Genetic algorithms in seismic waveform inversion

SUMMARY Recently a new class of methods, to solve non-linear optimization problems, has generated considerable interest in the field of Artificial Intelligence. These methods, known as genetic algorithms, are able to solve highly non-linear and non-local optimization problems and belong to the class of global optimization techniques, which includes Monte Carlo and Simulated Annealing methods. Unlike local techniques, such as damped least squares or conjugate gradients, genetic algorithms avoid all use of curvature information on the objective function. This means that they do not require any derivative information and therefore one can use any type of misfit function equally well. Most iterative methods work with a single model and find improvements by perturbing it in some fashion. Genetic algorithms, however, work with a group of models simultaneously and use stochastic processes to guide the search for an optimal solution. Both Simulated Annealing and genetic algorithms are modelled on natural optimization systems. Simulated Annealing uses an analogy with thermodynamics; genetic algorithms have an analogy with biological evolution. This evolution leads to an efficient exchange of information between all models encountered, and allows the algorithm to rapidly assimilate and exploit the information gained to find better data fitting models. To illustrate the power of genetic algorithms compared to Monte Carlo, we consider a simple multidimensional quadratic optimization problem and show that its relative efficiency increases dramatically as the number of unknowns is increased. As an example of their use in a geophysical problem with real data we consider the non-linear inversion of marine seismic refraction waveforms. The results show that genetic algorithms are inherently superior to random search techniques and can also perform better than iterative matrix inversion which requires a good starting model. This is primarily because genetic algorithms are able to combine both local and global search mechanisms into a single efficient method. Since many forward and inverse problems involve solving an optimization problem, we expect that the genetic approach will find applications in many other geophysical problems; these include seismic ray tracing, earthquake location, non-linear data fitting and, possibly seismic tomography.