Estimation of seismic waves parameters with application of a genetic algorithm

Abstract

A Genetic algorithm (GA) is a very important method for the solution of non-linear problems. The basic steps in GA are coding, selection, crossover, mutation and choice. Coding is a way of representing data  in binary notation. The algorithm must determine the fitness of the individual models. This means that  the binary information is decoded into the physical model parameters and the forward problem is solved. The resulting synthetic data is estimated, then compared with the actual observed data using the  specific fitness criteria. The selection of pairs of the individual models for the reproduction is based on  their fitness values. Models with the higher fitness values are more likely to get the selection than models with low  fitness values. A crossover caused the exchange of some information between the paired models thereby  generating new models. The mutation is a random change of binary state. The condition of the procedure of mutation: if a value obtained by a random number generator is less than a certain threshold value, the  mutation procedure is performed. The last basic step in GA is choice. We choose from each pairs a model,  which has the less fitness function. Then we produce the procedures: the crossover, the mutation and the  choice. This procedure is continued until we obtain the optimal model. We have used the GA for the  estimation of the velocity for the gradient layer. The synthetic seismogram was calculated by the finite- difference method. The obtained results showed a high effectiveness of GA for the seismic waves velocity estimation.