Transformada de Laplace na solução de problemas inversos dinâmicos da sísmica

Abstract

In this article we analyze several aspects of using the temporal Laplace and spatial Fourier-Bessel transforms in the solution of seismic inverse dynamic problems by optimization methods. Considering, as an example, thin layer models of media, we show that the real part of the Laplace parameter can be used as a regularization parameter in two principal stages of the solution of the inverse problem: solution of the direct problem, and combination of the theoretical solution of the direct problem with spectra of seismograms. It is shown that varying this parameter we can improve the properties of the misfit functional, accelerate the convergence of the method, and get a better initial approximation. Besides this, there was studied the influence of the parameter of Laplace and smoothing filters in the degree of similarity between two types of spectra: calculated using the seismograms (considering the limitation of the aperture of real observations) and obtained on basis of the analytical formulas. The results of this study made possible the development of computational proceedings, which aim to guarantee the good quality of the calculation of discrete spectra, using for this the Fourier-Bessel and Laplace transforms. © 2009 Sociedade Brasileira de Geof́i{dotless}sica.