Fourier Finite-Difference Migration for TTI Seismic Data
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Solution Overview
Problem
Current seismic data migration techniques for tilted transversely isotropic media are computationally expensive, particularly when dealing with three-dimensional models, due to the complexity of algorithms and increased computational cost in handling anisotropic media.
Innovation Solution
A method that generates numerical solutions for the exact three-dimensional dispersion relationship of seismic energy in tilted transversely isotropic media, using selected input values of polar and azimuth angles and Thomsen anisotropic parameters, and determines coefficients for a two-dimensional Fourier finite difference relationship to achieve a best fit, allowing for seismic data migration using a Fourier finite difference scheme.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If Kirchhoff methods or two-way wave equation methods are used for TTI migration, then imaging accuracy in dipping formations is improved, but computational cost increases significantly
Solution Approach 1:
The patent replaces traditional time-domain finite difference methods with frequency-domain Fourier finite difference methods. This substitution transforms the computational approach from solving wave equations in the time domain to using spectral methods in the frequency domain, achieving both accurate depth estimation in TTI media and reduced computational cost through efficient Fourier transforms
Solution Approach 2:
The patent changes the mathematical domain from time-domain to frequency-domain representation. By transforming the migration problem into the frequency domain using Fourier transforms, the method achieves computational efficiency while maintaining accuracy in imaging dipping formations with anisotropic velocity structures
2Device complexity
If explicit finite-difference methods are used for three dimensional TTI migration, then algorithm simplicity is maintained, but computational cost increases due to large convolution filters
Solution Approach 1:
The patent replaces convolution-based explicit finite difference methods with Fourier-based implicit finite difference methods. This substitution eliminates the need for large convolution filters by using spectral decomposition, thereby reducing computational cost while maintaining algorithmic simplicity through the efficiency of Fast Fourier Transform algorithms
Data Source
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AI summary
A method for migrating three dimensional seismic data in tilted transversely isotropic media ("TTI") is based on generating numerical solutions to an exact relationship for a three dimensional dispersion relationship of seismic energy traveling through TTI media. The numerical solutions use selected input values of polar angle φ and azimuth angle ψ of a transverse isotropic axis of symmetry, and selected values of Thomsen anisotropic parameters to generate tables of numerical values. Based on the tables of numerical values, optimized coefficients for a finite-difference relationship are estimated along multiple splitting directions. The seismic data are then migrated using a three dimensional Fourier finite difference extrapolation algorithm.