Majalah Ilmiah UNIKOM
Vol.6, No. 2
184
H a l a m a n
Assumption that reservoir rock has iso-
tropic character is no longer adequate in
geophysics data that requires high accu-
racy. Almost of crustal rocks have anisot-
rophic character. The anisotrophy causes
some mistakes in geophysics data such
as: mistake analysis of AVO, mistake in
reservoir elastic constant determination
like poisson ratio, bulk modulus, shear
modulus, and it cause some difficulties in
NMO analysis that is known as " hockey
stick effect
3)
, furthermore it causes split-
ting phenomenon or birefringence in S
wave. Due to transverse isotrophy fracture
is also anisotrophy case study, splitting
phenomenon is studied intensively in this
paper also. Studying existence of fracture
in reservoir plays important role in reser-
voir productivity and horizontal well drilling
design.
In this paper, we model seismic wave
propagation parameter and elastic con-
stant of fracture through Brown-Korringa
equation
4)
that is the extended version of
Gassmann equation. Then, we measured
the seismic wave parameter through the
real core sample data in fractured condi-
tion.
Generally in the anisotrophic fractured
rock, the seismic wave is depend on the
incident angle. The existence of fluid in
both vertical transverse isotrophy (VTI)
fracture and horizontal transverse isotro-
phy (HTI) fracture affects velocity increas-
ing. This velocity increasing is equivalent
linearly with fluid content of fracture. In
isotropic transverse fracture, this increase
is caused by increasing C
33
component
when the fracture is fluid saturated. In TI
medium, the attendance of fluid raises SV
(Shear-Vertical) wave. Theoretically, this
fluid affected velocity is caused by the sen-
sitivity of Thomsen parameter e to the
fluid saturation. While S horizontal(SH)
wave velocity is not affected by fluid satu-
ration, it is because C
55
stiffness compo-
nent is not sensitive to the fluid content.
The behavior of S wave in anisotrophy frac-
ture are different with one in isotrophy
case study. Change of S wave velocity be-
cause attendance of fluid saturant do not
happened in isotrophic case, and it can
not be explained by Gassmann equation,
therefore the extended of Gassmann
equation should be exercised through
Brown-Korringa equation
4)
.
BASIC THEORY
Relationship between stress tensor and
strain tensor in general, according to
Hooke’s law can be written as (1).
Where σ
ij
denotes stress tensor, C
ijkl
denotes stiffness tensor and ε denotes
strain tensor. In the case transverse
isotrophic fracture, the stiffness tensor is
expressed by equation (1) for vertical
transverse isotrophy (VTI) and equation (2)
for horizontal traverse isotrophy (HTI).
(2)
(3)
Brown dan Korringa
4)
have conducted an
extension of Gassmann theory for fluid
substitution in anisotrophy case, the
stiffness tensor of the extension o
Gassmann for anisothrophic in saturated
condition (fluid inclusion)
5)
is expressed
by equation (4)
kl
ijkl
ij
ε
C
σ
66
55
55
33
13
13
13
11
66
11
13
66
11
11
)
2
(
)
2
(
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
55
55
44
33
44
33
13
44
33
33
13
13
13
11
)
2
(
)
2
(
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
USEP MOHAMAD ISHAQ