Reverse Time Migration Using an Approximate Inverse Operator
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Solution Overview
Problem
Traditional least-squares reverse time migration technologies require numerous iterations due to the use of an adjoint operator that is not the inverse of the modeling operator, leading to lower imaging efficiency and accuracy.
Innovation Solution
A method utilizing an approximate asymptotic inverse operator for the scattering potential, derived based on the relationship between the reflectivity function and the scattering potential, reduces the number of iterations by using observed data or data residuals as boundary conditions for back-propagation, thereby obtaining a true-amplitude back-propagated receiver-side wavefield.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the adjoint operator is used as the migration operator in traditional least-squares reverse time migration, then the iterative inversion can be implemented, but the number of iterations required is large leading to low imaging efficiency
Solution Approach 1:
The patent changes the fundamental parameter of the migration operator from the adjoint operator to an approximate asymptotic inverse operator. This parameter change transforms the operator's mathematical properties, making it a true inverse of the modeling operator rather than just an adjoint, thereby reducing the number of iterations needed while maintaining imaging accuracy.
Solution Approach 2:
The patent constructs an approximate asymptotic inverse operator that copies the essential inverse properties of the modeling operator. By creating this approximate copy with optimized mathematical characteristics, the method achieves the inverse effect more efficiently without requiring numerous iterations of the traditional adjoint operator approach.
2Measurement precision
If numerous iterations are performed to achieve the inverse effect of the modeling operator, then imaging accuracy can be improved, but computational cost increases significantly
Solution Approach 1:
The patent changes the operator parameter from adjoint to approximate asymptotic inverse, which fundamentally alters the convergence behavior of the iterative process. This parameter change reduces the number of iterations required to achieve the same imaging accuracy, thereby lowering computational cost.
Solution Approach 2:
The patent performs preliminary construction of the approximate asymptotic inverse operator with optimized mathematical properties before the iterative inversion process. This preliminary action prepares the operator to achieve the inverse effect more directly, reducing the number of subsequent iterations and associated computational costs.
3Measurement precision
If the adjoint operator is used for iterative inversion, then least-squares migration can compensate for uneven illumination and enhance resolution, but the application efficiency is significantly limited
Solution Approach 1:
The patent changes the migration operator parameter from adjoint to approximate asymptotic inverse, which maintains the ability to compensate for uneven illumination and enhance resolution while dramatically improving application efficiency by reducing iteration requirements.
Solution Approach 2:
The patent creates an approximate asymptotic inverse operator that copies the beneficial properties of the adjoint operator for illumination compensation and resolution enhancement, while adding the improved property of requiring fewer iterations for convergence.
Data Source
AI summary
A least-squares reverse time migration method, system, terminal, and non-transitory computer-readable storage medium. The method includes: establishing a modeling operator based on the scattering potential, construct an approximate asymptotic inverse operator for the reflectivity function, build a relationship between the reflectivity function and the scattering potential, and obtain an approximate asymptotic inverse operator for the scattering potential based on the approximate asymptotic inverse operator for reflectivity and the relationship; acquiring seismic data collected by receivers as observed data, and performing imaging based on the approximate asymptotic inverse operator and the observed data to obtain an initial image; generating predicted data based on the initial image and the modeling operator, and calculating data residual between the observed data and the predicted data; iteratively updating the initial image based on the data residual and the approximate asymptotic inverse operator to obtain a target image. The imaging efficiency is improved.