Waveform-based velocity estimation from reflection seismic data

Abstract

The objective of this thesis is to investigate new methods in reflection seismology for estimating subsurface velocity models accurately and efficiently. Full waveform inversion (FWI) is a state-of-the-art approach that can yield high-resolution models. However, multiple problems, including high computational cost, spurious local minima and possible geologically-implausible solutions, have prevented widespread applications of FWI for reflection data. These problems correspond to the fact that we in practice must estimate numerous model parameters with inadequate data (e.g., limited aperture, insufficient low frequencies). To tackle the problems and achieve the goal of this thesis, I develop image-guided sparse-model FWI (IGFWI) and wave-equation reflection traveltime inversion (WERTI). IGFWI uses subsurface structures to constrain the inversion of a sparse model. I extract the subsurface structures from migrated seismic images. With the structures, I construct a sparse model, which can, with substantially fewer parameters, explain the subsurface in a geologically plausible way. The IGFWI optimization problem is then formulated with respect to the sparse model that is constrained by structures. With fewer parameters, IGFWI converges faster in fewer iterations than does conventional FWI; with structural constraints, estimated models are geologically plausible; with a sparse representation of the model, blocky updates mitigate the lack of low frequencies. I solve IGFWI using a image-guided conjugate-gradient method. With respect to the sparse model, I explicitly compute a projected Hessian matrix and its inverse using a projected BFGS (P-BFGS) method. Compared to the classic limited-memory BFGS (L-BFGS) method, P-BFGS substantially saves both computational time and memory, due to fewer model parameters of the sparse model. With the P-BFGS method, I propose an efficient quasi-Newton method to solve large-scale inversion problems, such as FWI. I also introduce WERTI to recover the low-wavenumber velocity background, and thereby mitigate local minima in reflection FWI with insufficient low frequencies. By alternating between WERTI and FWI, we can overcome the velocity-depth ambiguity in reflection traveltime inversion and estimate both the low- and high-wavenumber components of velocity models using only high-frequency reflection data .