Seismic Waveform Inversion Using Global Optimization Methods

A nonlinear optimization method based on the principles of natural selection is used to invert plane wave decomposed seismic data. We develop a genetic algorithm (GA) that uses an ensemble of subsurface models to create synthetic plane wave seismograms which are compared to observed seismic data. A normalized cross correlation function (fitness function) is used to compare the model seismograms to the data. The GA then selects the models with bigh fitness values to generate a new generation of trial models through the process of reproduction. We show that our GA works. We also show that its rate of convergence to a population with bigh fitness values can be significantly increased by defining the fitness function as a probability and using a control parameter analogous to the temperature employed in simulated annealing (SA) that decreases with each generation of modell. Further, we show that by repeating the process, we can estimate the mean model, the posterior probability density in model space and the posterior model covariance matrix.