Media Parameter Correction for Discontinuous Surface Simulation
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Solution Overview
Problem
Current seismic numerical simulation methods, particularly the finite difference method, face instability and reduced accuracy when dealing with high Poisson ratio media and complex discontinuous surfaces, leading to calculation challenges and high memory consumption, especially in simulating seismic waves near surfaces with strong impedance changes.
Innovation Solution
A media Parameter-modified method that corrects the constitutive relationship and density of non-horizontal points on free surfaces, allowing for adaptive expression of arbitrary discontinuous surfaces without altering the original finite difference method code, enabling accurate simulation by introducing the influence of free surfaces into the finite difference method code.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the finite difference method is directly applied to discontinuous surfaces with strong impedance comparison, then the calculation is unstable and numerical illusion is generated, but the method is simple to implement
Solution Approach 1:
The patent modifies the constitutive relationship parameters (elastic coefficients) at grid points adjacent to discontinuous surfaces by introducing correction coefficients. These coefficients are derived from the impedance contrast across the interface, allowing the finite difference method to handle strong impedance comparisons without generating numerical illusions or instability while maintaining the simplicity of the original method.
Solution Approach 2:
The patent applies local corrections only at grid points adjacent to discontinuous surfaces rather than throughout the entire model. By identifying interface-adjacent grid points and applying correction coefficients specifically at these locations, the method maintains calculation stability without increasing the complexity of the overall implementation approach.
2Measurement precision
If weak solution form methods such as spectral element method are used, then calculation accuracy is improved, but the algorithm theory is complicated and memory consumption is high
Solution Approach 1:
The patent achieves high-order calculation accuracy equivalent to weak solution methods by modifying the constitutive relationship parameters at interface-adjacent grid points. This parameter modification approach allows the use of simple finite difference algorithms while obtaining accuracy comparable to complex spectral element methods, avoiding the need for complicated algorithm theory and high memory consumption.
Solution Approach 2:
The patent extracts and addresses the specific issue at discontinuous surfaces by applying correction coefficients only at interface-adjacent grid points. This localized approach captures the essential physics of wave behavior at interfaces without requiring the complex theoretical framework and high computational resources of weak solution methods.
3Ease of operation
If direct discretization boundary conditions are used, then the implementation is simple, but the calculation accuracy is reduced near discontinuous surfaces
Solution Approach 1:
The patent maintains the simplicity of direct discretization boundary conditions while improving accuracy by applying local corrections at interface-adjacent grid points. The correction coefficients are calculated based on local impedance contrast, and only these specific grid points are modified, leaving the rest of the simple finite difference implementation unchanged.
Solution Approach 2:
The patent introduces asymmetric correction coefficients for grid points on different sides of the discontinuous surface. The correction coefficient for a grid point depends on the impedance contrast between adjacent media, creating an asymmetric modification that accurately represents the physical interface while maintaining implementation simplicity.
Data Source
AI summary
A media Parameter-modified method for realizing an adaptive expression of an arbitrary discontinuous surface, comprising the following steps: importing an initial forward model, importing anisotropic parameters; and setting a space step and a time step according to the initial forward model parameters; and then starting a stepped discretization of a free surface of the initial forward model; and using a corrected constitutive relationship to correct a first level parameter of the initial forward model; and bringing the corrected constitutive relationship into a displacement stress equation, and the influence of the free surface can be introduced in the case of the anisotropic media after series of operation. The present disclosure can make an accurate numerical simulation of a wave field near the discontinuous surface, and the accurate numerical simulation will contribute to the extraction and analysis of information from the seismic data.