Elastic full waveform inversion of multicomponent data

by Gustavo Catao Alves

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Abstract
Subsurface seismic imaging has relied on the acoustic wave-propagation model for many decades. This choice has been justifi ed by the greater availability of acoustic only data, i.e., ocean streamers, higher computational cost of shear-wave processing, and challenges in wave-mode separation methods.

However, in the last few years, seismic exploration has moved to more complex subsurface targets, such as sub-salt and sub-basalt. In these scenarios, including a greater range of physical processes is advantageous. Elastic modeling and inversion achieves that by accounting for both pressure and shear wave propagations. Therefore, a greater understanding of elastic wave-equation methods in seismic imaging becomes fundamental.

I formulate the imaging condition for the elastic wave-equation using the stress-velocity set of first-order partial diff erential equations. I show that the elastic imaging condition can be obtained similarly for density-Lame or density-velocity parameterizations of the model space. I demonstrate that these conditions are di fferent than the acoustic case and can be obtained by calculating the adjoint Born approximation of the nonlinear problem.

I discuss how elastic wave-equation modeling and imaging is computationally more intensive than acoustic methods. I propose solutions for memory cost and computational time optimizations and show performance gains in a simple synthetic example. Using the proposed formulation and computational improvements, I apply the elastic imaging condition to the Marmousi 2 synthetic model. I show an elastic reverse time migration (ERTM) result with model components in the density-Lame parameterization. I also show how this image can qualitatively indicate anomalies in a bulk-shear moduli ratio.

Finally, I combine all methodologies presented into an elastic full waveform inversion (EFWI) workflow. I apply this workflow to a 2D field data set acquired using four-component ocean-bottom nodes (4C OBNs). I obtain inversion results for density, P- and S-velocities up to 10 Hertz (Hz) frequency data. Finally, I combine P- and S-velocities to calculate a Vp/Vs model. The calculated model is composed of layers with Vp/Vs values between 1.5 and 2.3, which is consistent with the expected geology of the basin.

Reproducibility and source codes
This thesis has been tested for reproducibility. The source codes are made available for download. The source code included here covers both the elastic modeling and imaging described in Chapters 2 and 4, as well as the optimizations from Chapter 3 and the complete field data workflow for Chapter 5. Due to data usage permissions, the raw data used in Chapter 5 is not included in the download.

Defense presentation slides
All slides can be download as a .tar.gz file here.
For individual .pptx files, follow the links below. Please acknowledge the source when reproducing these slides.
Comparing acoustic and elastic data
Comparing single and multicomponent data
Chapter 2 - Theory
Chapter 2 - A visual example of ERTM
Chapter 3 - Random boundaries
Chapter 5 - EFWI of the Moere Vest data set
Appendix A - Reciprocity