Simulation of Seismic Real and Virtual Data Using the 3d Finite-difference Technique and Representation Theorem

Seismic modeling is a technique for simulating wave propagation through the subsurface. For a given geological model, seismic modeling allows us to generate snapshots of wave propagation and synthetic data. In my dissertation, for real seismic events I have chosen to implement the finite-difference modeling technique. When adequate discretization in space and time is possible, the finite-difference technique is by far one of the most accurate tools for simulating elastic-wave propagation through complex geological models. In recent years, a significant amount of work has been done in our group using 2D finite-difference modeling. For complex salt structures which exploration and pro- duction industries meet today, 2D finite-difference modeling is not sufficient to study subsalt imaging or the demultiple of subsalt models. That is why I have developed a 3D finite-difference modeling code. One of the key challenges that I have met in developing the 3D finite-difference code is to adapt the absorbing boundary conditions. Absorbing boundary conditions are needed to describe the infinite geological models by limited computing domain. I have validated the 3D finite-difference code by comparing its results with analytic solutions. I have used 3D finite-difference program to generate data corresponding to 3D complex model which describes salt and subsalt structures of Gulf of Mexico. The resulting data include reflections, diffractions and other scattering phenomena. I have also used finite-difference program in anisotropic context to show that we can effectively predict shear-wave splitting and triplication in the data. There are new sets of events that are not directly recorded in seismic data, they have been called virtual events. These events are turning to be as important as real events in modern data processing. Therefore we also have to learn how to model them. Unfortunately, they cannot yet be modeled directly from finite-difference. Here I will describe how to model these events by using cross correlation type representation theorem. As illustration of how important of virtual events for seismic data process- ing, I also described an internal multiple attenuation technique which utilized virtual events