10th Asian Regional Conference of IAEG (2015)

Dominating factors of the wave velocity anisotropy for TCDP borehole
Chang-No WU(1), Che-Ming YANG(1), Wen-Jie WU(1) and Jia-Jyun DONG(1)(1) Applied Geology Institute, National Central University, Chungli, Taiwan
E-mail:arnold790222@hotmail.com
Abstract
The direction of the fast horizontal shear wave velocity (FSH direction) is frequently
used as an indication of the direction of the maximum horizontal principal stress. However,
together with the stress induced anisotropy, the wave velocity anisotropy will also be
dominated by the inherent anisotropy including the effects of sedimentary and tectonic
structures. This study carefully evaluates the influence factors of wave velocity anisotropy
in Taiwan Chelungpu-Fault Drilling Project (TCDP) borehole. The anisotropic compliancetensors of sandstones and mudrocks were derived from the laboratory wave measurement.
The equivalently continue model was used to evaluate the compliance tensor of jointed
rocks, which considered the anisotropy distribution of discontinuities. The lithology was
identified as the most influential factor on the wave velocity anisotropy. The dip angle ofthe bedding plan is also a dominating factor. Surprisingly, the joints distributed in the rockmass are not significantly influencing the wave velocity anisotropy. Generally, themeasured FSH directions of sandstones can be accounted by the anisotropy of sandstones.
When the dip angles are steeper (in a depth greater than 1800 m), the measured FSH
directions of siltstones seems dominated by the dip direction of bedding planes. The spatial
variations of the FSH direction in siltstones could be related to the low inherent anisotropy.
This study demonstrated that determining the direction of the maximum horizontal principal
stress from the FSH directions should consider the influence of inherent anisotropy of rockmass base on the TCDP borehole data.
Keywords: TCDP, shear wave anisotropy, inherent anisotropy, fast shear wave velocity,maximum horizontal principal stress
1.

Introduction

Project (TCDP) was used (Lin et al., 2007; Yeh et al.,2007; Wu et al., 2008; Yabe et al., 2008; Louis et al.,2008; 2012; Hung et al., 2009; Haimson et al., 2010).
The appropriateness of using the direction of FSH toevaluate the direction of maximum horizontal
principal stress will be presented.

The directions of the fast horizontal shear wave
velocity (FSH) measured in boreholes are sometimes
used as indications of the maximum horizontal
principal stress (Boness and Zoback, 2006a).
However, the wave velocity anisotropy can orientfrom the inherent anisotropy of the medium (e.g.,alignment of minerals or grains; bedding plane,aligned macroscopic fractures, and faults) in addition
to the anisotropic stress state (Alford, 1986; Mueller,
1991; Sayers, 1994; Brie et al., 1998; Boness andZoback, 2004; Boness and Zoback, 2006b). In thiscase study, the influence of inherent anisotropy(including bedding planes and joints) on the directionof FSH is quantitatively evaluated. The available data,
includes the borehole logging and laboratory testingproduced from the Taiwan Chelungpu fault Drilling2.

Methodology

In this study, two sources of inherent anisotropyof rock mass were considered, namely: intact rocks(bedding plane and micro-fractures), and joints.
Christoffel equation (Musgrave, 1971) was used tolink the anisotropic wave velocity and the elastic
stiffness (or elastic compliance) of the medium. The
coordinate system used is showed in Fig. 1. Axes 1, 2,
and 3 represent East, North, and up directions,
respectively. Axes 1’, 2’, and 3’ are the dip direction,1

10th Asian Regional Conference of IAEG (2015)

strike, and normal directions of the bedding plane of
the sedimentary rocks.

rock) in 1-2-3 coordinate system can be expressed asfollows:

2.1 Elastic compliance of intact rocks
If the wave velocities parallel and perpendicular
to the bedding plane of the intact rocks are available,
we can easily obtain the elastic stiffness matrix (in thecoordinate system of 1’, 2’, and 3’) as follows:C
S ijkl (1 / h  1 / g ) Pijkl (1 / 4 g )( ik Pjl   jk Pil   il Pjk   jl Pik )where Pij , Pijkl are the crack tensors reflected thejoints characteristic (i.e. orientation ( n ), the volume

C11( M ) C12( M ) C13( M )000 C ( M ) C ( M ) C ( M )
0
0
0 
22
23
 21

(M )
(M )
(M )
C
C32 C33
000 (1)C IJ( M )   31
(M )
(M )
(M )
 0

0
0 C44
C45
C46
(M )
(M )
(M ) 
 0
0
0 C54
C55
C56

(M )
(M )
(M ) 
0
0 C64 C65 C66  0density of joint (  c ) and diameter of joints ( r )),which can be calculated as follows:(3)  r n n E n , r ddr
P   / 4  r n n n n E n , r ddr (4)Pij   c / 4The above elastic stiffness matrix (6*6) can be
expressed as a tensor by Voigt notation C(M )i ' j ' k 'l '

3

c

i



r

3



r

j

i

c

j k l

c

The h and g in Eq. (2) represent the averaged

tensor S i('Mj 'k)'l ' in the 1’-2’-3’ coordinate system canbe derived from C

rm

rm

ijkl

(Musgrave, 1971). Accordingly, the compliance(M )i ' j ' k 'l '(2)normal and shear stiffness, respectively, which can becalculated using Eqs. (5) and (6).

easily. After coordinate(M )of thesystem transformation, the compliance S ijkl

h  h  c n N ij (5)intact rocks in 1-2-3 coordinate system can beobtained.

g  g n N ij

(6)

N ij 

 n n E n d


i

j

c

(7)

The h and g in Eqs. (5) and (6) are constants. c
is aspect ratio which is introduced as a measure ofcrack shape. The ratio is assumed as a constant in thisstudy. The N ij is a directional density function that
describe the probability of the normal vectors in
different direction.

2.3 The velocity anisotropy of rock mass
To calculate the velocity of rock mass alongcertain direction, the Christofell equation (Eq. (8))
can be used.

Fig. 1 Coordinate system.

2.2 Elastic compliance tensor of jointed rock mass
Oda (1988) proposed an equivalent continuum
model for describing the elastic compliance of jointed
rock mass. The joints were represented by sets ofparallel plates connected by two springs in normal
and shear directions. The elastic compliance tensor of
the jointed rock mass (excludes the influence of intact

12
13  U 1 11  V 2
 21
22  V 2
23  U 2   0 (8) 3233  V 2  U 3 31(R) w w
ik  C ijkl
n j nl is the Christofell matrix, which is a2

10th Asian Regional Conference of IAEG (2015)

used. A can be calculated as follows:

function of the wave direction n wj and elastic

A  100 * V s2 fast  V s2 slow  / V s2 slow ,(R). The  andstiffness tensor of the rock mass C ijkl

(9)

V represent the density of rock and wave velocity
respectively. Based on the eigenvalue V 2 and theeigenvector U , the wave velocities and thepolarized direction of three waves (one is P-wave

where Vs2 fast and Vs2 slow are the fastest and slowest

velocity Vp , the others are S-waves Vs ) can be3.

shear wave velocity.

obtained.

Results

3.1 Observed velocity anisotropy from logging
Fig. 2 shows the measured anisotropy ratio ofshear wave velocity A (purple line, unit: %), andFSH direction DFSH (red line, unit: degree). The
fault zones (e.g. FZA1111, FZA1525, FZA1679)
were identified by Yeh et al. (2007) from core
analysis data. It can be observed that the DFSH is
influenced by the fault zones. Besides, it is obviousthat the changes of DFSH and A decrease withincreasing depth.
Furthermore, it appears that lithology is adominating factor of the anisotropy of shear wave
velocity. As shown in Fig. 2, DFSH in sandstone is

2.4 Data
The data of sonic wave velocity of host rock weused are from Louis et al. (2008; 2012). They
measured the P-wave velocity of the sandstone andsiltstone retrieved from TCDP hole A. Based on themeasured wave velocity, the siltstone is a transversely
isotropic material which is mainly dominated by thebedding plane. Sandstone is orthotropic underatmosphere pressure for the presence of micro
fractures normal to the bedding plane. However, withincreasing confining pressure, the orthotropic nature
gradually transformed into transversely isotropic(Louis et al., 2012). As the results, both siltstone andsandstone are considered as a transversely isotropic
material in this study. The measured P-wave velocityof Louis et al. (2008; 2012) was used to evaluate theelastic constants of intact rocks. The required S-wave
velocity of sandstone and siltstone was estimatedmostly distributed in 120° and A decreases withincreasing depth. However, DFSH and A ofsiltstone and shale are relatively scattered. The
general trend of DFSH and A are described asfollows:(1) The velocity anisotropy ratio A in sandstone
decreases from about 30% to 10% withincreasing depth.
(2) Generally speaking, FSH direction DFSH insandstone mostly distributed in 110° - 120°.
Above 750 m, DFSH is relatively scattered,
which abruptly approached to north (0°) or east(90°) than back to 120° soon, especially in
500m – 650m. Right below -1650 m, DFSH
abruptly approached to 180° and gradually
decreased to 60°, than back to 120°.
(3) The velocity anisotropy ratio A in siltstones
and shales (mudrocks) are more scattered than insandstone. The velocity anisotropy ratio A issignificantly influenced by fault zones. Notable,
A abruptly increases from 10% into 30% below
1785 m.
(4) Similar to the case of sandstones, FSH direction
DFSH in siltstones and shales are mostly
concentrated within 110° - 120°. However, themeasured DFSH for siltstone and shale isrelatively scattered. Apparently, the DFSH isalso influenced by the presence of fault zones.
Interestingly, at a depth greater than 1785m, thefrom velocity ratios ( R  Vp / Vs ) of 1.5 and 1.9(Castagn et al., 1985). Notable, the wave velocities
propagating through shales and siltstones are assumed
identical and these two rock types are represented as
mudrocks in the following analysis. That is, thelaboratory wave velocity measurement of siltstones
was used to represent the wave velocity of mudrocks.
To determine the parameters of equivalent model(normal vector of joints n and the volume densityof joint  c ), we use the borehole image of TCDP
hole A documented by Wu et al. (2008). The normal
stiffness proposed by Cheng (2006) and the shear
stiffness proposed by Oda (1988) was used.
To evaluate the velocity anisotropy, the velocity
anisotropy ratio A and FSH direction D FSH was3

10th Asian Regional Conference of IAEG (2015)

FSH direction DFSH concentrated at about
105° (The dip direction of formation). Notable,
the dip angle abruptly changed from 30° to about
60° below 1785m (Yeh et al., 2007).

assumed as transversely isotropic materials. The
isotropic plane of mudrock is bedding plane whilethat of the sandstone is the micro fracture which isperpendicular to the bedding plane. That is, theanisotropy of sandstone is only dominated by the
micro fractures. Since the shear wave velocities ofsandstones are confining stress sensitive, the pressure
dependent nature of sandstone was considered.
The elastic compliance tensor was derived fromthe measured P-wave velocity (Louis et al., 2008;2012) and the estimated S-wave velocity (from thevelocity ratios ( R  V p / Vs )). Based on the inferred
elastic compliance tensor, the A , DFSH , fastest andslowest shear velocity ( SVH ,F and SVH ,S ) of siltstoneand sandstones can be calculated by Eq. (8). Fig. 3
shows SVH ,F and SVH ,S of siltstone with different
dip angles, which propagating in vertical direction
and polarized in horizontal direction. The red andblue lines represent the fastest and slowest shear
wave velocities. The pink line is the velocity
anisotropy ratio A . From Fig. 3, A of siltstone isincreased with increasing dip angle. Notable, A islow (~5%) when the dip angle below 30 degree. A
of sandstone will not be influenced by the dip angleof bedding plane for the normal of the micro fractures
is on the horizontal plane. However, the DFSH will
identical to the dip direction of the bedding planesince the strike of the micro fractures is parallel to thedip direction. Meanwhile, the velocity anisotropy
ratio of sandstone is decreased with confining stress(Fig. 4) where a lower law is assumed to represent thestress dependence (Louis et al., 2012).

Fig. 2 The shear wave velocity anisotropy ofsandstone, siltstone and shale. Purple line represents
the velocity anisotropy ratio A . Red line represents
the FSH direction DFSH . FZA represents fault zone.

3.2 Calculated velocity anisotropy neglecting theinfluence of joints
Based on the Christoffel equation and the elastic
compliance matrix of intact rocks (sandstone andmudrock) derived from the wave velocity measured
by Louis et al. (2008, 2012), the anisotropy ratio A
and the FSH direction DFSH on arbitrary plane canbe calculated. It is indicated by Louis et al. (2008,2012) that the anisotropy of intact rocks is mainly
dominated by the bedding plane for mudrocks anddominated by the micro fractures which are parallelto the dip direction for sandstones. As aforementioned,
the orthotropic nature of sandstones transformed
gradually into transversely isotropic nature when theconfining stress increased. The studied rocks are

Fig. 3 Shear wave velocity anisotropy changes with
dip angle in siltstone.

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10th Asian Regional Conference of IAEG (2015)

Fig. 4 Shear wave velocity anisotropy changes withconfining pressure in sandstone.
Yeh et al. (2007) documented that the dip
direction is 105°. The dip angle is about 30 degree
above 1710 m and 60 degree below 1710 m. The
calculated and measured anisotropic shear wave
velocities are shown in Fig. 5. It is obvious that
DFSH and A of sandstone are decreased withincreasing depth. The spatial variation is insignificant.
That is, the anisotropy of sandstones is well depictedbased on the elastic compliance of intact rock.
However, in mudrock, there is a significant mismatch
between the predicted and measured anisotropy. It
indicated that other factors such as joints or in-situ
stress could dominate the anisotropy. Notable, thepredicted results in depth below 1785 m of mudrocks
are closed to the measured ones. The dip angle
abruptly increased from 30° to 60° (Yeh et al., 2007)
could account for the good prediction. That is, thewave anisotropy below 1785m is mainly dominatedby dip angle.

3.3 Calculated velocity anisotropy considering theinfluence of joints
Wu et al. (2008) reported TCDP core image.
Accordingly, the joint orientations required for Oda’s
equivalent model are available and the anisotropic
characteristics of the elastic wave of rock massaround TCDP hole-A. Six depth intervals wereselected with uniform lithology to calculate the
DFSH and A . The results are summarized in Table
1. The influence of joints on the anisotropy ofsandstone and mudrock is insignificant. It isreasonable for the anisotropy induced by joints will
decrease with increasing depth.

Fig. 5 Calculated and measured anisotropy (velocity
anisotropy ratio A and FSH direction DFSH ) of
the elastic wave velocities.

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10th Asian Regional Conference of IAEG (2015)

Table 1 The calculated wave anisotropy of the rockmass around TCDP hole A.
Depth
(m)

Lithology

700740sandstone

840856sandstone

8561012mudrock

13501529

mudrock

16001641

sandstone

17851855

mudrock

4.

Rock mass(neglecting
joints)Rock mass(considering
joints)

A (%)

27

A (%)

24

DFSH

105°

DFSH

105°

A (%)

26

A (%)

24

DFSH

105°

DFSH

106°

A (%)

5.5

A (%)

5.0

DFSH

15°

DFSH

14°

A (%)

5.5

A (%)

5.3

DFSH

15°

DFSH

14°

A (%)

23

A (%)

21

DFSH

105°

DFSH

106°

A (%)
DFSH

20
15°

A (%)
DFSH

20
14°

with the dip angle of the bedding plane. Above 1785
m, the anisotropy of the mudrocks is too low to
obtain an identical DFSH . For velocity anisotropy
ratio increased significantly below 1785 m (purple
color, left part of Fig. 3), the measured DFSH tends
to be dominated by the strike of the bedding plane(N15°E), which is illustrated in Fig. 6. The measured
anisotropy ratio is close to the calculated ones (20%).
The spatial variation of the measured DFSH ofthe sandstones is relatively low. The high anisotropy
ratio accounts for the stable DFSH . Meanwhile, themeasured anisotropy ratio support that anisotropy
ratio of sandstones will increase with increasing
depth (Fig. 4; pink dash line). Based on Fig. 4, theA decreased from about 30% to 20% when thedepth increased from 500 to 1860m (effective
confining pressure increased from 6 to 23 MPa if asubmerge unit weight of 1.22 g/cm3 is assumed).

Discussion

4.1 Host rock induced wave anisotropy factors
Based on the measured anisotropy (logging data),
lithology is the most important factors inducing wave
velocity anisotropy. Furthermore, the depth and dip
angle are also dominating factors on the wave
velocity anisotropy.
The measured and calculated DFSH and A are
listed in Fig. 5. The corresponding lithology are also
indicated (yellow: sandstone; brown: siltstone; green:
shale). Fig. 5 shows that the measured FSH direction
DFSH of sandstone (blue dots) is well predicted( DFSH is 105° for the dip direction of the bedding
plane is 105°; Fig. 6) using the laboratory obtainedelastic compliance of intact rocks although themeasured one demonstrated spatial variations. Fig. 7
is the histogram of DFSH (concentrated in about
100° – 120°) measured in sandstone from boreholelogging data. That is, the measured DFSH is well
depict only based on the elastic complianceanisotropy of intact rock DFSH .
The predicted DFSH of mudrock (siltstone andshale) is 15° (Fig. 5), which is highly deviated fromthe measured one. However, the measured DFSH
gradually changed below 1785 m and the direction
varied from east (90°) to north (0°). This difference iscaused by the variation of the dip angle changing
from about 30 degree to 60 degree. As indicated inFig. 3, the anisotropy of the mudrock will increase

Fig. 6 The sources of wave anisotropy of sandstones
and mudrocks.

Fig. 7 The histogram of DFSH measured insandstone from borehole logging data.

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10th Asian Regional Conference of IAEG (2015)

4.2 Influence of Joints on anisotropy of elastic
wave velocity

Besides, the joint length is uncertain in thisstudy because the data are from logging and core.
Besides, the vertical resolution of the averagetransmitter-receive spacing of DSI logger is about 4
meters (Schlumberger, 2004). Therefore, it is possiblethat the acute variation of A and DFSH is caused
by local change of joint orientation or existence of
longer joint. The Oda model (1986) is only valid for arepresentative elementary volume (REV) whichcontains enough number of cracks. The measurement
volume of velocity log is less than the REV of the
Oda model. We speculate that the model prediction
failed to capture the local variation of the wave
anisotropy which dominated by the abruptly change
of joint characteristics (e.g. length, orientation or joint
density).

The joint induced wave anisotropy decreases withincreasing depth (or stress), which is significant inshallow depth (Boness and Zoback, 2006a). To
demonstrate the influence of stress on the anisotropy,
the rock mass in the depth interval of 828 – 884m
(sandstones here is taken into account an isotopic
material) is evaluated. Fig. 8(a) shows theorientations of the joint distributed in the studied
depth interval. The parameters used were listed inTable 2.
Table 2 Parameters used in the Oda model.

r (m)h (MPa)
g (-)

0.2
360
200

5.

Fig. 8(b) shows that the anisotropy ratio isdecreased rapidly with increasing depth. It is becausethat the aperture decreased with increasing confining
stress rapidly. Therefore, the compliance tensor ofConclusions

This study used the laboratory wave velocity
measurement of intact rocks, equivalent continuum
model for describing the elastic compliance of jointed
rock mass, and discontinuities data to evaluate thedominating factors of the wave anisotropy. The
TCDP borehole A was used as a studied case. Basedon the logging data, it is obvious that the wave
anisotropy characteristics in sandstone and siltstone
are different. The wave anisotropy in sandstone ismainly dominated by confining pressure, but the
influence of bedding plane is significant for siltstone.
Based on the anisotropic elastic compliance ofsandstones and mudrocks derived from laboratory
wave velocity measurement, the calculated wave
anisotropy of intact rocks (neglecting the influence of
joints) generally comparable to the measured
anisotropy from borehole velocity logs. The
measured FSH directions of sandstones could bedominated by the micro fractures perpendicular to thebedding planes. When the dip angles become steeper(in a depth greater than 1785 m), the measured FSH
directions of mudrocks seems dominated by the dip
direction of bedding planes. It suggests that theinherent anisotropy of intact rocks accounts for thewave anisotropy.
Relatively, the influence of joints is insignificant
using the Oda model and assumed parameters,
especially at a depth greater than 500 m. However,the discontinuities separate the source and receiver ofthe velocity logging could explain the scatters of themeasured FSH directions and the wave velocity
anisotropy ratio.
To conclude, determining the direction of the
maximum horizontal principal stress from the(C )becomes smaller than the compliancejoints S ijkl

(M ). As depth reaches 800 m,
tensor of host rock S ijkl

the joint induced anisotropy ratio is only 3%.
Meanwhile, the predicted wave anisotropy A is
26% at -800m if the host rock (sandstone) is assumed
as a transversely isotropic material. It suggests thatthe wave anisotropy will be dominated gradually by
host rock with increasing depth. In TCDP logging
data (Fig. 2), the tendency of wave anisotropy A
gets smaller with depth is because the effect of joints
decreases gradually.

Fig. 8 (a) Orientations of the joints distributed in thedepth interval of 828 – 884 m. (b) The velocity
anisotropy ratio of rock mass in the studied depth
interval.

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10th Asian Regional Conference of IAEG (2015)

direction of the fast horizontal shear wave velocity
should carefully consider the influence of inherent
anisotropy of rock mass.

anelastic strain recovery method to three
dimensional in-situ stress determination, Terrestrial,
Atmospheric and Oceanic Sciences, Vol. 18, No. 2,
pp. 379–393.
Louis, L., Chen, N.T.M., David, C., Robion, P.,
Wong, T.F. and Song, S.R. (2008): Anisotropy ofmagnetic susceptibility and P-wave velocity in coresamples from the Taiwan Chelungpu-Fault Drilling
Project (TCDP), Journal of Structural Geology, Vol.
30, pp. 948–962.
Louis, L., David, C. Spacek, P., Wang, T.F., Fortin, J.
and Song, S.R. (2012): Elastic anisotropy of coresamples from the Taiwan Chelungpu Fault Drilling
Project (TCDP): direct 3-D measurements and weakanisotropy approximations, Geophysical JournalInternational, Vol. 188, pp. 239–252.
Mueller, M.C. (1991): Prediction of lateral variability
in fracture intensity using multicomponent shearwave seismic as a precursor to horizontal drilling,
Geophysical Journal International, Vol. 107, pp.
409–415.
Musgrave, M.J.P. (1971): Crystal acoustics,
Holden-ay, San Francisco.
Oda M. (1986): An equivalent continuum model forcoupled stress and fluid flow analysis in jointed
rock masses, Water Resources Res., Vol. 22, No. 13,
pp. 1845-1856.
Oda, M. (1988): An experimental study of theelasticity of mylonite rock with random cracks,
International Journal of Rock Mechanics andMining Sciences & Geomechanics Abstracts, Vol
25, No. 2, pp. 59-69.
Sayers, C.M. (1994): The elastic anisotropy of shales,
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767–774.
Schlumberger (2004): DSI dipole shear sonic imager,
Schlumberger marketing communications, Houston.,
2004
Wu, Y.H., Yeh, E.C., Dong, J.J., Kuo, L.W., Hsu, J.Y.
and Hung, J.H. (2008): Core-log integration studies
in hole-A of Taiwan Chelungpu-fault Drilling
Project, Geophysical Journal International, Vol. 174,
pp. 949-965.
Yabe, Y., Song, S. R. and Wang, C. Y. (2008): In-situ
stress at the northern portion of the Chelungpu fault,
Taiwan, estimated on boring cores recovered from a
2-km-deep hole of TCDP, Earth Planets Space, Vol.
60, pp. 809–819.
Yeh, E.C., Sone, H., Nakaya, T., Ian, K.H., Song,
S.R., Hung, J.H., Lin, W., Hirono, T., Wang, C.Y.,
Ma, K.F., Soh, W. and Kinoshita, M. (2007): Core
description and characteristics of fault zones fromHole-A of the Taiwan Chelungpu-Fault drilling
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Acknowledgements
The authors are grateful to the support from
MOST, Taiwan. The project numbers are MOST
103-2116-M-008-005 and 104-3113-M-008-001.
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