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Genetic algorithms have always been recognized
as powerful tools for inverting complex objective functions with complex
constraints either continuous or discrete Beasley et al. (1993a,b); Falkenauer (1998); Goldberg (1989); Haupt and Haupt (1998) but there is always a question mark about their
robustness in handling high-dimensional problems with reasonable accuracy and
speed. In a companion paper in this report Alvarez (2002) I show
that genetic algorithms, and in particular micro-genetic algorithms
Krishnakumar (1989), can be used
to solve a relatively high-dimensional problem. In this paper I give the details
of that problem: inverting a seismic data trace for the underlying interval
velocities assuming a layer-cake velocity model. This is a relatively simple
non-linear problem
that has been investigated for at least 20 years Lindseth (1982). Several
techniques have been proposed and various commercial software packages exist
with high levels of sophistication, using deterministic inversion or simulated
annealing.
If we can use genetic algorithms to efficiently solve this kind of problems, we can
then take advantage of the simplicity with which genetic algorithms handle all
kinds of continuous or discrete constraints to go
beyond the inversion of seismic data for interval velocities. Multiples,
wave mode conversion and other such complications may be equally handled.

In this paper I employ a micro-genetic algorithm to invert a synthetic seismic
trace for the underlying velocities that produced it. The seismic trace is
created from a real well log assuming normal-incidence, a layer-cake velocity
model and no multiples or absorption. I show that when the inversion is supplied
with an estimate of the velocity-depth trend obtained from the well log with a
33-point, sixth order Savitzky-Golay filter Press et al. (1992), the inversion yields
a very reasonable estimation of the input sonic log.

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Stanford Exploration Project

11/11/2002