Frequency-Domain Elastic Reverse-Time Migration Imaging
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Solution Overview
Problem
Subsurface imaging in elastic media is challenging due to the presence of P, S, and Rayleigh waves, which leads to undesired artifacts and high computational requirements, making it difficult to achieve accurate imaging of complex topographical structures.
Innovation Solution
The application of the Helmholtz decomposition theorem in the frequency domain allows for the division of seismic data into P- and S-wave potentials, using a back-propagation algorithm to express the imaging condition as a convolution of a virtual source with a wavefield displacement vector, thereby generating accurate migration images for P- and S-waves.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Helmholtz decomposition is applied to divide seismic data into P- and S-wave potentials, then imaging accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent applies Helmholtz decomposition to segment the elastic wavefield into P-wave potential and S-wave potential components. This segmentation allows separate processing of P-waves and S-waves, improving imaging accuracy by eliminating artifacts caused by wave type mixing while managing computational complexity through frequency-domain implementation.
2Productivity
If back-propagation algorithm is used to express imaging condition as convolution, then computing efficiency is improved, but memory requirements increase
Solution Approach 1:
The patent replaces time-domain back-propagation with frequency-domain convolution implementation. By transforming the back-propagation algorithm into the frequency domain, the patent achieves computing efficiency through convolution operations while managing memory requirements through efficient frequency-domain data structures.
3Measurement precision
If frequency-domain elastic reverse-time migration is implemented, then imaging of complex topography is improved, but computational cost increases
Solution Approach 1:
The patent transforms the migration problem from time domain to frequency domain, changing the mathematical parameters and representation of the wavefield. This parameter change enables more efficient computation of complex topography imaging by utilizing frequency-domain convolution properties and Helmholtz decomposition, reducing overall computational cost.
Data Source
AI summary
Provided are an apparatus and method for imaging a subsurface using frequency-domain reverse-time migration in elastic medium. The subsurface imaging method represents a frequency-domain imaging condition as convolution of measured data and a partial derivative wavefield. That is, the subsurface imaging method applies a back-propagation algorithm to represent an imaging condition as convolution of a virtual source and a back-propagated wavefield. Then, the subsurface imaging method divides a virtual source vector and the back-propagated wavefield represented by a displacement vector into P- and S-wave potentials through Helmholtz decomposition, thereby providing a new imaging condition.