Non-Stationary Matching Filters for Attenuation Compensation in Seismic Imaging
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Solution Overview
Problem
Current methods for compensating attenuation effects in Full Waveform Inversion (FWI) and Reverse Time Migration (RTM) are inefficient, leading to weak amplitudes in subsurface models and images, and require numerous iterations for convergence, due to the poor condition number of the Hessian matrix and high computational costs of wave propagation modeling.
Innovation Solution
The use of non-stationary matching filters (NMFs) to invert a pseudo-Hessian matrix, formed from viscoelastic and elastic wave propagation operators, to compensate for attenuation, providing a more stable and efficient solution by reducing the condition number and avoiding the need for decoupling phase and amplitude effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional attenuation compensation methods are used in FWI and RTM, then the Hessian matrix condition number remains poor, but the computational cost is high and convergence requires numerous iterations
Solution Approach 1:
The patent introduces non-stationary matching filters as an intermediary tool to invert the pseudo-Hessian matrix. These filters act as a mediator between the viscoelastic and elastic wave propagation operators, enabling attenuation compensation without requiring direct inversion of the ill-conditioned Hessian matrix, thus improving both reliability and productivity
Solution Approach 2:
The patent transforms the problematic Hessian matrix inversion problem into a filtering operation by changing the mathematical parameters and operations involved. Instead of directly inverting the pseudo-Hessian matrix with poor condition number, the method uses non-stationary matching filters that operate in the frequency-wavenumber domain, fundamentally changing the approach to achieve attenuation compensation
2Manufacturing precision
If wave propagation modeling is performed with high accuracy, then the subsurface model quality improves, but the computational cost increases significantly
Solution Approach 1:
The patent applies partial action by using non-stationary matching filters that selectively invert the pseudo-Hessian matrix only where needed for attenuation compensation, rather than performing full wave propagation modeling at high accuracy throughout the entire domain. This partial inversion approach achieves the necessary model quality while reducing overall computational cost
3Reliability
If the Hessian matrix is directly inverted for attenuation compensation, then the condition number remains poor, but the solution becomes unstable
Solution Approach 1:
Non-stationary matching filters serve as an intermediary that avoids direct inversion of the unstable Hessian matrix. The filters provide a stable computational pathway by operating in the frequency-wavenumber domain and applying regularization through the filtering process, thereby achieving both solution stability and improved condition number
Solution Approach 2:
The patent substitutes the mechanical matrix inversion process with a filtering operation in the frequency-wavenumber domain. This substitution replaces the unstable direct inversion mechanism with a more stable filtering approach that inherently regularizes the solution and improves the condition number
Data Source
AI summary
A method and apparatus for generating attenuation-compensated images of subsurface region, including: computing an image of the region utilizing elastic wave propagation, based on field data and subsurface model; generating forward-modeled data utilizing forward viscoelastic wave propagation, based on the image; computing secondary image by migration; computing NMF based on the images; and applying the NMF to the image to generate the attenuation-compensated image. A method and apparatus includes: iteratively computing attenuation-compensated gradient of the region utilizing an elastic wave propagation operator in the back-propagation and a viscoelastic wave propagation operator in the forward modelling, based on field data and subsurface model; computing search direction based on the attenuation-compensated gradient, searching for an improved model, and checking the improved model for convergence.