Improved Implementation of Seismic Waveform Inversion Using Gauss-Newton Method in Elastic Media

The purpose of this study is to make a seismic waveform inversion based on the Gauss-Newton method practicable. Seismic waveform inversion had been introduced in the 1980s but due to computational limitation, a noble approximation of the inversion based on the Gradient method has been usually used. In spite of amazing improvements in computing power, it is still a computationally demanding task to carry out seismic waveform inversion in its integrity. The major obstacle to solve a seismic waveform inversion is explicit calculation of the Jacobian and the approximate Hessian matrices. To overcome this, the reciprocity principle and the convolution theorem are employed. The inversion, however, still holds out huge amounts of memory and computation. The limitation can be surmounted by (1) multi-grid approaches in the spatial and in the time domain, (2) a reduction of the time window length, (3) a numerical scaling between the grid spatial size and the physical dimension of a virtual source, and (4) a parallelization of the computation via Message Passing Interface for massively parallel computers. From numerical experiments, it is shown that the Gauss-Newton method has significantly higher resolving power and convergence rate over the gradient method, and this study contributes greatly to making Gauss-Newton seismic waveform inversion efficient and demonstrates potential application to real seismic data.