Time-Varying Filter for Seismic Inversion Convergence
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Solution Overview
Problem
Local objective function optimization methods in seismic data inversion often get stuck in local minima due to the requirement of an accurate starting model, leading to incorrect solutions, as they fail to differentiate between global and local minima effectively.
Innovation Solution
Incorporating a time-varying high-cut filter into the objective function to reduce the number of local minima, where the filter's high-cut frequency decreases with increasing traveltime, allowing for more accurate initial model updates and eventual convergence to the global minimum.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If local objective function optimization is used for seismic data inversion, then computational efficiency is improved, but the method gets stuck in local minima and fails to converge to the global minimum
Solution Approach 1:
The inversion process is segmented into multiple stages with different objective functions. The first stage uses a simplified objective function with fewer local minima to obtain an initial model, while the second stage uses the original objective function to refine the solution. This segmentation allows the method to achieve both computational efficiency and reliable convergence.
Solution Approach 2:
A preliminary inversion stage is performed using an altered objective function to produce an initial model that is already close to the global minimum. This preliminary action prepares the starting model for the final inversion stage, ensuring that the efficient local optimization can converge to the correct solution without getting stuck in local minima.
2Reliability
If an accurate starting model is used for local inversion, then convergence to the global minimum is improved, but the accuracy requirements on the starting model become too strict
Solution Approach 1:
The method performs a preliminary inversion using an altered objective function to generate an initial model. This preliminary action relaxes the accuracy requirements because the altered objective function has fewer local minima, making it easier to obtain a starting model that is sufficiently accurate for the final inversion stage.
Solution Approach 2:
The objective function is altered by changing parameters such as the weighting matrix or regularization terms to reduce the number of local minima. This parameter change allows the use of less accurate starting models while still achieving reliable convergence to the global minimum in the final inversion stage.
3Reliability
If multi-resolution inversion is applied to reduce local minima, then the number of local minima is reduced, but computational cost increases
Solution Approach 1:
The inversion is segmented into two stages: a preliminary stage with an altered objective function that has fewer local minima, and a final stage with the original objective function. This segmentation reduces computational cost compared to full multi-resolution inversion because the expensive final stage only needs to refine a model that is already close to the solution, rather than performing complete inversion at multiple resolutions.
Solution Approach 2:
A preliminary inversion stage is performed to obtain an initial model close to the global minimum. This preliminary action reduces the computational cost of the final stage by starting from a better initial model, thereby reducing the number of iterations needed and lowering overall computational expense.
Data Source
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AI summary
An improved method for reducing the accuracy requirements on the starting model when performing multi-scale inversion of seismic data (65) by local objective function optimization (64). The different scales of inversion are brought about by incorporating a low-pass filter into the objective function (61), and then decreasing the amount of high- frequency data that is filtered out from one scale to the next. Moreover, the filter is designed to be time varying, wherein the filter's low-pass cutoff frequency decreases with increasing traveltime of the seismic data being filtered (62). The filter may be designed using Pratt' s criterion for eliminating local minima, and performing averages (or other statistical measure) of the period and the traveltime error only with respect to source and receiver location but not traveltime (63).