Poster: An Approximate Inverse to Extended Born Modeling Operator, Jie Hou, Rice University
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In seismic imaging, one tries to recover the subsurface reflector information from seismic reflection data. It usually depends on the linearized model of Born approximation. This process is essentially to compute the inverse to Born Modeling Operator. However, the common imaging technique, Reverse Time Migration(RTM), is only the adjoint of modeling operator. Though it can position the reflectors correctly, the migration operator will not produce the correct amplitudes or wavelet. An inversion will be the true-amplitude Reverse Time Migration. The "true-amplitude” here is meant in the ray-theoretic(asymptotic) sense. True amplitude migration was first developed for Kirchhoff migration by compensating the amplitudes. Ten Kroode(2012) gave a wave-equation-based Kirchhoff operator, which is an approximate inverse of the extended modeling operator in 3D. Inspired by him, I try to derive the approximate inverse mathematically in 2D. In this project, I apply asymptotic ray theory to depth-oriented modeling/migration operator using progressing wave expression. Then the Normal Operator is analyzed using principle of stationary phase. I determine that the adjoint operator differs from an asymptotic inverse only by application of several velocity-independent filters, which I identify explicitly. In addition to the theoretical derivation, I provide a numerical implementation and illustrate that effectiveness of the asymptotic inverse via computational examples.This is very rewarding. Because the amplitude information itself, on one hand, is very useful to detect the reservoir. On the other hand, this new operator can be used as a preconditioner for Full Waveform Inversion, a process which iteratively improves an initial model by matching the measured data and modeled data. The new preconditioner will speed up the the convergence of iterations dramatically.

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In seismic imaging, one tries to recover the subsurface reflector information from seismic reflection data. It usually depends on the linearized model of Born approximation. This process is essentially to compute the inverse to Born Modeling Operator. However, the common imaging technique, Reverse Time Migration(RTM), is only the adjoint of modeling operator. Though it can position the reflectors correctly, the migration operator will not produce the correct amplitudes or wavelet. An inversion will be the true-amplitude Reverse Time Migration. The "true-amplitude” here is meant in the ray-theoretic(asymptotic) sense. True amplitude migration was first developed for Kirchhoff migration by compensating the amplitudes. Ten Kroode(2012) gave a wave-equation-based Kirchhoff operator, which is an approximate inverse of the extended modeling operator in 3D. Inspired by him, I try to derive the approximate inverse mathematically in 2D. In this project, I apply asymptotic ray theory to depth-oriented modeling/migration operator using progressing wave expression. Then the Normal Operator is analyzed using principle of stationary phase. I determine that the adjoint operator differs from an asymptotic inverse only by application of several velocity-independent filters, which I identify explicitly. In addition to the theoretical derivation, I provide a numerical implementation and illustrate that effectiveness of the asymptotic inverse via computational examples.This is very rewarding. Because the amplitude information itself, on one hand, is very useful to detect the reservoir. On the other hand, this new operator can be used as a preconditioner for Full Waveform Inversion, a process which iteratively improves an initial model by matching the measured data and modeled data. The new preconditioner will speed up the the convergence of iterations dramatically.

Thursday March 6, 2014 4:30pm - 6:30pm PST

BRC Exhibit Hall*Rice University 6500 Main Street at University, Houston, TX 77030*

BRC Exhibit Hall