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In-Depth Information

seismic wave energy at a planar interface, and

then subsequently many others (notably Shuey

1985
) developed approaches for determining

rock properties from seismic waves. Because

there is a relationship between the reflection

coefficient, R, and the angle of incidence,

different volumes with the reservoir - well data

needs to be upscaled and seismic data needs to be

downscaled (depending on the grid resolution

and seismic resolution of the case in hand). This

is where the Bayesian method comes into play.

Buland et al. (
2003
) developed a particularly

elegant and effective method for estimating rock

properties from AVO data, employing Bayesian

inference and the Fourier transform. This

approach allows the reservoir modeller to recon-

cile different scales of data (seismic versus well

data, using the Fourier transform) within a robust

Bayesian statistical framework: what is the best

seismic inversion given the well data - a P(A|

,

analysis of seismic amplitude variations with

offset (AVO) or angle (AVA) allows rock

properties of specific rock layers to be estimated.

The simplest form of the AVO equations,

known as the Shuey approximation is:

R

ʸ

G
sin
2

ðÞ
¼

R0

ðÞþ

ʸ

ð

3

:

28

Þ

Where R(0) and R(

ʸ

) are the reflection

)

problem. Nair et al. (
2012
) have illustrated this

workflow for reservoir characterization, combin-

ing elastic properties (from seismic) with facies

probability parameters (from wells) to condition

probabilistic property models.

Having first extracted elastic properties (V
P
,

V
S
and

Β

coefficients for normal

incidence and offset

angle

ʸ

and G is a function of V
P
and V
S
, given

by:

2
V
S

V
P

1

2
ʔ

V
P

V
P

ʔˁ

ˁ
þ

2
ʔ

V
S

V
S

G

¼

ð

3

:

29

Þ

Subsequently, using empirical correlations, it

is then possible to estimate porosity from V
P
,V
S

and

from the seismic AVA data (Fig.
3.25
),

the challenge is then to relate elastic properties

to flow properties.

Since flow properties are essentially estimated

from well data (cores and logs), we need to

merge (or correlate) the seismic elastic properties

with elastic and flow properties at the wells.

This is a complicated process. We need a veloc-

ity model to convert seismic data from time to

depth and we need a way handling the scale

ˁ

. Assuming that information on rock

properties can be gained from seismic data, the

next challenge is to find a way of integrating

seismic information with well data and the

underlying geological concepts. The real chal-

lenge here is that well data and seismic data

rarely tell the same story - they need to be

reconciled. Both seismic data and well data

have associated uncertainties. They also sample

ˁ

Fig. 3.25
(
a
) Angle stacks and (
b
) corresponding

inverted elastic parameters from seismic inversion

case study (From Nair et al.
2012
)(Redrawnfrom

Nair et al.
2012
,
#
EAGE reproduced with kind

permission

of EAGE Publications B.V., The

Netherlands)