Fast Line Search in Frequency Domain FWI
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Solution Overview
Problem
The existing seismic data inversion methods, particularly in the frequency domain, require repeated and computationally expensive matrix factorizations during line searches in FWI, leading to increased CPU time and memory usage due to changes in model parameters, especially in 3D problems.
Innovation Solution
A fast, perturbation-based approach that leverages stored matrix factors to efficiently update the wavefield by computing model updates through perturbation theory, reducing the need for repeated factorizations during line searches by using small model parameter changes and stored factors for quick wavefield evaluations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If matrix factorization is performed repeatedly during line search in frequency domain FWI, then accurate wavefield evaluation is achieved, but CPU time and memory usage increase significantly
Solution Approach 1:
The matrix factorization is performed once in advance before the line search, and the factors are stored. During the line search, these pre-computed factors are reused to evaluate wavefields for different model parameters, avoiding repeated factorizations and significantly reducing CPU time while maintaining evaluation accuracy
Solution Approach 2:
The matrix factors obtained from a single factorization are made universal and can be used to evaluate wavefields for multiple different model parameter values during the line search, making the factorization result applicable to multiple scenarios without re-computation
2Measurement precision
If matrix factorization is performed repeatedly during line search in frequency domain FWI, then accurate wavefield evaluation is achieved, but memory usage increases due to storing multiple factorizations
Solution Approach 1:
The matrix factorization is performed once in advance and the factors are stored in memory. During the line search, these pre-computed factors are reused for all wavefield evaluations, avoiding the need to store multiple separate factorizations and thus reducing memory usage
Solution Approach 2:
Instead of performing separate factorizations for different model parameters (which would require storing multiple factorization results), the method changes the approach by using the same factorization factors with updated model parameters, reducing memory requirements while maintaining accuracy
3Measurement precision
If complete new wavefield computation is performed at each line search step, then accurate misfit computation is achieved, but computational cost increases significantly
Solution Approach 1:
The matrix factorization is performed once in advance, and the factors are stored for reuse. During line search, wavefields are computed using these pre-computed factors with updated model parameters, avoiding complete re-computations and significantly improving computational efficiency while maintaining misfit computation accuracy
Solution Approach 2:
Instead of performing complete new wavefield computations at each line search step, the method uses partial updates by reusing the pre-computed matrix factors and only recomputing the necessary components with updated model parameters, reducing computational cost while maintaining sufficient accuracy
Data Source
AI summary
Method for rapidly computing updates to frequency-domain seismic wave fields by utilizing a matrix perturbation approach. The method speeds up model (e.g., velocity) parameter estimation by iterative inversion of measured seismic data. The method applies to the line search where the optimal size of the model update is estimated by testing different size updates to see which one generates the minimum objective function. By treating the model update as a perturbation, perturbation theory is used to relate the model perturbation to a corresponding wavefield perturbation. Thus, the Helmholtz equation is solved only once per iteration cycle.