Agreement DE-FC26-02NT15342, Seismic Evaluation of ...

saturation from seismic data. Validations of SVM regression on the gas andlow saturation
gas show it is possible to separate commercial gas and low saturation gas at deep water
reservoirs. Low saturation gas or “fizz” refers that the percentage of gas in the pore
volume is small (less than 25%). The discrimination between low saturation gas and
economical gas attracts much attention because wells are classified as “dry holes” even
when small amounts of hydrocarbons exist in the reservoir. Discrimination between fizz
and economical gas will reduce exploration cost and improve efficiency.
At low-pressure condition (shallow depth < 2000 m), gas modulus is much less than 0.1
GPa. The presence of a small amount of gas can dramatically reduce the P-wave velocity
of the reservoir, so “fizz” and economic gas saturations have nearly the same seismic
responses. This well known physical phenomena can be modeled by Gassmann’s
equation (Domennico, 1976). Under higher pressure condition (depth greater than 2000
m), modulus of gas-water mixture shows progressive decrease with increasing gas
saturation (Han and Batzle, 2002). This improves the chances to discriminate low
saturation gas from commercial gas with seismic data.
Our objective of this study is to estimate the water saturation from seismic volume at
deep-water reservoir. We first train a Support Vector Machine (SVM) to learn the water
saturation log from seismic trace nearest to the wellbore. With this SVM, we estimate
water saturation with all the traces in the seismic volumes from the commercial gas
reservoir and low saturation gas reservoir.
An SVM is an algorithm using selected subset of data (known as support vectors) in
function estimation. We explain this algorithm in detail in the following section.
SVM regression
Support Vector Machines were introduced to the computer learning community in the
mid 1990s (Vapnik, 1995) and are just beginning to applied in geophysical field (Kuzma,
2004; Li and Castagna, 2003; Zhao et al., 2005). They are most commonly used to solve
very large classification problems such as handwritten digit recognition and document
sorting. However, SVMs can also be used for regression (Smola and Scolkopf, 2004).
This part introduces SVM regression based on Smola and Scolkopf’s tutorial.
Suppose we are given training data {(x 1 , y 1 ), …, (x l , y l )}, x i ∈ R d is “d” dimension vector,
y i ∈ R. In ε–insensitive Support Vector regression, our goal is to find a function f(x) that
has at most ε deviation from the actually obtained targets y i for all the training data, and at
the same time is as flat as possible. In other words, we do not care about errors as long as
they are less thanε, but will not accept any deviation larger than this. Suppose our target
function has a linear form
f ( x)
= 〈 w,
x〉
+ b with w ∈ R d , b∈ R (1)
where 〈⋅,⋅〉 denotes the dot product in R d . Flatness in the case of (1) means that one
seeks a small w. One way to ensure this is to minimize the norm, i.e. || w || 2 = 〈 w, w〉. We
can write this problem as a convex optimization problem:
Agreement DE-FC26-02NT15342, Seismic Evaluation of Hydrocarbon Saturation 19