Optimal Seismic Reflectivity Inversion: Data-driven ℓ -loss-ℓ -regularization Sparse Regression.

Area of Science:

• Geophysics
• Seismic Data Processing
• Inversion Techniques

Background:

• Seismic reflectivity inversion is crucial for detailed subsurface understanding, often relying on the convolution model and optimization.
• The L1 norm is commonly used for regularization in seismic inversion to mitigate noise, but its optimality is not definitively proven.
• Existing methods face limitations in noise/interference vulnerability and may not represent the best choice for regularization.

Purpose of the Study:

• To propose an optimal seismic reflectivity inversion approach that moves beyond unproven fixed regularization norms.
• To develop a method that adaptively selects regularization parameters for more accurate and detailed reflectivity profiles.
• To enhance seismic inversion results by optimizing the damping factor using K-fold cross-validation.

Main Methods:

• Implementation of a non-convex constraint for seismic inversion utilizing L_p-loss-L_q-regularization (p=2, 0
• Application of the majorization-minimization algorithm for solving the optimization problem.
• Utilization of K-fold cross-validation to determine the optimal damping factor (λ).

Main Results:

• The proposed method estimates a more accurate and detailed reflectivity profile by adaptively adopting L_p-loss-L_q-regularization.
• Optimization of the damping factor through K-fold cross-validation further improves seismic inversion outcomes.
• Validation of the approach through synthetic examples and a field dataset from the Bohai Bay Basin, China.

Conclusions:

• The adaptive L_p-loss-L_q-regularization approach offers a superior alternative to fixed L1 norm regularization in seismic inversion.
• The integration of K-fold cross-validation effectively optimizes the damping factor, leading to enhanced inversion performance.
• The proposed method demonstrates significant potential for improving the accuracy and detail of subsurface imaging in geophysical exploration.