Subspace Approach to Inversion by Genetic Algorithms Involving Multiple Frequencies

Abstract

Based on waveguide physics, a subspace inversion approach is proposed. It is observed that the ability to estimate a given parameter depends on its sensitivity to the acoustic wavefield, and this sensitivity depends on frequency. At low frequencies it is mainly the bottom parameters that are most sensitive and at high frequencies the geometric parameters are the most sensitive. Thus, the parameter vector to be determined is split into two subspaces, and only part of the data that is most influenced by the parameters in each subspace is used. The data sets from the Geoacoustic Inversion Workshop (June 1997) are inverted to demonstrate the approach. In each subspace Genetic Algorithms are used for the optimization — it provides flexibility to search over a wide range of parameters and also helps in selecting data sets to be used in the inversion. During optimization, the responses from many environmental parameter sets are computed in order to estimate the a posteriori probabilities of the model parameters. Thus the uniqueness and uncertainty of the model parameters are assessed. Using data from several frequencies to estimate a smaller subspace of parameters iteratively provides stability and greater accuracy in the estimated parameters.