**This is an old revision of the document!**

**Downloads**

- Thesis pdf

**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 justified 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 differential 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 different 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