Introduction

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.