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.

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Integration of rock physics template to improve Bayes’ facies classification

Introduction

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):

n

i

ii

iii

cpcxp

cpcxpxcp

1

|

|| or

ionnormalizat

priorliklihoodposterior

(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.

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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).

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:

3

2

3

4

K

Vp and

sV (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.

The relationship between seismic velocities and seismic

impedances can be written as:

pVIp and sVIs (3)

where, Ip is the P-impedance and Is is the S-impedance.

From equations (2) and (3) we can define the Lame

parameters:

22222 3;;2 IsIpIsIsIp (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.

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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. )()( foilP . 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)

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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. REFERENCES

Avseth, P., Mukerji, T. and Mavko, G., 2005, Quantitative seismic interpretation: Applying rock physics tools to reduce interpretation risk: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511600074.

Hossain, Z., and L. MacGregor, 2014, Advanced rock-physics diagnostic analysis: A new method for cement quantification: The Leading Edge, 33, 310–316. http://dx.doi.org/10.1190/tle33030310.1.

Hossain, Z., and T. Mukerji, 2011, Statistical rock physics and Monte Carlo Simulation of seismic attributes for greensand: Presented at the 73rd Annual International Conference and Exhibition, EAGE.

Mukerji, T., A. Jørstad, P. Avseth, G. Mavko, and J. R. Granli, 2001a, Mapping lithofacies and pore

Mukerji, T., A. Jørstad, P. Avseth, G. Mavko, and J. R. Granli, 2001b, fluid probabilities in a North Sea reservoir: Seismic inversions and statistical rock physics: Geophysics, 66, 988–1001. http://dx.doi.org/10.1190/1.1487078.

Stigler, S. M., 1983, Who discovered Bayes’ theorem?: The American Statistician, 37, no. 4, 290–296. http://dx.doi.org/10.2307/2682766.

Takahashi, I., 2000, Quantifying information and uncertainty of rock property estimation from seismic data: Ph.D. thesis, Stanford University.

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