1997 Annual Report of the Rice Inversion Project

Kidane Araya and William W. Symes, Acoustic Asymptotic Inversion and AVO

Abstract:
Prestack asymptotic linearized acoustic inversion, like other forms of prestack depth migration, produces image volumes exhibiting amplitude-versus-offset variation which may be indicative of hydrocarbon accumulations. A careful analysis a seismic line from the offshore Gulf of Mexico suggests that the prestack acoustic inversion volume may be more consistent with the physics underlying AVO analysis than are other possible input data volumes, yielding more consistent predictions of gradient and intercept across a wider range of angles.

Kidane Araya and William W. Symes, 2.5D Common-Offset Inversion of Mobil North Sea AVO Data Set

Abstract:
This short report deals with the application of TRIP 2.5D Common-offset inversion algorithm on a field data set from the North Viking Graben in the North Sea. This data set was donated to TRIP by Mobil Exploration and Production Technical Center, a sponsor of TRIP, to evaluate our inversion code. We show: a) inversion of each offset gives a "true amplitude" depth map of the subsurface, b) post-inversion stack produces a clearer image by reducing the noise in the data and c) common-image gathers (coherency pannels from different offset inversion) near a well indicate flat events with different amplitude. The offset dependent depth map might be used in the AVO analysis of reflection seismic data.

Philippe Ecoublet, William W. Symes and Stewart Levin, Seismic Inversion for Porosity using a Backpropagation Neural Network

Abstract:
Fluid properties in seismic reservoirs are commonly assessed from the computation of seismic attributes. We investigate both qualitatively and quantitatively how seismic inversion results can improve fluid property predictions in reservoir characterization by implementing a neural network as an inversion tool. This study is first conducted locally by comparing log-to-log elastic prediction of porosity with seismic inversion prediction and with direct seismic attributes prediction, before tackling multi-offset seismic data. We also investigate the performance achieved from using different classes of neural networks for prediction and pattern classification, including the popular backpropagation network and the radial-basis function networks.

Maissa A. El-Mayeed, Seongjai Kim and William W. Symes, 3-D Kirchhoff Migration Using Finite Difference Traveltimes and Amplitudes

Abstract:
Imaging techniques based on high frequency asymptotic representation of the 3-D acoustic Green's function require efficient solution methods for the computation of traveltimes and amplitudes. Second-order finite difference schemes solve the eikonal and transport equations on regular grids with usable accuracy. Since the transport equation includes the gradient and the Laplacian of the computed traveltime field, special superconvergent difference formulas must be employed to guarantee accurate amplitudes. Upwind finite differences are requisite to sharply resolve discontinuities in the derivatives, while centered differences improve accuracy and enjoy extra-order accuracy for the averaged gradient of the traveltime field. A two-level, second-order, upwind, essentially non- oscillatory (ENO) scheme satisfies these requirements. The computed amplitude is at least first-order accurate, while the traveltime is second-order accurate. we embed the eikonal/ transport solver in a 3-D Kirchhoff migration algorithm, resulting in accurate and efficient depth migrations.

Christopher D. Belfi, Second and Third Order ENO Methods for the Eikonal Equation

Abstract:
The first arrival time problem may in some cases considered as a Hamilton-Jacobi initial value problem. Such a problem can be solved by a very simple finite difference method. The second and third order essentially nonoscillatory (ENO) extensions to this method are relatively straight-forward and result in significant accuracy and efficiency gains.

Chaoming Zhang, The Immersed Interface Method for Elastic Wave Propagation in Heterogeneous Materials

Abstract:
The immersed interface method is applied to solve elastic wave equations with discontinuous coefficients, whose solutions are discontinuous or nonsmooth across the interfaces between different material properties. High resolution multi-dimensional flux-limiter methods are used on a Cartesian grid to help reduce the dispersion and eliminate nonphysical oscillations. Near the interface, special formulas are employed using the imersed interface method that incorporate the jump conditions and give pointwise second order accuracy even when the interface is not aligned with the grid. This work is an extension of previous work on acoustics.

Chaoming Zhang, A Fourth Order Method for Acoustics Waves in Heterogeneous Media

Abstract:
We present a fourth order finite difference method for the simulation od acoustic waves in heterogeneous media. We derive the numerical jump conditions from the physical jump conditions at the interface of the heterogeneous media, and build the numerical jump conditions into a special stencil to obtain fourth order methods.

Chaoming Zhang and Wiliam W. Symes, An Overview of Numerical Methods for Maxwell's Equations and Ground-penetrating Radar

Abstract:
The literature on numerical methods for Maxwell's equations and groud-penetrating radar (GPR) includes discussion of finite difference, finite element, finite volume, asymptotics, pseudospectral methods. We propose further investigation of finite difference schemes using 1) nonlinear flux limiters to control dispersion and 2) special stencils to maintain accuracy at coefficient discontinuities.

Wiliam W. Symes and Chaoming Zhang, A Finite Difference Time Stepping Class

Abstract:
The abstract C++ class FDTD expresses the common characteristics of explicit finite difference schemes for initial boundary value problems. The advantages of abstract specification are especially apparent when linearized and adjacent simulation modules are required, as is the case for example when the simulator drives the optimization of fit error to solve a parameter estimation problem.

Philippe Ecoublet and William W. Symes, An introduction to the Backpropagation Neural Network Code Developed at TRIP

Abstract:
A backpropagation neural network algorithm has been developed at The Rice Inversion Project as an inversion tool for seismic reservoir characterization. Neural networks can be implemented in a straighforward way for tackling a broad variety of prediction and classification problems as an alternative to model based inversion methods. This document is an introduction to the backpropagation neural network, probably one the most widely used neural network, and describes the procedure for using the program available at TRIP.