Spectral Shaping for Seismic Inversion Convergence
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Solution Overview
Problem
Iterative inversion methods in geophysical prospecting, such as full wavefield inversion, are computationally expensive due to the high number of simulations required for convergence, making them impractical for field-scale 3D applications, especially when high-resolution subsurface models are needed.
Innovation Solution
The method employs spectral shaping by applying a filter to the gradient of the cost function in the model parameter space to match the known or estimated frequency spectrum of the subsurface region, reducing the number of iterations needed for convergence by ensuring the inversion generates models with the desired frequency spectrum from the first iteration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If iterative inversion methods are used to generate accurate subsurface models, then manufacturing precision is improved, but productivity deteriorates due to the high number of simulations required
Solution Approach 1:
The patent applies spectral shaping filters to the input seismic data and source wavelet before the inversion process begins. This preliminary action pre-adjusts the frequency content of the data to match the expected subsurface spectrum, so that the inversion algorithm starts with optimally conditioned input. This prevents the algorithm from wasting iterations adjusting for spectral mismatches, thereby accelerating convergence while maintaining model accuracy.
Solution Approach 2:
The patent modifies the frequency spectrum parameter of the input data by applying spectral shaping filters. This changes the distribution of energy across different frequencies in the seismic data and source wavelet, aligning it with the target subsurface frequency spectrum. This parameter transformation enables the inversion to converge faster by eliminating spectral mismatches that would otherwise require numerous iterative corrections.
2Productivity
If the number of iterations is increased to improve convergence, then productivity is improved, but use of energy worsens due to computational cost
Solution Approach 1:
By applying spectral shaping filters to the input data and source wavelet before inversion, the patent performs a preliminary conditioning step that reduces the number of iterations needed for convergence. This preliminary action eliminates spectral mismatches in advance, so the inversion algorithm does not need to expend computational energy correcting these issues during the iterative process, thereby reducing overall energy consumption while improving convergence speed.
Solution Approach 2:
The patent transforms the frequency spectrum parameter of the input data to match the target subsurface spectrum. This parameter change optimizes the input conditions for the inversion algorithm, enabling it to converge in fewer iterations and thus reducing the total computational energy required for the inversion process.
Data Source
AI summary
Method for speeding up iterative inversion of seismic data (106) to obtain a subsurface model (102), using local cost function optimization. The frequency spectrum of the updated model at each iteration is controlled to match a known or estimated frequency spectrum for the subsurface region, preferably the average amplitude spectrum of the subsurface P-impedance. The controlling is done either by applying a spectral-shaping filter to the source wavelet (303) and to the data (302) or by applying the filter, which may vary with time, to the gradient of the cost function (403). The source wavelet's amplitude spectrum (before filtering) should satisfy D(f)=fIp(f)W(f), where f is frequency, D(f) is the average amplitude spectrum of the seismic data, and Ip(f) is the average amplitude spectrum for P-impedance in the subsurface region (306,402) or an approximation thereof.