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

*by Yaxun Tang*

**Table of contents**

- Opening pages: Abstract; Preface; Acknowledgments; Contents
- Chapter 1: Introduction
- Chapter 2: Target-oriented wavefield least-squares migration
- Chapter 3: Target-oriented wavefield tomography
- Chapter 4: 3-D field-data examples
- Chapter 5: Conclusions
- Appendix A: Convergence property of plane-wave phase encoding
- Appendix B: Convergence property of random phase encoding
- Appendix C: Wave-equation tomographic operator
- Appendix D: 3-D conical-wave migration
- Appendix E: Seismic visibility analysis

**Abstract**

This thesis develops a novel target-oriented inversion framework that uses wavefields as carriers of information to image both low- and high-wavenumber components of the earth model in complex geological settings, such as subsalt regions. The low-wavenumber component of the earth model is often known as the background velocity, whereas the high-wavenumber component of the earth model is often known as the reflectivity. I address the problem of reflectivity imaging with target-oriented wavefield least-squares migration, and the problem of velocity estimation with target-oriented wavefield tomography.

Reflectivity images of the subsurface are commonly produced by prestack depth migration. When the overburden is complex and the reflectors are unevenly or insufficiently illuminated, the migration operator alone is inadequate to provide an optimal image.

I tackle the problem of distorted illumination in reflectivity imaging by wavefield least-squares migration. I formulate least-squares migration in the image domain and solve it in a target-oriented fashion. In the image-domain formulation, explicit computation of the Hessian operator (the resolution function that measures the illumination deficiency of the imaging system) is the most important and challenging step. I develop a novel method based on phase encoding to efficiently and accurately compute the target-oriented Hessian operator. By design, the phase-encoded Hessian converges to the exact Hessian either deterministically (for plane-wave phase encoding) or statistically (for random phase encoding), while having the important advantages that no Green's functions need to be stored during computation and that the number of wavefield propagations is also drastically reduced. The target-oriented Hessian operator is then used to recover the reflectivity by iterative inverse filtering. I regularize the inversion with dip constraints, which naturally incorporate interpreted geological information into the inversion.

Accurate imaging of the reflectivity also requires an accurate background velocity model. High-quality velocity model-building in complex geology requires wavefield-based velocity analysis to properly model band-limited wave phenomena. However, the high cost and lack of flexibility of target-oriented model-building prevent this method from being widely used in practice.

I overcome the cost and flexibility issues of wavefield-based migration velocity analysis by developing target-oriented wavefield tomography. Target-oriented wavefield tomography is achieved by synthesizing a new data set specifically for velocity analysis. The new data set is generated based on an initial unfocused target image and by a novel application of generalized Born wavefield modeling, which correctly preserves velocity kinematics by modeling both zero and non-zero subsurface-offset-domain images. The new data set can be synthesized for a chosen target region with velocity inaccuracies. The reduced data size and computation domain, therefore, greatly improve the efficiency and flexibility of wavefield tomography, allowing fast and interpretation-driven interactive wavefield-based velocity analysis, where different geological scenarios or hypotheses can be tested in quasi-real time.

The proposed target-oriented inversion framework successfully estimates subsalt velocities and recovers subsalt reflectivities from distorted illumination from 2-D synthetic and 3-D field data.