paul sava


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© 2007 PC Sava

Page updated on
October 8, 2014

Thesis


Here are links to my thesis (PDF) and to my defense presentation (PPT).



table of contents

Chapter 1 Introduction
Chapter 2 Riemannian Wavefield Extrapolation
Chapter 3 Angle-domain common image gathers
Chapter 4 Prestack residual migration
Chapter 5 Wave-equation migration velocity analysis
Chapter 6 Examples
Chapter 7 Conclusions

abstract


The goal of this thesis is to design new methods for imaging complex geologic structures of the Earth's Lithosphere. Seeing complex structures is important for both exploration and non-exploration studies of the Earth and it involves, among other things, dealing with complex wave propagation in media with large velocity contrasts.

The approach I use to achieve this goal is depth imaging using acoustic waves. This approach consists of two components: migration and migration velocity analysis. No accurate imaging is possible without accurate, robust and efficient solutions to both components. The main technical requirements I impose on both imaging components call for the use of as much information as possible from the recorded wavefields, design of methods consistent with one-another, and accurate modeling of wave phenomena within the constraints of the available computational resources.

I address both migration and migration velocity analysis in the general framework of one-way wavefield extrapolation. In this context, both imaging components are consistent and use the entire acoustic wavefields with accurate, robust and computationally feasible techniques.

The migration state-of-the-art involves downward continuation of wavefields recorded at the Earth's surface. I introduce Riemannian wavefield extrapolation as a general framework for wavefield extrapolation. Downward continuation or extrapolation in tilted coordinates are special cases. With this technique, I overcome the steep-dip limitation of downward continuation, while retaining the main characteristics of wave-equation techniques. Riemannian wavefield extrapolation propagates waves in semi-orthogonal coordinate systems that conform with the general direction of wave propagation. Therefore, extrapolation is done forward relative to the direction in which waves propagate, so I achieve high-angle accuracy with small-angle operators. Riemannian wavefield extrapolators can also be used for diving waves that cannot be easily handled using conventional downward continuation.

The velocity estimation state-of-the-art involves traveltime tomography from sparse reflectors picked on migrated images. I introduce wave-equation migration velocity analysis as a more accurate and robust alternative. With this technique, I overcome the instability of traveltime tomography caused by ray tracing in areas with high velocity contrasts. I formulate wave-equation MVA with an operator based on linearization of wavefield extrapolation using the first-order Born approximation. I define the optimization objective function in the space of migrated images, in contrast with wave-equation tomography with objective function defined in the space of recorded data. Since the entire images are sensitive to migration velocities, I use image perturbations for optimization, in contrast with traveltime tomography which employs traveltime perturbations picked at selected locations. I construct image perturbations with residual migration operators by measuring flatness of angle-domain common image gathers, or by measuring spatial focusing of diffracted energy.