Application Of Nonlinear Optimization Method In Static Correction Of Converted Wave

As multi-component seismic exploration can provide more information underground so that people can describe the properties of earth media more accurately, it develops rapidly these years. The data processing has also attracted the concern of academics. In the data processing of multi-wave and multi-component seismic exploration, the converted wave data processing is important and difficult. Because of the dissymmetrical ray path (the downgoing wave is P wave and the upgoing wave is S wave), conventional P-wave approach is difficult to apply to converted wave processing. It's necessary to find a specific approach to process the data of converted wave exploration. It uses the probability distribution function of SAStatic correction is an important part in the seismic data processing. The aim of static correction is to remove the impact of the low velocity layer in the surface. A high-quality static correction is an essential precondition of getting high-quality stack section. For P wave data, following the field static correction, the residual static measurements are generally small. Normally it is smaller than half of the wavelet period. In that case, the residual static problem only has one extreme value. Routine linear static correction is base on this context. But for the converted wave, since the converted shear wave velocity is low and lateral variations. After the field static correction there still has large residual static measurements. The measurements are no longer meet the hypothesis that less than half of the wavelet period. This residual static correction is a nonlinear, multi-extreme and multi-parameter inversion. Using linear method to solve such problems is difficult to obtain the global optimum. To solve this large converted wave static problem we have two ideas: The first idea is a two-step correction. First use a reasonable method to reduce the static correction in order to meet the hypothesis that the residual static measurements are less than half of the wavelet period. Then we can use the routine linear static correction method to solve the problem. The second idea is the use of nonlinear global optimization methods (such as Particle Swarm Optimization, Simulated Annealing Algorithm) to solve the converted wave static problem.For the first idea of this paper we deduce that when the offset is small, the time distance curve equation of converted wave can be approximated by a parabolic equation. Based on this conclusion we can give the idea of using polynomial fitting to solve the residual static correction: First use least square method to fit a single shot converted wave record for the parabola. Get the initial residual static as the actual travel time values minus the fitted values. Then use routine linear static correction method to correct the seismic record after the initial static correction. For the second idea, we gather the particle swarm algorithm and simulated annealing algorithm methods to solve the residual static correction of converted wave.Particle swarm optimization (PSO) algorithm is a population search algorithm. It has some features such as fast convergence, easy to implement, less call parameters. But the disadvantage is easy to fall into local optimum. Simulated annealing algorithm (SA) is a random search method based on probability. It has features such as robust and easy to implement. It has the ability to avoid the trap of local optimum and find the global optimum. But the disadvantages are that it needs a high enough initial temperature, slow cooling, a low enough terminative temperature and sufficient number of sampling at each temperature. Usually it doesn't get the ideal result when dealing with practical problems because the cooling schedule is not ideal. In addition the convergence rate is not good.In order to avoid the shortcomings of the two algorithms and give full play to their strengths. We combined the PSO and SA and get a new algorithm called PSOSA. It uses the probability distribution function of SA to get the initial population of PSO. And transform the scale of the target function. It increases the global optimization ability of PSO and prevents its premature. The numerical test also approved that PSOSA is an advisable solution of residual static correction of converted wave.