Seismic Imaging Time Dispersion Error Compensation
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Solution Overview
Problem
Current seismic imaging methods, particularly those using finite difference (FD) methods for wave propagation, suffer from significant time dispersion errors that distort seismic data and images, especially at high frequencies and long offsets, leading to inaccurate positioning of reflectors and increased computational costs when trying to reduce these errors.
Innovation Solution
The method involves calculating and compensating for predicted time dispersion errors using a Forward Time Dispersion Transform (FTDT) and Inverse Time Dispersion Transform (ITDT), which estimate and correct phase shifts in seismic wave data, allowing for accurate seismic imaging with reduced computational overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If large sampling rate of discretization is used to improve efficiency of wave propagation calculation, then computational efficiency is improved, but numerical dispersion errors increase severely
Solution Approach 1:
The patent applies spectral methods which fundamentally change the mathematical approach from finite difference to frequency-domain processing. This parameter change in the calculation method allows achieving both high computational efficiency and high accuracy by using Fourier transforms and wavenumber filtering, avoiding the numerical dispersion problems inherent in time-domain finite difference methods with large time steps
Solution Approach 2:
The patent replaces the mechanical finite difference approximation with a spectral approach using Fourier transforms. This substitution changes the fundamental mechanism from discrete difference equations to continuous frequency-domain operations, eliminating numerical dispersion while maintaining computational efficiency through optimized spectral algorithms
2Manufacturing precision
If spectral methods are used to reduce spatial dispersion, then spatial accuracy is improved, but time extrapolation errors increase due to one side extrapolation
Solution Approach 1:
The patent extracts and corrects the time dispersion component separately from the spatial processing. By identifying and removing the one-sided extrapolation error through inverse time dispersion transform, the method retains the spatial accuracy benefits of spectral methods while eliminating the time domain inaccuracies
Solution Approach 2:
The patent introduces an intermediary correction step using inverse time dispersion transform between the forward and backward propagation processes. This intermediary operation compensates for the time extrapolation errors without affecting the spatial accuracy already achieved by the spectral methods
Data Source
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AI summary
A method, system and non-transitory computer-readable medium for forming a seismic image of a geological structure are provided. After obtaining seismic wave data including a plurality of seismic wave traces at a first region of the geological structure, a predicted time dispersion error of an actual time dispersion error that results from a use of a finite difference approximation in calculating predicted seismic wave data at a second region of the geological structure as if a seismic wave propagates from the first region to the second region of the geological structure, is calculated. A corrected predicted seismic wave data at the second region of the geological structure is calculated by applying the finite difference approximation to the seismic wave data at the first region of the geological structure compensated with the predicted time dispersion error. A seismic image of the second region of the geological structure is generated using the corrected predicted seismic wave data, such that the actual time dispersion error is negated by the predicted time dispersion error.