Numerical experiments for Full-wave tomogrpahy (2)-Source inversion

摘要

Seismic waveform is influenced not only by medium property but by source parameters, hence source parameter inference is important task in Full-wave tomography (FWT). As discussed in Tsuchiya (1997a), the mechanism of explosive borehole source can be described by the diagonal components of moment density tensor; two time series of vertical and in-plane horizontal vector dipoles, in case of 2D FWT. Moreover it can he assumed that they are determined by the combination of the normalized common time series (source function) and two maximum values of each vector dipole (MVD's).While we have some possibility for prior estimate of the source function, the direct measurement of directivity parameter (the ratio of two MVD's) is difficult. This fact suggests us to infer the source parameters through the FWT calculation.Because the source inversion as well as the property parameter inversion in FWT is a nonlinear problem, the method proposed by Tsuchiya (1997a) in which the source parameters are infered jointly with the property parameters is naturally thought out. Thus the numerical experiments to study practical procedure of his method were implemented and are discussed in this paper.Conclusions are as follows. (1) Accurate evaluation of source parameters is important for inference of Vp and Vs distribution. (2) Joint inversion of source parameters with Vp and Vs is effective. (3) Source parameter inversion in terms of the gradient method tends to converge towards local minimum. This effect is mainly caused by coupling of the prior errors of MVD's and source function. (4) One possible way to solve this problem is to deal with the averaged time series as unknown until the property parameters are sufficiently restored.