Institutionen för Geovetenskaper – Geofysik
UNIVERSIDAD SIMÓN BOLIVAR Earth Science Department – Geophysical Engineering
Processing of shear waves from VSP data at the Forsmark site investigation
Master's Thesis Gwendal Georges Salmon Chatelet Uppsala, Spring 2008 TABLE OF CONTENT
1. Introduction...... 7
2. Geology of the area
2.1. Regional Geology...... 9
2.2. Local Geology; The Forsmark site...... 13
3. Seismic theory and VSP
3.1. Bases of Seismic Theory...... 15
3.2. The Wave Equation...... 16
3.3. Vertical Seismic Profile...... 17
3.4. VSP processing...... 18
4. Seismics in anisotropic media
4.1. Anisotropic mediums ...... 20
4.2. Shear waves splitting analyzing methods...... 24
4.3. Real anisotropy in the subsurface...... 30
5. Equipment and data acquisition process
5.1 The seismic equipment...... 34
5.2. The acquisition process...... 35
6. Data Processing...... 36
6.1. Polarization estimation...... 44
6.2. Velocity analysis...... 52
7. Results and interpretation...... 54
8. Discussions and conclusions...... 57
9. Further work...... 59
2 10. Acknowledgment...... 60
11. References...... 61
12. Internet Sources...... 63
3 LIST OF FIGURES
1. Figure 1.1. Location of borehole KFM01 and the 10 shot points. Cosma et al. (2005)...... 8
2. Figure 2.1.1. Main Precambrian units in southern Fennoscandia. Åhäll K., Connelly J. (2008)..9
3. Figure 2.1.2. Major tectonic units in the Fennoscandian Shield. Hermansson et al (2008)...... 10
4. Figure 2.1.3. A) Bedrock map of the Fennoscandian Shield. Bergman et al. (2008)...... 11
B) Bedrock map of south-central Sweden and Southern Finland...... 11
5. Figure 2.1.4. a) Tectonic domains in the western part of the Svecofennian orogen...... 12
b) Structural style of the Forsmark area. Hernansson et al. (2008)...... 12
6. Figure 2.2.1. The Forsmark investigation site. Cosma C. et al. (2005)...... 13
7. Figure 3.1. Representation of axial stress in a cylinder. http://physics.uwstout.edu/...... 15
8. Figure 4.1.1. Medium with vertical hexagonal symetry and horizontal propagation.
Caicedo M., Mora P., (2004)...... 22
9. Figure 4.1.2. Birefringence for the shear waves in two bodies with horizontal
and vertical fracture planes. Caicedo M., Mora P., 2004...... 23
10. Figure 4.1.3. Polarization of the shear wave depending of the relation
between incidence polarization and fractures direction. Juhlin C., (1990)...... 24
11. Figure 4.2.1. Wave propagating through an anisotropic medium and recorded
by a geophone. MacBeth C. and Crampin S. (1991)...... 25
12. Figure 184.108.40.206. Polarization diagrams. MacBeth C. and Crampin S. (1991)...... 27
13. Figure 220.127.116.11. Particle motion discriminants. MacBeth C. and Crampin S. (1991)...... 28
14. Figure 18.104.22.168. Ellipsoid of motion described by the particle motion.
MacBeth C. and Crampin S. (1991)...... 29
15. Figure 22.214.171.124. Propagator matrix between horizontal components of two adjacent
4 geophones. From MacBeth C. and Crampin S. (1991)...... 30
16. Figure 126.96.36.199 Splitting of shear waves in two anisotropic medium with different direction
of the fracture's planes. MacBeth C. and Crampin S. (1991)...... 31
17. Figure 188.8.131.52. a) Polar map with the direction of the fast and slow shear waves...... 32
b) Three receptor at different angles with the source. MacBeth C. and
Crampin S. (1991)...... 32
18. Figure 5.1.1. One of the VIBSIST-1000 sources used for the at Forsmark.
Cosma et al. (2005)...... 34
19. Figure 6.1. Shot S01 without (a) and with (b) spherical divergence correction ...... 37
20. Figure 6.2. Horizontal and vertical components...... 37
21. Figure 6.3 a) Seismic traces for the vertical (V) and horizontal components from
receiver 37 in S06...... 38
b) Hodograms before and after azimuth and incident angle rotation from
receiver 37 in S06...... 39
22. Figure 6.4 a, b, c, e, f and g. Shots S01, S02, S03, S05 S06 S08 and S09 respectively
after rotations of horizontal and vertical components...... 40-41
23. Figure 6.5. Frequency range in S06...... 42
24. Figure 6.6. Shot S05 before and after balancing...... 43
25. Figure 6.7. Seismograms from shot S06. Fill holes process...... 43
26. Figure 6.1.1a, b, c, e, f and g. Shots S01, S02, S03, S05 S06 S08 and S09
respectively. Hodograms and seismograms with LMO...... 44-50
27. Figure 7.1 Mid Ocean Ridge. Minster et al. (1974)...... 55
28. Figure 8.1. Shot S02, Receiver 75. Representation on particle motion for a shear wave
in the two horizontal components...... 57
5 LIST OF TABLES
1. Table 2.2.1. Main groups of rocks at Forsmark. T. Hermansson et al. (2007)...... 14
2. Table 4.1. Crystalline structures and the number of independent coefficient.
Modified after Caicedo M. and Mora P., 2004...... 20
3. Table 4.2.1. Applications of several methods in different areas. MacBeth C.
and Crampin S. (1991)...... 26
4. Table 5.2.1. Coordinates of borehole KFM01A. Cosma et al. (2005)...... 35
5. Table 5.2.2. Coordinates of the source positions for the VSP survey at KFM01A.
Cosma et al. (2005)...... 35
6. Table 6.1.1 Rotation angles from hodograms for every shot...... 51
7. Table 6.1.2 Incidence angles at the first and last receptor for every shot...... 51
8. Table 6.2.1. Velocities in both shear wave components measured directly in t
he seismic sections...... 52
9. Table 6.2.2. Shear waves velocities for H1 and H2 components using the method
described by Li et al. (1988)...... 53
10. Table 7.1. Rotation angles and direction of the fast coordinate of the shear wave...... 54
11. Table 7.2. Velocity in the fast and slow components...... 55
12. Table 7.3. Anisotropy estimation using velocities...... 56
6 1. Introduction
The Forsmark Nuclear Plant is one of the largest in Sweden and produces around one sixth of the total electrical energy in the country. It is situated on the east coast of Sweden in the Uppland region. Nuclear waste has to be properly handled every year and Forsmark is one site proposed for long-term storage of all spent fuel from Swedish nuclear power reactors. This potential high-level repository (a low-level one already exists in the area) will be based on the KBS-3 design process, which consists of 6000 iron-copper capsules where the waste will be stored for 30 years and finally buried 500 m down, isolated from the environment for100.000 years.
Before using the disposal site, numerous investigations must be done in the area so the risks are reduced as much as possible. These investigations include drilling of cored boreholes down to 1000 m depth. In this study the KFM01A borehole (figure 1.1) was used with different shot points to analyze possible anisotropy in the subsurface. The anisotropy in rocks can be due to different mechanisms as crystal and mineral grain alignment, crack and pore space alignment and thin layer anisotropy (Rowlands J. et al., 1993). For this purpose a shear wave splitting analysis was done in an attempt to determine both orientation and density of fractures.
Shear wave splitting has shown to be a very effective method detecting fractures, providing an unique ability to measure anisotropic seismic attributes that are sensitive to fractures (James E. Gaiser, 2004). This can be useful in many domains as in oil companies to improve reservoir management (James E. Gaiser, 2004) or as an imaging tool in fracture-controlled geothermal reservoirs, to monitor fluid pressure in the cracks and changes in crack density (Tang Chuanhai, 2005). Shear wave splitting studies have also been done in seismology for crustal studies (Rowlands J. et al., 1993).
When shear waves enter anisotropic medias they split in two approximately orthogonal components, where the faster and slower components will travel parallel and perpendicular to the fracture planes respectively. The time delay will depend of the amount of anisotropy and the path length. Different methods can be used to evaluate the anisotropy; polarization diagrams (Crampin et al., 1986), linear moveout plots of the horizontal components (Li et al.,1988).The procedure described by Li et al. (1988) are the techniques that are used in the present study.
The fractures orientation is also analyzed and compared with the general stress components in the area using well bore information from previous studies, as well as the general tectonic characteristics of the zone.
7 Figure 1.1. Location of borehole KFM01 and the 10 shot points. Taken from Cosma et al. (2005)
8 2. Geology of the area
2.1 Regional Geology
Three major Proterozoic crustal segments, namely the Svecofennian Domain (~1.9 Ga), Transscandinavian Igneous Belt (TIB; 1.8-1.7 Ga) and Gothian orogen (1.7-1.5 Ga) were accreted after the southwestward growth of the Proterozoic crust of the Fennoscandian shield (K.-I. Åhäll, J.N. Connelly, 2008). Following growth and successive stabilization of these lithotectonic segments, episodic 1.7-1.2 Ga intracratonic magmatism also swept westward (K.-I. Åhäll, J.N. Connelly, 2008).
Figure 2.1.1. Main Precambrian units in southern Fennoscandia: Svecofennian Domain, Askersund suite (AS), Oskarshamn-Jönköping Belt (OJB), Transscandinavian Igneous Belt (TIB), Klarälven-Ätran segment (K and Ä), Idefjorden terrane (Id), Western Gneiss region (WGR) and Telemarkia terrane. B, Ba and Ko mark the Begna, Bamble and Kongsberg sectors, and MZ the Mylonite Zone. From K.-I. Åhäll, J.N. Connelly, 2008
The Svecofennian orogen is located within the Fennoscandian Shield, bounded in the Northeast by an Archean continental nucleus and in the Southwest by the Sveconorwegian orogen. In the Northwest and Southwest sides it is bordered by the Caledonian orogen and by the Neoproterozoic and Palaeozoic cover sedimentary rocks and intrusions, respectively (Figure 2.1.2; Hermansson et al, 2008).
9 Figure 2.1.2. Major tectonic units in the Fennoscandian Shield. From Hermansson et al (2008)
Most parts of the continental crust in the Svecofennian Domain of the Baltic Shield were formed between 1.90 and 1.86 Ga. The exception is a narrow belt in the Archean Domain which contains ophiolites from 1.97 Ga, although this could derive from marginal rifts in the Archaean crust (Gorbatschev R. et al, 1993).
The Skellefte District, the Bothnian Basin, the Ljusdal Batholih and the Bergslagen Province form the eastern part of the Svecofennian orogen in Sweden (figure 2.1.3), while the Los area in Finland is in the eastern part. The Skellefte District and the Bothnian Basin are the northernmost groups and they are formed by metavolcanic rocks, overlain by metasedimentary rocks (Allen et al., 1996a; Billström and Weihed,1996) and by the metagreywacke belonging to the lower Svecofennian Härnö formation (Lundqvist, 1987; Lundqvist et al., 1990), respectively.
10 Figure 2.1.3. A) Bedrock map of the Fennoscandian Shield. ACWF: Arc Complex of Western Finland, ACSF: Arc Complex of Southern Finland and HSZ: Hassela Shear Zone. B) Bedrock map of south-central Sweden and Southern Finland. L: Los area. From Bergman et al. (2008)
The dextral Hassela Shear Zone system separates the Bothnian Basin from the 1.86-1.84 Ga Ljusdal Batholith (figure 2.1.3A). Also in the boundary area between the Ljusdal Batholith and the Bergslagen Province (figure 2.1.3A) there is a steep shear zone system (Högdahl et al., 2006).
This central western part of the Svecofennian orogen in central Sweden can be divided in four parts (figure 2.1.4; Hernansson T. et al., 2008):
11 a. Tectonic domain 1. It was affected by a penetrative ductile deformation and metamorphism under amphibolite and granulite facies around or after 1.85 Ga (Högdahl and Sjöström, 2001). The tectonic domain 1 is characterized by a bedrock composed of different calc-alkaline rocks, ranging from granodiorite to tonalite (Delin, 1993). b. Tectonic domain 2. A deformation belt of tens of kilometers crosses this domain in a WNW to NW direction (Hermansson T. et al, 2008). This domain contains the Singö shear zone, referred to as the Singö deformation zone (SKB,2004) and the Eckarfjärden and Forsmark deformation zones. c. Tectonic domain 3. As in tectonic domain 1 major folding of penetrative ductile fabric affected the rocks prior to 1.85 Ga (Hermansson T. et al., 2007). The domain is dominated by calc- alkaline granitoids, accompanied by minor volumes of alkali-calcic rocks (Stålhös,1972). d. Tectonic domain 4. It also contains a deformation belt of highly strained rocks, deformed under amphibolite-facies metamorphic conditions (Hermansson T. et al, 2008).
Figure 2.1.4. a) Tectonic domains in the western part of the Svecofennian orogen, central Sweden. b) Structural style of the Forsmark area with ductile high-strain belts (lined areas) that anastomose around tectonic lenses with lower ductile strain. From Hernansson et al. (2008)
12 2.2. Local Geology; The Forsmark site
The Forsmark site (figure 2.2.1) has been subjected to three main geological events, which characterized the “hot” period in the history of the Forsmark bedrock. The first was a volcanic activity period that took place 1,885 Ga. This was followed by the penetration into the Earth's crust of granitoid rocks between 1,865 and 1,885 Ga. The last event was a magmatic one, with mainly dyke intrusions between 1,845 and 1,865 Ga (Kenneth Ozaveshe Lawani,2007).
In the lens chosen as the possible target for the disposal of radioactive material, two contrasting structural domains can be identified. In the Southwest and Northeast a higher degree of ductile deformation and SL-tectonites (planar fabric is more developed than lineation) is present. On the other hand, the central zone shows a lower degree of ductile deformation (Kenneth Ozaveshe Lawani, 2007).
Figure 2.2.1. The Forsmark investigation site. DS indicates the borehole location, KFM01A (DS1). The red line shows the candidate area for the Swedish Nuclear Waste Co. (SKB). The shot points are indicated with black dots . From Cosma C. et al. (2005)
13 The Forsmark site is formed by four main rock groups which underwent different phases of structural deformation (Page et al., 2004); the first one is formed by felsic to intermediate metavolcanic rocks and the other three by meta-intrusive rocks. A lithological description of each group can be found in table 2.2.1 . The most important deformation zones are in a northwest direction and they include the Forsmark, Eckarfjärden and Singö zones (Kenneth Ozaveshe Lawani,2007).
Table 2.2.1. Main groups of rocks at Forsmark. Modified by T. Hermansson et al.,2007 after Stephens et al.; 2003
14 3. Seismic theory and VSP
3.1. Bases of Seismic Theory
The basis of the seismic surveying is the propagation of elastic waves through the earth's interior. Using detectors the travel times and waveforms of these reflected and refracted waves can be recorded and finally converted into depth sections. Nevertheless, the behavior and way the seismic waves travel in the subsurface depends upon the elastic properties of the rocks, which can be studied with two fundamental concepts: stress and strain (Telford W. M., Applied Geophysics, 1976).
– Stress: is defined as the ratio of the force to the area on which the force is applied. It can be “axial or normal stress” when the force is perpendicular to the area (also called pressure) or “shear stress” when it is tangential to the area (Figure 3.1).
– Strain: is defined as the relative changes in shape or dimension of a body when a stress is applied to it. The strains can be “normal strains” which refer to the dimension changes in the main directions (e.g. x- and y- axis) or “shearing strains” which refer to the changes of a right angle with the body in the xy plane when the stress is applied, that means the body undergoes a change in shape.
Figure 3.1. Representation of axial stress in a cylinder. From http://physics.uwstout.edu/StatStr/indexfbt.htm
These two terms can be related with the Hooke's law, which can be used when the strains are small and it states that the strain is directly proportional to the stress applied to the medium. The Hooke's law is given by equation:
σij = Cijkl ekl
But it can be shown that in an isotropic media, the elastic tensor C can be reduced from 81 to only two components, so the equation can be approximated as:
ii= ij2eii i=x,y,z
15 where is the stress eis the strain and are the Lame's constants is the dilatation
The dilatation or volumetric deformation can be expressed as = eii + ejj+ ekk
3.2. The Wave Equation
Starting with the equation of motion from Newton's second law:
Fi + Tij,j - Üi = 0
where F is the force T is the stress U is the displacement vector and the density
The Hooke's relation for isotropic mediums can be substituted in to get:
Fiij2eii , j−U¨ i=0
∂ ∂ 1 ∂ U i ∂U j Fi 2[ ]−Ü i =0 ∂ X j ∂ X j 2 ∂ X j ∂ X i
∂ 2 Fi ∇ U i−Ü i=0 ∂ X i
Assuming there are no external forces, the equation can be rewritten in a vectorial form:
∇ ∇ ²U i=Ü i
To reach the compressional and shear wave equations, divergence and curl operators need to be used. Taking the divergence of both sides of the last equation gives:
∂² ∇ ²∇ ² ∇ .U = ∂t²
Using the identity ∇ U = and dividing by the equations for the p-wave can be deduced:
2 ∂² ∂² ∇ ²= or 2 ∇ ²= ∂t² ∂t²
16 2 where = is the p-wave velocity Now taking the curl instead of the divergence:
∂2 ∇ x U ∇ X ∇ ∇ 2∇ X U = ∂ t 2
Knowing the curl of the divergence is zero, so X = 0 We finally have:
∂2 ∇ X U ∂2 ∇ X U ∇ 2∇ X U = or 2 ∇ 2 ∇ X U = ∂t 2 ∂t 2
where = is the shear wave velocity
Using the Helmholtz theorem, this equations can be written as functions of a scalar and an arbitrary vector :
∂² ∂2 2 ∇ ²= 2 ∇ 2 ∇ x U = ∂ t² ∂t 2
So solving for and the displacement's components can be obtained.
These two wave equations are fundamental in seismic studies and both show important properties. The fact that the divergence of a shear wave gives zero means that shear waves are dilatation free, so no changes in volume occurs, but only transversal movements. On the other hand, p- waves have compressional movements with volume changes. Even if these equations are based on assumption of isotropic mediums, they are commonly used in velocity analysis for real data.
3.3. Vertical Seismic Profile
Vertical Seismic Profile (VSP) involves recording seismic energy sources with detectors clamped at many levels of the borehole wall (Lee M. and Balch A., 1983). When the shot point is located at the wellhead vertically above the borehole detectors the method is known as zero-offset VSP and if there is an offset between shot and wellhead so that the rays travel along inclined ray paths the methods is known as offset VSP (Kearey P. book).
In contrast to the conventional surface seismic method, VSP allows us to observe the wave as it is going down from the subsurface at different levels in the well and downgoing waves can be separated from upgoing (after reflection at interfaces) waves. Events whose travel time increase with depth represent downgoing waves and events whose travel time decreases with depth represent upgoing
17 waves for zero-offset VSP.
Important information about reflectivity, attenuation, mode conversion, velocity and other rock properties can be deduced from VSP surveys (Lee M. and Balch A., 1983). Furthermore, ties between surface seismic and well logs can be done with the VSP information, reducing the ambiguity that particular events observed in conventional seismic are primary or multiple reflections (Kearey P. book). Due to the fact that in VSP ray paths are shorter than in conventional seismic, there is a lower degree of attenuation and therefore better horizontal (Fresnel zone) and vertical resolution, resulting in an improved accuracy of the data.
3.4. VSP processing
Each set of VSP data is unique and the processing steps to be applied depends on many different factors, starting by the source type, ground characteristics till the sensor placement and quality. Following the classification of Lee and Balch (1983), a general procedure with the most common techniques to process VSP data will be presented, keeping in mind that some extra steps can be needed for particular situations.
Every shot is plotted for a visual quality inspection, so noise and undesired events can be removed. Timing error, if any, must also be corrected. This is a subjective process and can have different interpretations depending on the person in charge of the processing.
Since surface sources are generally weak, the source has to be generally energized several times and all the recordings must be stacked at the same level. This process improves the signal, enhancing the coherent events and eliminating the incoherent noise so the S/N ratio improves at approximately √N, where N is the stack fold. The stacking is generally not used for explosive sources because they usually have enough energy in one shot.
● Shot static correction
When the sources are buried, the depth and even the location can change significantly during the survey due to hole damage. A common formula for static corrections is:
d d−2H2d T=T −T =T [ 1 1 −1] 2 1 1 2 − 2 l H d 1
Where d1 and d2 are the depths of two shots in the same hole d = D2 - D1 T1 and T2 are the direct arrival time from d1 and d2 respectively l is the horizontal distance from the hole to the well and H is the depth of the receiver
18 Static corrections are generally not needed when surface sources are used.
● Frequency analysis and band-pass filtering
This processing step can improve remarkably the S/N relation, suppressing tube noise and random noise. Spectral analysis to determine the frequency range of the different events must be used and if the desired signal lies in a band outside the noise and tube wave, an effective band-pass filter can be applied.
● Amplitude analysis
Geometrical spreading, loss in downward-traveling energy due to upward reflection, intrabed multiple effects and inelastic attenuations are the main causes of amplitude decay between receivers. For the amplitude compensation at each receiver the following formula is used:
ce− R or cR n R
Where R is the distance from the source to the receiver and c,n and are constants
R corrects for the geometrical spreading and does not depend on the frequency. The n and parameters correct for transmission losses and attenuation, so they can vary for different frequencies.
● Multichannel velocity filtering
In VSP surveys, both upgoing and downgoing waves are recorded. The multichannel velocity filter is an effective way to separate these two waves. It uses apparent velocity of coherent events from adjacent receiver to distinguish between desired and undesired signals (incoherent events and coherent events with a wrong apparent velocity). This step is one of the most important in VSP processing because it allows us to identify a reflected event and the reflecting point, as well as the changes of the downgoing waves with depth.
● Downgoing wave train deconvolution
As the wave propagates downward, multiple reflections occur between the layers so the signal recorded at the receivers are not a simple impulse or wave but a complicated wavetrain, complicating the geological interpretation. The deconvolution uses a short pulse or spike to compute the data as if it were recorded with this spike. This process is called spiking deconvolution and it is based on the autocorrelation of the recordings at each level.
● Impedance log estimation
The final goal of seismic processing is generally to estimate the acoustic impedance function with depth. In VSP this process is much more accurate than in surface seismic since the data is recorded directly or near the reflecting sequence of interest. This process usually uses an iterative process with a transfer function assuming some reasonable initial impedance.
19 4. Seismics in anisotropic media
4.1. Anisotropic mediums
In seismics, an anisotropic medium can be defined as a medium where the velocity depends on the direction (angle) of propagation of the wave (Caicedo M., Mora P., 2004). The underground can present an anisotropic behavior due to many reasons like aligned crystals, aligned fabric, periodic thin layering and aligned cracks due to stress (Crampin, 1987). This last reason, called by Crampin extensive-dilatance anisotropy (EDA) is one of the most important and one of the biggest interests for studying seismic data. Cracks and fractures represent possible paths for gas and oil and the detection of them can notably help the production.
To understand the anisotropy of a material it is first necessary to look at the symmetric characteristic of it. Depending of the crystal structure, minerals can be divided in 230 space groups, 32 crystal classes, 14 bravais lattices and 7 crystalline structures (Wikipedia). Table 4.1 shows the 7 crystalline structures, which are used to designate the anisotropic media, and the independent coefficients in the elastic tensor equation for each one of the structures.
Crystalline structures Independent Coefficients Triclinic 21 Monoclinic 13 Orthorhombic 9 Tetragonal 6 Rhombohedral 7 Hexagonal 5 Cubic 3
Table 4.1. Crystalline structures and the number of independent coefficient. Modified after Caicedo M. and Mora P., 2004.
The elastic tensor equation in 3D for an isotropic media is given by:
Cijkl = λδij δkl + μ(δik δjl + δil δjk )
We already saw that in an isotropic media it can be reduced to two components but in anisotropic media this reduction cannot be applied anymore. A really useful symmetry in exploration geophysics is the hexagonal crystalline structure, where the elastic tensor has 5 independent coefficient and is given by (Caicedo M., Mora P., 2004):
The general Christoffel equation in 3D for anisotropic media can be written as:
Γik(xs,pi ) = aijkl(xs )pjpl ,
where pi = ∂τ /∂xi and aijkl = Cijkl /ρ,
pi represent the components of the phase vector, τ is the travel time along the ray, ρ is the bulk density, xs are the Cartesian coordinates for position along the ray, s=1,2,3 (Tariq Alkhalifah, 1998).
These coefficients can be reduced for an hexagonal system in the Kelvin-Christoffel matrix to (Caicedo M., Mora P., 2004):
2 2 2 Γ11 = C11 nx + C66 ny + C44 nz 2 2 2 Γ22 = C66 nx + C22 ny + C44 nz 2 2 2 Γ33 = C44 nx + C44 ny + C33 nz Γ12 = Γ21 = (C11 − C66 ) nx ny Γ13 = Γ31 = (C13 + C44 ) nx nz Γ23 = Γ32 = (C44 + C23 ) ny nz .
If the equations are solved for horizontal propagation in a medium with vertical hexagonal symmetry (figure 4.1.1), simulating an anisotropic media with horizontal planes of fractures, the Kelvin-Christoffel matrix will be diagonal with coefficients:
Γ11 = C11 Γ22 = C66 Γ33 = C44
21 Figure 4.1.1. Medium with vertical hexagonal symetry and horizontal propagation (Caicedo M., Mora P., 2004)
Solving the matrix, the following velocities are obtained:
C Vp= 11
C Vs = 66 1
C Vs = 44 2
Where Vp is the p-wave velocity and Vs1 and Vs2 are the s-wave velocities in the component parallel and perpendicular to the fractures respectively.
If the same problem is solved but with vertical propagation, the velocities will be:
C Vp= 33
22 C Vs= 44 This equations show very interesting results:
– When the wave front (or ray) propagates perpendicular to the plane of fractures there is only one p- wave velocity and one s-wave velocity, but when the propagation in parallel to the planes of fractures two different s-wave velocities are present, which vibrate perpendicular each other and the p-wave propagration direction. – The s-wave velocity of the component parallel to the fractures is higher than the perpendicular component, so they are generally called fast and slow shear wave respectively.
This polarization and time delay between the two components of the s-waves is called birefringence. Figure 4.1.2 explains the process of birefringence for a medium with vertical symmetry axis and horizontal fracture planes (VTI) and another medium with a horizontal symmetry axis and horizontal fractures (HTI). In the VTI model it can be seen that when the wave propagates in a direction perpendicular to the fracture planes that they cross the medium without any change in their polarization and within the same time. In contrast, when they cross the medium in a direction parallel to the fractures the two shear wave components will take different time to pass through the body, with the faster component parallel to the planes of fractures as should be expected.
Figure 4.1.2. Birefringence for the shear waves in two bodies with horizontal and vertical fracture planes. Taken from Caicedo M., Mora P., 2004.
In the HTI model the same process occurs but the axises are rotated 90 degrees, so the direction of the fast and slow s-waves are switched.
When the initial polarization of the s-waves is in the direction of the fractures the wave passes through the system without polarization changes but if they do not fit, the wave will be separated in two waves parallel and perpendicular to the fracture planes (figure 4.1.3). This can be analyzed from a
23 practical point of view: because the s-wave component perpendicular to the fractures will constantly cross and pass through the fractures, it will pass a lower density zone, i.e. low velocity (gas, water or other low density material), while the parallel component will propagate parallel to the fractures but beside these ones in the hard rock.
The velocity difference between the fast and slow shear waves can be used to calculate the anisotropy, using the maximum velocity difference normalized by the faster one (Juhlin C., 1990).
Figure 4.1.3. Polarization of the shear wave depending of the relation between incidence polarization and fractures direction. In a) andb) the slow and fast shear waves respectively have the initial polarization. In c) the initial polarization changes totally to align with the fracture planes. From (Juhlin C., 1990).
4.2. Shear waves splitting analyzing methods
In the simple case of a shear wave propagating through a homogeneous anisotropic medium with planes of fractures in one direction, the shear wave will split in a fast (parallel to the planes) and a slow (perpendicular to the planes) component with a time delay t. The information of the splitting can be obtained from polarization diagrams of the horizontal plane. If the signal is recorded on a 3C geophone, the energy of the two shear waves will be divided between the two horizontal components of the geophone (H1 and H2), unless they agree with the polarization direction (figure 4.2.1). In this case it would be enough rotating the horizontal components about the vertical axis till the maximum energy of the faster shear wave is in one component and the maximum energy of the slower shear wave in the other component. Knowing the angle of rotation, the final position of the geophone components would indicate the direction of polarization, therefore, the fracture plane directions.
24 Figure 4.2.1. Wave propagating through an anisotropic medium and recorded by a geophone. From MacBeth C. and Crampin S. (1991)
Once this is done the time delay between the two components can be calculated directly from the time delay between the two signals in H1 and H2, using for example a cross-correlation function which will show a maximum at time t. Finally, knowing the velocity of the shear waves the percentage of anisotropy (fractures) can be estimated.
These simple ideas about shear wave splitting carry forward to many sophisticated methods that can be applied to the real life situations. MacBeth C. and Crampin S. (1991) divided the methods for estimating shear wave splitting in four groups, often with different applications: direct inspection of polarization diagrams, particle motion discriminants, the covariance matrix approach and the use of different geophone levels of a VSP. Table 4.2.1 shows the application of the four methods in different areas.
25 Table 4.2.1. Applications of several methods in different areas. From MacBeth C. and Crampin S. (1991)
26 4.2.1. Polarization diagrams
The direct inspection of polarization diagrams is a common method for analyzing shear wave splitting (figure 184.108.40.206). These diagrams show the particle motion projected onto the horizontal plane. The direction of the fast and slow shear waves can be estimated rotating the horizontal components till a maximum energy is centered in one of the components, obtaining near cruciform patterns, nevertheless subjective judgment is required when small delays are present giving rise to elliptical or circular polarization patterns. Authors propose different minimum time delays between 0.25T to 0.7T (where T is the dominant signal period) before the effect of anisotropy can be identified.
The time delay can be estimated either looking for an abrupt change in the slow component of the seismogram after the leading wave or using a correlation function between the two reoriented components, although for this be done it is required that the two split shear waves are orthogonal, which is not always the case (MacBeth C. and Crampin S., 1991).
In spite of polarization diagrams being a time consuming process and subjective to different interpretations, Crampin (1978) suggests that plotting of polarization diagrams may be the only reliable way to identify shear wave splitting if the anisotropy is weak.
Figure 220.127.116.11. Polarization diagrams. From MacBeth C. and Crampin S. (1991)
27 4.2.2. Particle motion discriminants
This method acts directly on the time series, rotating the recorded horizontal seismograms till some discriminant function is optimal (figure 18.104.22.168). Discriminant functions can be the projected energy on one component of the geophone (Di Siena, Gaiser and Corrigan, 1985) or the cross- correlation function between the two horizontal geophone components (Garrota and Marechal, 1987) . The time delay can be estimated by the time-lag between the peaks in the correlation function (MacBeth C. and Crampin S., 1991).
Figure 22.214.171.124. Particle motion discriminants. F is the discriminant function. From MacBeth C. and Crampin S. (1991)
4.2.3. Covariance matrix
The covariance matrix approach (figure 126.96.36.199) can provide accurate estimates of the type of polarization (linear, elliptical or ellipsoidal) and orientation of the motion as a function of time (Kanasewich 1981). The method uses the eigenvector analysis of a covariance matrix formed using the three components of the recorded seismogram; basically it relates the average covariance between the three recorded components of motion analyzing the shape of the particle motion (MacBeth C. and
28 Crampin S., 1991). It can be applied in both the frequency and time domains depending on the nature of the data and noise content. If the waveform has essentially the same polarization over almost all frequencies the time domain is more useful, otherwise, if scattering is present the frequency domain is preferable (Park, Vernon and Lindberg 1987).
Figure 188.8.131.52. Ellipsoid of motion described by the particle motion. The polarization directions is determined by the axes of the ellipsoid. From MacBeth C. and Crampin S. (1991)
4.2.4. Techniques using a group of geophones
As in the previous method, a correlation matrix that can be set both in the frequency or time domain is used to estimate the anisotropy of the medium (figure 184.108.40.206). This matrix can be interpreted as the transfer function between two receivers at different depth levels. The polarization is estimated by the angle of rotation of both geophones that produces a maximum correlation between the two x- and y- components and a minimum in the cross terms of the matrix. This method assumes an homogeneous medium between the two geophones but has the advantage that the differential attenuation can be calculated between two levels (MacBeth C. and Crampin S., 1991).
29 Figure 220.127.116.11. Propagator matrix from cross-correlation between horizontal components of two adjacent geophones. From MacBeth C. and Crampin S. (1991).
Another common method is the use of linear moveout (LMO) plots of the horizontal components (Li et al, 1988). The two horizontal components are plotted for different rotational angles and when a maximum separation is achieved, the components should be aligned with the slow and fast direction. This application has also the advantage that velocities of both components can be calculated with the LMO.
4.3. Real anisotropy in the subsurface
Different problems appear in real media that make it difficult for the splitting analysis. Some methods try to take into account real situations, but it is practically impossible to deal with all of them. However, some of these problems will be introduced.
4.3.1. Variance of anisotropic material.
To assume a homogeneous anisotropic medium with a constant direction for the planes of fractures along the profile can be a good approximation, but is generally (or almost always) not the case
30 in the subsurface. Figure 18.104.22.168 shows a model of varying anisotropic properties, with two media with different alignment of the cracks. When the shear wave passes through the first medium, both components are polarized in the direction of the fractures and have a time delay of t1. But when the two components reach the second medium, each one will split again in two components polarized according to the fracture direction in the new medium. The final result will be four shear waves with the polarization of the last medium, where the time delay between the two fast or slow components will depend of the degree of anisotropy of the first medium and the delay between fast and slow shear waves (t1) will be due to the second medium. This process can be repeated many times for different anisotropic media and for many reflections, getting a complicated wave train with a total length that will be the sum of the individual time delays (MacBeth C. and Crampin S., 1991)
This varying anisotropic properties can also lead to differential attenuation of the components of the shear waves, so the waveform may be different for each component complicating the cross-correlation function between the two horizontal components of the geophone.
Figure 22.214.171.124 Splitting of shear waves in two anisotropic medium with different direction of the fracture's planes. Taken form MacBeth C. and Crampin S. (1991).
4.3.2. Non-orthogonality between slow and fast components of shear waves.
Many of the methods outlined above attempt to estimate shear wave polarization assuming orthogonality between the fast and slow components, nevertheless, this is not true for all the cases, and vertical incidence must be assumed in many methods, which also simplifies notably the calculations.
MacBeth C. and Crampin S. (1991) show in figure 126.96.36.199 a polar map with the direction of the fast (solid bar) and slow (broken bar) shear waves components for different incident () and azimuth () angles. In this case the extensive dilatancy anisotropy (EDA) is in the W-E direction, so the fast
31 component should be in that direction too. The inner circle in figure 188.8.131.52a marks the window for angles between 0°-35°, with the middle of the circle representing vertical incidence. It can be seen that a receiver inside this circle will have both shear waves components separated by a angle close to 90° but receivers outside this circle (as the geophones 2 and 3 in figure 184.108.40.206b), for particular azimuth angles, do not have orthogonality between the fast and slow shear wave components. The last paragraph shows that orthogonality of split shear-waves is only present for near vertical propagation (<35°) or when the propagation is parallel to the planes of fractures (in a W-E direction for the last case), otherwise, the polarization of the shear waves components will not be orthogonal (Crampin 1978). The reason of this is that even if:
“The polarization of plane split shear-waves are strictly orthogonal for the same direction of phase propagation, since the group-velocity (ray velocity) deviates from the phase-velocity direction (often by substantial amounts), the two split shear-waves traveling along similar raypaths are not usually orthogonal because their directions of phase propagation are not, in general, parallel to the ray” (MacBeth C. and Crampin S., 1991)
The same authors state that even in a comparatively weak anisotropic media the angles between the two shear wave components can differ about 5°-20° from orthogonality. On the other hand, even if the displacement of shear wave components is perpendicular each other and perpendicular to the compressional waves, the last one is not necessarily parallel to the direction of propagation (Juhlin C., 1990).
Figure 220.127.116.11. a) Polar map with the direction of the fast (solid bar) and slow (broken bar) shear waves at different azimuth and incident angles. b) Three receptor at different angles with the source. Taken from MacBeth C. and Crampin S. (1991)
32 4.3.3. Anisotropy reasons.
Shear wave splitting is generally due to the strike direction and amount of cracks in the medium, nevertheless, as it has already been mentioned, anisotropy can be due to several factors in the subsurface that affect the wave propagation. For example, in sedimentary basins, the anisotropy is due mainly to thin layer sequences and in a minor scale to the cracks, so the final shear wave polarization is generally not the same as the strike of the cracks (MacBeth C. and Crampin S., 1991).
33 5. Equipment and data acquisition process
5.1. The seismic equipment
The source used for the VSP survey was the VIBSIST-1000, which is based on the Swept Impact Seismic Technique (SIST) (Park et al. 1996; Cosma and Enescu, 2001) and can produce both shear and compressional waves.
The VIBSIST-1000 sources used were two tractor/excavator-mounted hydraulic rock-breakers, equipped with hammers delivering 1,500 and 2,500 J/impact at 400-800 impacts/minute, powered through a computer controlled flow regulator (figure 5.1.1). The shot points were located at different azimuths around the borehole KFM01A (Figure 1.1) and between 5 to up to 10 shots were made in each shot point so an high signal-noise ratio was achieved. The VIBSIST source was activated for a period of 15-20 seconds with different impact frequency ranges (Cosma C. et al., 2005).
For the receivers the 3 component chain Vibrometric R8-XYZ-C was used. The 24-28 Hz geophones were placed 5 meters distance between each other and a down-hole preamplifier was used for each channel. 136 levels were used so a distance of 675 m along the wellbore was covered. The z direction was placed along the hole and the x and y components perpendicular to this one. The frequency range was from 40 to 1000 Hz (Cosma C. et al., 2005).
A PC-based acquisition system was employed, consisting of an ICS 32-channel, 24-bit acquisition board, with LabView based acquisition interface (Cosma C. et al., 2005).
Figure 5.1.1. One of the VIBSIST-1000 sources used at Forsmark. Taken from Cosma et al. (2005)
34 5.2. The acquisition process
Figure 1.1 shows the coordinates of the borehole KFM01 and the 10 shot points in a lateral and panoramic view. The field work was carried out between the 2nd and the 22nd of august 2004.
The coordinates and elevation of the borehole and shot points are shown in tables 5.2.1 and 5.2.2 (Cosma C. et al., 2005). The dipping angle of the wellbore is of 84.7° from horizontal so the true depth and the distance from the zero depth to the last receiver differs by around 3,32 meters only. The distances from the top of the boreholes to shot points used for the VSP surveys range from 38 for SP-03 to 1.168 meters for SP-07.
Table 5.2.1. Coordinates of borehole KFM01A. Dipping and azimuth angle are measured from the horizontal and clockwise from the North respectively.
Table 5.2.2. Coordinates of the source positions for the VSP survey at KFM01A.
35 6. Data Processing
The data processing was done using Claritas Sofware in a Linux operating system.
The first step before the data processing was incorporating the geometry information in the headers of the program, including the real position of the well after calculations with the dipping angle and azimuth. A visual inspection of the 10 shots recorded in the VSP was also done. All the shots had relatively good data quality, excepting shots S04, S07 and S10 which didn't seem to show clear s-wave arrivals. The last two are at large offset shots (Figure 1.1) and the incidence angles varies from the first to the last receiver from 5°-34° and 5°-35° for the shots S07 and S10, respectively. As has been seen before (figure 4.3.2), for shots with incidence angles (angle between horizontal and ray) lower than 55°, the polarization of the shear waves will not be orthogonal unless the propagation is in the direction of the fracture. Both shots that were ruled out have incidence angles lower than 55° so they probably wouldn't show good results estimating the polarization. Furthermore, shots S06 and S09 are approximately in the same direction relative to the the well as shots S07 and S10, respectively, so rejection of these shots should not result in too much information loss.
Once the selection of shots was done, different processing steps were applied. First a spherical divergence correction was applied to all shots (Figure 6.1). This process clearly removes the high amplitude noise in the upper part of the seismograms (short time). Subsequently, rotations of horizontal and vertical components were done (Figure 6.2). The horizontal components were rotated using a window around the first compressional wave arrival, so the maximum energy (positive amplitude) of the p-wave was in the H1 component. With this the H1 component is in the plane source-well and H2 is in a perpendicular plane. The fact that p-waves can be recorded in the horizontal components has two main reasons:
– When the incidence is not vertical so the horizontal components of the receivers are not in a perpendicular plane to the propagation direction, some of the p-wave energy can be recorded in H1 and H2. After rotation of these two horizontal components, H1 is in a plane parallel to the propagation direction and H2 is in a perpendicular one, explaining why the p-wave energy disappear in H2. – In the case of near zero offset, that is, near vertical incidence as in S03 (with incidence angles between 69°-87°) the problem gets a bit more complex. The former reason can stand for the first shallower receivers, but for the deepest ones, with angles higher than 80°, a possible reason for the detection of compressional waves in the horizontal components can be the fact that in anisotropic media, the p-waves are generally not parallel to the propagation direction (Juhlin C., 1990). This would be equivalent to a wave arriving to the geophones with non vertical incidence, so with components in H1 and H2.
These two are theoretical reasons, but in real applications other effects can appear as for example wrong layout of the geophones along the well, with the horizontal components dipping in relation to the vertical plane. The dipping angle of the wellbore could also have an important role in this case.
36 Figure 6.1. Shot S01 without (a) and with spherical divergence correction (b)
Figure 6.2. Horizontal and vertical components. Both azimuth () and incident (i) angles were rotated.
37 After the horizontal rotations, the incident angle was rotated too, so the energy of the same p- wave in H1 was minimized and maximized in the vertical component (V). By this way, the vertical and H1 components are forming a plane parallel to the propagation direction, with the vertical component pointing in the propagation direction and the two horizontal components in a plane perpendicular to V.
Figure 6.3 shows an example of the energy in the first p-wave arrival before and after the two rotation steps. In the first seismograms and the corresponding first hodogram column, it can be seen how the energy is almost uniformly distributed in the three components. After rotating the horizontal component, the second seismogram shows a higher amplitude in H1 and a flat trace in H2. In the H1- H2 hodogram, the energy is centered along the H1 component only. The same trend is present in the V- H2 hodogram. The final incident angle rotation, focuses all the p-wave energy in the vertical component (negative amplitude).
Figure 6.3a. Seismic traces for the vertical (V) and horizontal (H1 and H2) components from receiver 37 in S06.
38 Figure 6.3b. Hodograms before (first column) and after azimuth (second column) and incident (third column) angle rotation from receiver 37 in S06
Once all the rotations were done, the p-wave energy was centered in the vertical component and the s-waves, which are perpendicular to the compressional wave, was divided between both horizontal components (Figures 6.4a-6.4g). A frequency band-pass filter was applied to all the data to remove undesired signal. Figure 6.5 shows the frequency range of the seismograms; a maximum frequency content was kept so only clearly noisy events were filtered. In this case a band pass filter of 15-30-250-400 Hz was used.
Figure 6.4a, b and c. Shots S01,S02 and S03 respectively after rotations of horizontal and vertical components
Figure 6.4 d, e, f and g. Shots S05,S06,S08 and S09 respectively after rotations of horizontal and vertical components.
41 Figure 6.4 shows clearly the p-wave arrival in the vertical component, with a higher amplitude and velocity. The shear waves can be seen at different times depending of the shots; in the near zero- offset section (shot S03), both shear and compressional waves arrive almost at the same time at the first receiver but there is a clear difference in the slope between both waves types. For the more distant shots (S06, S08 and S09) there is a big delay between the p and s waves arrivals.
All the shots excepting the near offset (2nd and 3th), show approximately in the first 40 receivers a positive or near horizontal slope, which is especially clear in the horizontal components. This event could be an upgoing wave reflected in an boundary between two different layers. Another interesting pattern that can be seen in almost every shot (green square in H1 component in figure 6.4d and 6.4f ) is the wave showing the same moveout as the shear waves, but starting almost at the same time as the compressional wave. This is a P-S wave which was transformed near the the first receiver, so its arrival time for the firsts geophones is almost the same as for a p-wave but after that it continues with an s- wave slope.
Figure 6.5. Frequency range in S06. Events below 30 Hz and above 250 Hz are clearly noisy events.
A trace balancing was also used (Figure 6.6), enhancing the important reflections. This process scales individual traces by a constant factor so all the traces have the same average amplitude (Claritas help manual). The trace balance unlike other methods as AGC (Automatic Gain Control) does not alter the frequency content and is a horizontal process (in space and not in time as AGC).
42 Figure 6.6. Shot S05 before and after balancing.
The following step was to kill the traces with bad data quality using the balance process with zero as the scalar factor and fill the traces using the fillholes process. This application fills holes in an ensemble of data from the adjacent traces scaled by the reciprocal of the distance of the ensembles from the trace to be filled (Claritas help manual). Figure 6.7 shows an example of two traces (trace 74 and 82) killed and filled using information from the two adjacent traces.
Figure 6.7. Seismograms from shot S06. Look traces 74 and 82 before (a) and after (b) the fillholes process was applied.
43 6.1. Polarization estimation
Subsequently, the polarization of the shear waves were estimated. Polarization diagrams (hodograms) were used to determine the direction of the fast and slow shear waves, using the the near cruciform pattern explained by Crampin et al (1986). Some of the hodograms picked are shown in figure 6.1.1. for the different shot points, as well as seismic sections rotated with the estimated angle and LMO.
Figure 6.1.1a. Shot S01. Hodograms and seismograms with LMO in the two horizontal components rotated according to the angle of polarization (35°)
44 Figure 6.1.1b. Shot S02. Hodograms and seismograms with LMO in the two horizontal components rotated according to the angle of polarization (18°)
45 Figure 6.1.1c. Shot S03. Hodograms and seismograms with LMO in the two horizontal components rotated according to the angle of polarization (25°)
46 Figure 6.1.1d. Shot S05. Hodograms and seismograms with LMO in the two horizontal components rotated according to the angle of polarization (30°)
47 Figure 6.1.1e. Shot S06. Hodograms and seismograms with LMO in the two horizontal components rotated according to the angle of polarization (45°)
48 Figure 6.1.1f. Shot S08. Hodograms and seismograms with LMO in the two horizontal components rotated according to the angle of polarization (14°)
49 Figure 6.1.1g. Shot S09. Hodograms and seismograms with LMO and the two horizontal components rotated according to the angle of polarization (33°)
50 An average of the angles from the different hodograms in every shot was done and used to plot the seismic sections rotated with this angle (Table 6.1.1). To these rotated-sections an LMO was applied, using a velocity that emphasizes as much as possible the shear wave slope differences between the two sections.
S01 S02 S03 S05 S06 S08 S09 Rotation 18 40 46 33 11 7 17 47 26 28 30 17 39 30 19 42 52 62 46 80 17 20 0 23 36 41 29 36 Angles 26 47 43 21 17 10 7 32 31 25 23 18 15 46 0 36 21 48 12 32 10 36 20 42 44 25 35 43 48 17 23 9 17 45 44 23 Average 35 18 25 30 45 14 34 Table 6.1.1 Rotation angles from hodograms for every shot
These angles represent the rotation clockwise for the fast component to be in H1 for the shots S01, S02 and S05. For the other shots it is the rotation angle necessary for the fast component to be in H2. The representation of these angles in geographic coordinates will be presented in the next section.
The selection of hodograms with cruciform patterns was not an easy task. As was said before, for the cruciform pattern to be identified in seismograms, a time delay between components of about 0.7T is necessary (Edelman, 1988), which implies that a strong anisotropy must be present or very short period wavelets (high frequency) must be used. This is one of the restrictions of this technique and could have been one of the reason for the few cruciform patterns detected. Moreover, noise and deformed wavelet degrades the particle motion representation in the hodograms. The fact that other arrivals (noisy signal) were before the shear wave first arrival is a problem because the end of this noise will interfere in the slow component at the beginning of the window chosen to see the cruciform patterns. Furthermore it affects the signal shape itself.
As can be observed in the hodograms, they all correspond to receivers below the 48th geophone, excepting for shot S03 were hodograms with cruciform patterns for the first receivers of the wellbore were detected. This could be due either to the interception of the shear waves with the upgoing wave for this upper part of the well or by the fact that for angles of incidence lower than 55° (from the horizontal) for shots non parallel to the plane of fractures, the shear wave components are not orthogonal. Table 6.1.2 shows the incidence angles for the different shots at the first and last receiver.
Shots Incidence angle for the first receiver Incidence angle for the last receiver S01 9.4585 52.2058 S02 25.5560 74.8802 S03 68.8045 87.1318 S05 13.8957 62.4248 S06 7.1047 43.9710 S08 6.8209 42.7934 S09 7.2127 44.4076 Table 6.1.2 Incidence angles at the first and last receiver for every shot.
51 Nevertheless, it is unlikely that the incidence angle is the reason for the lack of cruciform patterns in the hodograms in the first receivers. Having several shot points, each one of them should start showing orthogonalization between shear wave components at different depths depending on the offset, but they all start showing polarization around the 50th-60th receiver. Moreover, with shots at so many different azimuths, some of them should be close to parallel to the fracture planes, so they should have orthogonal components for any incident angle.
6.2. Velocity analysis
Two different methods were employed for the velocity analysis. The first uses the seismograms after rotations with the angle of polarization already estimated and calculates directly the velocity of the shear waves in both horizontal components. The velocity calculation is done using the ruler tool of the Claritas Xview window and confirmed using LMO plots with the velocity estimated.
Table 6.2.1 shows the velocity of three shear waves in all the shots for both components. An average is considered as the true velocity of the shear waves.
Shots H1 velocities (m/s) H1 average velocity (m/s) H2 velocities (m/s) H2 average velocity (m/s) S01 3781 3694 3695 3723.33 3704 3743 3712 3719.67 S02 3547 3532 3583 3554 3482 3519 3500.5 S03 3432 3512 3544 3496 3516 3575 3518 3536.33 S05 3316 3327 3296 3313 3281 3204 3267 3250.67 S06 3378 3393 3402 3391 3453 3501 3418 3457.33 S08 3673 3618 3742 3677.67 3802 3864 3753 3806.33 S09 3943 3875 3837 3885 3880 3942 3911
Table 6.2.1. Velocities in both shear wave components measured directly in the seismic sections.
Only the second component of shots S02 and S09 did not show three clear shear waves, so only two waves were used for that cases.
The second method is the one proposed by Li et al. (1988). The velocity of the p-wave must be calculated, and a LMO with this velocity is applied to the horizontal components. Finally the slopes of the s-waves are measured and plugged into the equation:
app 1 V = s 1 1 V p S
app Where Vs is the apparent shear wave velocity, Vp is the p-wave velocity and S is the slope of the s-wave after LMO was applied with Vp.
52 For the true velocity, the apparent one must be multiplied by the cosine of the incidence angle:
app V s=V s cos
The incident angle was taken as the average between the first and last receiver used for the beginning and end of the slope. Table 6.2.2 shows the slopes, average apparent and true shear wave velocities for both horizontal components. The compressional wave velocities are also provided in the last column. As for the first method, three shear waves were taken for each component, excepting H2 for the shots S02 and S09.
Shots Slope (m/s) Av Vsapp(m/s) True vel (m/s) Slope (m/s) Av Vsapp(m/s) True vel (m/s) Vp (m/s) S01 13175.65 4237.87 3634 12954.55 4287.93 3550.42 6300 12500 13157.89 13181.82 14210.53 S02 11176.47 3783.19 3120.73 10454.55 3768.81 3068.12 5850 10694.44 10735.29 10277.78 S03 8916.67 3477.34 3414.4 9298.25 3623.28 3548.24 5750 8790.32 8898.31 8688.52 11416.67 S05 9347.83 3605.57 3031.99 8191.49 3440.94 2852.28 5650 10595.24 8953.49 10000 9302.33 S06 13181.82 3885.83 3432.87 12727.27 3887.45 3408.02 5500 12916.67 14000 13636.36 13095.24 S08 16428.57 4331.57 3892.93 26000 4645.22 4103.57 5630 18500 32500 22058.82 22647.06 S09 17750 4549.12 4058.63 15681.82 4601.37 4071.66 6150 18684.21 21562.5 16136.36
Table 6.2.2. Shear waves velocities for H1 and H2 components using the method described by Li et al. (1988)
53 7. Results and interpretation
The polarization angles can be used to know how much the H1 component in the well has to be rotated for each shot pointing to the propagation direction to be in the fast polarization direction. Table 7.1 shows the azimuth angles (counterclockwise from the north) for every shot, the polarization angle and the difference of both, which represent the fastest component. Assuming orthogonality between components, 90 degrees was added to shots S03, S05, S06, S08 and S09 so the fast direction is not in H2 anymore, but in H1.
Shots Azimuth Rotation for H1 to be in the Direction of fast Geographic direction of (degrees) fastest component (degrees) component the fast component (degrees) S01 47.2955 35 12.3 N12.3W - S12.3E S02 72.0069 18 54.01 N54.01W - S54.01E S03 332.5098 25+90 37.15 N37.15W - S37.15E S05 237.2614 30 27.26 N27.26W - S27.26E S06 196.3162 45+90 61.32 N61.32W – S61.32E S08 166.3145 18+90 58.31 N58.31W – S58.31E S09 115.7511 33+90 172.75 N7.25E – S7.25W
Table 7.1. Rotation angles and direction of the fast coordinate (counterclockwise) of the shear wave
Taking an average of all the directions, the fast components lie in the plane N60W – S60E. Nevertheless, it can be seen that shots S01 and S09 differ significantly from the other shots, pointing almost in a N-S direction. If these two shots are excluded, the new average is N48W – S48E with a standard deviation of ±15°. This direction represents the one parallel to the fracture planes, with the slow component perpendicular to this one. Lawani K. (2007) determined, using borehole breakout, a direction for the average maximum horizontal stress in well KFM01A of about N39±8W. This value seems to agree with the average obtained using the shear-wave polarization.
The main cause of the horizontal stresses in the region is the mid-Atlantic-ridge (Juhlin C., personal communication), which is spreading in a direction approximately according to the results obtained (Figure 7.1). Following the extensive dilatancy anisotropy (EDA) criteria from Crampin (1985), the fractures should align in the direction of the main stress so the fast shear wave component should agree with that direction.
To determine the degree of anisotropy, the velocity difference must be analyzed. Table 7.2 shows the velocity for both shear wave components, with the direct and the Li et al. (1988) methods as well as an average of both. The velocity estimated differs using one or the other method, but the trend
54 of the fastest components is consistent. It can be seen that shots as S05 and S08 have a considerable velocity difference between their components, while shot S01, S06 and S09 have almost the same velocity in both components, so a high degree of anisotropy can be expected for the first ones and a low value for the last ones.
Figure 7.1 Mid Ocean Ridge After Minster et al. (1974)
H1 (all measures are in m/s) H2 (all measures are in m/s) Shots Direct Li et al. Average Direct Li et al. Average measure method measure method S01 3723.33 3634 3679±63 3719.67 3550 3635±120 S02 3554 3121 3338±306 3500.5 3068 3284±306 S03 3496 3414 3455±58 3536.33 3548 3542±8 S05 3313 3032 3173±199 3250.67 2852 3051±282 S06 3391 3433 3412±30 3457.33 3408 3433±35 S08 3677.67 3893 3785±152 3806.33 4104 3955±210 S09 3885 4059 3972±123 3911 4072 3992±114
Table 7.2. Velocity in the fast and slow components
55 In table 7.3, the anisotropy coefficient was calculated using the velocity difference in both components divided by the fastest velocity component. The depth was estimated for every shot from the depth of the first geophone were visible polarization patterns were appreciated till the last receiver. Another parameter that can be used for anisotropy calculations is the density of aligned fractures parameter (), which is best thought of as the ratio of the cube of the fracture radius to the unit volume enclosing the fracture (Leary et al., 1987). To estimate this parameter the formula of Hudson (1981) was used:
0.5 16 2 2 2 2 V =V [1− cos −sin ] st s 3 32
where Vst is the velocity of transversal (or slow) shear wave component Vs is the velocity of the shear wave velocity is the incidence angle from the vertical and are the Lame's constants and is the density of aligned fractures parameter
The fast shear wave component was used as Vs and the Lame's constants were calculated from the s and p wave equations, using a density of 2.65 g/cc (granite density), due to the dominance of igneous intrusive rocks in the region. The fracture parameter estimated is consistent with the anisotropy calculated using only the two shear waves components, with a high anisotropy between shot S08 and the well and a very low anisotropy from shot S09. It can also be seen the percentage of anisotropy appears to have some relation with the p-wave velocity, which decreases in the zones of high anisotropy.
The very low degree of anisotropy in shots S01 and especially in S09 can be the reasons for the difference in the polarization angle calculated before. This low amount of fracture produces little velocity delay between the components, so the cruciform patterns are not common. These two shots are also in the same region to the west of the well (see Figure 1.1), so it is possible that anisotropy is less to the west of the well that in the other parts.
Shots Depth (m) Anisotropy Density of aligned fractures Vp (m/s) S01 388-771 1.2 % 2.1 % 6300 S02 343-771 1.6 % 1.3 % 5850 S03 154-771 2.5 % 1.9 % 5750 S05 393-771 3.8 % 2.8 % 5650 S06 353-771 0.6 % 1.5 % 5500 S08 328-771 4.3 % 6.2 % 5630 S09 388-771 0.5 % 1.0 % 6150
Table 7.3. Anisotropy estimation using velocities
56 8. Discussions and conclusions
Shear wave splitting analysis has shown to be an useful tool for anisotropy estimation, with consistent estimations in 5 out of 7 wells. The results show a preferential direction for the plane of fractures of N48W - S48E ±15° which seems to be consistent with the main horizontal stress direction from previous studies of borehole breakout and with the regional stresses in the zone due to the Mid- Atlantic Ridge (MAR). The anisotropy was noticed between approximately 350 and 771 m (bottom of the well) depth. The shallower receivers did not have a clear signal and, furthermore, the low degree of anisotropy makes a short time delay between slow and fast wave components, making difficult the interpretation of the hodograms and the velocity difference estimation.
Shots S01 and S09 showed different anisotropy directions than the other shots and even if these two shots are located more to the west than the other ones, it is unlikely that the geology presents so drastic regional changes in short distances. Other reasons can also explain this difference, like the low degree of anisotropy in this zone (especially in well S09) which complicates the estimation of polarization directions. Figure 8.1 shows an example of a shot where there is a clear delay between the two horizontal components, but the low degree of anisotropy prevents a time difference high enough to form cruciform patterns in the hodograms. Processing errors could also have had some influence in the results, taking into account that the hodogram selection process is a subjective method, experience and knowledge have a fundamental role for this method
Figure 8.1. Shot S02, Receiver 75. Representation on particle motion for a shear wave in the two horizontal components.
The degree of anisotropy calculated for the area in shots S02, S03, S05, S06 and S08 was relatively low, with an average of 2.6% ± 1.5% and a density of aligned fractures of 2.7% ± 2%. The results were calculated using two different methods for the velocity analysis. Both had the same trend but the values of the velocities used in the two methods did not exactly agree. Nevertheless, the velocity estimates are always subject to a margin of error, so using two different ways to estimate velocities reduced this uncertainty.
The only exception in the anisotropy calculations was shot S08, were a relatively high anisotropy was obtained. This difference could be due to local structural deformation or fracturing, or to a lithological feature (thin layer or mineral grain alignment). Nevertheless other studies must be done
57 to see the possible reason of this high anomaly. Personal mistakes in the processing cannot be ruled out either as a possible reason for the high anisotropy in S08.
In general terms, polarization diagrams and the velocity analysis methods used in this work, have the disadvantage of been very time consuming due to the fact that every trace must be analyzed individually, nevertheless, as was already mentioned before, it is one of the most common and reliable methods to study the anisotropy and can offer results that cannot be reached with only compressional wave processing.
The results obtained confirm that the northwestern part of the Forsmark investigation site could be a feasible region to bury and store the nuclear waste. The amount of anisotropy found in this study proves, assuming most part of the anisotropy present is due to fractures, there are no big leakage paths for the waste in the area.
58 9. Further work
The work carried out so far shows some important conclusions, but more studies must be performed in the area to check the trends obtained and, especially, using the other wells, so information from the southeastern part of the Forsmark investigation site can be related with the one of this work. Due to the low degree of anisotropy, other more accurate methods can be implemented to estimate the direction of polarization and amount of fractures. Correlation matrices between components of the geophones at the same or different levels could be a useful and more exact method to study the shear wave splitting, and even not so time consuming as the direct study of polarization diagrams.
Finally, well logs are also an important tool that should be used to tie the VSP data, taking advantage of the several wells in the area and the relatively short distance between them, so depth maps of the region can be produced with the location the lithological layers, fractures and other important patterns of interest.
59 10. Acknowledgment
I would like to thank, above all, my parents and my sister for their steady support along my studies and during all this year abroad, keeping me motivated and always believing in me. A special thanks to my relatives in France, Italy and Scotland too, who even if I don't see very often I know I can always count on them.
To the Simon Bolivar University (home University) and Uppsala University (host University) that made possible this wonderful exchange year program in Sweden, contributing noticeably to my personal and professional formation.
Deepest gratitude to my supervisor Christopher Juhlin, who was abundantly helpful and offered invaluable assistance, support and guidance every time I had problems with my thesis.
To all the geophysics department's staff and students, who, as well as having been important for my studies, provided a great atmosphere and made of this a pleasant place to work, offering enjoyable moments and making from every day a special and different day.
Finally, but not less important, I have to thank my friends in Venezuela (Calabozo and Caracas) and here in Uppsala for all the marvellous time and amazing moments we have shared together, being everyone an essential part in the development of my life.
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