# SEP-178 (2019)

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**Contents**

##### Chapter 1. Introduction

##### Chapter 2. Theory and Formulation

##### Chapter 3. Sensitivity and Parameterization

##### Chapter 4. Rock physics guided velocity model building

##### Chapter 5. Field Data Application 89 6 GPU Implementation and Adaptation

##### Appendix A: Symbolic derivation of wave equation operators

##### Appendix B: Adjoints of general two-step recursions

##### Appendix C: Visco-elastic anisotropic wave equations

##### Bibliography

**Abstract**

Full Waveform Inversion (FWI) seeks to recover a subsurface model from which simulated seismic data best match the observed data. By minimizing an objective function that measures the difference between the two data sets, FWI can potentially give a model with higher spatial resolution than traveltime-based tomographic techniques. When inverting for all components (reflections and refractions) of the seismic data including multiple azimuths and offsets, the isotropic assumption breaks down by not accounting for directional velocity variation, leading to inconsistent kinematics along azimuths and offsets. This can result in biased velocity models that misposition key reflectors in seismic images. Hence, in order to obtain an accurate subsurface velocity model, FWI needs to take anisotropy into consideration. Anisotropy can arise as an intrinsic property of rocks (for example shales) and minerals (for example clay), but most commonly as an effective property of layered or fractured media. Anisotropy provides a better description of the subsurface and seismic wavefields. To include anisotropy in FWI, however, one needs to extend the search space and invert for not only a single velocity model but also anisotropic parameters which describe how velocity varies with direction. Sadly there is often an ambiguity in determining whether a change in the seismic data recorded on the surface comes from a perturbation in velocity or anisotropic parameters in the subsurface. This means there may be a number of subsurface anisotropic models that, for a given objective function, fit the observed data equally well. To address this uncertainty problem in anisotropic FWI, I constrain the inversion vi with bounds derived from a rock physics workflow that models the relationship between velocity and pore pressure. This workflow combines various sources of data such as well logs, drilling data, basin history, and shale diagenesis to build velocity templates which are consistent with our rock physics models and understanding of pore pressure behavior in the subsurface. In a 3D field data application, enforcement of the derived constraints improves the final seismic image in terms of focusing and continuity of reflectors and better flattens the common image gathers we use to assess velocities. In addition, the resulting anisotropic velocity models are more physically plausible and better suited for subsequent exploration workflows such as pore pressure prediction and geo-hazard prevention. Anisotropic FWI is computationally costly. For the simplest anisotropic model, constant-density acoustic vertical transverse isotropy (VTI), the number of wavefields double and the number of medium parameters triple compared to isotropic FWI. Not only requiring more memory, the amount of computation needed to solve the VTI wave equations also increases three to four times. To cope with these problems, I implement a pipeline algorithm for the time-domain finite difference solver on Graphics Processing Units (GPUs). This algorithm takes advantage of the locality of the difference stencil to divide a 3D volume into blocks and perform multiple time stepping on these blocks to overlap data transfer between the CPU host and the device. This design is very suitable for a cloud environment and allows me to process an arbitrarily large 3D volume with a single GPU and compute extended images in device.