paul sava



wsi course




© 2007 PC Sava

Page updated on
October 8, 2014


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


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.