Velocity inversion of a seismic trace with a micro-genetic algorithm

Gabriel Alvarez

gabriel@sep.stanford.edu

ABSTRACT

An ever present goal of seismic processing and inversion is to extract meaningful geologic information from seismic data. The simplest possibility is to invert for seismic impedance, or, considering density constant, invert for velocity. Here I use a micro-genetic algorithm program to achieve this goal. A micro-genetic algorithm is different from a standard genetic algorithm in that it evolves a very small population that must be restarted whenever genetic diversity is lost. I use a real sonic log to compute a synthetic seismic trace and then use that trace as input to the micro-genetic algorithm program to invert for the velocity log. Without further input, the velocity inversion cannot hope to recover the general velocity-depth trend because this information corresponds to the very low frequencies which are absent in the seismic data. In order to achieve a good match between the real and the inverted sonic log, the inversion must be suppled with an estimate of the velocity-depth trend. Here I use a 33-point Savitzky-Golay filter with a sixth-degree polynomial to smooth the velocity log and show that with this trend the velocity log is reasonably well recovered. I used both the L₁ and the L₂ norms of the sample-to-sample difference between the reference and the inverted trace and show that the results with both norms are similar.