Seismic Modeling and Imaging Using Duplex-Wave and Low-rank Approximation

Abstract

A foremost aim of exploration is to distinguish locations of reservoirs to drill new wells. Increasingly, the resolution of subsurface images leads to the identification of geological properties and improved knowledge of the Earth’s subsurface. Subsequently, in seismic exploration, approaches to solving wave equations include finite-difference and pseudo-spectral algorithms. However, these approximations can cause numerical instability and dispersion artifacts. Accordingly, the sampling intervals in time or space require a rigorous limit. This thesis is divided into two parts. The first part focuses on wavefield extrapolation methods. I proposed a method that is theoretically exempt from numerical instability and dispersion artifacts for seismic imaging. The new approach is established with a fast implementation of a Fourier Integral Operator (FIO) obtained from the solutions of the wave equations. I show that the new algorithm is stable and able to propagate waves using large time-step sizes. However, it comes with an additional cost to the extrapolation. Next, I present a new spectral method of using a residual formulation that employs a second-order Taylors series expansion to lower the cost and promote accuracy. The new residual application depends on the velocity perturbation. The second part of the thesis is devoted to a new modified method for imaging the Earth based on a variation on Reverse Time Migration (RTM). The core of seismic imaging algorithms like RTM depends on the wavefield time extrapolation. I have developed a new depth migration technique, Duplex-Wave Reverse Time Migration (DRTM), to improve the image considering the complexity of near-surface structures. DRTM utilizes the direct arrival as a source to propagate a forward wavefield and then reversely extrapolates the recorded data and finally applies the zero-lag crosscorrelation imaging condition. The new algorithm can be used to improve the current RTM method for imaging the shallow areas, without additional computational costs. I have studied the reconstruction of missing near-surface offset seismic data. By applying seismic interferomerty to retrieve the missing near-offset recorded data, we can resolve the issue of getting a poor image using the DRTM algorithm. This will in turn enhance the image in areas with complex near-surface structures and get a better image compared to the image produced with the missing near-offset recorded data.