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 within-facies 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 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.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
14 July 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
7 July 2008
- Manuscript approved:
26 July 2008
- Version of record:
29 December 2008
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