Anisotropic Regularization for CSEM Inversion Stability
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Solution Overview
Problem
Current electromagnetic inversion methods for subsurface geological exploration, such as mCSEM, face challenges with non-uniqueness and un-physical results due to ill-posedness and lack of representation of geological geometry, leading to difficulties in interpreting resistivity profiles effectively.
Innovation Solution
A Tikhonov-type structural smoothing regularization approach is introduced, which uses seismic data to determine the directionality and strength of regularization, discretizing the model to conform with stratigraphic surfaces and varying weights based on seismic chaos attributes, ensuring smoother profiles where data is confident and allowing variations where uncertain, thus aligning regularization with geological structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If uniform smoothing regularization is applied in horizontal and vertical directions, then the inversion problem becomes better conditioned and produces stable results, but the results fail to represent geological geometry and produce un-physical resistivity profiles
Solution Approach 1:
The patent applies different regularization strengths in different spatial locations and directions. Specifically, it uses an anisotropic regularization operator that applies stronger smoothing perpendicular to geological interfaces and weaker smoothing parallel to interfaces, allowing the regularization to adapt to local geological structures rather than applying uniform smoothing throughout the model space.
Solution Approach 2:
The patent introduces directional information by considering the orientation of geological interfaces. It transforms the conventional isotropic regularization into an anisotropic one by incorporating the dip angle and strike direction of interfaces, effectively adding directional dimensions to the regularization process to better constrain the inversion along geologically meaningful directions.
2Device complexity
If the regularization term is weighted uniformly, then the optimization problem is simpler to solve, but the trade-off between data fidelity and regularizing information cannot be properly balanced
Solution Approach 1:
The patent makes the regularization weights dynamic and adaptive rather than static and uniform. The weights are calculated based on local geological properties such as interface dip angles and seismic data quality, allowing the regularization strength to vary automatically across different regions of the model based on local confidence and geological complexity.
3Stability of the object's composition
If conventional smoothing regularization is used, then the resistivity profile becomes smooth and stable, but sharp geological interfaces are blurred and interpretation becomes difficult
Solution Approach 1:
The patent applies different regularization strengths in different spatial locations and directions. Specifically, it uses an anisotropic regularization operator that applies stronger smoothing perpendicular to geological interfaces and weaker smoothing parallel to interfaces, allowing the regularization to adapt to local geological structures rather than applying uniform smoothing throughout the model space.
Data Source
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AI summary
A method of estimating electromagnetic parameters of a geological structure, comprising: providing controlled source electromagnetic, CSEM, data of the structure, calculating a numerical model representing electromagnetic parameters of the structure and generating simulated CSEM data, discretising the numerical model based on prior knowledge of the structure, defining a functional for minimising the distance between said simulated CSEM data and said CSEM data, wherein the functional comprises a regularisation term which depends on prior knowledge of said structure.