Seismic Migration Image Distortion Reduction via Least-Squares Regularization
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Solution Overview
Problem
Seismic migration in geological tomography is often distorted due to poor acquisition geometry, limited aperture, noise, and illumination effects, leading to poor quality and blurred images of the Earth's subsurface.
Innovation Solution
The implementation of an image-domain least-squares migration (LSM) technique that approximates the Hessian through point spread functions (PSFs) with L 1 -norm or L 2 -norm regularization and total variation (TV) regularization to reduce artifacts and maintain structural continuity, improving image resolution and reducing migration distortions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional seismic migration is used, then the imaging process is computationally efficient, but the image quality is poor with blurring and artifacts
Solution Approach 1:
The patent applies L1-norm and L2-norm regularization constraints to modify the optimization parameters in the least-squares migration process. These parameter changes constrain the solution space to produce sharper images with reduced artifacts while maintaining computational feasibility through iterative optimization methods.
Solution Approach 2:
The patent implements an iterative least-squares migration process where the migration image is continuously refined by comparing it with the observed seismic data and adjusting the reflectivity model accordingly. This feedback mechanism progressively reduces artifacts and improves image quality through multiple iterations of forward modeling and inversion.
2Measurement precision
If acquisition geometry is improved to reduce distortion, then image accuracy improves, but acquisition cost and complexity increase
Solution Approach 1:
The patent introduces regularization terms as intermediary constraints in the migration optimization process. These intermediary mathematical constraints compensate for the limitations of the acquisition geometry by guiding the inversion process toward solutions that are physically plausible and reduce artifacts, effectively mediating between limited data and high-quality imaging.
3Manufacturing precision
If deblurring is applied to reduce artifacts, then image sharpness improves, but structural continuity may be disrupted
Solution Approach 1:
The patent employs total variation (TV) regularization as a parameter constraint that specifically preserves edges and discontinuities while removing artifacts. The TV norm allows large gradients at geological interfaces while penalizing small-scale noise, thereby maintaining structural continuity during the deblurring process unlike conventional L2-norm methods that tend to oversmooth.
Data Source
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Figure 2
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AI summary
A system and method for reducing migration distortions in migrated images of the Earth's subsurface. Recorded seismic data may be migrated, using a migration velocity model, to generate a migration image comprising distortions. Synthetic seismic data may be generated, using the migration velocity model, for a grid of scattered points. The synthetic seismic data may be migrated, using the migration velocity model, to generate impulse responses for the scattered points. The impulse responses are used as point spread functions (PSFs) which approximates the blurring operator, e.g., the Hessian operator. An optimal reflectivity model may be selected using image-domain least-squares migration (LSM), based on the PSFs, with a regularization of the difference between the migration image and a reflectivity model and a total variation (TV) regularization of the reflectivity model. An image of the optimal reflectivity model may be generated that has reduced migration distortions compared to the original migration image.