SEISMIC MODELING AND IMAGING OF REALISTIC EARTH MODELS USING NEW FULL-WAVE PHASE-SHIFT APPROACH

Seismic modeling is a valuable tool for seismic interpretation of oil and gas reservoirs and is an essential part of seismic inversion algorithms. In this thesis, we have developed and verified the new full-wave phase-shift (FWPS) approach for solving seismic modeling and imaging problems. FWPS approach is based on a new way to generalize the “one-way” acoustic wave equation using a phase-shift structure. Our approach solves the full acoustic wave equation by separating the problem into an equation consisting of two coupled first-order partial differential equations for wave propagation in depth, in which the initial waves are purely one-way, but solving the equations for downgoing initial waves and then for upgoing initial waves, retaining the full two-way nature of the Helmholtz equation. This produces a complete set of linearly independent solutions, that is used to construct the correct, causal full wave solution that includes waves propagating both up and down. The initial conditions for the modeling problem are generated by solving the Lippmann-Schwinger integral equation formally, in a non-iterative fashion and converting the problem into a Volterra integral equation of the second kind. Reflection and wraparound from boundaries are effectively dealt with employing correct absorbing boundary conditions. We validate the new FWPS method by applying it to forward modeling and inversion. Time snapshot results are given for standard velocity models, as well as a realistic earth velocity model. We compare the realistic earth velocity model results from new FWPS approach to those obtained by finite differences (FD), with correct scattering boundary conditions imposed. We have stabilized our results by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing evanescent waves, while retaining all of the propagating waves and exponentially decaying evanescent waves. Our approach is easily parallelized to achieve approximate N2 scaling, where N is the number of coupled equations. We discuss the parallelization techniques used to optimize the algorithm and improve the computational cost. We show the presence of evanescent waves in a realistic earth velocity model by comparing the reflection matrix both with and without decaying evanescent waves.