3D Elastic Full-Waveform Inversion

Abstract

Full Waveform Inversion (FWI) is a depth imaging technique that takes advantage of the full information contained in recorded seismic data. FWI provide high resolution images of subsurface properties, usually seismic velocities or related parameters, although in theory it could image any property used to formulate the wave equation. The computational cost of the methodology has historically limited its application to 3D acoustic approximations but recent developments in hardware capabilities have increased computer power to the point that more realistic approximations are viable. In this work the traditional acoustic approximation is extended to include elastic effects by introducing the elastic wave equation as the governing law that describes wave propagation. I have developed a software based on finite-differences to solve the elastic wave equation in 3D, which I applied in the development of a full-waveform inversion algorithm. The software is fully parallelised for both distributed and shared-memory systems. The first level of parallelisation distributes seismic sources across cluster nodes. Each node solves the 3D elastic wave equation in the whole computational domain. The second level of parallelisation takes advantage of present multi-core computer processor units (CPU) to decompose the computational domain into different volumes that are solved independently by each core. Such parallel design allows the algorithm to handle models of realistic sizes, increasing the computational times only a factor of two compared to those of 3D acoustic full-waveform inversion on the same mesh. I have also implemented a perfectly matched layer absorbing boundary condition to reproduce a semi-infinite model geometry and prevent spurious reflections from the model boundaries from contaminating the modelled wavefields. The inversion algorithm is based upon the adjoint-state method, which I reformulated for the wave equation that I implemented, which was based on particle-velocities and stresses, providing a comparison and demonstration of equivalence with previous developments. To examine the performance of the code, I have inverted several synthetic problems of increasing realism. I have principally used only pressure sources and receivers to assess the potential of the method's application to the most common industry surveys: streamer data for offshore and vertical geophones (only one component) for onshore exploration surveys. The results show that the imaged properties increase with the heterogeneity of the models, due to the increase in P-S-P conversions which provides the main source of information to invert shear-wave velocity models from pressure sources and receivers. It remains to demonstrate the inversion of field datasets and my future research project will focused on achieving this goal.