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