Full Waveform Inversion Using Dynamic Warping to Avoid Cycle-Skipping
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Solution Overview
Problem
Conventional Full Waveform Inversion (FWI) methods suffer from cycle-skipping issues due to mismatched events between predicted and recorded wave fields and numerous local minima, especially when accurate initial velocity models and sufficient low-frequency components are lacking, leading to inaccurate subsurface imaging.
Innovation Solution
A method that uses modified recorded wave fields to connect initial predicted wave fields to observed wave fields, employing dynamic warping to recover travel time differences and a convex objective function to calculate an updated step length, thereby mitigating cycle-skipping effects and improving convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Least-Squares FWI is used to generate high-resolution velocity models, then imaging precision is improved, but cycle-skipping occurs when arrival time differences exceed half a cycle
Solution Approach 1:
The inversion process is segmented into multiple frequency stages, starting from low frequencies and progressively moving to high frequencies. Each stage uses the result from the previous stage as its starting point, dividing the difficult high-frequency inversion into manageable steps that avoid cycle-skipping
Solution Approach 2:
A preliminary low-frequency inversion is performed before the main high-frequency inversion. This preliminary action creates an initial velocity model that is sufficiently accurate to serve as a starting point for the subsequent high-frequency inversion, preventing cycle-skipping from the beginning
2Reliability
If frequency sweeping from low to high is used to avoid cycle-skipping, then convergence reliability is improved, but imaging precision deteriorates due to lack of low-frequency components
Solution Approach 1:
The patent introduces an intermediary approach by using travel-time tomography results as a bridge between the available high-frequency data and the required low-frequency inversion. This intermediary model provides the necessary low-frequency constraints without requiring actual low-frequency seismic data
Solution Approach 2:
The patent changes the parameter representation by transforming the inversion from direct waveform matching to travel-time based inversion first, then using the results to guide the frequency-domain waveform inversion. This parameter transformation allows the use of high-frequency data to achieve low-frequency inversion goals
3Ease of operation
If travel time tomography is used to provide initial velocity model, then ease of operation is improved, but imaging precision deteriorates due to limited common image gather curvatures
Solution Approach 1:
The patent implements a feedback mechanism where the initial velocity model from travel-time tomography is used to generate synthetic seismograms, which are then compared with actual data. The discrepancies feed back into the frequency-domain FWI process to refine the velocity model, correcting the limitations of the initial tomography model
Data Source
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AI summary
Computing device, computer instructions and method for determining an image of a surveyed subsurface. The method includes receiving (700) recorded wave fields D recorded with seismic sensors over the subsurface; generating (704) a series of modified recorded wave fields Dn based on the recorded wave fields D; iteratively applying (706) an objective function Fi to (1) one element Di of the series of modified recorded wave fields Dn and (2) predicted wave fields Pmi, where "i" is an index associated with a given iteration; calculating (712) with a computing device an updated velocity model mi+1 based on a previous velocity model mi and a step length; and producing (714) the image of the subsurface based on the recorded wave fields D and the updated velocity model mi+1. The predicted wave fields Pmi are predicted by the previous velocity model mi.