Seismic Full Waveform Inversion Using Matching Filter Misfit
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Solution Overview
Problem
Traditional full waveform inversion (FWI) methods face challenges such as cycle skipping, cross-talk issues, and instability due to the use of conventional misfit functions like the l2 norm and optimal transport, especially in complex reflectivity regions and with broadband data, leading to inaccurate subsurface model updates.
Innovation Solution
The method introduces a Radon transform to separate seismic events, uses a Rytov approximation for the adjoint source, and selects a misfit function that measures the distance between a matching filter and a Dirac Delta function or travel time shift, preserving the phase and amplitude of seismic data to stabilize the inversion process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the l2 norm misfit function is used for its simplicity and potential for high-resolution models, then manufacturing precision is improved, but reliability deteriorates due to severe cycle skipping limitations and susceptibility to local minima
Solution Approach 1:
The patent changes the parameter of the misfit function from the conventional l2 norm to a matching filter-based misfit function that measures the distance between the matching filter and a Dirac Delta function. This parameter change resolves the cycle skipping issue by transforming the comparison from point-to-point subtraction to a global deconvolution-based comparison, thereby improving reliability while maintaining model resolution capability.
2Reliability
If the matching filter based misfit function is used to resolve cycle skipping, then reliability is improved, but device complexity increases due to the extended function computation using deconvolution
Solution Approach 1:
The patent introduces a matching filter as an intermediary element that when applied to the observed or predicted seismic data reproduces the other dataset. This intermediary approach simplifies the misfit function computation by avoiding direct deconvolution of the entire trace, thereby reducing computational complexity while maintaining the reliability benefits of the matching filter approach.
3Reliability
If the extended function by deconvolution is used for global comparison, then reliability is improved by resolving cycle skipping, but object-generated harmful factors worsen due to unwanted cross-talk of different events
Solution Approach 1:
The patent extracts and isolates the matching filter computation from the full trace deconvolution process. By focusing the matching filter on specific seismic events and using it to reproduce the other dataset, the method separates the useful signal comparison from the harmful cross-talk between different events, thereby maintaining reliability while eliminating cross-contamination.
4Ease of operation
If traditional misfit functions are used in complex reflectivity regions, then ease of operation is maintained, but measurement precision deteriorates due to cross-talk and hampered effectiveness
Solution Approach 1:
The patent applies local quality by making the matching filter event-specific rather than applying a uniform misfit function across all seismic data. The matching filter is computed and applied locally to match specific seismic events between observed and predicted data, thereby improving measurement precision in complex reflectivity regions while maintaining operational feasibility through the systematic matching filter application process.
Data Source
AI summary
A method for calculating a velocity model for a subsurface of the earth. The method includes receiving (200) measured seismic data d; calculating (204) predicted seismic data p; selecting (206) a matching filter w that when applied to one of the measured seismic data d or the predicted seismic data p reproduces the other one of the measured seismic data d or the predicted seismic data p; selecting (208) a misfit function J that calculates (1) a distance between the matching filter w and a Dirac Delta function or (2) a travel time shift associated with the measured seismic data; and calculating (218) a new velocity model using the misfit function J, the measured seismic data d, and the predicted seismic data p. The measured seismic data d includes wavefields generated by a seismic source and the wavefields propagate through the subsurface where they are attenuated and reflected, and the attenuated and reflected wavefields are recorded by plural seismic receivers.