Generalized Spectral Decomposition for Seismic Resolution
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Solution Overview
Problem
Current seismic spectral decomposition methods, such as DFT and CWT, face challenges in achieving balanced temporal and spectral resolution, with DFT being inadequate for short events and CWT providing high temporal but poor spectral resolution, while also being difficult to parameterize and prone to instability.
Innovation Solution
A computer-implemented method for constructing a seismic image using a generalized spectral decomposition that allows for flexible wavelet design with three parameters: frequency, number of cycles, and phase, enabling enhanced control over vertical and frequency resolution, and avoiding the use of 'scale' and 'number of vanishing moments' parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If DFT method is used for evaluating spectral characteristics of long windows, then spectral resolution is improved, but temporal resolution deteriorates
Solution Approach 1:
The patent segments the long window into multiple shorter windows, each processed with DFT to achieve both good spectral resolution and improved temporal resolution through overlapping analysis segments
Solution Approach 2:
The patent dynamically adjusts the window length and overlap based on the local characteristics of the seismic signal, allowing adaptive optimization of the trade-off between spectral and temporal resolution
2Measurement precision
If SWFT method uses a long wavelet, then spectral resolution is improved, but vertical resolution deteriorates
Solution Approach 1:
The patent employs dynamic wavelet length adjustment where the wavelet length varies adaptively based on the local frequency content and signal characteristics, enabling simultaneous achievement of good spectral and vertical resolution
3Loss of time
If CWT method uses a short wavelet, then temporal resolution is improved, but spectral resolution deteriorates
Solution Approach 1:
The patent segments the analysis into multiple frequency bands, applying short wavelet transforms at higher frequencies for temporal resolution while using longer wavelets at lower frequencies for spectral resolution
Solution Approach 2:
The patent dynamically adjusts the wavelet scale and shape based on the local signal characteristics, allowing the wavelet to adapt its length to maintain optimal temporal and spectral resolution across different frequency content
4Measurement precision
If MEM method is used, then spectral resolution may be improved, but parameterization difficulty and instability increase
Solution Approach 1:
The patent replaces the complex and unstable MEM parameterization with simpler, more robust wavelet-based parameters that are easier to control and produce more stable results while maintaining spectral resolution
Data Source
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AI summary
A method for decomposing a signal includes receiving sampled data. A wavelet is built using the sampled data that includes a plurality of samples. The wavelet includes a number of oscillations per sampling unit, and a length of the wavelet corresponds to the number of oscillations. The wavelet is time-shifted. The wavelet is then scaled such that the samples proximate to one or both ends of the wavelet decay toward zero. The wavelet is also scaled such that an amplitude at a peak frequency of the wavelet, when transformed into a Fourier domain, is substantially unity. The method may include a flexible and natural parameterization, which may allow the user to design any wavelet shape in the continuum between short-window Fourier Tranform (SWFT) and continuous wavelet transform (CWT).