Using Local Born and Local Rytov Fourier Modeling and Migration Methods for Investigation of Heterogeneous Structures

Abstract

During the past few years, there has been interest in developing migration and forward modeling approaches that are both fast and reliable particularly in regions that have rapid spatial variations in structure. The authors have been investigating a suite of modeling and migration methods that are implemented in the wavenumber-space domains and operate on data in the frequency domain. The best known example of these methods is the split-step Fourier method (SSF). Two of the methods that the authors have developed are the extended local Born Fourier (ELBF) approach and the extended local Rytov Fourier (ELRF) approach. Both methods are based on solutions of the scalar (constant density) wave equation, are computationally fast and can reliably model effects of both deterministic and random structures. The authors have investigated their reliability for migrating both 2D synthetic data and real 2D field data. The authors have found that the methods give images that are better than those that can be obtained using other methods like the SSF and Kirchhoff migration approaches. More recently, the authors have developed an approach for solving the acoustic (variable density) wave equation and have begun to investigate its applicability for modeling one-way wave propagation. The methods will be introduced and their ability to model seismic wave propagation and migrate seismic data will be investigated. The authors will also investigate their capability to model forward wave propagation through random media and to image zones of small scale heterogeneity such as those associated with zones of high permeability