Gauß-Newton Full-Waveform Inversion for Acoustic Media

This thesis investigates the performance of the Gauss-Newton (GN) method in Full-
waveform inversion (FWI) in acoustic media in the time domain. FWI aims to estimate
subsurface properties by iteratively minimizing the misfit between observed and synthetic
seismic data. While the Steepest-descent (SD) method is commonly used in FWI, this study
demonstrates that the GN method offers superior performance, achieving higher resolution
and faster convergence. However, the GN method requires significant computational
resources due to the calculation of the Jacobian matrix. To address these challenges, we
calculate the partial derivative field for the Jacobian matrix using virtual sources and the
reciprocity principle. These wavefields are explicitly obtained by convolving the forward
propagated wavefields from each source with the reciprocal wavefields from each receiver.
Then the Jacobian matrix is used to calculate the approximate Hessian matrix and the
gradient used in the GN method. Numerical experiments reveal that the GN method
outperforms the SD method across various geometries with different numbers of receivers
and sources, delivering significantly higher resolution and faster convergence rates.