Seismic Trace Analysis Using k-Space Fourier Coefficient Re-orthogonalization
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Solution Overview
Problem
Seismic surveys often produce sparsely and unevenly sampled data, which is incompatible with data processing and visualization systems that require densely and regularly sampled data, leading to issues with aliasing and energy leakage.
Innovation Solution
A method that estimates Fourier coefficients using a discrete Fourier transform, applies a coherence criterion to reduce aliased energy, re-orthogonalizes the coefficients in k-space, and uses an inverse Fourier transform to produce regularized seismic data, effectively addressing the problem of aliasing and energy leakage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If seismic survey data is used as-is, then the data represents actual subsurface information, but the data is sparsely and unevenly sampled causing aliasing and energy leakage
Solution Approach 1:
The patent applies parameter changes by transforming the seismic data from the time domain to the frequency-wavenumber domain using Fourier transforms. This changes the representation parameters of the data, allowing aliasing to be identified and corrected in the frequency domain while preserving the original time-domain information integrity.
Solution Approach 2:
The patent uses an intermediary approach by introducing a coherence criterion as a mediator between the raw seismic data and the final processed data. This criterion acts as a filter that separates true subsurface signals from aliased energy, allowing the system to work with irregularly sampled data while producing regularly sampled output.
2Ease of operation
If data is transformed to have appropriate sampling basis, then data processing systems can process the data, but aliasing energy is introduced or exacerbated
Solution Approach 1:
The patent converts the harmful aliasing effect into a beneficial filtering opportunity. By transforming to the frequency domain, the aliasing appears as distinct patterns that can be identified and removed using the coherence criterion, turning the aliasing problem into a signal processing advantage for separating true signals from artifacts.
Solution Approach 2:
The patent extracts and removes aliased energy from the data by applying the coherence criterion in the frequency-wavenumber domain. This extraction process separates the harmful aliased components from the useful subsurface information, allowing the data to be transformed back to the time domain with reduced aliasing.
3Measurement precision
If coherence criterion is applied to reduce aliased energy, then aliasing is reduced, but computational complexity increases
Solution Approach 1:
The patent segments the complex data processing task into distinct manageable steps: forward Fourier transform, coherence criterion application, re-orthogonalization, and inverse Fourier transform. This segmentation allows each step to be optimized independently and makes the overall complex process more manageable and implementable.
Data Source
AI summary
Seismic data are processed to reduce or eliminate aliasing due, for example to sparse or irregular sampling. An iterative method includes an inhibiting function used in conjunction with a function evaluating a magnitude of Fourier coefficients that together act to reduce the effects of aliased energies and preferentially select true energies. Computational steps are conducted primarily in k-space, without returning to x-space, thereby reducing computational costs.