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Elastic full waveform inversion of multicomponent data

by Gustavo Catao Alves

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Table of contents

  • Chapter 1: Introduction
  • Chapter 2: Elastic wave-equation and adjoint formulation
  • Chapter 3: Computational optimization of elastic modeling and imaging
  • Chapter 4: Elastic imaging in the Marmousi 2 model
  • Chapter 5: Elastic full waveform inversion of the Moere Vest 2D data set
  • Appendix A: Reciprocity in multicomponent elastic data
  • Appendix B: 3D Equations
  • Bibliography

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

Defense presentation slides
Chapter 1
Chapter 2
Chapter 3
Chapter 4

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