A Widely Convergent Generalized Pulse‐ Spectrum Methods for 2‐D Wave Equation Inversion

Abstract

Combining the widely convergent homotopy method applied to the inversion process of operator identification with the Tikhonov regularization method for ill-posed problem, a new Widely Convergent Generalized Pulse-Spectrum Technique (WCGPST) for 2-D wave equation inversion is constructed. And constraint inversion is preformed with data of well logs. Many numerical simulations and tests of anti-noise indicate that this method is effective.

An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation

“…Recently, a large amount of literature is devoted to the homotopy method for parameter estimation. The homotopy method is applied to the parameter identification of an elliptical equation [26], the parameter identification of twodimensional acoustic wave equation [27,28], the parameter identification of two-phase viscoelastic media [29], the PEM identification of ARMAX models [30] the reconstruction of mountain surface [31] and the well-log constraint waveform inversion [32][33][34]. The homotopy method for nonlinear inverse problems is given in [35] and the homotopyprojection method for the parameter estimation problems is given in [36].…”

A Regularization Homotopy Method for the Inverse Problem of 2-D Wave Equation and Well Log Constraint Inversion

“…In 1991, we applied the homotopy method to solve the inverse problem in well-log [5] , this may be the first work for applying the homotopy method to solve inverse problems. Then, we spread the method to the general parameter identification problem in a differential operator, and the inverse problem of wave equation in seismic prospecting [6,7] . Vasco [8] used the homotopy method to solve inverse problems and illustrated its use for traveltime tomography.…”

“…Bao and Liu [14] suggested a homotopy-regularization method to solve inverse scattering problem with multi-experimental limited aperture data. Feng and Han [7] combine the homotopy method with the generalied pulse-spectrum technique to solve the inverse problem of 2-D wave equation. Zhang et al [15] studied the homotopy method for obtaining the impedance profile for 1-D wave equation.…”