paul sava
© 2007 PC Sava
Page updated on October 8, 2014


Thesis
table of contents 
Chapter 1 
Introduction 
Chapter 2 
Riemannian Wavefield Extrapolation 
Chapter 3 
Angledomain common image gathers 
Chapter 4 
Prestack residual migration 
Chapter 5 
Waveequation 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 nonexploration 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 oneanother, 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 oneway 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 stateoftheart 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 steepdip limitation of downward continuation, while retaining the main characteristics of waveequation techniques. Riemannian wavefield extrapolation propagates waves in semiorthogonal 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 highangle accuracy with smallangle operators. Riemannian wavefield extrapolators can also be used for diving waves that cannot be easily handled using conventional downward continuation.
The velocity estimation stateoftheart involves traveltime tomography from sparse reflectors picked on migrated images. I introduce waveequation 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 waveequation MVA with an operator based on linearization of wavefield extrapolation using the firstorder Born approximation. I define the optimization objective function in the space of migrated images, in contrast with waveequation 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 angledomain common image gathers, or by measuring spatial focusing of diffracted energy.

