Near-Surface Correction on Seismic and Gravity Data

Home , Gravimetry

Journal of Earth Science, Vol. 26, No. 6, p. 851–857, December 2015 ISSN 1674-487X Printed in China DOI: 10.1007/s12583-015-0546-7

S. Bychkov*, I. Y. Mityunina Perm State University, Mining Institute of Ural Branch of Russian Academy of Sciences, Perm 614001, Russia

ABSTRACT: It is important and urgent to work out better statics correction methods to facilitate seismic prospecting. This paper presents a new method of statics correction calculation based on development of a seismic-gravity model of the near surface. Gravity interpretation includes determination of the local component caused by the near surface effects and calculation of the near-surface rock density by solving the linear inverse gravity problem. To obtain the near-surface velocities, priori seismic data such as time fields of the first waves recorded in the initial part of common depth point (CDP) seismograms are used. An optimal near-surface model is retrieved on the basis of the successive solution of the inverse and forward seismic problems, correlating with the observed seismic data. Matching of seismic and gravity model of the near surface yields the maximum coefficient of correlation between the values of velocities and densities. At the end of the interactive iterative process we get values of the near-surface seismic wave velocities, used for statics evaluation, and values of gravity anomalies, calculated with a variable density of the interbedded layer. The applications of the proposed method at geophysical exploration of oil and gas confirm the possibility of calculation of statics correction using the gravimetric data by constructing a coherent seismic-gravity model of the near surface. KEY WORDS: gravity, near-surface velocity, seismic-gravity model, statics correction.

0 INTRODUCTION yono et al., 2014; Colombo et al., 2013, 2010, 2008; Opfer, In common depth point (CDP) survey, statics preparation 2003). To solve the inverse problem, initial data such as the is carried out by the times of first arrivals on reflection seismo- observed gravity field and its local components obtained by grams. A near-surface velocity model can be derived from au- particular means are used. However, significant errors in the tomated methods (Zhu et al., 2014; Raef, 2009; Cox, 1999). The statics corrections arise due to limitations of these methods, main disadvantage of the majority of these methods is that they namely, formal selection of the local component of the gravity do not guarantee high precision results in many regions since field, the use of the near-surface model in a form of a plane they try to solve the inverse problem with simplified models of layer, and the absence of regression equation between velocity subsurface structure. Therefore, it is necessary to work out bet- and density in the near-surface formation in particular explora- ter methods to calculate near-surface velocity, heterogeneity tion areas. and statics correction in seismic prospecting. In areas where three-dimensional seismic works have been 1 SOLUTION ALGORITHM done, there are generally sufficient 2D seismic profiles and oil We suggest the following algorithm to interpret gravity da- wells are drilled deeper there, in which up-hole velocity surveys ta to calculate the near surface rock density with further statics (UVS) and areal gravity explorations on different scales have computation. been previously conducted. Due to a close correlation between (1) Determine the average near-surface rock density (inter- seismic wave propagation and rock density (Gardner et al., bedded layer), with respect to which anomalous densities for 1974), the near-surface heterogeneity influences both seismic further calculations will be determined. For this purpose, conven- and gravity fields. It allows using gravity data to interpret seis- tional methods using gravity data and terrain relief altitudes can mic data, particularly, to determine first-estimate statics before be applied. Previous experience of such works shows that simple 3D seismic works. Nettleton’s method is the most effective (Nettleton, 1940). The existing methods of applying gravity data for statics (2) Allocate the gravity field component determined by the calculation mainly reduce themselves to the solution of the near surface effects. All data available and possible methods to linear inverse problem, i.e., calculation of near-surface rock divide the field including geological reduction, frequency filter- densities with their further interval velocity-conversion (Seti- ing and correlation transformation should be used. (3) Calculate the near-surface rock density by solving the *Corresponding author: [email protected] linear inverse gravity problem using the field component ob- © China University of Geosciences and Springer-Verlag Berlin tained at the previous stage. For the first approximation, the Heidelberg 2015 average near surface rock density is used. Decision problem forward and inverse gravity in 2D or 3D option to layer limited Manuscript received January 5, 2015. above terrain, bottom-datum. Approximation of layer is made of Manuscript accepted April 7, 2015. rectangular set boxes, each of which is specified with the

Bychkov, S., Mityunina, I. Y., 2015. Near-Surface Correction on Seismic and Gravity Data. Journal of Earth Science, 26(6): 851–857. doi:10.1007/s12583-015-0546-7. http://en.earth-science.net 852 S. Bychkov and I. Mityunina

density of σij. The solution of inverse linear problem is carried out on the Earth’s surface points {xi, yj} by the formula

nn1inmod  ij ij()gg ij ij where n-number of iteration, Δgin and Δgmod-initial and model fields accordingly, α-parameter of regularization. This parameter α is selected experimentally. It is smaller than that of the slower convergence of the iteration process, but with higher accuracy. At high values of the parameter, consistent approximation may disagree. End of iteration process criterion is a coincidence within the specified accuracy of initial and model fields or achieving a certain number of iterations. (4) Determine correlations between a priori velocities of elastic waves and the obtained densities. Obviously, the coefficient of correlation between the values of elastic wave velocities and densities can serve as a criterion of reliability of the interpretation as the whole method is based on the strength of this correlation. (5) Solve the forward gravity problem for the near surface Figure 1. Solution of the forward problem of gravity. (a) Pat- formation with the obtained densities and specify the local field terns of initial and model gravity fields; (b) near-surface density component. The iterative process of selecting a local component curve; (c) geo-density model. 1. Source; 2. model field at con- ends with the maximum coefficient of correlation between the stant near-surface density; 3. model field at variable near- values of velocities and densities reached, and the coincidence surface; 4. retrieved near-surface densities; 5. average rock within the given error of the observed and calculated gravity densities (g/cm3); 6. density interfaces. fields. (6) Elastic wave velocity-conversion of values of the rock model errors and regional background represent in the first density using established correlation and statics evaluation. place the influence of unconsidered near-surface heterogeneities. The interpretation process can be repeated after the first To solve the linear inverse problem, differences between the stage of determination of statics corrections, i.e., by using the priory and determined anomalies are converted into variable established correlation we obtain a set of the near-surface rock rock densities. The iterative process of density retrieval ends densities, solve the forward problem, and obtain the local com- with the coincidence of the observed and calculated curves g ponent of gravity field. At the end of the interactive iterative within the desired precision or error of gravity observations. As process, we get values of the near-surface seismic wave veloci- Fig. 1b shows the systematic mismatch between the observed ties, used for statics evaluation, and values of gravity anomalies, and model fields g is completely removed due to the increase calculated with a variable density of the interbedded layer. Thus, of the near-surface density from 2.40 to 2.60 g/cm3 by the end the solution of the problem reduces to the building of a detailed of the profile. seismic-gravity model of the near surface. Thus, in the result of the first stage of the model development we get a set of near-surface rock densities on the 2 DEVELOPMENT OF A SEISMIC-GRAVITY MODEL profile, satisfying the gravity data. OF THE NEAR SURFACE For this area, a set of velocities of seismic wave propaga- The building of the model is complicated due to general tion in the near surface can be calculated by using seismic data. lack of information on the near-surface rock density. Therefore, In this case, the iterative process of the interpretation of wave the first stage of the building of the model is to determine and fields recorded during seismic survey is carried out. Based on specify the correlation between the near-surface velocity and the successive solution of the inverse and forward seismic prob- rock density for a particular exploration area. For this purpose lems, an optimal near-surface model retrieves, correlating with- on the basis of drilling data, seismic information, well-log data in the accuracy limits of observations with the observed seismic and effective densities obtained from gravity data (Nettleton, data (Fig. 2). At the same time, practice proves that it is appro- 1940) a detailed geologic-geophysical (geo-density) model of priate to use as a priori seismic data time fields of the first the whole investigated section is established (Fig. 1c). The waves, recorded in the initial part of CDP seismograms (Mityu- gravity response of the section is excluded from the gravity nina et al., 2003). This allows the use of the correlations be- anomaly in the course of the solution of the forward problem. tween time fields of the first waves and fields of the vertical Since the original model was built with a constant density of time, for making the wavefield continuation into subsurface rocks, calculated gravity anomaly does not coincide with the velocity profiles more efficiently. observed. For example, in Fig. 1a variance curves have syste- Plotting the correlation dependence between the values of matic characteristics of -2 mGal at the beginning of the profile the obtained velocities and densities and calculating coefficients to +2 mGal in the end. of pair correlation and the regression equation (Fig. 3a) we get a It is believed that the residual anomaly together with the new set of densities and use them to solve the forward gravity

Near-Surface Correction on Seismic and Gravity Data 853

Figure 4. Block diagram of the algorithm for the best-fit gravity-seismic model establishment.

Figure 2. Time fields of the first waves. (a) The observed; (b) model after the first stage of iteration.

Figure 3. Correlation between rock velocity and density for the original (a) and retrieved (b) near-surface models. problem. In this case, the iterative process ends with the maximum coefficient of correlation reached (Fig. 3b) and the coincidence within a specified error of the observed and determined gravity fields. The next stage of the model building is conversion of density values by the determined correlation dependence to seismic Figure 5. CDP stacks obtained with different statics technique. wave velocities and making them more precise by solving the (a) Statics correction plots; (b) terrain relief; (c) time section forward seismic problem. The obtained velocity values are with standard statics technique; (d) stack with static corrections checked once again by solving the forward gravity problem, i.e. corresponding to gravity anomalies. 1. Standard statics tech- the completely iterative process is repeated (Fig. 4), at the same nique plot; 2. statics plot calculated corresponding to gravity time, the behavior of the regional gravity trend is made more anomalies; 3. wells with vertical-velocity survey. precise, and the model of deep parts of the section is corrected. The procedure of converting rock density to velocity and vice ues of the gravity anomaly, determined with variable density of versa with the correction of their values continues until the best- the interbedded layer and values of the velocity of seismic fit seismic gravity model, satisfying both methods, is established. waves in the near surface, which is used for statics calculation. In the result of the interactive iterative process, we get val- As Fig. 5a shows values of uphole-based statics and calculated

854 S. Bychkov and I. Mityunina from the gravimetric data differed by almost 10 ms. Compari- density heterogeneities in suprasalt and salt formations. son of CDP sections obtained with different statics technique This area is particularly convenient to test the method of revealed (Figs. 5c, 5d) that use of the statics corrections calcu- the building of the best-fit gravity-seismic model of the near lated from the gravimetric data significantly improved the con- surface for statics calculation due to the previous 2D seismic tinuity of practically all reflecting horizons. This is most clearly survey and a sufficient number of the wells in which uphole noticeable in the middle part of the profile (x=2.3–3.0 km), velocity survey (UVS) was made. Besides, on the margins of where by gravity data it is possible to find low-velocity near- the investigated area there are two-and-a-half-inch conditional surface anomalies, which do not correlate with the elevations of gravity anomaly maps used to calculate edge effects at field surface topography (Fig. 5b). What is more, the obtained corre- continuation. lation between the rock velocity and density can be used to The interbedded layer density, nearest to the true density of develop a first approximation near-surface model for areas with the rocks composing the relief, was determined by Nettleton’s similar geological structures. method. For each profile, a series of Bouguer anomaly curves was plotted, calculated at different densities of the interbedded 3 A PRIORI STATICS CALCULATION IN AREAL layer. From the series, one curve was selected, which least cor- SURVEYS related with the relief. Fig. 6a shows position of two lines (7 We consider an example of the interpretation of geophysi- and 101) for which Bouguer gravity profiles are displayed (Fig. cal information in one of the areas situated in the Solikamsk 6b). Nettleton’s method found that the average rock density of depression of the Cis-Ural foredeep within the spread of the interbedded layer for the whole area was about 2.40 g/cm3. Verkhnekamskoe potassium accumulation at the depth of 200– This density was used for Bouguer anomaly calculation and 400 m. The formation of salt interferes with seismic imaging further solution of the forward and inverse problems. and causes high-amplitude gravity anomaly significantly ex- As it has been mentioned, the main density contrast in this ceeding the effect of target geological features. Under the salt area is the top of salt with density differences 0.2–0.3 g/cm3. formation at the depth of 1.9–2.1 km there is an oil deposit dat- The morphology of salt surface was investigated by salt explo- ing to Late Devonian reefs. In the area of detailed study of the ration holes and was then enhanced by gravity data, which geological structure of the oil deposit 3D seismic (OJSC renders it reasonable to exclude the influence of this formation “Permneftegeofizika”) and gravimetry scaled 1 : 10 000 (Min- from the observed gravity field, i.e., to use geological reduction. ing Institute of UB of RAS) were set. Gravity observations were As Fig. 7, presenting reduction results, shows a change in abso- made by using Autograv CG-5 gravimeters on 3D seismic pro- lute elevation of the top of salt of more than 100 m in this area files over a network 250×300 m in increments of 50 m. The root- (Fig. 7b) and causes gravitational effect over 3 mGal, whose mean-square error of determining Bouguer anomalies was 0.028 exclusion results in a significant change of the gravity field mGal. The main task of the gravity measurements was to study morphology (Fig.7c). density structure of the region and first of all the localization of The next problem is to obtain the local field component

Figure 6. Determination of the interbedded layer density by Nettleton’s method of (a) terrain relief, (b) graphics of gravity anomalies for different densities of the interbedded layer (curve parameter-density, g/cm3).

Figure 7. Gravity reduction of gravitational field. (a) Original gravity anomaly map; (b) top of salt map (points represent holes); (c) residual gravity map.

Near-Surface Correction on Seismic and Gravity Data 855 determined by the near-surface influence. As is mentioned field transforms, calculated in the VECTOR system with differ- above, this problem is ambiguous and can be solved to some ent sizes of k, that local component is selected, which best cor- extent by a way of vector scanning developed at the Mining relates with the “fixed” values of near-surface velocities calcu- Institute of UB of RAS (Bychkov at al., 2003). The compute- lated on the UVS data. based system VECTOR, realizing the procedure of vector scan- The results of dividing gravity field into components are ning, allows dividing gravity field into components, characteriz- shown in Fig. 8. The source (reduced) field (Fig. 8b) is divided ing particular intervals of the geological cross-section and get- into local components, calculated with different parameters of ting a three-dimensional image of the interior density. It is the VECTOR k transformation (Fig. 8c). The obtained local based on stable calculation of horizontal derivatives, their anomalies were compared with the near-surface velocity map processing, and transformation with further integration of the (Fig. 8a). Relationship between the original field of gravity results. All transformations are carried out within horizontal anomalies and the velocity of elastic waves in the upper part of gradients space. Smoothing data using running window in con- the section is practically absent (the correlation coefficient R is sideration of vector direction gives an opportunity for determi- 0.204) (Fig. 8d). For the local component of the field calculated nation local and regional components of gravity field. Subse- in the VECTOR at k=0.15, the correlation coefficient is 0.802 quent integration of the component allows obtaining reconstruc- (Fig. 8e), indicating that it may be used to calculate the velocity tion field. Gravity response of deep sources reduction achieved of elastic waves. by vector scanning is caused by different characteristics of at- The linear inverse problem was solved by retrieving densi- tenuation of gravity field and its horizontal gradient within large ty of the layer, limited from above by the terrain relief and from distance from the source. Transformation parameter is a factor k, below-datum plane. Layer approximation was carried out by a which determines the relative size of the running window. As set of rectangular parallelepipeds. Figure 9 presents retrieved the size of the running window increases averaging vectors of near-surface rock densities. The densities were retrieved at horizontal gradient over a larger area, decreasing the frequency points on the land surface (Fig. 9b). The mean square error of content of the local component of the field and to some extent, retrieval made 0.028 mGal. The result of the calculations––a we can assume that increases the depth of the scanning field. map of the near-surface density values––is shown in Fig. 9c. To estimate the near-surface gravity influence from a set of

Figure 8. Dividing gravity field. (a) Velocity map of elastic waves in the near-surface (points represent UVS wells); (b) the observed gravity field; (c) field transforms calculated in the vector system at different values of k; (d) correlations between velocities and observed gravity anomalies; (e) correlations between velocities and the field transform at k=0.15.

856 S. Bychkov and I. Mityunina

Figure 9. Results of the near-surface rock density retrieval. (a) Map of gravity local anomalies; (b) terrain relief; (c) retrieved near- surface rock densities.

Figure 10. Maps of statics corrections calculated by different methods. (a) by refracted waves (Millennium complex programs); (b) by gravity data (points on map represent UVS wells).

Using the obtained regression equation a velocity map of the calculated densities, we will get the interbedded layer varia- the near surface was constructed for the whole exploration area ble density correction in the Bouguer anomaly analogical to and was further converted with the calculation of the near- terrain correction. This will allow removing anomaly interfe- surface thickness into a map of statics corrections (Fig. 10b). rence, which is of no interest in studying oil prospective fields Comparison of the obtained data with the corrections, calcu- at great depth. lated during the processing of first arrivals of the whole of 3D seismic records in a complex of the Millennium (Green Moun- 4 CONCLUSIONS tain Geophysics, USA) programs at OJSC Permneftegeofizika For important seismic CDP problem of determining a (Fig. 10a) shows their good convergence. It proves reliability priori statics, we propose a method based on the construction of of the results and the possibility of predicting the near-surface a coherent seismic-gravity model. processing Our method velocity heterogeneities on gravity data before 3D seismic mainly differs from the existing methods using gravity data in works. In case of absence of UVS wells in the area for a priori the seismic data by the following three features. data on elastic wave velocities, results of the previous 2D seis- (1) Division of the gravity field on the components and the mic data interpretation can be used. release of the one that best agrees with a priori values of elastic The near-surface seismic wave velocities, converted to wave velocities. rock densities, can be further used for gravity data interpretation. (2) Gravity inversion of the selected components with the Thus, if to solve the forward problem for the layer, bounded calculation of the density of near-surface rocks. from above by terrain relief and from below-datum plane, with (3) Determination of the regression coefficients between the

Near-Surface Correction on Seismic and Gravity Data 857 values of calculated densities and seismic velocities from which Conference & Exhibition incorporating SPE EUROPEC, converts the density near-surface section into the velocity one. London. 1–5 To implement the method, we have developed an Cox, M. J. G., 1999. Static Corrections for Seismic Reflection interactive iterative process, the output of which has velocities Surveys. SEG, Tulsa of seismic waves in the near surface. That is used for the Mityunina, I. Y., Spassky, B. A., Laptev, A. P., 2003. First calculation of statics corrections, and the values of gravity Waves in Seismic Reflection Seismograms and Near- anomalies, computed with variable density of the interbedded Surface Studies. Geophysics, 5: 5–12 (in Russian with layer. The method can be used in 2D, and 3D seismic surveys. English Abstract) Nettleton, L. L., 1940. Geophysical Prospecting for Oil. REFERENCES CITED McGraw-hill Book Company, New York, London. 452 Bychkov, S., Novoselitskiy, V., Prostoloupov, G., et al., 2003. Opfer, R., 2003. Imaging Seismic Data with High Resolution The Computer-Based System VECTOR as a Tool for De- Gravity Data. VIII Symposia Bolivariano-Exploration tection and Localization of Both Gravity and Magnetic Petrolera en las Cuencas Subandinas, Colombia. 438–442 Field Sources and Its Applications at Geological Interpre- Raef, A., 2009. Land 3D-Seismic Data: Preprocessing Quality tation. Abstracts of Contribution of the EGS-AGU-EUG Control Utilizing Survey Design Specifications, Noise Joint Assembly, Nice. 5: EAE03-A-01497 Properties, Normal Moveout, First Breaks, and Offset. Colombo, D., Cogan, M., Hallinan, S., et al., 2008. Near- Journal of Earth Science, 20(3): 640–648. Surface P-Velocity Modeling by Integrated Seismic, EM, doi:10.1007/s12583-009-0053-9 and Gravity Data: Examples from the Middle East. First Setiyono, K., Gallo, S., Boulanger, C., et al., 2014. Near Sur- Break, 10: 91–102 face Velocity Model of the Dukhan Field from Microgravi- Colombo, D., Mantovani, М., Sfolciaghi, M., et al., 2010. Near ty and Resistivity to Enhance PSDM Seismic Imaging. Surface Solutions in South Rub Al-Khali, Saudi Arabia Expanded Abstracts of 76th EAGE Conference & Exhibi- Applying Seismic-Gravity Joint Inversion and Redatuming. tion, Amsterdam. 1–5 First Break, 2: 77–84 Zhu, X. S., Gao, R., Li, Q. S., et al., 2014. Static Corrections Colombo, D., Rovetta, D., Curiel, E. S., et al., 2013. 3D Seis- Methods in the Processing of Deep Reflection Seismic Da- mic-Gravity Simultaneous Joint Inversion for Near Surface ta. Journal of Earth Science, 25(2): 299–308. doi: Velocity Estimation. Expanded Abstracts of 75th EAGE 10.1007/s12583-014-0422-x