Integration of rock physics template to improve Bayes’ facies classification
Zakir Hossain*, Stefano Volterrani and Felix Diaz, ION Geophysical,
Paul Constance, HighMount Energy,
Summary
Reliable facies prediction is a key problem in reservoir
characterization. Facies classification using an arbitrary
selected zone is the simplest method. However, the
problem is that the interpretation result strongly depends on
the size of the selected zone. Using an RPT (rock physics
template), we can define an accurate zone instead of
defining an arbitrarily sharp cutoff for the zone. The next
level of sophistication is using a statistical technique,
whereby we can calculate not only the best zone, but also
the probability of occurrence of that zone. Baye’s theory is
normally used for probabilistic facies classification.
However, the prior belief is a fundamental part of Bayesian
statistics. The posterior probabilities are heavily influenced
by the prior probabilities, so any error caused by the
interpretation of the prior probability will be amplified in
the posterior probability. The objective of this study is to
improve the prior probability predictions using rock
physics analysis for quantitative facies classification. We
use an RPT as a guidance to define these prior
probabilities. For seismic reservoir characterization, well
data along with rock physics theory via RPT are used to
define the prior probability. We found that Baye’s
prediction increases as we define the prior probabilities
from the RPT.
Figure 1 Four different facies classification workflows: (a) Using an arbitrary sharp cutoff method, (b) using a rock physics template (RPT),
(c) using probability density function (PDF), and (d) integrating RPT with PDF.
© 2015 SEG
SEG New Orleans Annual Meeting
DOI http://dx.doi.org/10.1190/segam2015-5900545.1
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Integration of rock physics template to improve Bayes’ facies classification
Introduction
posterior 
Reliable facies prediction is a key problem in reservoir
characterization. For reservoir facies characterization, three
different methods are normally used (Figure 1a, 1b, 1c).
We combined method 2 (Figure 1b) and Method 3 (Figure
1c) to improve facies classification for quantitative seismic
interpretation (Figure 1d). Facies classification using an
arbitrarily selected zone is the simplest method (Figure 1a).
However, the problem is that interpretation results strongly
depend on the size of the selected zone. Using an RPT, we
can define an accurate zone instead of defining an arbitrary
sharp cutoff for the zone (Figure 1b). Using a statistical
technique (Figure 1b), we can calculate not only the best
zone, but also the probability of occurrence of that zone.
Bayes’ theory is normally used for probabilistic facies
classification. This theory primarily involves a prior to
posterior updating technique. Mathematically Bayes’
theory is given by (Stigler, 1983):
pci | x  
px | ci   pci 
n
 px | c  pc 
i 1
i
i
or
liklihood  prior
normalization
(1)
where, p(ci) is the prior probability, p(ci|x) is the posterior
probability for our observation, p(x|ci) is the likelihood of
obtaining our particular observation ci, under the
supposition that any of the possible states of the variable x
were actually the case.
Bayes’ theory guarantees the maximum likelihood rock
properties and minimum prediction errors (Takashashi
2000). However, the prior belief is a fundamental part of
Bayesian statistics. When we have few data about the
parameter of interest, our prior beliefs dominate inference
about that parameter. It is often difficult to obtain the prior
probability. The posterior probabilities are heavily
influenced by the prior probabilities, so any error caused by
the interpretation of the prior probability will be amplified
in the posterior probability. In any application, effort
should be made to model our prior beliefs accurately. The
objective of this study is to improve prior probability
predictions using rock physics analysis for quantitative
Figure 2 Graphical representation of prior to posterior updating using three different methods: (Top) method 1 with constant and equal prior
probabilities, (Middle) method 2 with constant and non-equal prior probabilities, and (Bottom) method 3 with continuous and non-equal prior
probabilities defined from the RPT.
© 2015 SEG
SEG New Orleans Annual Meeting
DOI http://dx.doi.org/10.1190/segam2015-5900545.1
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Integration of rock physics template to improve Bayes’ facies classification
facies classification. We used the RPT as a guide to define
these prior probabilities. The measured data are the most
important information in reducing uncertainty and
improving facies prediction (Mukerji et al. 2001).
Incorporating rock physics with the statistical method may
reduce the uncertainty even more (Hossain and Mukerji,
2011).
4
2
 
K 
3
3
and Vs 
Vp 





(2)
where, K is the bulk modulus,  is the rigidity or shear
modulus;  is the Lame’s constant; Vp is the compressional
wave velocity, and Vs is the shear wave velocity.
Method
In order to improve facies predictions using Bayes’ theory,
we need to integrate more rock properties with Bayesian
statistical techniques. To achieve this, we may assume that
the prior probability represents our knowledge about rock
properties. Then, the prior probability should be consistent
with our geological knowledge, rock physics theories of
objective rocks as well as measured data. We used an RPT
as a guide to define these prior probabilities because an
RPT guides the manual classification of lithology and
fluids. The RPT has an advantage because it places
everything in perspective, combining rock physics theory
with geology to describe the rock properties from measured
data (Avseth et al. 2005). For seismic reservoir
characterization, well data along with rock physics theory
via RPT can be used to define the prior probability. To
generate an RPT we used the interrelationship between the
elastic constants.
For homogeneous isotropic media, two elastic constants,
involving the bulk density () will describe the seismic
body wave velocities, as given by:
The relationship between seismic velocities and seismic
impedances can be written as:
Ip  V p
and
Is  Vs
(3)
where, Ip is the P-impedance and Is is the S-impedance.
From equations (2) and (3) we can define the Lame
parameters:
  Ip 2  2Is 2 ;   Is 2 ;     Ip 2  3Is 2 (4)
The relations between lp, ls, , Vp/Vs, E are
shown in Figure 1b. An RPT combining multiple attributes
in the Ip,Vp/Vs cross-plot can be used to describe the
various reservoir properties from seismic data (Hossain and
MacGregor, 2014). Laboratory data show that in the
lp,Vp/Vs cross-plot, constant describes the effects of
pore fluid and pore-filling clay minerals; while constant 
Figure 3 Facies classification using the RPT, an example from the Buffalohorn unconventional reservoir (Mississippi lime and Woodford
reservoir intervals). (Left) P-impedance from seismic inversion, (Right) Facies classification using the RPT.
© 2015 SEG
SEG New Orleans Annual Meeting
DOI http://dx.doi.org/10.1190/segam2015-5900545.1
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Integration of rock physics template to improve Bayes’ facies classification
describes the effects of matrix supported clay minerals. In
addition, constant Is describes the effects of porosity and
pressure (Hossain, 2015). Absolute values of these third
attributes have quantitative predictive capabilities for
measurements of porosity, pressure, clay and fluids. We
used the third attribute in the lp,Vp/Vs cross-plot to define
the prior probability, e.g. P(oil )  f (   ) . We
emphasize that these prior probabilities are defined from
the RPT combined with well log data and rock physics
theories, and that these prior probabilities are independent
from seismic data.
Results
Figure 2 gives a graphical representation of prior to
posterior updating using three different methods: method 1
with constant and equal prior probability, method 2 with
constant and non-equal prior probability and method 3 with
continuous and non-equal prior probability. For gas bearing
facies we define posterior probabilities of 0.71 using
method 1, 0.81 using method 2, and 0.95 using method 3 in
which the prior probability was defined using an RPT.
Further investigation of examples in Figure 2 shows the
influence of prior probabilities on posterior probabilities.
The posterior probabilities are changed when the prior
probabilities are changed and the conditional probabilities
are kept identical. In example 1 when the prior probabilities
are constant and equal, the posterior probabilities are
increased, but the separations between the facies are
remained identical. However, in example 3 when the prior
probabilities are continuous and the prior probabilities are
estimated from the RPT, the posterior probabilities are
increased and the separations between the facies are also
increased. The posterior probabilities change to narrower
and taller. The Bayes’ prediction increases as the difference
between the prior probabilities for the two fluids becomes
greater. When the existence of fluid 1 is impossible, then
the prior probability of fluids 1 is zero, hence, the posterior
probability of fluid 1 is zero and the posterior of fluid 2 is
one. Application of this method for quantitative seismic
interpretation is shown in Figures 3 and 4.
Conclusions
For seismic reservoir characterization, we provided a
method to improve Bayes’ facies classification. In order to
improve facies predictions using Bayes’ theory, we
integrated an RPT with Bayesian statistical techniques
assuming that the prior probability represents our
knowledge about rock properties and the prior probability
is consistent with our geological knowledge, rock physics
theories of objective rocks as well as measured data. We
showed Bayes’ prediction increases as we define the prior
probabilities from the RPT. Probabilistic facies
classification method provided in this study can be used for
litho-facies
classification
for
conventional
and
unconventional reservoirs.
Acknowledgments
The authors thank EnerVest for allowing this work to be
published. There are a number of individuals at ION that
contributed to this work, including Howard Rael and
Shihong Chi in the reservoir group. Doug Sassen and Scott
Singleton are acknowledged for helpful discussions and
comments.
Figure 4 Facies classification combining RPT with PDF, an example from the Buffalohorn unconventional reservoir (Mississippi lime and
Woodford reservoir intervals)
© 2015 SEG
SEG New Orleans Annual Meeting
DOI http://dx.doi.org/10.1190/segam2015-5900545.1
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EDITED REFERENCES
Note: This reference list is a copyedited version of the reference list submitted by the author. Reference lists for the 2015
SEG Technical Program Expanded Abstracts have been copyedited so that references provided with the online metadata for
each paper will achieve a high degree of linking to cited sources that appear on the Web.
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© 2015 SEG
SEG New Orleans Annual Meeting
DOI http://dx.doi.org/10.1190/segam2015-5900545.1
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