Inversão tomográfica em modelos de velocidade representados por funções de base radial

Abstract

Tomography is today the standard tool in velocity model building. It is a fundamental part of the seismic method, whose purpose is to obtain accurate images of the interior of the planet. In this work, a traveltime tomography based on the discretization of velocity models by radial basis functions was proposed. The tomographic inversion can be divided in two major steps. The first one is the direct problem, whose purpose is to obtain the traveltimes and raypaths. It was solved with an algorithm based on the eikonal equation. The second step is the inverse problem, that aims to recover the coefficients of the radial basis functions. The Gauss-Newton method was used in conjunction with the conjugate gradient. It has been shown that using the eikonal equation in the forward modeling allows positioning sources and receivers in any region of the model, without the need for further processing of the traveltime matrix. Other advantages are the possibility of working with high velocity contrasts and the absence of shadow zones. The radial basis functions can represent velocity models with a reduced number of parameters. The points can be positioned without prior information. However, the σ parameter of the Gaussian radial base function has a high sensitivity. The results of the experiments show that the developed inversion tool is able to retrieve the parameters of the models represented by these functions.