Geoscience Reference

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transition, since well data has high frequency

content not present in the seismic data. Using

Bayesian reasoning, Buland et al. (
2003
) and

Nair et al. (
2012
) use the following steps:

(i) Assign the elastic properties from well data

as a prior probability model, p(m);

(ii) Treat the seismic AVA data (d) as a likeli-

hood model, p(d|m);

(iii) The Bayesian inversion is then posterior

probability model, p(m|d).

To handle the band-limitations of the seismic

data a low frequency background model is

needed. This is estimated from vertical and lat-

eral trends in the well log data using Kriging to

generate a smoothed background model. This

background model itself should capture the

underlying geological concepts (sand fairways,

porosity trends) but is also critical to the seismic

inversion. Figure
3.26
shows an example com-

parison of raw versus inverted V
p
logs, an impor-

tant step in quality control of the process.

The solutions to seismic AVA inversion are

non-unique and entail large amounts of data

- wavelets and reflection coefficients for each

offset angle throughout the volume of interest.

By transferring the data into the Fourier domain

(the frequency spectrum), Buland et al. (
2003
)

used a fast Fourier transform to handle the seis-

mic covariance matrices and to separate the sig-

nal and noise terms. Figure
3.27
compares AI

from seismic inversion (the prediction) with

two stochastic realisations of simulated AI,

incorporating both seismic data and well data.

Notice the finer resolution of simulated cases

because of inclusion of higher frequency well

data with the seismic data in this Bayesian

workflow.

The potential for deriving rock properties

from seismic data is enormous. The V
p
/V
s
versus

impedance plot (e.g. Fig.
3.28
) is widely used as

a rock physics template, giving the potential for

estimation of facies and flow properties from

seismic data. Exactly how successfully this can

be done depends on the case at hand and the data

quality. We should add a cautionary reminder to

seismic inversion enthusiasts - the transform

from elastic properties to flow properties is not

a simple one, and there are many pitfalls. How-

ever, in the hands of an experienced reservoir

Fig. 3.26
Comparison of raw V
p
logs (
dashed lines
) with

V
p
logs extracted along the well from the inverted 3D seismic

data (
continuous lines
), from Nair et al. (
2012
)(Redrawn

from Nair et al. 2012,
#
EAGE reproduced with kind

permission of EAGE Publications B.V., The Netherlands)

modeller the Bayesian statistical framework

offers a rather elegant way of making that leap

from 3D seismic data to predictive flow property

models.