Seismic Facies Identification and Classification Using Simple Statistics

Seismic Facies Identification and Classification Using Simple Statistics Abraham K. John,* Larry W. Lake, Carlos Torres-Verdin, and Sanjay Srinivasan, The University of Texas at Austin

Summary The identification and mapping of rock facies is important to reliable reservoir characterization. Traditionally, facies identification and mapping are based on inspection of core data and/or well-log signatures, a procedure that has subjective aspects because it is relies on samples from only a very small portion of the reservoir. Such identification is also difficult to perform at the onset of the exploration stage because of lack of sufficient well data. This paper demonstrates a simple practical approach to identify and classify facies from seismic-amplitude data using basic statistical concepts. Within a geologic facies, measured properties [in this case acoustic impedance (AI)] are assumed to differ mainly as a result of random additive events and are modeled by a normal distribution, as justified by the central-limit theorem. The facies are identified by estimating the combination of facies volume fractions and distribution parameters (means and standard deviations of the facies probability-density function) that best fit the population distribution of AI. A simple form of Bayes theorem is then used to compute the probability of occurrence of each of the facies at the measured locations. This generates a volume of facies probabilities corresponding to the seismic volume. Such a volume can be used to perform facies-specific petrophysical analysis or be a starting point to generate multiple realizations of petrophysical properties. The approach is simple and transparent to use, with no significant computational requirements even on large data sets. We describe an application of the procedure to a synthetic reference data set and a Gulf of Mexico AI data set. Mapped probabilities of the individual facies show the spatial continuity and geologic character of the underlying depositional environment. Property values within the mapped regions are substantially less variable than the original data across the entire region. The withinfacies semivariograms exhibit much less spatial correlation than across all facies. Since the facies are mapped across an exhaustive data volume, this approach considerably reduces the need for the geostatistical construction of property distributions within them as long as a high correlation exists between the seismic attribute and petrophysical properties. Introduction One of the first steps involved in building a reservoir model is to identify the facies present and to map their spatial distribution. This typically is performed using the geological information available from early well logs and cores and the interpretation of seismic-amplitude data. Knowledge of the facies present in the area of study results in better application of correlations that are used to generate spatial maps of petrophysical properties. However, at the onset of the exploration process, accurate identification of the facies and mapping their distribution across the entire reservoir is challenging. This is because not enough well data are available to calibrate and transform the seismic-amplitude data on the basis of crossplots of AI and log-measured properties. This motivates the need to have an automated procedure to help identify directly possible facies from the seismic-amplitude data and then to be able

* Now with Shell International Exploration and Production. Copyright © 2008 Society of Petroleum Engineers This paper (SPE 96577) was accepted for presentation at the SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October, and revised for publication. Original manuscript received for review 14 July 2005. Revised manuscript received for review 7 July 2008. Paper peer approved 26 July 2008.

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to generate maps of their probable spatial distributions using the same seismic-data volume. A seismic facies can be defined as a group of seismic amplitude variations with characteristics that differ distinctly from those from other facies. A seismic facies is the manifestation of the underlying geologic facies or structural feature in the seismic-amplitude data. Different approaches can be used to search and identify these from the seismic data. These could be based on analysis of either the seismic waveforms or the seismic attributes. Statistical classification techniques, which work on seismic attributes such as amplitude, have found increasing use within traditional interpretation workflows (Johann et al. 2001; Fournier et al. 2002). The objective of these techniques is to be able to describe the variability of the data and highlight details of the underlying geologic features. Statistical classification techniques may be supervised on the basis of established identification rules or they may be unsupervised (Coléou et al. 2003) on the basis of automated recognition of patterns in data. The most commonly used supervised technique is that of artificial neural networks (Saggaf et al. 1984). Supervised techniques, though flexible, need substantial training effort based on available data or prior knowledge. This is usually time-consuming, case-specific, and, at times, not possible because of the paucity of data. Techniques such as cluster analysis and principal-component analysis, which are unsupervised, are used typically to establish relationships between data attributes and to eliminate data redundancy. All of the above are essentially similar in that they make use of statistical properties of data either to group or to separate them. But they differ in their ability to capture geologic features efficiently, and in their applicability and interpretability. Given the large uncertainty at this preliminary stage of modeling, it is important to have a technique that is transparent so that it lends itself to easy interpretation. This paper demonstrates such an approach, which is based on partitioning the probability distribution of the measured attribute into multiple parent distributions (Sinclair 1976). The procedure can help identify facies only on basis of the probability distribution of AI data. The law of total probability is used along with a parametric mixture model for the facies probability distributions. Bayes theorem is used subsequently to compute the probability of occurrence of each facies at every spatial location, given the presence of measured seismic amplitude. The paper is outlined as follows: The basic theory underlying the classification procedure is discussed first. This is followed by an introduction and description of Bayes theorem and its use in generating facies probability maps. Application of the technique to two data sets is shown next. Theory Facies Identification. A geologic facies is a sedimentary unit that has characteristic structural and mineral properties that reflect its depositional environment and diagenesis. The resulting set of petrophysical properties for a facies is unique; often the properties can be used to distinguish between them. But an exhaustive set of measurements is never available; hence, it is desirable to be able to identify the major facies from a minimal set of attributes or in this case, from only the univariate distribution of AI. If there were only one facies present, then the probability distribution function (PDF) of AI across the reservoir would be unimodal. If multiple facies are present, the nature of the PDF changes and new modes arises. The probability distribution of the seismic attribute across the entire reservoir is thus a mixture of the individual facies distributions whose number, parameters, and proDecember 2008 SPE Reservoir Evaluation & Engineering

portions are to be estimated. This mixing rule follows from the law of total probability that states N

P共Z ⬍ z兲 =

兺 P共F = i兲P共Z ⬍ z | F = i兲, . . . . . . . . . . . . . . . . . . (1) i=1

where Z is a random variable denoting AI; F is a categorical random variable denoting facies type; P(Z