10 m apart, and (1) 1 m calcite cemented beds 10 m apart. The numbers to the right of the curves indicate the number of calcite cemented beds in the stack. 48 Chapter 4. A nalyses of tuning amplitudes (a) (b) 1. 0.6- Model N Model O* Calcite bed: 1.0-18 r Calcite bed: 1.0 m Sand bed : O m Sand bed: 1 a: 14m 10 to 4 !:o -- 1------1------r-- o —i------1------r.— 200 400 600 800 lOOO 1200 200 400 600 800 1000 1200 Offset [mj Offset [m] Figure 4.8: Tuning curves for calcite cemented layers with velocity 6520 m/s, versus offset (up to offset for critical reflection), (a) For one layer of increasing thickness 1-18 m. The stippled curve is the response from a very thick calcite cemented layer (no interference). Compare with low contrast model A (Figure 4.5); note the different offset scales, (b) Increasing number of 1 m calcite cemented beds separated by 1 m sands. an interface between non-cemented and calcite cemented sandstones, reveals that the actual amplitude from the low velocity calcite cemented layer model is generally about 70% of the high velocity calcite cemented layer model for corresponding layer thicknesses or stacks of calcite cemented layers. 4.5 Analyses In Figure 4.9 the zero-offset normalized tuning amplitudes are plotted versus number of calcite cemented beds in the stack for 0.5 m and 1.0 m thick calcite cemented beds. Adding a calcite cemented bed to the bottom of the stack does not seem to affect the top-stack amplitude if the total stack thickness is more than approximately 25 m thickor a quarter of the dominant wavelength (Ad. = V'caicitejfd — 3810 ™/40 Hz = 23.8 m). For further analyses, the zero-offset tuning amplitudes were grouped within constant windows of 10, 15, and 20 m. All stacks thinner than 10 m were grouped within the 10 m window, all stacks thinner than 15 m within the 15 m window and so on. The calcite fraction within each window was then calculated: A single 1 m thick calcite cemented bed has a calcite frac tion of 10% in the 10 m window, 6.7% in the 15 m window, and 5% in the A nalyses 49 £0.6- 2 0.2- 2 0.2- 45.0 m Number of calcite beds Number of calcite beds Figure 4.9: Zero-offset normalized amplitude versus number of calcite ce mented beds for different calcite cemented bed spacing intervals, (a) 0.5 m calcite cemented beds and (b) 1.0 m calcite cemented beds. Spacing between calcite cemented beds is indicated to the right of the curves. 20 m window. The data were grouped like this to increase the data points within each total stack thickness to allow for statistical analyses. For all three windows the zero-offset tuning amplitude can be linearly related to calcite fraction within the window for normalized amplitudes less than 1.2 (Figure 4.10). The flattening at high amplitudes and high calcite fractions is especially evident for the 20 m window. Linear regression analyses (for all data points having normalized amplitudes less than 1.2) shows a high correlation (r2 > 0.90) between amplitude and fraction calcite. The differ ent slopes for the regression lines (Figure 4.10) may partly be explained by the fact that several data points fall within all three windows. These points plot with different calcite fraction in the different windows, but the same amplitude. In Figure 4.11a the zero-offset tuning amplitude has been plotted as a function of vertical stack size (measured from the top of the uppermost to the bottom of the lowermost calcite cemented bed in the stack), for total stack size less than 25 m, and percentage calcite within the stack. There is a clear trend of increasing zero-offset amplitudes with increasing stack size or increasing calcite fraction. For high calcite content in the stacks, the 50 Chapter 4. A nalyses of tuning amplitudes =5.1.0- Fraction calcite Fraction calcite (4 (b) Fraction calcite (c) Figure 4.10: Normalized zero-offset tuning amplitudes versus calcite fraction within constant windows of (a) 10 m, (b) 15 m, and (c) 20 m and regression lines (for all data points having normalized amplitude less than 1.2). amplitude is mostly a function of stack size, whereas for low calcite content the amplitude is mostly a function of calcite content within the stacks. In the TOGI area stacks of calcite cemented beds have generally low calcite content and the amplitudes should therefore primarily be a function of the calcite content. This will be further analysed in Chapter 5. To describe the variation with offset for the offset dependent tuning A nalyses 51 curves (Figure 4.5 to 4.7) the sum of estimated polynomial coefficients Stack size (m) (a) (b) Figure 4.11: (a) Normalized zero-offset tuning amplitudes, (b) and the sum of cti and a2 plotted versus vertical stack size (for stacks less than 25 m) and percentage calcite in the stack. Data points are indicated by black dots. 52 Chapter 4. A nalyses of tuning amplitudes 4.6 Discussion Although single beds give relatively small seismic reflections, the stacking of several beds which is expected to occur around sequence stratigraphic bounding surfaces, produce significant reflections. The tuning amplitudes vary only slightly with offset and there is probably little to gain from work ing in this domain. The contributions of locally converted waves and internal multiples are controlled by shear-wave ratios and compressional wave ratios respectively. Based on petrophysical analyses (Chapter 3) more realistic seismic velocities were found for the calcite cemented beds in TOGI. More significant contributions from locally converted waves and internal multiples may therefore be expected. For sub-critical reflections the analysis, however, has shown that there is insignificant variation with offset for the normalized tuning amplitude also for these models. One effect of going critical at rel atively short offsets may be that deeper reflectors fall in a shadow zone, and decreases in amplitude versus offset may be expected for these reflec tions. This, however, has not been further investigated here. At zero-offset the amplitude from the top of the stack is affected by layers within a quar ter wavelength. Assuming constant vertical stack thicknesses the zero-offset tuning amplitude is quite linearly related to the percentage calcite within the stack. The amplitude, however, is also dependent on the thickness of the stack. Meckel and Nath (1977) analysed seismic visibility for one layer as a func tion of layer thickness and acoustic impedance contrast. They found a similar relationship as shown in Figure 4.11a. The composite seismic response in creases in amplitude as the layer thickness (or stack size here) increases or acoustic impedance contrast (or calcite content here) increases. In order to use this dependency for predicting calcite cementation using amplitudes, it is necessary to quantify the relationship. The use of regression analyses for quantifying the relationships is described in the next chapter. Chapter 5 Prediction of lateral variation in calcite cementation using zero-offset tuning amplitudes 5.1 Introduction Calcite cemented layers occur in networks or stacks around sequence strati graphic bounding surfaces. In the previous chapter the zero-offset tuning amplitude was shown to be dependent on calcite content in the stack and vertical stack size. In this chapter the relationships are quantified using a regression analysis based on extensive seismic modelling. The results of the regression analysis are then used to predict calcite distribution in a synthetic and real data example. 5.2 Seismic modelling A stochastic modelling tool (see Chapter 6) has been used to generate 500 ID models of calcite distribution. The 500 models are grouped into 5 wedge models containing 5, 10, 25, 50, and 75% calcite cemented beds. Individual calcite cemented beds are 0.25 m thick on average. The wedges range in ver tical extent from 0 to 25 m, and are 2000 m in horizontal length (Figure 5.1). The stochastic modelling tool was used as a quick technique for gen erating a large number of models with statistically defined characteristics. 53 54 Chapter 5. Zero -offset tuning amplitudes (a) Horizontal length [m] (b) Figure 5.1: Two of the wedge models used to quantify how the composite reflected amplitude and pulse-length depend on vertical stack size and per centage calcite in the stack. For expected calcite percentage of: (a) 5% and (b) 75%. Calcite cemented beds are shown in white. Seismic modelling 55 Figure 5.2: Variation in stack size and percentage calcite within the stack for the ID models (500 models totally) used to establish empirical relations for zero-offset tuning amplitude and pulse-length. The use of a stochastic model also introduce the desired natural (random) variability. Figure 5.2 shows the variation in stack size and percentage cal cite of the 500 models. The stack size has been measured from the top of the uppermost calcite cemented bed to the bottom of the lower-most calcite cemented bed in the stack. The models were placed at a depth of 1500 m in a homogeneous back ground of gas sand. The seismic parameters for the gas sand were found as an average of the non-cemented sands in the five TOGI wells. These values and the velocity and density of the calcite cemented sandstones are given in Chapter 3. The seismic modelling was done using full waveform elastic reflectivity modelling. A 40 Hz zero-phase Ricker wavelet has been applied, and to avoid source and receiver ghosts the modelling was done without a free surface. Figure 5.3 shows the seismic response from the two wedges in Figure 5.1 for expected calcite percentage of 5% and 75%. Note that when the percentage calcite is low and the stack size large the shape of the composite reflected pulse changes. The zero-offset seismic responses 56 Chapter 5. Zero -offset tuning amplitudes (a) Total wedge thickness [m] Figure 5.3: Seismic response from the two wedge models in Figure 5.1: (a) 5% and (b) 75% expected percentage calcite in the stack. Note that the amplitudes in (a) have been scaled up ten times compared to those in (b). were corrected for geometric spreading and normalized with the seismic re sponse from the top of a very thick calcite cemented layer as described in the previous chapter. In addition to the normalized tuning amplitudes, lengths of the composite reflected pulses were measured from the seismic response to 500 ID models. Figure 5.4 and 5.5 show how tuning amplitude and pulse-length vary as functions of stack size and percentage calcite. The plots are based on 425 measurements (shown in Figure 5.4b and Figure 5.5b). The remaining 75 data-points have been removed due to abnormal behavior, mainly caused by Regression analyses 57 too large of a distance between calcite cemented beds. This problem will be addressed later (Chapter 5.4.2). Both tuning amplitude and pulse-length increase with increasing stack size and increasing percentage calcite. The pulse-length, however, is generally less sensitive to changes in percentage calcite than the tuning amplitude. Note also that for low calcite contents (less than 25%) thetuning amplitude does not differ much for different stack sizes and is primarily a function of calcite content. 5.3 Regression analyses Regression analyses were performed on the two datasets (Figure 5.4 and 5.5) to establish mathematical expressions for how the tuning amplitude and the pulse-length vary as functions of stack size and percentage calcite in the stack. Several regression models were investigated and the best results were obtained from the following models: A = &oP^= (5.1) and I = (5.2) where A is the zero-offset tuning amplitude, L is the pulse length, P is percentage calcite in the stack, S is the stack size, and &o, &i, ^o, h, and Z2 are regression constants. These regression models were transformed to logarithmic expressions in order to simplify the regression analyses: InA = In&o + AqlnP &2lnS (5.3) and InZ = Info + filnP + f2ln& (5.4) After regression analyses the final expressions can be written as: A = 1.31 • 10-3P1-150-53 (5.5) and 2, = 18.3P°-i5,S°-i*. (5.6) In Figure 5.6 the regression surfaces for the tuning amplitude and the pulse length as functions of stack size and percentage calcite in the stack (equations 5.5 and 5.6) are shown. 58 Chapter 5. Zero -offset tuning amplitudes Figure 5.4: Tuning amplitude contour maps: (a) contour map with 3D im age below, (b) contour map with data points overlaid, (c) trend surface, and (d) residual map (contour map subtracted from trend surface; contour interval 0.1). Regression analyses 59 Figure 5.5: Pulse length contour maps: (a) contour map with 3D image below, (b) contour map with data points are overlaid, (c) trend surface, and (d) residual map (contour map subtracted from trend surface; contour interval 5 ms). 60 Chapter 5. Zero -offset tuning amplitudes (a) Figure 5.6: Regression surfaces for (a) tuning amplitude and (b) pulse length as functions of stack size and percentage calcite. 5.4 Synthetic data example The empirical relations for how the tuning amplitude and the pulse length vary as functions of stack size and calcite content in thestack have been used Synthetic data example 61 to predict lateral variation in calcite content on a synthetic seismic dataset. Stochastic modelling has been used to generate a synthetic model with sand and calcite cemented bed geometries reminiscent of the geometries for the TOGI area of the Troll Field (see Chapter 2 and 3). In Figure 5.7 a vertical cross-section through a 3D realization is shown. Note the concentrations of calcite cement around and above the sequence stratigraphic bounding surfaces. In such a reservoir, laterally extensive calcite cemented barriers will especially influence the vertical permeability. The seismic response from the model (Figure 5.7) has been modelled using full waveform reflectivity modelling (Figure 5.8). Seismic parameters for the calcite cemented and non-cemented sandstones were the same as those used to establish the empirical relations in the previous section (see also Chapter 3). The model was placed at 1500 m depth with an overburden having the same seismic parameters as the sandstones in the reservoir. The zero-offset seismic response was modelled every 25 m, resulting in a total of 80 traces. A high degree of interference in the seismic response makes the measurement of pulse length difficult for one stack of calcite cemented beds. To avoid interference effects a single stack of calcite cemented beds was isolated and placed at 1500 m depth in a background of gas sand. The relatively calcite-rich 5C zone was used (Figure 5.9a). The zero-offset seismic response from this isolated stack (Figure 5.9b) shows little lateral variation in pulse shape, whereas theamplitude of the composite seismic reflection varies considerably. This is in agreement with observations of how amplitude and pulse length vary as functions of stack size and calcite content. 5.4.1 Prediction of calcite cementation The amplitude at the maximum of the first peak in the composite reflected signal and the pulse length which were measured laterally across the seismic section (Figure 5.10a and b) were used together with the empirical relations (equations 5.5 and 5.6) to predict lateral change in percentage calcite and stack size (Figure 5.10c and d). The prediction of percentage calcite is good compared to the values measured from the model, but the prediction of stack size is more variable. When the stack size is larger than approximately 20 m, the prediction method is unstable. For smaller stack sizes the predicted stack size is close to the measured. Lateral variation in predicted calcite content and stack size follow the same lateral trend as measured amplitude and pulse length. CO Chapter 5. Zero -offset tuning amplitudes where which Figure boundaries based ’ ■5 r 9) 8 E E 1 0 0 ---- on sandstones have 5.7: ■ calcite (SB) Model been -- observation have analysed. are of 500 shown the been * reservoir ■ identified To in in — Horizontal yellow the the section five left --- (shown color : 1000 -- 1 is TOGI ...... a in length and 2D to the wells, calcite the vertical TOGI .. [m] ...... far where cemented 1500 right). area, cross-section » ...... — three ----- Troll 1 Also ------beds ' flooding ...... Field. indicated --- --- in through .... - --- blue. - .. The surfaces 0 proportion Calcite L r t ; r * are — a calcite 3D 50 the (FS) slur - 5M 3C 4C sc eM 6C stochastic nine proportion [%] 100 and zvwx ---- /VWXSB2 /vw\SB / — aaazxsb A/wvSB reservoir — wva — six — - realization — — — sequence curve SB SB FS FS FS2 zones 1 3 4 3 5 6 1 is CO Synthetic data example «© was seismic Figure jZ 2 E used 1.380 1.360 1.340 1.320 1.300 1.280 1.260 1.400 5.8: has in Zero-offset been the 0 seismic plotted seismic modelling. with normal response 500 polarity. Horizontal to the 2D To model the 1000 length right in Figure is [m] the 40 5.7. Hz 1500 Lateral zero-phase dimension Ricker is 2000 wavelet 2000 m. which The Chapter 5. Zero -offset tuning amplitudes to Figure proportion " model 5.9: curve based (a) and Stochastic the 40 on Hz observations 500 realisation zero-phase Horizontal in of Ricker the the 1 ooo length (b) (a) five wavelet calcite TOGI [m] cemented which wells, 1500 was and barriers used (b) synthetic in in the reservoir seismic zero-offset o Calcite proportion modelling. zone so seismic 5C 100 [%] and wv\ -VXAASB response SB calcite 3 4 Synthetic data example 65 = 0.20- CB 0.15— K0.10- E 0.05- Z 0.00 1000 Horizontal length [m] sz 50- ® 45- 1000 Horizontal length [m] 1000 Horizontal length [m] "to 20-, 1000 2000 Horizontal length [m] Figure 5.10: Prediction input: (a) normalized zero-offset tuning amplitude and (b) pulse length, and prediction results: lateral variation in (c) calcite content and (d) stack size of reservoir zone 5C. Predicted values in dotted curves and measured values in solid curves. 66 Chapter 5. Zero -offset tuning amplitudes 30 — 20 — IQ- 500 1O0O 1500 2000 Horizontal length (m) Figure 5.11: Predicted calcite content in reservoir zone 5C using the mea sured tuning amplitude (Figure 5.10a) and a constant stack size of 7.9 m. Predicted values in dotted curves and measured values in solid curves. The calcite content has also been predicted assuming a constant stack size. The stack size was assumed to be constant for the middle part of the stack of calcite cemented beds in reservoir zone 5C, equal to 7.9 m (shown by the red arrow to the left of the model in Figure 5.9). The lateral variation in calcite content (Figure 5.11) is predicted very well using constant stack thickness. This a consequence of the fact that the tuning amplitude varies little with change in stack size for a low calcite content (Figure 5.4). Note that as the constant vertical stack size is smaller than the whole stack asso ciated with reservoir zone 5C, the measured (and predicted) calcite content is larger than the measured values for the whole stack (Figure 5.10c). 5.4.2 Complicating factors Interference Pulse length as an independent measurement for predicting stack size and percentage calcite has been shown to be clearly affected by interference. To investigate how interference influences reflected amplitudes from stacks of cemented beds, the tuning amplitudes from the isolated stack (Figure 5.9b) were compared with theamplitudes measured from the top of the same stack of calcite cemented beds included in the whole model (Figure 5.8). For these events the lateral variations in tuning amplitude are almost identical (Fig- Synthetic data example 67 ffl 0.25 (0 0.15- E 0.05- Zo.00 Horizontal distance (m) Figure 5.12: Comparison of lateral change in normalized tuning amplitude from the isolated reservoir zone 5C (solid) and from the reservoir zone 5C included in the whole model (dotted). ure 5.12). The predicted variation in calcite cementation (using a constant stack size) would likewise be very similar. Even if there are calcite cemented beds above the stack of calcite cemented beds in reservoir zone 5C, these are either too far away or too thin to change the amplitudes significantly. The same, however, can not be assumed for other events related to other stacks of thin calcite cemented beds. Comparing the seismic response to the iso lated stack of calcite cemented beds in reservoir zone 5C (Figure 5.9b) and the seismic response to the whole model (Figure 5.8), the second positive lobe in the composite reflected signal from the stack calcite cemented beds in reservoir zone 5C clearly interferes with the response from the underlying stack of calcites in reservoir zones 5M and 4C. Distribution Tuning amplitude (and pulse length) has so far been assumed to be de scribed as a function of stack size and calcite content in the stack. Another factor which may affect amplitudes is the distribution of calcite cemented beds within the stack. To analyse this factor stacks with total vertical thicknesses of 20 m all with 20% calcite content but with different calcite cemented bed thicknesses, were placed in a homogeneous background of gas sandstones (Figure 5.13). These stacks were placed at 1500 m depth (overburden has 68 Chapter 5. Zero -offset tuning amplitudes SAND [m]: Effective 0.3 1.7 3.0 3.8 5.0 7.5 15.0 CALCITE [m]: medium 0.1 0.5 0.9 1.0 1.3 1.7 2.5 Total stack: 20 m 20 % calcite (c) Figure 5.13: Seismic response to stacks of calcite cemented beds all with vertical stack size 20 m and 20% calcite content, but with different calcite cemented and non-cemented sandstone bed thicknesses. The stacks (calcites cemented beds in black and non-cemented sandstone beds in yellow) are shown at the top with individual calcite cemented and non-cemented sand stone bed thicknesses indicated. The seismic response to each stack is shown below together with the 40 Hz zero-phase Ricker wavelet (far left) which was used in the full waveform reflectivity modelling. the same seismic parameters as the sands in the stacks) and the zero-offset seismic responses were modelled (Figure 5.13b-h) using full waveform re flectivity modelling. Effective medium parameters for the stacks were also calculated, according to Backus (1962) and the seismic response modelled (Figure 5.13a). The pulse shape changes gradually as bed thicknesses increase except for the model with thickest calcite cemented and non-cemented sandstone beds (Figure 5.13h for two 2.5 m thick calcite cemented beds separated by 15 m Synthetic data example 1.5 /(h) Effective medium (a) 1.0 X... (b) X. (c) X—X---X"-...... —x 0.5 0 0 2 4 6 8 10 12 14 16 18 Sum of thickest sand and calcite [m] Figure 5.14: Normalized amplitude versus sum of thickest calcite cemented and non-cemented sandstone beds for stacks of calcite all with vertical stack size 20 m and 20% calcite content but with different calcite cemented and non-cemented sandstone bed thicknesses. The amplitudes have been nor malized to the amplitude from the effective medium. The letters (a) to (h) refer to the different stacks in Figure 5.13. sand) where the pulse shape is drastically changed. Note that the onset of the first peak comes in at earlier time as the bed thicknesses increase. This is probably due to internal multiples. The amplitude of the first peak in the different seismic responses are plotted in Figure 5.14 versus the sum of the thickest calcite cemented and non-cemented sandstone bed in each stack. The amplitudes have been nor malized to the amplitude of the effective medium (horizontal dotted line). The amplitude corresponding to the first peak in the composite reflected signal decreases as individual bed thicknesses increase to about 78% of the effective medium amplitude at 5.0 m sand and 1.3 m calcite cemented bed Chapter 5. Zero -offset tuning amplitudes E 0.2- 0 500 1000 1500 2000 Horizontal length [m] <1)45- 1000 Horizontal length [m] Figure 5.15: Comparison of (a) tuning amplitude and (b) pulse length mea sured from synthetic seismic for isolated reservoir zone 5C (solid) and for reservoir zone 5C replaced by an effective medium (dotted). thickness and then starts to increase again. A decrease in amplitude of 22% for an assumed constant stack size of 20 m would mean that the calcite content in the stack would be predicted (using the empirical relation, equa tion 5.5) to 16% instead of the correct 20%. For the stack consisting of two 2.5 m thick calcite cemented beds and 15 m non-cemented sandstone beds, the amplitude is almost 50% higher than the effective medium amplitude. Again assuming a constant stack size of 20 m, this amplitude would predict a calcite content of 29%. To analyse the effect of layer distribution in the synthetic dataset from reservoir zone 5C, the isolated stack was replaced by effective medium param eters. The seismic response was modelled and processed as before. Tuning amplitude and pulse length were measured and compared to those of the layered medium (Figure 5.15). The effective medium pulse length shows only minor deviations from that of the layered medium. The tuning amplitude for the effective medium is lower than the amplitude from the layered medium, except for the region 1200 m - 1600 m. This is also the region which has the highest calcite Synthetic data example 71 content (Figure 5.10c) and where the calcite cemented layers are closest together. The largest differences between the effective medium amplitude and layered medium amplitude are around 500 m. This is also a region where the calcite content was predicted too large, both when the stack size was predicted (Figure 5.10c) and when it was kept constant (Figure 5.11). The spacing of thin calcite cemented beds clearly affect the amplitudes of the composite reflected signals, but the random distribution of calcite cemented beds which the empirical relations for amplitude and pulse length are based on, capture to some degree this effect. The largest effect is when the calcite cemented beds are separated by thick non-cemented sandstones. In this case the calcite content will be predicted to be higher than it is. Variations in the background sandstones In this chapter the non-cemented sandstones have so far been considered homogeneous. Variations in acoustic properties within the non-cemented sandstones may, however, also give rise to reflections. Acoustic impedance histograms reveal similar average values of 4625 and 4775 ™ for the clean and micaceous sandstones respectively (Figure 3.5). These values are much lower than the 17474 associated with the calcite cemented beds. A series of ID modelling experiments has been carried out to quantify the relative contributions of the non-cemented sandstones and calcite ce mented layers to the total seismic response. The overlapping histograms for clean and micaceous sandstones suggest that there should be insignificant reflections from the porous non-cemented lithologies. In a first experiment impedance averages for each clean and mica zone were used as input. The seismic response to models with and without calcite cemented barriers was then simulated. Amplitudes in the model where the barriers were removed (Figure 5.16a) are very small compared with amplitudes in the model con taining barriers (Figure 5.16b). The results from this first simulation suggest that the seismic response within the TOGI reservoir will be dominated by the presence of thin high impedance calcite cemented beds. Another simulation, however, has been carried out where vertical trends in the non-cemented lithologies have been introduced. The trends, which are observed in all five wells, are especially pronounced in one of the mica zones which reflects highstand progradation (at about 1.35 s in Figure 5.16c and d). When these trends are included in the model significant reflections are gen- 72 Chapter 5. Zero -offset tuning amplitudes Impedance Impedance Impedance Impedance [g/crr? m/s] [g/crr? m/s] [g/cm 3 m/s] [g/cm 3 m/s] 4000 7000 10000 4000 10000 20000 4000 700010000 4000 10000 20000 © 1.35 (a) Figure 5.16: Acoustic impedance logs (logarithmic scale) and seismic (zero- offset) response from acoustic impedance variations in non-cemented sand stones only (a and c), and with calcite cemented beds (b and d). In (a) and (b) average acoustic values for clean and mica sandstones are used, whereas in (c) and (d) vertical trends in the background are introduced. A zero-phase 40 Hz zero-phase Ricker wavelet was used in the modelling. erated from the non-cemented lithologies alone (Figure 5.16c). These reflec tions are of the same order of magnitude as those from the stacks of calcite cemented beds (Figure 5.16d). The direct prediction method presented in this chapter depends on good well ties and an understanding of how much of the reflected signal is caused by calcite cemented beds and how much is caused by other factors such as reflections from the non-cemented sand stones, interference from other events, and noise. In the relatively small TOGI area, vertical trends in the non-cemented sandstones are larger than the lateral variation (Figure 3.6). The use of tuning amplitudes to predict calcite content, however, cannot deterministically distinguish between lat- Real data example 73 eral variation in calcite content and lateral variations in the non-cemented sandstones. 5.5 Real data example The use of reflection amplitudes as a direct indicator for calcite cementation within stacks associated with sequence stratigraphic boundaries, has been tested on real seismic data from the TOGI area. The seismic data (Fig ure 5.18) are a near-offset stack processed to enhance resolution, suppress noise, and preserve amplitudes. 5.5.1 The 2D seismic dataset The 3D seismic survey over the Troll East gas province was acquired in 1992. Two vessels were used in the dual source and five streamer operation. From this survey, a 2D line has been extracted and especially processed with the goal of preserving amplitudes in the offset domain. The 2D line is located in a north-south direction approximately 130 m west of the 6H well (top reservoir level) in the TOGI area (Figure 5.17). A summary of the acquisition parameters for the 3D survey is given in Table 5.1. The seismic data were acquired with two vessels; one vessel had the two source arrays and three streamers, and the other two streamers. The two sources were fired every other time (flip flop shooting), thereby record ing ten CMP lines for every swath. Due to positioning problems between the vessels, a CMP line from the vessel towing the sources was chosen for this study. Processing The goal of the processing of the 2D seismic line was to preserve amplitudes, improving resolution (horizontally and vertically), and minimizing noise. The data has been converted to minimum phase by applying a recorded far field signature. A summary of the main steps in the processing sequence is given in Table 5.2. The near-offset stack section is shown in Figure 5.18 with acoustic impedance logs in the two wells. 74 Chapter 5. Zero -offset tuning amplitudes North t 31/5 -B -5H 31/5-B -B-4H 1/5 -B -3H 31/5-B Distance [m] Figure 5.17: Location map of the 2D near-offset seismic line relative to the TOGI wells. Well calibration The near-offset stack section has been calibrated to well 6H. The procedure for doing this is described in Chapter 7, and only the main results will be presented here. The impedance log in well 6H was edited and blocked, and the wavelet was estimated using the HIGHRES method (also described in Chapter 7). The estimated wavelet in the 6H well position is shown in Figure 5.19. The synthetic seismogram was generated with full waveform reflectivity modelling and compared with the real seismic in the well position (Figure 5.20). Even though the well is located 130 m away from the seismic line, the tie is fairly good. Real data example Figure been E o converted 1.54 1.62 1.60 1.58 1.56 1.70 1.68 1.66 1.64 5.18: North Real to minimum seismic Well Acoustic Impedance near-offset 31/5-B-6H phase and log Distance stack is plotted section, between CMP with located number normal wells 130 polarity. 565 m west m Well of Acoustic Impedance wells 31/5-B-2H 6H and log South 2H. The contact Gas Top reservoir data fluid has 76 Chapter 5. Zero -offset tuning amplitudes Source M/V Explorer Number of arrays 2 Source array type Point source Distance between array centers 50 m Strings per array 3 Volume each array 2620 cu. in. Pressure 2000 psi Shot interval 18.75 m (37.5 m between odd SPs) Source depth 4 m (+/- 0.5 m) Streamer M/V Explorer + M/V 0stervold Number of streamers 3 + 2 Streamer separation 100 m Length 2990 m Group interval 12.5 m Number of groups per streamer 240 Depth 5-6 m Recording Recording length 5120 ms Sampling interval 2 ms Filter setting 3-218 Hz Table 5.1: Acquisition parameters for the 3D survey. 5.5.2 Prediction of calcite cementation The seismic data have been converted to minimum phase and therefore have a different wavelet than the one used to establish the empirical relation (equation 5.5). Both the frequency content and the time length of the main lobe in thewavelet are about the same as for the Ricker wavelet used earlier, and the relation between amplitude and calcite content is therefore assumed to be valid. The empirical relation was calibrated to well 6H assuming a constant stack size of 19.1 m, based on interpretation of the well. The anal ysed event is marked with a red arrow in Figure 5.18. Seismic modelling indicated that 87% of the total amplitude in the well position is caused Real data example 77 (a) (b) E -20- 20 40 60 80 100 120 Frequency [Hz] (c) ® 0- 100 120 Frequency [Hz] Figure 5.19: Estimated wavelet in well 6H using the HIGHRES method for the 2D near-stack data, (a) Time signal, (b) amplitude spectrum, and (c) phase spectrum. 78 Chapter 5. Zero -offset tuning amplitudes 1. Filter: Instrument phase compensation using recorded far-field signature. Correc tion for recording, signature record ing and processing bandpass filters. Bandpass filter 3.5 Hz 18 dB/oct - 120 Hz 72 dB/oct. 2. Correction: 2.5 dB/s for inelastic attenuation. 3. NMO: using velocities picked every 62.5 m (every 10th trace). 4. Multiple removal: Radon filter: 70 P values -100 to 600. 30 ms taper. 6-120 Hz. Subtract model method. 5. Inverse NMO: Before migration. 6. Migration: Prestack common-offset migration (Ekren and Ursin, 1995). 7. Correction: For geometrical spreading (Ursin, 1990 and Ekren and Ursin, 1995). 8. NMO: After new velocity analysis. 9. Stack: Near-offset stack (850 m). Table 5.2: Main steps in the processing sequence for the 2D seismic data. by the calcite cemented layers in reservoir zone 5C. The remaining 13% is caused by interference from neighboring reflectors, vertical variations in the non-cemented sandstones and random noise. To minimize the contribution from random noise the calibration was also done using the average over five traces around the well. This had only minor effect on the final prediction result. To account for random noise away from the well position, the pre diction results (Figure 5.21) were filtered to show the low frequency trend. The reflected amplitude from the stack of calcite cemented beds analysed is little affected by interference from shallower reflections in the well position. Further away from the well, interference becomes a problem (Figure 5.18) and the prediction results are less reliable. In well 2H the amplitude of the event analysed clearly interferes with reflections from shallower calcite ce mented beds. Measured and predicted calcite content in reservoir zone 5C in the well positions are given in Table 5.3. Real data example 79 Acoustic impedance [g/cm 3m/s] 0 5000 10000 15000 20000 (a) (b) (c) Figure 5.20: Calibration of seismic at 6H well position, (a) Blocked acoustic impedance log in well 6H (reservoir zone 5C is at 1.595 s to 1.607 s), (b) synthetic seismogram (repeated zero-offset trace), and (c) real seismic data (repeated stack trace). Well 6H Well 2H Well 2H Measured Predicted Measured Calcite [%] 13.0 15.1 12.1 Stack size [m] 19.1 19.1 16.1 Table 5.3: Well measurements and prediction results for calcite cemented sandstone content in reservoir zone 5C, real data example. 80 Chapter 5. Zero -offset tuning amplitudes Well 31/5-B-6H Well 31/5-B-2H (used to calibrate) (blind well) CMP number 1020 1060 Figure 5.21: Lateral variation in calcite content in reservoir zone 5C using the empirical relation, equation 5.5, and a constant stack size of 19.1 m. The solid curve is the prediction result while the dotted curve is the low frequency trend. Well 6H was used to calibrate the prediction method, and well 2H was used to check the result. Black crosses indicate calcite content in the wells. 5.6 Conclusions Calcite cemented beds generate significant seismic reflection events although they are very thin. This is due to their very high acoustic impedance. In dividual beds produce relatively small reflections and it is the stacking of several calcite cemented beds around bounding surfaces which produce sig nificant reflections. Based on extensive seismic modelling, empirical relations for zero-offset tuning amplitudes and pulse length as functions of stack size and percentage calcite in the stack have been established. Both amplitude and pulse length increase as stack size and percentage calcite increase. In reservoirs such as the Troll reservoir, reflections from closely spaced stacks of calcite cemented beds will interfere and make the use of the pulse length problematic for prediction purposes. Calcite content may be predicted using amplitude information alone, assuming constant stack sizes. As long as interference between reflections from different stacks of calcite cemented Conclusions 81 beds is minimal the method gives good results. Other factors also affect the amplitudes, such as distribution of calcite cemented beds within the stacks and reflections from the non-cemented sandstones. Good well calibration is therefore required for the direct use of amplitudes for predicting lateral vari ation in calcite cementation. Lateral variations in the non-cemented sand stone are small in the shallow marine Troll Field reservoir. Such variations will however superpose the predicted lateral variation in calcite content. The prediction method has been tested on real data from the Troll Field where many of the above mentioned complicating factors are present. Spe cially interference between seismic responses from different stacks of calcite cemented beds, as well as from different non-cemented sandstones is a prob lem. This work has demonstrated that the description of calcite cemented beds in shallow marine sandstone reservoirs is not a deterministic problem. In the next chapters seismic inversion and sequence stratigraphy interpreta tion of well data have been combined in a probabilistic approach to produce models of calcite cemented barriers constrained by a maximum amount of information. 82 Chapter 5. Zero -offset tuning amplitudes Chapter 6 Application of seismic data for constraining a stochastic model of calcite cementation - synthetic Test 6.1 Introduction In this chapter a prototype procedure for modelling the spatial distribution of calcite cemented barriers in shallow marine sandstones is presented. The procedure integrates geometrical data from held analogue studies, sequence stratigraphy, and seismic data within a stochastic modelling framework. • Analogue data are used to define the a priori geometry of calcite ce mented beds. • The sequence stratigraphic interpretation along with well data are used to define a priori vertical trends in the distribution of calcite cemen tation, and to guide seismic inversion. • Seismic data are used to define lateral variations in cementation around sequence stratigraphic bounding surfaces. The integration of the three techniques produces models of calcite cemented barriers which are constrained by a maximum amount of information. Seis mic inversion constrained by well data and seismic interpretation is used 83 84 Chapter 6. Seismic inversion - synthetic data to overcome the problem of interference between reflections from different stacks of calcite cemented beds (and other reflections in the reservoir) which was demonstrated to be a problem for the direct prediction method presented in Chapter 5. The stochastic models for calcite cementation are outlined first before describing the results of the testing which has been carried out using data from the Troll reservoir in the TOGI area. The modelling procedure has been tested on a synthetic seismic data set based on stochastic simulations of the geology in the TOGI area and real seismic data from the same area. The synthetic data example is presented in this chapter, and the real data example will be presented in Chapter 7. 6.2 Stochastic model for calcite cementation Omre et al. (1990) have developed and applied a 2D Markov field model for describing geometries of calcite cemented beds in a shallow marine reservoir formation. As calcite cementation occurs in zones around bounding surfaces, and not necessarily directly on the bounding surface, a 3D model is desirable. It is not straightforward to extend a 2D Markov model to 3D, and in this work a modified indicator model developed by British Petroleum (BP) has been adopted. This model can capture the most important features of the conceptual model presented in Chapter 2. An indicator model is a grid based model where a discrete variable (in dicator) is simulated at each grid node. For purposes of the work presented here the indicator model is binary with only two indicators (cemented or non-cemented) . The most important input parameter to an indicator model are the proportions of the different lithologies, and variograms in orthogonal directions. Vertical variograms control bed thickness, and horizontal vari ograms control lateral continuity of the cemented and non-cemented sand stones. A sequential indicator simulation (SIS) algorithm (Journel and Alabert, 1990) has been used. The algorithm involves estimating the indicator prob abilities at each node in the model in a sequential manner. Monte Carlo sampling from the probability distributions is then used to assign indicator values to the nodes. The probabilities for the indicators at each node are estimated by indicator kriging (Isaaks and Srivastava, 1989) which uses the following input to the kriging equations: Stochastic modelling constrained by sequence stratigraphy 85 1. well data and previously simulated indicator values within a neighbor hood search radius; 2. indicator variograms; and 3. a priori probabilities (proportions) for each indicator. In a conventional SIS model a stationary held is assumed and the a priori probabilities for each indicator are constant. In the modified SIS algorithm used here spatial trends in the a priori probabilities are introduced. As will be described later, the most important challenge is the definition of the spatial trends which are used to introduce sequence stratigraphic and seismic constraints in the heterogeneity model. 6.3 Stochastic modelling constrained by sequence stratigraphy The observed concentrations of calcite cemented beds around bounding sur faces are incorporated in the stochastic model as a vertical trend in the a priori probabilities (proportions) for the cemented and non-cemented litholo gies. The conditional probabilities describe theprobability for different facies (indicator) given the depth in the model P(fi\di) where /*• is the facies (ce mented or non-cemented) at node i and di is the depth with respect to the bounding surface at node i. The other main parameter in the stochastic model is the indicator var- iogram which controls the geometry of the individual beds. The vertical variogram can be estimated from well data. Horizontal variograms are dif ficult to estimate using well data alone, and uncertainty in the horizontal variograms should be included in the stochastic model. Data from outcrop analogues suggest that the calcite cemented beds within highstand systems tracts are characterized by slightly longer horizontal correlation lengths than those occuring within lowstand systems tracts. The less continuous beds within the lowstands reflects the erosional depositional setting characterized by local channeling etc. Two stochastic realisations of calcite cement distribution within the up per part of the TOGI reservoir are illustrated in Figure 6.1 and 6.2. The first realisation is associated with longer horizontal correlation lengths than the second. Vertical correlation lengths are slightly shorter in Figure 6.1 than 00 CO C hapter 6. Seismic inversion - synthetic data defined surfaces sand Calcite Figure orange. 6.1: by cemented (SB the Stochastic and Note calcite FS). layers the 250 proportion The realisation concentrations 31/5-B-2H are "V vertical u, blue, 500 curve of Horizontal non-cemented distribution distribution of shown cemented 750 to length of of the clean calcite beds calcite right. [m] around quartz cemented cemented 31/5-B-6H * sand and beds above beds yellow, 1250 is within sequence constrained and reservoir non-cemented N 1450 stratigraphic by Vertical a zones 0 proportion Calcite trend 0.25 (trend) micaceous 5C bounding 0.50 which control to 0.75 3C. is 00 Stochastic modelling constrained by sequence stratigraphy is Figure simulated o s 6.2: The with effect shorter 250 of changing 31/5-B-2H horizontal * correlation Horizontal and longer lengths 750 vertical length on correlation geometries [m] 31/5-B-6H of lengths calcite 1250 than cemented the 1450 N realsation beds. Vertical 0 proportion Calcite This in 0.25 (trend) Figure realisation 0.50 control 0.75 6.1. 88 Chapter 6. Seismic inversion - synthetic data in 6.2. The first realisation is characterized by 500-1000 m laterally contin uous barriers whereas more discontinuous barriers are present in the second realisation. Both realisations are constrained by the same a priori vertical trend. In terms of reservoir performance, the first realisation is associated with relatively low vertical connectivity and will tend to behave as a layered system. The second realisation is associated with a much higher degree of vertical connectivity. 6.4 The synthetic “true earth model” A heterogeneous acoustic earth model has been built to test the procedure for predicting variation in calcite cementation. The model is based on well data in the TOGI area, and includes variation in the velocity and density of the non-cemented sandstones and variation in calcite cemented bed geometries. The seismic parameters for the calcite cemented barriers were kept constant for reasons explained in Chapter 3. This acoustic model was used to test procedures for: • extracting information from seismic data; and • using seismic data to condition the stochastic model. The model is treated as a “true earth model ” which acts as a standard for objectively testing the results of the seismic inversion and the method for constraining the stochastic model. The heterogeneous “true earth model ” has been generated in four steps using two stochastic simulators. 1. First a statistical analysis of the TOGI well data was carried out to provide input parameters to the stochastic modelling. 2. Velocity and density variations within the non-cemented sandstones fa cies were then modelled as 3D Gaussian fields (Journel and Huijbregts, 1978). 3. The distribution of calcite cemented layers was simulated using an indicator model described earlier in this chapter. The synthetic “true earth model ” 89 4. Finally the models of calcite cemented bed geometries and non-cemented sandstones were amalgamated by inserting the simulated calcite ce mented bed geometries into the models for density and velocity of the non-cemented sandstones. A total of nine reservoir zones were analysed and modelled independently. Models were also generated for two buffer zones describing the overlying and underlying strata. The reservoir zones and the buffer zones were stacked vertically to create one continuous “true earth model ”. A very high vertical grid resolution of approximately 0.25 m was required to reproduce the thin calcite cemented bed geometries. The horizontal grid resolution is 50 m in both x (East-West) and y (North-South) directions. The model dimensions are 2000 m * 1500 m * 140 m, and the center-point grid is defined by 40 * 30 * 553 grid nodes. The gas-fluid contact is not included in the model and it is assumed that all the reservoir sandstones are gas saturated. Gaussian fields are conventionally used for modelling petrophysical vari ables such as porosity and permeability for use in reservoir simulators (Jour- nel and Huijbregts, 1978). They are also ideal for modelling density and velocity in 2D and 3D as realistic variance and spatial continuity is eas ily captured. Mean values, vertical trends, variance and vertical variograms were calculated for density and velocity for each of the TOGI reservoir zones using data from the five wells. Spherical variogram models with vertical correlations lengths of between 1 and 4 m were fitted to the experimen tal variograms for velocity and density in the various zones as described by Isaaks and Srivastava (1989). Horizontal correlation lengths of between 400 m and 1000 m were used to model different continuity between wells in different zones. Figure 6.3 shows a cross section through a 3D realisation of the acoustic impedances for the non-cemented sandstones for part (zone 5C to 3C) of the reservoir in the TOGI area. This section illustrates the acoustic impedance variation for the non-cemented sandstones in the “true earth model ”. The geometries of calcite cemented beds were generated using rather long correlation lengths of 750 m and a spherical variogram model. Vertical variograms with a correlation length of 1 m were assigned to the calcite cemented beds in all reservoir zones. A cross-section of the calcite model which has been used in the building of the “true earth model ” is shown in Figure 6.1. o Chapter 6. Seismic inversion - synthetic data Note Figure before 5C 2 s ■E E 8 o s to specially 3C). and 6.3: 0 s after Acoustic The the micaceous blocking. vertical 250 impedance 31/5-B-2H trend sandstones 3000 Acoustic variations in Horizontal the 4000 have 4M impedance in zone. generally the 5000 750 length “ true The 6000 higher [g/cm earth inserted [m] 31/5-B-6H 3 model impedance "V m/sj ■g, 7000 logs ” show for the 1250 than variations non-cemented the clean N 1450 in acoustic quartz Reservoir sandstones zone sandstones. impedance (zone Seismic modelling 91 Before the simulated geometries of calcite cemented beds were inserted into the models for density and velocity of the non-cemented sandstones, the 553 density and velocity values for each vertical profile were blocked to between 100 and 200 layers. This was done to reduce computer time in the seismic modelling. In Figure 6.3 are the original and blocked logs shown in well 6H. 6.5 Seismic modelling Synthetic zero-offset sections were generated by a series of ID experiments; one for each x-y node in the “true earth model ”. The seismic modelling was performed using the same full waveform reflectivity modelling as in previous chapters. This modelling gives the correct seismic response to a ID medium and includes primary reflections, transmission loss, and all internal multiples. The modelling was done elastically without a free surface to avoid source and receiver ghosts. A three lobes, zero-phase Ricker wavelet with a center frequency of 40 Hz was used. This produces a similar frequency spectrum to that observed in the real seismic data in the TOGI area. Two synthetic seismic data sets have been generated, one including the calcite cemented barriers and the other with the calcite cemented barriers removed. The model with the calcite cemented barriers removed produces a relatively simple seismic section (Figure 6.4) with a good continuous reflec tion associated with a high acoustic impedance zone at the base of the 4M reservoir interval (Figure 6.3). A number of significant, but discontinuous, reflections were generated within the uppermost reservoir interval. This in terval is characterized by relatively high variances for density and velocity (not shown in Figure 6.3). The model with calcite cemented barriers produces a more complex sec tion with generally higher reflection amplitudes (Figure 6.5). The inclusion of calcite cemented barriers within the 4C and 5C zones in particular pro duces significant reflection which are not present in the response from the model with the calcite cemented beds removed. Also shown in Figure 6.5 (in colors) are seismic horizons for top reservoir, and top and base of stacks of calcite cemented beds (as indicated by the cal cite proportion curve to the right). These horizons are based on calculated times from thicknesses and velocities in the “true earth model ”. From an interpretation point of view it would be quite easy to interpret the calcite 02 Chapter 6. Seismic inversion - synthetic data with calcite Figure used in some cemented 6.4: the of seismic North-South the beds reservoir modelling. removed. synthetic zone boundaries The seismic log shows section indicated. the through acoustic To the wells impedance right 2H is and the 6H (on 40 from Hz logarithmic zero-phase an earth scale) model Ricker in with well wavelet the 6H o> CO Seismic modelling seismic 4C, in Figure Interpreted the and non-cemented 6.5: modelling. 5C. seismic Synthetic To the The horizons right sandstones seismic log are shows show calcite section as the top in proportion from Figure acoustic and an base 6.4, impedance earth curve of but stacks model with and in the of the with well calcite 40 calcite the 6H Hz cemented same (on zero-phase cemented logarithmic variation beds beds Ricker in in scale) (Figure reservoir acoustic wavelet . 6.1) used impedance zones included. in 4M, the 94 Chapter 6. Seismic inversion - synthetic data stack in zone 4M. This is mainly due to the high acoustic boundary between non-cemented sandstones of zone 3C and 4M which is continuous and easy to follow. For the stacks in zone 4C and 5C interference (between reflections from different calcite stacks as well as from the non-cemented sandstones) is a problem for lateral interpretation of the stacks. These synthetic data examples show how difficult it may be to use seismic data for reservoir char acterization. 6.6 Inversion of synthetic seismic data The synthetic seismic data set (Figure 6.5) has been inverted using a con strained sparse spike inversion algorithm from Jason Geosystems B.V. Sparse spike inversion The convolutional model of a seismogram can be expressed by: s(t) = w(t) * r(t) + n(t), (6.1) where w{t) is the seismic wavelet, r(t) is the reflectivity, n(t) is the additive noise, s(t) is the seismic data as function of two-way traveltime t and * means convolution. The purpose of deconvolution is, given a measurement s(t), to retrieve the reflectivity function r(t). The objective of post-stack seismic inversion is to find acoustic impedance £, which in the ftth layer is defined as: & = pkVk, ' (6.2) where pk and % are density and velocity respectively. The acoustic impedance is related to the reflectivity coefficients by: (6.3) There exist infinitely many acoustic impedances which will reproduce the observed seismogram; some of these may reasonably describe the earth impedances, other will not. Using the seismic data as the only source of information and assuming a known wavelet an inverse filter applied to the seismogram (equation 6.1) will produce estimated reflectivity series which Inversion of synthetic seismic data 95 are averages of the true reflectivities (Fullagar, 1985). To reduce the non uniqueness, the earth’s reflectivity may be assumed to be composed of a series of large events superimposed on a Gaussian background of smaller events. The sparse spike assumption or the layered earth model may be expressed as: L r(t) = ^ rkS(t - rk), where (6.4) k~l where L is the total number of layers, rk is the reflection coefficient at the interface between the Mh and (k + l)th layer, rk is the travel-time to the kih layer, and t is travel-time. This assumption reduces the non-uniqueness because there exist many acceptable reflectivity series, r(i), which cannot be written in this form. The sparse spike deconvolution and inversion techniques have developed over the last two decades with contributions amongst others by Taylor et al. (1979), Levy and Fullagar (1981), Oldenburg et al. (1983), Fulla gar (1985), and Debeye and Van Riel (1990). Sparse spike inversion is a recursive, single trace algorithm which assumes normal incidence data. The sparse spike inversion algorithm used in this work is described by Debeye and Van Riel (1990) and Debeye and Schellinger (1996). In this algorithm the Zg-norms of both the reflectivity and the noise are minimized in the time domain. The objective function may be expressed on matrix form as: = rTr + Anrn, (6.5) where r is the reflectivity vector, A is a weighting factor, n is the noise vector given by d — s (real data minus modelled data), and T denotes trans pose. The problem is solved iteratively using least squares techniques. The synthetic seismic data are generated with the convolutional model. The weighting factor, A, is used to weigh the data match versus the reflection coefficient term. Global constraints in the vertical direction are available impedance well logs and horizons interpreted on the seismic data. A low frequency trend model is built from the logs and the interpreted seismic horizons. The solution is constrained to lie within some large percentage of this trend. Another factor which introduces non-uniqueness into the problem is the inversion of thin beds. Obviously, the inversion will not be able to pick up 96 Chapter 6. Seismic inversion - synthetic data every thin calcite cemented bed. In Chapter 4 and 5, it was shown that the amplitude of the composite reflection from a stack of calcite cemented beds was correlated with the vertical stack size and the percentage calcite in the stack. Russell (1988) showed that sparse spike inversion fails to resolve bed thicknesses below one-quarter of the dominant period in the seismic signal. Even if the total stacks of calcite cemented beds are replaced by effective medium layers, their thickness will in this case be less than one-quarter of the dominant period. This problem is omitted in the constrained sparse spike inversion by the interpreted seismic horizons. They define the top and the base of the most prominent stacks of calcite cemented beds and within certain limits fix the stack sizes. The acoustic impedance between these interpreted horizons are then estimated by the sparse spike algorithm. Input to the inversion algorithm The input to the inversion is the seismic data, a wavelet, a low frequency trend model, and interpreted seismic horizons. In addition a number of performance parameters have to be set before the inversion can be done. The most important parameter is the weighting factor, A. This factor has to be set so that it strikes a balance between generating acoustic impedance traces that are not overly detailed versus getting an acceptable data fit. A low A means fewer spikes, resulting in little detail in the acoustic impedance model and a poor data fit. Too high A may result in multiple spikes being used to model a single seismic event and/or spurious events being modelled. The objective is to select a low frequency trend model, constraints, and a A that optimize the match between the acoustic impedance trace and the well log, and that optimize the match between the real and synthetic seismic traces. For inversion of thin beds (stacks of calcite cemented layers) in this work high A values of 150 were chosen. The solution was further constrained to lie within 25% of the low frequency trend. The inversion of the synthetic data-set has been done using well data from well 6H and quality controlled in well 2H. The wavelet extraction method used in thereal data example (Chapter 7) has been also been tested on the synthetic data to check the method. The seismic wavelet has been estimated using the HIGHRES inversion method introduced by Ursin and Holberg (1985) and modified and tested on real data by Brevik and Berg (1986) and Brevik et al. (1990). A stacked seismic trace is assumed represented as the discrete convolution of a reflection coefficient Inversion of synthetic seismic data 97 series with a pulse, plus a noise term: Nr Si — ^ ] r jWl—j -)- Til: l — [0, Ag] i (6-6) i=0 where s; is the sampled seismic trace, rj is the sampled reflection coefficient series as a function of two-way travel-time, wi-j is the seismic pulse and ni is the noise term. Ns is the number of time samples to be considered in the inversion. In the HIGHRES method the noise is allowed to have non-white spectra (i.e. the noise can be correlated), and the noise is expressed as: Nc ni = ^2c3e‘-E (6 .7 ) 3=0 where the cj’s are coefficients of a Moving Average (MA) process of order Nc and the sequence {e;_y} is a realisation of a zero-mean white-noise process having a Gaussian distribution. In the wavelet estimation the reflection coef ficient series is known from the well log, and the seismic pulse and the noise coefficients, Cj, are estimated from the actual time window of the seismic data at the well position using a maximum-likelihood principle. Acoustic impedance logs for the entire reservoir section, converted to time and densely sampled to include the thin calcite cemented beds were used together with the seismic data as input to the HIGHRES wavelet esti mation. Even with a perfect match between the acoustic impedance log in the well and the seismic data, the wavelet is not estimated exactly. Com pared to the 40 Hz Ricker wavelet which was used in the seismic modelling (Figure 6.6a), the estimated wavelet is longer in time and contains more side-lobes (Figure 6.6b). These differences are also reflected in the phase spectra of the two wavelets (Figure 6.6e and f). The amplitude spectrum of the estimated pulse, however, is close to that of the Ricker pulse (Figure 6.6c and d). The HIGREStechnique assumes that the seismic trace can be rep resented by the convolutional model plus noise (equation 6.6). The seismic data has been modelled with a more sophisticated method which includes transmission loss and internal multiples. An explanation for the mismatch between the wavelet used in the seismic modelling and the estimated may be that the noise term in equation (6.6) cannot compensate for the above mentioned factors. A total of 10 seismic horizons delineating stacks of calcite cemented beds and important acoustic impedance boundaries were used to constrain the 98 Chapter 6. Seismic inversion - synthetic data (a) (b) -0.04 -0.04 Time [s] Time [s] -10- -10- -20- -20- -40- -40— Frequency [Hz] Frequency [Hz] Q) 0- Frequency [Hz] Frequency [Hz] Figure 6.6: The 40 Hz Ricker wavelet (a, c, e) used for seismic modelling. The estimated wavelet (b, d, f) using the HIGHRES method. Time signals (a, b); amplitude spectra (c, d); and phase spectra (e, f). Stochastic modelling constrained by seismic data 99 sparse spike inversion. Seven of the horizons are shown in Figure 6.5 and all the horizons crossing well 2H are shown in Figure 6.8. In the synthetic data example these seismic horizons were estimated exactly in time from the “true earth model ” using the velocity information . The horizons are between 12 m and 35 m apart. Inversion The result of the sparse spike inversion is an acoustic impedance section in time. This has been depth converted (Figure 6.7) using the known velocity field. Lateral trends in the inverted impedance result within the 4C and 5C reservoir zones partly mirror the lateral variation in the proportion of calcite cemented beds seen in the “true earth model ” (Figure 6.1). For example, the clustering of calcite cemented beds in the lower left and upper right of the 5C zone of the “true earth model ” (Figure 6.1) is reflected in higher impedances in the inverted section (Figure 6.7). The inversion result has been checked in well 2H (Figure 6.8) which was not used as input to the inversion, and there is good agreement between the filtered impedance log and the inversion result. The generally excellent match between the true and inverted impedance demonstrate that a sparse spike inversion has potential to extract useful information from seismic data which can be used to constrain the modelling of calcite cemented barrier distribution within the TOGI area. The success of theinversion was partly related to the tight constraints imposed using the ten interpreted seismic horizons, i.e. the seismic inversion was dependent on a sequence stratigraphic understanding of the reservoir geometries. 6.7 Stochastic modelling constrained by seismic data Acoustic impedance marginal distributions have been established for the ce mented and non-cemented sandstones using the results of the inversion of the synthetic seismic data (Figure 6.9a). Although the marginal distribu tions are overlapping there is a partial separation with the non-cemented sandstones having a higher probability density distribution at low acoustic impedance values and the cemented sandstones having higher probabilities at high acoustic impedance values. This is reflected in the population statistics Chapter 6. Seismic inversion - synthetic data I * section Figure r (Figure 8 o 75 50 25 o S 6.7: of 6.1) Figure Depth and with 6.5. converted acoustic Compare 31/5-B-2H 4500 inverted Acoustic impedance with impedance the 5000 impedance distribution variations section 5500 in [g/cm of the for calcite non-cemented 31/5-B-6H 3 reservoir m/s] 6000 cemented zones sandstones beds 3C to in 5C, N the (Figure based “ true Vertical proportion 0 Calcite on earth 6.3). 0.25 (trend) the 0.50 control model seismic 0.75 ” Stochastic modelling constrained by seismic data 101 Acoustic Impedance [g/cm 3 m/s] Acoustic Impedance [g/cm 3 m/s] 0 5000 10000 15000 -5000 0 5000 10000 Top reservoir 1.52- -1.52 1.54- ® 1.56- 1.58- 1.60- -1.60 (b) Figure 6.8: Inversion result in blind well position, (a) Acoustic impedance well log in well 2H; and (b) filtered (5-75 Hz) acoustic impedance log (solid) and filtered (5-75 Hz) inversion result (dotted). The ten seismic horizons, used to constrain the sparse spike inversion, are indicated. where the non-cemented sandstones have acoustic impedance mean values of 5181 -A? ir and 5418 respectively. The marginal distributions can be directly transformed to conditional probability functions and scaled through the classic Bayes theorem (Davies, 1986): g{sj\fi)p{fi) (6 .8) S{si\fi)p{fi = sand) T = calcite) where g{si\fi) is the probability density function of the acoustic impedance given the facies (non-cemented and cemented sandstone), and p(fi) is the facies proportion of non-cemented and cemented sandstone. Figure 6.9b shows the conditional probabilities which are not yet scaled for facies pro portions. The slope of the functions are related to the information content 102 Chapter 6. Seismic inversion - synthetic data (a) s I 4600 5100 5600 6100 Acoustic impedance [c^cm m/s] (b) 4600 5100 5600 6100 Acoustic impedance [^mr m/s] 0.8 - 0.6 - 0.4 - 0.2 - 4600 '100 5600 Acoustic impedance [t^crrr m/s] Figure 6.9: (a) Marginal distributions for non-cemented and cemented sand stone, (b) conditional probability functions without scaling for facies pro portions, and (c) scaled conditional probability functions. Non-cemented sandstones are shown as solid curves and calcite cemented as dashed curves. Stochastic modelling constrained by seismic data 103 in the seismic data. If the functions are vertical the prediction problem be comes deterministic and the seismic data can be used to define uniquely the facies distribution. If the functions are horizontal the seismic data will not contribute with useful information on facies distribution. At intermediate slopes, such as in this example (Figure 6.9b), seismic data can be used in a probabilistic framework for predicting facies distributions. Although the cor rectly scaled functions (Figure 6.9c) are relatively flat, the consistent slopes demonstrate that the inverted acoustic impedance can be used to assist the prediction of distribution of calcite cemented beds. For example an inverted acoustic impedance of 5100 ^3 ™ is associated with a conditional probabil ity of 0.03 whereas an acoustic impedance of 5600 ^3 ™ is associated with a conditional probability of 0.1, which is more than a three-fold increase. The seismic constraints P(/z|sz-) are used to introduce lateral trends su perimposed on the vertical trends defined by well data and sequence stratig raphy P(fi\di). The integration of the two trends involves first normalizing P(fi\si) within each layer of the simulation model, followed by a rescal ing with respect to P(/,-|d,) to produce conditional probabilities P(/j|d,-, s,). This is a rather ad hoc method, and alternatively more rigorous Bayesian methods for integrating the two trends should be developed. Figure 6.10 il lustrates the conditional probabilities P(/,-|d 4-, s,j which have been used as an external trend for modelling distribution of calcite cemented beds within the 5C to 3C reservoir zones. The trend has captured the layering implicit in the sequence stratigraphic interpretation, and the seismic data have generated significant lateral variation along each horizon. Stochastic simulations constrained by both sequence stratigraphy and seismic data using this a priori trend are illustrated in Figure 6.11 and 6.12. The realisation in Figure 6.11 includes a distribution of calcite cemented beds which is remarkably similar to the geometries in the “true earth model ” (Figure 6.1). Note for instance that the concentration in cementation above SB 4 is high to the right and decreases to theleft, whereas theopposite trend can be seen above SB 3. This is in good agreement with the trends in the “true earth model ”. Correlation lengths are similar to the ones used in the generation of the “true earth model ”. The other realisation (Figure 6.12) is also reminiscent of the “true earth model ”, but also includes a number of significant differences. This is a natural consequence of the fact that the description of calcite cemented beds is not a deterministic problem. 104 Chapter 6. Seismic inversion - synthetic data seismic Figure 6.10: constraints Conditional P(fi\di 1 probabilities Si). 0.0 Compare Horizontal 0.1 Probability for with 0.2 calcite Figures length of 0.3 cementation calcite 6.1 [m] 0.4 and 31/5-B-6H 6.7. based 0.5 on both sequence Vertical stratigraphy Calcite proportion (trend) control and Conclusions 105 6.8 Conclusions The multidisciplinary procedure for modelling the spatial distribution of calcite cemented barriers in shallow marine sandstones has been tested on a realistic synthetic seismic data-set. Knowing the facies distribution of the subsurface it has been possible to test procedures for extracting informa tion from seismic data and for using seismic data to condition a stochastic model. Sparse spike inversion tightly constrained by interpreted seismic horizons provides valuable information which may used to condition the stochastic modelling. However, due to interference of reflections from stacks of calcite cemented beds and from the non-cemented background litholo gies intra-reservoir seismic interpretation is difficult. The inverted acoustic impedances and the known facies distribution have been used to establish conditional probabilities for facies given the inverted acoustic impedance. These conditional probability functions reveal that seismic data can be used in a probabilistic framework for predicting facies distribution within the TOGI reservoir. Geometries of calcite cemented beds from stochastic sim ulations constrained by both sequence stratigraphy and seismic data are in good agreement with geometries of the “true earth model ”. In the next chapter the procedure has been tested on real seismic data from TOGI. Figure generation data 3C. Vertical th ick n ess[m] The using o S 6.11: distribution of the Stochastic the spatial “ true 250 of trend earth calcite realisation 31/5-B-2H * illustrated model cemented 500 Horizontal 1 ” . of Compare distribution in beds Figure 750 is length with constrained 6.10. of the [m] calcite The “ true 31/5-B-6H * by same cemented earth by correlation both model 1250 sequence beds ” (Figure within lengths stratigraphy N 1450 6.1). reservoir were Vertical 0 Calcite proportion used (trend) 0.25 zones and 0.50 as control seismic in 5C 0.75 the to o O i> o % o z (A fA Figure Vertical th ick n ess [m] 75 50 25 0 o s 6.12: Stochastic 250 31/5-B-2H realisation * 500 Horizontal 2 of distribution 750 length of [m] cemented 31/5-B-6H beds within 1250 reservoir 1450 N zones Vertical Calcite 0 proportion 0.25 (trend) 5C 0.50 to control 3C 0.75 108 Chapter 6. Seismic inversion - synthetic data Chapter 7 Application of seismic data for constraining a stochastic model of calcite cementation - real test 7.1 Introduction In the previous chapter, a procedure for modelling spatial distribution of calcite cemented barriers in shallow marine sandstones was presented. The procedure integrates information from outcrops, sequence stratigraphic in terpretation of well data, and seismic inversion results in a stochastic mod elling framework. The procedure was successfully tested on synthetic seismic data. In this chapter, the procedure is tested on real seismic data from the TOGI area. The seismic data used in this chapter is a 3D seismic line located very close to the 2H and 6H wells in the TOGI area. 7.2 The 3D seismic dataset The 3D line is located in a North-South direction (Figure 7.1), 20 m to the east of well 2H (at top reservoir level). This seismic line is from the same survey as the 2D data used in the real data example in Chapter 5. The 3D line is closer to the wells and may therefore be easier to tie. The 109 110 Chapter 7. Seismic inversion - real data North t 1500 1 8 31/5 -B -5H 31/5-B -6H * i ^ 1000 ----- yi£------ 31/5 -B -4H 3 1/5 -B -3H 1 * * 31/5-B -2H o 500 i & 0 0 500 1000 1500 2000 Distance [m] Figure 7.1: Location map of the 3D seismic line relative to the TOGI wells. reflections in the 3D data are more continuous than in the 2D data. The acquisition parameters for the 3D survey are listed in Table 5.1. The Troll East 3D seismic survey has been processed by CGG. The main steps in the processing sequence are summarized in Table 7.1. Full 3D processing involves steps like binning and 3D migration which have apparently improved the data quality of the 3D line (Figure 7.2) com pared to the 2D processed seismic line presented in Chapter 5 (see Fig ure 5.18). The processing of the 2D line was aimed at preserving amplitudes at all offset and only the near-offset traces were stacked. AVO effects in the data possibly due to critical reflections from stacks of calcite cemented beds (see Chapter 4) would then not affect the near-offset response. On the other hand random noise will be dampened less with the stacking of fewer traces. In this chapter the 3D processed line has been used. The main reason for this is the improved data quality, but also the fact that this line is located Well calibration 111 1. Filter: low cut 6 Hz 18 dB/oct 2. Minimum phase conversion: using far-field signature 3. Adjacent trace sum: of adjacent traces with NMO wraparound applied 4. Spherical divergence correction: 1 /tv2 5. Predictive deconvolution: 24 ms gap, 200 ms operator length 6. Velocity analysis: every 2 km 7. Multiple removal: fk demultiple 8. 2D DMO: using Kirchhoff Integral Algorithm 9. Intelligent binning: using 75% overlap. Cell length: 37.5 m. Cell width 25.0 m 10. NMO correction: using velocities picked ev ery 0.5 km 11. Stack 12. Predictive deconvolution: water bottom gap, 100 ms operator length 13. 3D random noise attenuation 14. Pre migration time variant filter 15. 3D finite difference migration 16. Attenuation compensation 17. Zero-phase conversion 18. Time and space variant filter Table 7.1: Main steps in the processing sequence for the 3D seismic data. very close to the wells. 7.3 Well calibration Well calibration includes log editing, wavelet estimation, creation of syn thetic seismograms and establishing a correlation between thesynthetic seis mograms, the surface seismic data, and the geologic features. 112 Chapter 7. Seismic inversion - real data with limiting Figure low 7.2: stacks frequency 3D seismic of calcite trends section cemented and through estimated beds wells concentrated wavelets 2H and is 6H the around with input impedance bounding to the seismic logs surfaces. and inversion. interpreted This information seismic horizons together Well calibration 113 The 3D seismic data used in this real data example is zero-phase con verted and plotted with reverse polarity following the SEG standards. In the zero-phase conversion of this data-set, an operator was designed based on an estimated wavelet in one well (located about 10 km away from the study area). The wavelet, however, cannot be assumed constant. It will vary as a function of both time and space. Before synthetic seismograms could be created a wavelet had to be esti mated. To get a good estimate of the wavelet, a good correlation between the logs and the real seismic data is needed. This correlation, however, is difficult to achieve without a good understanding about the wavelet. Well calibration is therefore an iterative process. Log-editing Full logging suites in the TOGI wells cover only from 40 m above the reser voir to 20 m below the gas fluid contact. Velocity and density logs have been edited for caving, specially in the upper part of the reservoir in well 2H. Fur ther, the calcite cemented intervals have been assigned constant velocity and density values (6520 m/s and 2.68 g/cm 3) for reasons explained in Chapter 3. Shoulder effect due to the thin calcite cemented beds, will also affect the measurements in the sands, yielding to high log readings directly above and below the calcites cemented beds. No editing was, however, done to correct for this. Sonic and density readings will also be affected by mud filtrate in the gas saturated formation. Velocity and density readings will therefore be too high in the gas sands. This is not thought to be of major importance and has not been corrected for. To find a good velocity and density model for the overburden, well in formation from nearby wells and check-shot data from well 6H were used. The top of the reservoir is characterized by an overall drop in velocity and density going from the overlying shaly Heather Formation into the gas sat urated sands of the Sognefjord Formation. Assuming a zero-phase reverse polarity wavelet, the seismic response from the top of the reservoir is a strong peak. Positive (downwards) shifts of 12.5 ms and 15.8 ms for well 2H and 6H respectively, were necessary to align the synthetic seismograms with the real seismic data. The gas fluid contact is characterized by increase in both velocity and density and gives a prominent trough on the seismic section. To fit the synthetic seismograms to the real seismic data at the gas fluid contact and keep the top of the reservoir, it was necessary to compress the 114 Chapter 7. Seismic inversion - real data logs 8 ms and 3 ms for well 2H and 6H respectively. This was done by ad justing the velocities (in the non-cemented sandstones) to keep the correct layer thicknesses. This compression lead to an increase of velocities of the non-cemented sandstones of 8% in the well 2H and 3% in well 6H. Wavelet estimation A good estimate of the seismic wavelet traveling at the depth considered is necessary to obtain a good calibration between the well logs and the real seismic data. In this work theestimated pulse has also been used as input to the seismic inversion. This wavelet will be different from the pulse generated from the source at the surface due to transmission through overlying layers, attenuation, and data processing. Wavelets have been estimated in both well 2H and well 6H lying on the seismic section (Figure 7.1), using the HIGHRES method described in the Chapter 6. Because of the short logging intervals, special attention had to be paid to edge effects in the pulse estimation. The edge effects were reduced by tapering the error trace (seismic trace minus the sum of synthetic and the estimated noise trace) near the ends of the time windows. Several combinations of different number of noise coefficients (equation 6.7) and pulse lengths were evaluated in order to obtain stable wavelet estimates in the two wells. Figure 7.3 shows the estimated wavelets in time, their amplitude spectra, and their phase spectra. For well 2H a pulse length of 40 ms and 9 noise coefficients were used and for well 6H the pulse length was 70 ms with 9 noise coefficients. Both wavelets have a center frequency of about 40 Hz. The pulse estimated in well 6H is most similar to a zero-phase wavelet, whereas the pulse estimated in well 2H is not. The phase spectra show that both wavelets are mixed phase. Correlation between the synthetic seismograms, the surface seis mic data, and the geologic features Synthetic seismograms were made for both well positions using full-waveform reflectivity seismic modelling. Figure 7.4 and 7.5 show synthetic seismograms for well 2H and 6H with estimated wavelets in the two wells applied, together with the acoustic impedance logs in the wells, the filtered acoustic impedance logs (10-75 Hz), and the real seismic data. Also shown are the seismic picks for top and base of interpreted stacks of calcite cemented layers used in the Well calibration 115 (a) (b) Time [s] (c) -10- -10- -20- -40” 40 60 80 100 120 Frequency [Hz] Frequency [Hz] (e) (f) 20 40 60 80 100 120 40 60 80 100 120 Frequency [Hz] Frequency [Hz] Figure 7.3: Estimated wavelets in well 2H (a, c, e) and 6H (b, d, f) using the HIGHRES method. Time signals (a, b), amplitude spectra (c, d), and phase spectra (e, f). 116 Chapter 7. Seismic inversion - real data Acoustic impedance [g/ctn ’m/s] Acoustic impedance [g/cm ’m/s] 0 5000 10000 15000 0 6000 10000 15000 ireseivoir E 1.62 Figure 7.4: Well tie well 2H. (a) Acoustic impedance log, (b) filtered acous tic impedance log (10-75 Hz) with seismic picks, (c) synthetic seismogram (repeated zero offset trace) using the wavelet estimated in well 2H, (d) syn thetic seismogram (repeated zero offset trace) using the wavelet estimated in well 6H, and (e) real seismic data (repeated stack trace). seismic inversion. As seen in Figures 7.4 and 7.5, the calibration between well data and real seismic data is difficult. Even if the wells are only 565 m apart, the estimated wavelets are quite different. Bad quality log measurements in well 2H due to caving, may be one reason for this. In well 6H the estimated wavelet is closer to a zero-phase wavelet, but the match between the synthetic seismo gram and the real seismic is not perfect. The lateral extent of single calcite cemented beds away from the well is an uncertain factor. Some knowledge may be drawn from the vertical position in a sequence stratigraphic context and may be from geochemical composition (Chapter 2). The lateral extent of one single calcite cemented bed, however, is not so important for the seismic tool. It is the concentration of calcite cemented beds around the sequence Well calibration 117 Acoustic impedance [g/cm ’m/s] Acoustic impedance Jg/cm ’m/s] 0 5000 10000 15000 0 5000 10000 15000 Figure 7.5: Well tie well 6H. (a) Acoustic impedance log, (b) filtered acous tic impedance log (10-75 Hz) with seismic picks, (c) synthetic seismogram (repeated zero offset trace) using the wavelet estimated in well 2H, (d) syn thetic seismogram (repeated zero offset trace) using the wavelet estimated in well 6H, and (e) real seismic data (repeated stack trace). stratigraphic bounding surfaces that gives the seismic response related to the calcite cemented beds. The occurrence of beds around sequence bounding surfaces, however, is thought to be a more lateral extensive phenomenon. All calcite cemented beds observed in the wells have therefore been included in the well calibration process. Even in the synthetic data example (Chapter 6) with perfect match be tween log and seismic, the wavelet was not estimated perfectly. This was explained by the fact that the wavelet estimation method uses the convolu tion model, whereas the a more sophisticated method was used modelling the synthetic seismic data. The same will be true in this real data exam ple. This, however, cannot explain the difference between the two estimated wavelets (well 2H and 6H). The seismic inversion has been done with both 118 Chapter 7. Seismic inversion - real data Figure 7.6: Inverted acoustic Acoustic impedance impedance section [g/cm 3 including m/s] well information from 4M 4C Gas 3C 50 Top 6C calcites calcites calcites calcites calcites well reservoir fluid contact 2H. Sparse spike inversion 119 wavelets and will be compared in the next section. 7.4 Sparse spike inversion The same inversion technique was used on the real data as for the synthetic data example. Input to the inversion was seismic data, acoustic impedance log (only one can be used at the time), low frequency trend model, inter preted seismic horizons, and estimated wavelet. The output is an acoustic impedance section in time. The 3D seismic line with impedance logs (well 2H and 6H) and interpreted seismic horizons are shown in Figure 7.2. Inter preted seismic horizons limit the interpreted stacks of calcite cemented beds concentrated around bounding surfaces. Two inversions have been performed on the 3D seismic section; one in cluding 2H well information (estimated wavelet, impedance log, and low frequency information) and one including 6H well information. The output acoustic impedance sections are shown in Figure 7.6 and 7.7. In both sections the low impedance gas saturated reservoir can be clearly seen be tween the high impedance shaly cap rocks and underlying water-saturated sandstones. In the gas reservoir high and low impedance bands are visible, reflecting stacks of calcite cemented beds and different sand types (micaceous and clean quartz sands). The two inversion results are generally similar, but the result including the 6H well information seems to be generally more varying than the other. To visualize the similarity the two sections have been plotted against each other sample by sample (2 ms sample interval) in a scatter plot in Figure 7.8a. Including the low frequency trends, the two inversions results have a correlation factor of 0.86. The result of a linear regression analysis of the two datasets is shown by the line in the plot. Too tight constraints set on the low frequency trend model cause the sharp edges in the high impedances. Figure 7.8b shows a scatter plot of the two inver sion results after applying a 10 Hz low-cut filter. Without the low frequency trend, the sample by sample difference in the two inversion results is caused only by the fact that two different wavelets have been applied in the inver sion. The correlation coefficient has now dropped to 0.80. The estimated wavelet is important for the inversion result, but there is also a good cor relation between results using the two different wavelets estimated in each well. The inversion result including the 6H well information will be used further to constrain the stochastic modelling of calcite cemented barriers. In 120 Chapter 7. Seismic inversion - real data Figure 7.7: Inverted acoustic Acoustic •4000 impedance impedance 5000 section [g/cm 3 sooo m/s] including well information from well 6H. Sparse spike inversion 121 (a) 7000 —I----- «------1------<----- j------«------4000 5000 6000 7000 Acoustic impedance [g/cm s m/s], wavelet 1 well 6H (b) li I -1000 0 1000 2000 Acoustic impedance [g/cm 3 m/s], wavelet 1 well 6H Figure 7.8: Correlation plots of the inversion results from well 2H with estimated wavelet in well 2H and from well 6H using the wavelet estimated in well 6H. (a) Including the low frequency trend, and (b) without the low frequency trend (low cut filter 10 Hz applied). Also shown are the regression lines. 122 Chapter 7. Seismic inversion - real data Acoustic impedance [g/crn m/s] Acoustic impedance [g/crn m/s] 0 5000 10000 15000 0 5000 10000 15000 1.56 - reservoir 1.58 - 1.60 - 1.62 - 1.64 - 1.66 - — Gas-fluid contact Figure 7.9: (a) acoustic impedance log in well 2H, and (b) filtered (10-75 Hz) impedance log (solid) and inversion result (dotted). Well 2H was not used actively in the inversion, only well 6H. Also indicated are the seismic picks used to constrain the seismic inversion. Figure 7.9 the inversion result including the 6H well information is checked in well 2H. There is generally a very good match between the inversion result and the filtered acoustic impedance log from well 2H. D epth conversion 123 7.5 Depth conversion Conversion of interpreted seismic horizons or maps in time to depth are most commonly done integrating stacking velocity information with well data and check-shot data. This normally gives a velocity field with low frequency lateral and vertical trends. In areas with good well control, as in the TOGI area, linear interpolation of velocities measured in the wells is an alternative method. Commercial software packages (e.g. from Jason Geosystems B.V.) have the possibility to do linear interpolation of well velocities constrained by interpreted seismic horizons (to account for stratigraphic dip) in combination with stacking velocities. This method will give a velocity field with better vertical resolution, but equally low lateral resolution to the first method mentioned. When the seismic data have been inverted to acoustic impedance, a more logical approach is to use the 2D (or 3D) impedance model to steer velocity variations away from the wells. A kriging approach has been adopted for this purpose and to ensure correct velocity values at well locations. The velocity model is: vi(t,x) = a + b£(t,x)+ e(t,x), (7.1) where £ is the inverted acoustic impedance as a function of time, t, and space, x, tq is the velocity field, a and b are regression coefficients, and e is a noise term. The coefficients, a and b, are obtained from a regression analysis of the velocity measurements in the wells (after applying a 75 Hz high-cut filter) and the inverted acoustic impedance at the well positions. The regression analysis gave the following regression model: %2 (Z, %) = 990 + 0.31f (Z, %), (7.2) where the velocity is given in ™, and the acoustic impedance is given in The noise term, e(Z, z), in equation (7.1) is added to the velocity field, ug, found using equation (7.2) so that the resultant velocity field, ui, matches the velocities measured in the wells. To ensure correct velocity values at thewell positions the noise term is found using a kriging technique (Abrahamsen, 1993). The noise has been modelled using a spherical variogram model with correlation length of 10 m and 1300 m in the vertical and horizontal directions respectively. The variance of the noise is 27225 which corresponds to a standard deviation of 165. The final 2D velocity field is shown in Figure 7.10. 124 Chapter 7. Seismic inversion - real data wells. Figure Also 7.10: shown Velocity are field interpreted based 2000 on seismic the inversion horizons Velocity 2600 [m/s] result and 3000 velocity and constrained logs in the by wells. velocity observations in the two Constrained modelling of calcite cemented barriers 125 The spatial trends in the velocity model are partly given by the inverted impedance result and partly by the variogram function. The long horizontal correlation length will tend to generate a horizontally layered velocity field. As long as the layering, given by the inversion result, is sub-horizontal (in the region between the wells, Figure 7.10) the algorithm works well. At the edges of the model there is a slight stratigraphic dip, and the velocity layering becomes inconsistent with the stratigraphic layering because of the long horizontal correlation length. This could be solved either by using a shorter horizontal correlation length or preferably by using a variogram function that is dip dependent. The depth conversion was performed using the velocity field in Fig ure 7.10, and flattened at the gas fluid contact (1547 m) (Figure 7.11). 7.6 Constrained modelling of calcite cemented bar riers Conditional probability functions for facies given the impedance values have been estimated using the results of the inversion at the well locations and the facies distributions observed in the wells (Figure 7.12a). The marginal dis tributions are overlapping, but as for the synthetic data example described in Chapter 6, there is a partial separation with non-cemented sandstones having a higher probability density distribution at low acoustic impedance values and the cemented sandstones having higher probabilities at high acoustic impedance values. The mean value for non-cemented sandstones is 4824 — and for calcite cemented sandstones 4922 These val- ues are somewhat lower and closer than for the synthetic example. In the synthetic example the distributions were based on the whole earth model, whereas in this real example only the two wells could be considered. The marginal distributions are transformed to conditional probability functions and scaled through the Bayes theorem (equation 6.8). Figure 7.12b and c show the conditional probabilities before and after scaling for facies propor tions. The conditional probability functions are quite similar to those found in the synthetic example (Figure 6.9b and c). As described in Chapter 6 for the synthetic data example, the seismic constraints were used to introduce lateral trends superimposed on the verti cal trends defined by well data and sequence stratigraphy. The vertical trend 8 Chapter 7. Seismic inversion - real data seismic Figure 7.11: horizons Inverted and impedance impedance well Acoustic result •4000 logs. (including impedance 5000 [g/cm well 3 6000 information m/s] in well 6H) in S depth 4M 4C Gas 3C 6C Top 5C calcites calcites calcites calcites calcites reservoir fluid with contact interpreted Constrained modelling of calcite cemented barriers 127 (a) 0.008 c 0.006 - £ 0.004 - sandstone 0.002 - 4700 5200 Q Acoustic impedance [g/cm m/s] a 0.6 - C 0.4 ■O 0.2 5200 5700 Acoustic impedance [g/cm m/s] (c) a 0.8 - a 0.6 - C 0.4 4200 5700 Acoustic impedance [gtamr m/s] Figure 7.12: (a) Marginal distributions for non-cemented and cemented sandstone, (b) conditional probability functions without scaling for facies proportions, and (c) scaled conditional probability functions. Non-cemented sandstones are shown as solid curves and calcite cemented as dashed curves. (N oo Chapter 7. Seismic inversion - real data seismic Figure of caicite 7.13: constraints. cemented Conditional beds To the in probabilities all right five is 0.05 TOGI the for Probability vertical wells. caicite 0.15 trend cemented of caicite or the 0.35 beds caicite based proportion on both curve sequence based stratigraphic on Caicite 0 proportion 0.25 observation 0.50 0.75 and Constrained modelling of calcite cemented barriers 129 is the same as for the synthetic data example and is based on calcite cement observations in all five TOGI wells and sequence stratigraphic interpretation. Figure 7.13 shows the conditional probabilities which have been used as an external trend for modelling distribution of calcite cemented layers within reservoir zones 4M, 4C, 5M, and 5C, where three sequence boundaries (SB) and one flooding surface (FS) have been interpreted. There is considerable lateral variation implied by the seismic data along SB 4, but less along SB 2 and SB 3. Compared to the conditional probability for the synthetic data example (Figure 6.10) the lateral variation is less in the real data example. The synthetic seismic data was modelled trace by trace assuming local ID medium, and consequently the lateral resolution will be better than what can be expected for real seismic data. Another reason may of course be that the stacks of calcite cemented beds are more lateral extensive than antici pated. Based on the spatial conditional probability functions (Figure 7.13) capturing both sequence stratigraphy and seismic data information, stochas tic simulations of geometries of calcite cemented layers have been done. The same indicator model which was used for the synthetic data example (Chap ter 6), has been used in this real data example. Figure 7.14 and 7.15 show two realisations of distribution of calcite cemented beds in the TOGI area using spherical variogram models with correlations lengths as for the syn thetic data example in Chapter 6 (750 m horizontally and 1 m vertically). These realisations, equally probable, are constrained by a maximum amount of information about calcite cemented beds. 130 Chapter 7. Seismic inversion - real data observation quartz 4M. Figure using Distribution the sandstones 7.14: o N spatial of Stochastic calcite trend of in 31/5-B-6H calcite light cemented illustrated realisation yellow. Horizontal cemented beds in To 1 Figure in the of beds 500 length all distribution right five is 7.13. [m] constrained is TOGI the Micaceous of vertical 31/5-B-2H wells. * calcite by sandstones trend both cemented or sequence 1000 the are beds calcite colored stratigraphy within proportion in 1250 dark reservoir s and yellow Vertical curve proportion Calcite seismic zones (trend) and based control 5C clean data on to CO Co n s t r a in e d m o d e l l in g o f c a l c it ec e m e n t e db a r r ie r s 4M. Figure 7.15: o N Stochastic 31/5-B-6H * realisation Horizontal 2 of 500 length distribution [m] of 31/5-B-2H * calcite cemented 1000 beds within 1250 reservoir s Vertical 0 proportion Calcite zones 0.25 (trend) control 0.50 5C 0.75 to 132 Chapter 7. Seismic inversion - real data 7.7 Conclusions Within a stochastic modelling framework geometrical data from field ana logue studies, sequence stratigraphy, and seismic data have been integrated to produce calcite cemented barrier models which are constrained by a max imum amount of information. A non-stationary indicator model with an arbitrary spatial trend in the indicator proportions is a suitable model for describing the geometries and distribution of calcite cemented beds in shal low marine sandstone reservoir. The work has shown that sequence strati graphic interpretation provides a framework for defining vertical trends in the distribution of calcite cement within shallow marine sandstone reservoirs. The concentration of thin calcite cemented beds around bounding surfaces produces a measurable seismic response. Sparse spike inversion, tightly con strained by a sequence stratigraphic interpretation, can be used to extract information concerning the lateral distribution of calcite cementation around flooding surfaces and sequence boundaries. The seismic data used is a 3D seismic data set of good quality. The data is assumed to resemble a zero-offset section, and no attempt has been done to process for AVO effects. For well calibration it is important to correct calcite cemented bed velocities and densities for layer thickness effects. A good esti mate of the seismic wavelet is also important to get a good calibration of the seismic data to the well data. Even for closely spaced wells as in the TOGI area, rather different wavelets may be estimated. The different wavelets will yield different seismic inversion results. For depth conversion purposes a ve locity field has been obtained integrating well information with the inverted acoustic impedance field. This method yields a more lateral variability in the velocities than would be obtained using for instance stacking velocities. The synthetic (Chapter 6) and real data examples have proved that seismic data can provide valuable information on distribution of calcite cemented beds in reservoirs where the background sandstones are relatively homoge neous. This modelling procedure where stochastic simulation is used as a framework for multidisciplinary data integration, can be used to assist reser voir management of shallow marine reservoirs containing calcite cemented barriers. Appendix A Thin-layer AVO effects N.E. Bakke and B. Ursin A.l Abstract Tuning caused by closely spaced impedance boundaries affect seismic ampli tudes. At zero-offset the shape of the composite reflected signal approaches the time-derivative of the original pulse as the layer thickness decreases. For layers thinner than half of the tuning thickness, the reflected ampli tude is modified by a factor equal to twice the time-thickness of the thin layer. Offset dependent tuning can be approximated by the time differences between primary reflections. For high velocity contrasts locally converted waves will also affect the total reflected seismic response. The contribution from intrabed multiples can in most cases be ignored. Correction for offset dependent tuning should be considered before conventional AVO analysis. A.2 Introduction AVO analysis has in many cases proved to be a useful tool in estimating the contrasts in seismic (elastic) properties of the subsurface. These properties might again be related to lithology and fluid content. The fundamental ba sis for AVO analysis is the Knott-Zoeppritz equations which describe how transmission and reflection coefficients vary with angle for plane wavefronts impinging upon a single interface separating two half-spaces. Seismic am plitude variation with offset, however, are affected by many other factors 133 134 A ppendix A. Thin -layer AVO effects of which some are offset dependent (Ursin and Dahl 1992; Castagna 1993). Seismic data processing should aim at removing the effects of these other factors, so that the corrected data-set depends only on reflection and trans mission coefficients. Dealing with a layered medium consisting of more than one boundary, makes AVO analysis more complex. At zero-offset interference or tuning is a function of thelength of the pulse, often 20-100 msec, and the spacing of the acoustic impedance boundaries in time. The latter is again a function of the interval velocity of the thin bed. Widess (1973) showed how the composite reflection amplitudes from a thin layer vary as a function of layer thickness for a cosine wavelet. For a thin layer interbedded in a homogeneous background of lower acoustic impedance Widess found that the maximum constructive interference for a zero-phase wavelet occured when the bed thickness was equal to one quarter of the dominant wavelength in the signal. This is also called the tuning thickness. When the layer thickness was one-eight of the dominant wavelength, the composite response approximated the derivative of the original signal. Widess called this thickness the theoretical threshold of resolution. For even thinner layers, the shape of the composite response stayed the same but decreased in amplitude. Chung and Lawton (1995) developed expressions for the normal incidence amplitude response of a thin layer for the general case of unequal reflection coefficients at the top and base of the bed. As a function of offset, the bed-tuning also becomes a function of differ ential moveout. Depending on the layer thickness, differential moveout can cause an amplitude increase or decrease with offset. Swan (1988) described AVO analysis in a finely layered medium and found that AVO distortions due to tuning may be larger than the underlying lithologic AVO effect. Tun ing caused by NMO convergence may be considered to be noise for some methods, like AVO analysis, while it provides additional information for other methods. Ball (1988) used the additional information from the offset domain to extend the conventional zero-offset tuning analysis which relates layer thickness to impedance of the thin bed. Different approaches to correct for AVO tuning before conventional AVO analysis, have been proposed. Hindlet and McDonald (1986) decomposed the total offset response from a thin layer into top and bottom responses. The decomposition was achieved by taking the difference between two offset reflections and applying amplitude calibrations based on tuning ratios. Their Seismic response from a thin layer 135 method was found to suffer from inaccuracies for layers thinner than half the tuning thickness. Lin and Phair (1993) extended the work by Widess (1973) to include the offset domain. They assumed that the thin layer was inter- bedded in the same media above and below, that their zero-phase wavelet approximated a cosine wave, and that intrabed P-wave multiples and locally converted waves could be neglected. We analyse thin-layer tuning effects and present tuning correction fac tors for a general seismic wavelet and for both zero-offset and offset data, extending the work by Widess (1973) and Lin and Phair (1993). A.3 Seismic response from a thin layer We consider a thin elastic layer of thickness Az and P-wave velocity v. embedded in two half-spaces, as shown in Figure A.l. The response from the thin layer may be approximated by the two primary P-wave reflections (Ursin and Dahl 1992): (A.1) Layer 1 Layer 2 Layer 3 Figure A.l: Layered elastic model with primary reflections. 136 A ppendix A. Thin -layer AVO effects where t denotes time and y offset. R(y) is reflection amplitude, g(y) is geometrical spreading and T(y) is two-way travel-time. Index 1 denotes reflection from the top of the layer and index 2 from the bottom of the layer. In the formula above we have neglected the offset dependent effects of the source and receiver array directivity, visco-elastic attenuation and transmission through the overburden. The seismic wavelet p(t) represents the incident wavelet. In order to simplify the analyses we shall assume thatthe two half-spaces have identical elastic properties and that the layer is thin compared to the depth (distance to the source and receivers). This means that J?2(y) = -Ri(y) and gi(y) ~ <72(2/) (see Appendix A-l). Correcting for offset depen dent geometrical spreading (as given in Appendix A-l) and normal moveout corresponding to the top of the layer results in the corrected data-set: 4*,3/) = - AT(y))], (A.2) where AT(y) = ?2(y)—Ti(y) is the difference in two-way travel-time between the bottom and the top of the thin layer. Assuming that this travel-time difference is small compared to the length of the pulse p(t) results in the approximation: 4W = (A.3) where p'(t) is the time-derivative of the pulse. By using the approximation in Appendix A-2 we obtain: 4t,y) = #)AT(0)C(y)/(f), (A.4) where (A.5) is an offset-dependent AVO tuning factor. For small velocity contrasts (vs % v), the last term in equation (A.5) can be ignored and we get the alternative AVO tuning factor: For a thick layer, the corrected data consist of the primary reflection from the top of the layer is 4W = (A.7) Synthetic data examples 137 The thin-layer effects are therefore, see equation (A.4): 1. The pulse-shape is changed from p(t) to p'(t), 2. The zero-offset amplitude is changed from 72(0) to R(0)AT(0) , and 3. The AVO-response is modified by the term C(y) or alternatively by the term Ci(y). In Appendix A-3 it is shown that for the wavelet p{i) = cosio0t, equa tion (A.4) gives the formula of Lin and Phair (1993) and, for zero-offset, of Widess (1973). A.4 Synthetic data examples The proposed thin-layer effects have been analysed on synthetic seismic data sets; one set based on a model with high contrasts in seismic parameters and one with low contrasts. To substantiate the validity of the assumptions made in the previous section, seismic data-sets have been generated with different modelling algorithms. A.4.1 Seismic modelling Dynamic ray tracing with the possibility to specify different modes (Cerveny et al. 1977) and the commercially available full waveform, elastic, reflectivity modelling OSIRIS from 0degaard & Danneskiold-Samspe have been used for seismic modelling. Reflectivity modelling gives the correct seismic response to a stratified medium, and includes all events such as primary reflections, intrabed multiples, and locally converted waves. Locally converted waves are waves which propagate as P-waves in the overburden, but convert to S-waves, and have one or two legs as S-waves, within the thin layer. For thin layers, the travel-times of these converted waves and the intrabed multiples will be approximately the same as the primary reflections. In ray tracing all events have to be specified, and its accuracy may be questionable for thin layers. The seismic simulations were set up with a receiver spacing of 50 m and a maximum offset of 2000 m. A point source and the same source pulse were applied in both ray tracing and reflectivity modelling. The source pulse contains both source and receiver ghosts, and was modelled by the program 138 A ppendix A. Thin -layer AVO effects (a) (b) o 6 12 30 36 Figure A.2: (a) Source pulse and (b) its time-derivative. The original pulse has been up-scaled 1000 times compared to the derivative. Modgun from PGS Seres. The center frequency in the source pulse is 60 Hz. The pulse and its time-derivative are shown in Figure A.2. A simple model consisting of only three layers has been considered (Fig ure A.l). The depth to the top of the thin layer was kept constant at 1500 m. The thickness of layer number 2 was constant in each modelling, but was varied in different modelling examples from 1 to 20 m. A.4.2 Data processing for AVO analysis For an homogeneous overburden, the geometrical spreading is equal to the travel path distance: (A.8) where D is the depth to the first interface. This corresponds to equa tion (A. 10) with vs = vq. All data-sets were amplitude corrected by multi plying with g{y) given above. For the purpose of analysing thin-layer effects (as given by equation A.4), the synthetic data was also corrected for offset- dependent PP-reflection coefficient (Cerveny et al. 1977). The data was further processed for AVO effects with a robust AVO anal ysis technique (Ursin and Ekren 1995). This technique aligns a time window horizontally for each zero offset sample in a CMP-gather using static time- shifts in the NMO correction to avoid NMO stretch. Inaccuracies in this alignment are reduced by a residual NMO correction. The length of the time window is approximately equal to the composite pulse duration. The travel-time corrected data is modelled as a constant pulse multiplied by an Synthetic data examples 139 amplitude function that is approximated by a polynomial in the offset coor dinate (Ursin and Dahl 1992). This gives the signal estimate: d(t,y) = [l + b1 y2+ b2y4]w(t). (A.9) The polynomial coefficients, b\ and 62, and the estimated pulse, w(t), are found by a separable least-squares algorithm. Comparing the estimated dataset given by equation (A.9) with the thin- layer data expression (equation A.4) after dividing by the reflection coeffi cient, R(y)), we can now analyse the proposed thin-layer effects. The offset- dependent tuning factors, C(y) and C\(y) in equations (A.5) and (A.6), may be compared directly with the polynomial in equation (A.9), and the esti mated pulse, w(t) in equation (A.9), may be compared with the zero-offset tuning factor AT(0)p'(t) in equation (A.4). A.4.3 High contrast layer The seismic parameters for the high contrast models are given in Table A.l. These parameters are typical for a calcite cemented sandstone (layer num ber 2) in a gas sand reservoir (layer number 1 and 3). Simmons and Backus (1994) found that the contributions from intrabed multiples and local converted waves from a thin layer depend on the con trasts in Vp and Vs. Seismic modelling has been performed with reflectivity modelling and ray tracing (with primaries only) to substantiate the valid ity of the assumption that the response from this thin-layer model can be approximated by the primary reflections. In Figure A.3 the contribution from primary reflections, intrabed multiples (up to third order), locally con verted waves (single-leg, PPSP and PSPP, and double-leg, PSSP), and Layer Lithology P-velocity S-velocity Density number [m/sec] [m/sec] [g/cm 3] 1 Gas sand 2465 1643 2.12 2 Cemented sand 3810 2241 2.70 3 Gas sand 2465 1643 2.12 Table A.l: Seismic parameters used in the synthetic data example, high contrasts in the seismic parameters. 140 A ppendix A. Thin -layer AVO effects the sum of all these events are shown for a 8 m thick layer. Compared to the primary reflections, the intrabed multiples are veiry weak and probably can be neglected. The locally converted waves, however, give a considerable contribution to the total reflected seismic response for this model. Analyses at zero-offset In Figure A.4 wedge plots of zero-offset data are shown for reflectivity mod elled data, d(t, 0), estimated data ,w(t), using the robust AVO analysis tech nique, and the derivative of the source pulse scaled by the time-thickness of the thin layer, p'(t)AT(0). Figure A.5 shows corresponding difference plots. As expected, both reflectivity modelling and ray tracing give very simi lar zero-offset responses even for this high contrast model. The robust AVO analysis technique manages to estimate both modelled data-sets very well, and there are only small differences. For all layer-thicknesses the shape of the composite reflected pulses are similar to that of the derivative of the pulse. There are, however, time-shifts between the modelled data and the scaled derivatives which increase with increasing layer thicknesses. It is also evident that multiplying the derivative of the pulse by the time-thicknesses of the layers yield too large amplitudes for layers thicker than 8 m. The differences seen in Figure A.5 between the scaled pulse derivatives and the other data-sets are partly due to amplitude differences and partly due to the mentioned time-shifts. The actual amplitude scaling factor at zero-offset due to thin-layers ef fects has been estimated from the synthetic data-sets and compared with the proposed factor AT(0) (Figure A.6). The actual scaling-factors were estimated by direct amplitude measurements and by a least squares method and give similar results. The maximum of the estimated scaling factors oc cur at the tuning thickness, which is at 14 m for this model. The proposed scaling factor AT (0) is similar to the actual scaling factor for layers thinner than half of the tuning thickness. Analyses at offset Figure A.7 shows the offset dependent tuning curves for thin layers (1-20 m) estimated by the robust AVO analysis technique shown for (a) the ray tracing data-set (with primaries only) and (b) reflectivity modelled data-set. Also shown are the two proposed correction factors, C(y) and C\ {y). Note that Synthetic data examples 141 (a) Offset [m] 500 1000 1500 2000 1.20 — 1.26 LA ] U =5 — 1.32 A 1.38 1.44 1.50 ' 4 (b) Offset [m] 500 1000 1500 2000 1.20 1.26 1.32 1.38 1.44 1.50 (c) Offset [m] 1.20 ! 1.26 ' * 1.32 1.38 | 1.44 1.50 I ! I (d) Offset [m] 500 1000 1500 2000 1.20 L-j ! 1.26 - 1.32 1.38 1.44 I I 1 1.50 Figure A.3: Seismic response from a 8 m thick layer (with high contrasts in seismic parameters) modelled with ray tracing for (a) primary reflections from top and base, (b) intrabed multiples, (c) locally converted waves, and (d) the sum of all the events mentioned above. 142 A ppendix A. Thin -layer AVO effects Modelled data, d(t,0) Estimated data, w(t) (a) Reflectivity modelling (c) From reflectivity data 2 4 6 8 10 12 14 16 18 20 1.218 J I!!I L 1.218 £L 0) 1.230 I 1.242 |I 1.242 1.254 (b) Ray tracing (d) From ray tracing data 2 4 6 8 10: 12 14 16 18 20 1 2 4 6 8 10 12 14 16 18 20 J- V3 1.218 1 1 1.218 1.230 >> i > ) s 1.230 FE I 1.242 1.254 1.254 (e) P'(t) AT(0) 10 12 14 16 18 20 "L Figure A.4: Wedge plots of zero-offset data, high contrast models: (a) and (b) modelled data, (c) and (d) estimated data, and (e) derivative of the source pulse scaled by twice the time-thickness of the thin layers. The wedge thickness in metres is indicated above each trace. these factors are independent of the layer thickness. The large contrast in velocities for these models causes a significant difference between the two correction factors. The ray tracing data-set shows that for decreasing layer thicknesses the tuning curves approach the correction factor C(y). For layers thinner than 6 m, the tuning curves have abnormal behaviors, which are caused by the failure of ray tracing for such thin layers. The tuning curves for the reflectivity modelled data-set show no such abrupt changes for the thinnest layers. Also for this data-set, the responses approach the correction Synthetic data examples 143 Reflectivity modelling Ray tracing (a) d(t,0) - w(t) (d) d(t,0) - w(t) 1 2 4 6 8 10 12 14 16 18 20 1 2 4 6 8 10 12 14 16 18 20 1 J 1 1.218 CO | | i i g ' S 1.230 uJ L J I 1.242 I F 1.254- m f m 1.254 (b) d(t,0)-p'(t)AT(0) (e) d(t,0) - p'(t) a T(0) 1 2 4 6 8 10 12 14 16 18 20 1518 - - 1530, 1542- 1554 - (C) w(t) - p'(t) a T(0) (f) w(t)-p'(t)AT(0) 10 12 14 16 18 20 1518 SL (g) Reflectivity data - ray tracing data 1 2 4 6 8 10 12 14 16 18 20 1518 .to. 1530 I 1542 1554 Figure A.5: Difference plots for zero-offset data-sets; high contrast models: (a) and (d) modelled data minus estimated data, (b) and (e) modelled data minus derivative of source pulse times time thickness of the thin layer, (c) and (f) estimated data minus derivative of the source pulse scaled by the time-thickness of the thin layers, and (g) reflectivity data minus ray tracing data. The wedge thickness in metres is indicated above each trace. 144 A ppendix A. Thin -layer AVO effects AT(O) = 2Az/v From amp. measurements Least squares estimates Q> 8- •4= 4- Wedge thickness [m] Figure A.6: Proposed, AT(0), and estimated actual scaling factors at zero- offset due to thin-layer effects for high contrast data-set. factor, C{y), as the layer thicknesses decrease, but due to contribution from locally converted waves, never reach it. For these models with high contrast in velocities the correction factor Ci(y) will better correct for thin-layer tuning effects than the factor C(y). Synthetic data examples 145 (a) 1 m calcite 2 m calcite 0.9 -i ^0.7 - Tuning curves for thin layers (1-20 m) Correction factor C(y) Correction factor C, (y) Offset [m] 5 0.9 ==0.7 Tuning curves for thin layers (1 -20 m) Correction factor C(y) Correction factor C, (y) Offset [m] Figure A.7: Tuning curves for (a) ray tracing and (b) reflectivity modelled high contrast data-set. Also shown are the two correction factors C(y) and Ci{y). The arrows indicate increasing layer thicknesses, 6 - 20 m in (a) and 1 - 20 m in (b). 146 A ppendix A. Thin -layer AVO effects A.4.4 Low contrast layer Thin-layer effects have also been analysed for a thin gas sand layer encased in shale with low contrasts in seismic parameters (Table A.2). Computation shows that for this model the contributions from locally converted waves and intrabed multiples are negligible compared to the primary reflections. Layer Lithology P-velocity S-velocity Density number [m/sec] [m/sec] [g/cm 3] 1 Shale 2743 1394 2.06 2 Gas sand 2835 1762 2.04 3 Shale 2743 1394 2.06 Table A.2: Seismic parameters used in the synthetic data example; low contrasts in the seismic parameters. Analyses at zero-offset The same analysis has been performed as for the high contrast data-set to analyse the proposed thin-layer effects. Seismic modelling has been per formed only with reflectivity modelling as locally converted waves and in trabed multiples can be neglected for these models. Wedge plots of modelled data, d(t, 0), estimated data, w(t), and the derivative of the pulse scaled by twice the time-thicknesses of the thin layers, p'(t)AT(0), were also computed in this case. The same conclusions can be drawn from these plots as for the analyses of the high contrast data-sets. Again the robust AVO analysis technique estimates the modelled data well. The pulse-shape of the com posite reflected signals approaches the shape of the derivative of the pulse for decreasing layer thicknesses. Due to lower velocity for the thin layers in these models the pulse-shape changes more for increasing layer thicknesses than in the high contrast data-set. The differences between the scaled pulse derivatives and the other data-sets are to a higher degree due to pulse-shape changes than for the high contrast models in addition to amplitude differ ences and time-shifts. The actual amplitude factor at zero-offset due to thin-layer effects has been estimated in the same ways as for the high contrast data-sets and again Synthetic data examples 147 To 14------AT(0) = 2Az/v ...... - From amp. measurements O) 4- Wedge thickness [m] Figure A.8: Proposed, AT(0), and estimated actual scaling factors at zero- offset due to thin-layer effects for low contrast data-set. the same conclusions can be drawn (Figure A.8). The maximum of the estimated scaling factors occur at the tuning thickness, which is at 10.5 m for this model. The proposed scaling factor AT(0) is again similar to the actual scaling factor for layers thinner than half of the tuning thickness. Analyses at offset Figure A.9 shows the offset dependent tuning curves for the seismic responses from the gas sand (1-18 m) encased in shale together with the two correction factors C(y) and C\{y). Due to the small contrast in velocities, the correc tion factors are almost identical for all offsets. The AVO response due to tuning from a 6 m thick gas sand layer will be nearly perfectly corrected for. Thinner layers will be slightly under-corrected, while thicker layers will be over-corrected by an amount depending on the layer thickness. 148 A ppend ix A. Thin -layer A VO effects "O 0.8- ------Tuning curves for thin layers (1-18 m) 0.6 - — Correction factor C(y) • • • • Correction factor C,(y) Offset [m] Figure A.9: Offset dependent tuning curves for the low contrast data-set. Also shown are the two correction factors C(y) and Ci(y). The arrow indi cates increasing layer thicknesses, 1 - 18 m. A.5 Real data The AVO response correction has been applied to a real data example from the Troll Field in the Norwegian North Sea, Block 31/6. The seismic event analysed is the response from the Early Paleocene Maureen Formation; a 21 m thick limestone encased in a thick homogeneous shale. Table A.3 gives the seismic parameters for the thin layer and the layers above and below, based on wire-line logs from well 31/6-8. The S-velocities are based on Vp/Vg-ratios from wells in the Troll West area. The seismic data-set is from a 2D seismic line acquired as part of a 3D seismic survey, acquired in 1992 and processed by Statoil. To increase the signal-to-noise ratio, six CMP-gathers around the well position have been summed to a super CMP-gather. The near trace in this super CMP-gather is at 130 m offset and the far trace at 1480 m offset. The receiver interval is 75 m. Processing for AVO effects has been performed with the same robust AVO analysis technique as described earlier. After NMO correction, the data within the time window has been corrected for offset dependent geometrical spreading, according to Ursin (1990) (Appendix A-l). Conclusions 149 Lithology P-velocity S-velocity Density [m/sec] [m/sec] [g/cm 3] Shale 2030 1041 2.00 Limestone 3410 2273 2.40 Shale 2100 1077 2.15 Table A.3: Seismic parameters based on well logs, real data example. Figure A.10 shows the AVO response in the seismic data (ideally only due to PP-reflection coefficient and tuning), and the AVO responses after applying correction factor C(y) and C\ (y). Due to relatively high contrasts in velocities between the thin layer and the overlying layer the two correction factors yield different results. To check the accuracy of the corrected data sets, reflectivity modelling was performed down to the top of the thin layer. The model is based on well information and includes 63 layers above the thin layer. The same AVO processing has been applied to this synthetic dataset as to the real data. Compared with the modelled response including only the top of the thin layer, the correction factor C(y) over-corrects the seismic data. This is due to contributions from locally converted waves in the thin layer. The AVO response after applying factor Ci(y), however, is very similar to the modelled response. These results are in agreement with the analyses of the synthetic data examples. A.6 Conclusions We have analysed thin-layer AVO tuning effects. For zero-offset data the shape of the reflected pulse approaches the derivative of the source pulse as layer thickness decreases. This is consistent with earlier published work, e.g. Widess (1973). For layers thinner than half of the tuning thickness the zero-offset reflected amplitude is scaled with a factor equal to twice the time-thickness of the thin layer. Seismic data is often converted to zero-phase in seismic processing, which yields a symmetrical pulse as a result. Thin-layer tuning effects should al ways be considered before conventional AVO analysis if the shape of the 150 A ppendix A. Thin -layer AVO effects ■O 0.8- co 0.6- ------Seismic data ...... Seismic data after applying C(y) • • • • Seismic data after applying C,(y) ------Modelled top Offset [m] Figure A.10: AVO curves estimated by the robust AVO analysis technique for the real data example for the seismic data before correction, after correction with factors C(y) and Ci(y), and for seismic modelling including the top of the thin layer. reflected pulse of the interesting seismic event is asymmetrical. The data may in this case be corrected for offset dependent AVO tuning by dividing by the factor Ci(y) given in equation (A.6), as demonstrated in the real data example. Acknowledgments We would like to thank Statoil for getting access to data and computer facilities and Terje Dahl for letting us use his ray tracing program. Nils Erik Bakke thanks Mobil Exploration Norway Inc. for financial support. Conclusions 151 Appendix A-l: Geometrical spreading correction The offset-dependent geometrical spreading for a primary P-wave reflection is approximated by (Ursin 1990): / vs \ 2 2 1 r 1 11 g(y) = Sfif(0)2 + 0 + (A.10) l2 W - xJ .^0 where vq is the velocity at the source and receiver, vs is the stacking veloc ity, and T(0) is the two-way normal-incidence travel-time. The zero-offset geometrical spreading is: 0(0) = -- 53 ^Zkvk, (A.ll) vo % Y where Az& and % are the layer-thickness and interval velocity of layer num ber k, and the sum is over all layers above the reflecting interface. The zero-offset geometrical spreading factors from the thin layer are re lated by: 92(0) = 9l(0) + ^^. (A.12) Vo The zero-offset amplitudes are related by: 1^1 2Az v _ 1 v0vAz (A.13) 02(o)~m(o) %0i(o)^ gi(o) This means that the amplitude-difference is roughly proportional to 7^, where D is the depth of the thin layer. This amplitude-difference is very small. For non-zero offset it is of the same order of magnitude, and we may use the approximation: 0iW«02((/). (A. 14) Appendix A-2: Travel-time difference The two-way travel-time to the top of the thin layer is approximated by: (A. 15) r(y) = T(0): + ,2‘ 152 A ppendix A. Thin -layer AVO effects The two-way travel-time from the base of the thin layer is then: T2(s) = y[T(0) + AT(0)]2 + (A.16) where AT(0) = ^==- (A.17) is the two-way, normal-incidence travel-time in the thin layer. The change in the stacking velocity is computed from: [T(0) + AT(0)][^ + A^ = T(0)^ + 2„Az, which gives: (A.18) The travel-time-difference can now be approximated by: ATW = T2(y)-T(;/) 2T(0)AT(0) ^A^ fl + -T(%) (A.19) T( 0) V2 — v2 AT(!/) 1 + 2T(0)2u4 Appendix A-3: Comparison with previous work Lin and Phair (1993) give the AVA-response from a thin layer by (their equation (2) in our notation): Bt(6)=WoAT(0)coa0E(g), (A.20) where lvq is the dominant frequency of the wavelet, AX’(O) is the two-way normal-incidence travel-time in the thin layer, and R(0) is the reflection coefficient from the top interface. Using the travel-time approximation in equation (A.15) gives: dT yy sin6 — v (A.21) Conclusions 153 and then cosO = r(Q) A , (A.22) T(0) u? — u2 1 + T(y) 2T(0)2u Assuming the wavelet is p(t) = cosojqI. our equation (A.4) gives equation (A.20) above with cosO given i equation (A.22). For 0 = 0 (zero-offset) this reduces to equation (3) and (4) in Widess (1973). 164 A ppendix A. 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