Jacques Leveille

An optimized wave equation for seismic modeling and reverse time migration

The acoustic wave equation has been widely used for the modeling and reverse time migration of seismic data. Numerical implementation of this equation via finite-difference techniques has established itself as a valuable approach and has long been a favored choice in the industry. To ensure quality results, accurate approximations are required for spatial and time derivatives. Traditionally, they are achieved numerically by using either relatively very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, known as numerical dispersion, is present in the data and contaminates the signals. However, either approach will result in a considerable increase in the computational cost. A simple and computationally low-cost modification to the standard acoustic wave equation is presented to suppress numerical dispersion. This dispersion attenuator is one analogy of the antialiasing operator widely applied in Kirchhoff migration. When the new wave equation is solved numerically using finite-difference schemes, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite-difference scheme with little additional computational cost. Numerical tests on both synthetic and field data sets in both two and three dimensions demonstrate that the optimized wave equation dramatically improves the image quality by successfully attenuating dispersive noise. The adaptive application of this new wave equation only increases the computational cost slightly.

Practical Strategies for Waveform Inversion

The term “waveform inversion” refers to a collection of techniques that use the information from the times and waveform shapes of seismic data to derive high fidelity velocity models for seismic imaging. Waveform inversion was first introduced by Lailly, Tarantola, and Mora(Lailly, 1983; Tarantola, 1984; Mora, 1988). Since these pioneering efforts many researchers have attempted to use various strategies and computational schemes to make waveform inversion implemented either in the time or the frequency domain a processing tool for real data sets. The attractiveness of waveform inversion lies mainly in its lack of approximations, at least in a formal theoretical sense, in contrast to other traditional velocity determination techniques such as semblance or tomography. However, a whole raft of approximations must be made to make the technique viable with today’s computing technology and restrictions of seismic data acquisition. Some of these approximations are rather severe, such as restriction to acoustic waveform inversion while others are made simply to speed up the process. These are collectively referred to as “waveform inversion strategies”, which turn the whole process into a very manpower intensive art form. This paper discusses these various strategies and their influences on the velocity models that are obtained from waveform inversion. One cannot exhaustively test all the choices of strategies, and for that reason the paper focuses on the choices that in our experience create the most difficulties. These approaches will be illustrated on data from offshore Brazil.

Reverse Time Migration of P-wave and C-wave Data from a 3D VSP over a Deep Subsalt Prospect in the Gulf of Mexico

Summary Difficulties in imaging subsalt data in the Gulf of Mexico are well documented. Even with the lates t wide azimuth acquisition technology the quality of imaging subsalt is quite variable. 3D VSPs offer the potential to improve reservoir imaging as compared to surface data and to calibrate the reservoir to the surface seismic. The major drawbacks to 3D VSPs are that they are quite expensive due to the rig time required and by their very nature offer a narrow illumination window around the wellbore. To extract more information from 3D VSPs than standard Pwave processing two avenues were investigated: 1) The utilization of the reverse time migration (RTM) imaging algorithm which offers the possibility to increase the lateral coverage of 3D VSPs because it honors two-way propagation and all multiples in the model. 2) Processing for converted wave modes of energy.

Practical strategies for waveform inversion

The term “waveform inversion” refers to a collection of techniques that use the information from the times and waveform shapes of seismic data to derive high fidelity velocity models for seismic imaging. Waveform inversion was first introduced by Lailly, Tarantola, and Mora(Lailly, 1983; Tarantola, 1984; Mora, 1988). Since these pioneering efforts many researchers have attempted to use various strategies and computational schemes to make waveform inversion implemented either in the time or the frequency domain a processing tool for real data sets.

Introduction to special section: Salt basin model building, imaging, and interpretation

Salt basins such as the Gulf of Mexico, Brazil, and West Africa have proven to be prolific areas for hydrocarbon discoveries. In these basins the salt usually presents a high velocity contrast, with fast salt juxtaposed against slower sediments creating substantial imaging challenges, making

Phases in One Way Wave Equation Migrations

In this paper, we investigate phases in different one way wave equation based migration algorithms. We found that poststack migrations preserve the characteristics of the input wavelet. However, like Kirchhoff migration, prestack shot and plane wave migration require a phase rotation to match the phase of the image to that of the input data. We use a single impulse response and a flat reflector model to demonstrate our conclusions.

Application of elastic modeling to subsalt interpretation

Staggered grid finite difference elastic modeling is used to synthesize point-source responses to a two-dimensional subsurface model derived from three-dimensional preand post-stack depth migrated data volumes. The modeled data are then processed as if they were the result of a real field acquisition process. Comparisons between real data and synthetic responses provide additional confidence in validation of interpretations and drilling decisions.