Seismic Signal Interpolation via Iterative Basis Function Selection
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Solution Overview
Problem
Existing seismic interpolation methods, such as Yen's Interpolator and anti-leakage Fourier transformation (ALFT), face challenges with irregular sampling grids, leading to significant errors, especially when dealing with high-wavenumber content and aliased signals, and are not well-suited for multichannel data or gradient measurements.
Innovation Solution
An iterative method that selects and combines basis functions, characterized by n parameters, to represent seismic signals, minimizing the residual between measured and represented signals at each iteration, using techniques like Matching Pursuit and the Lomb spectrum to optimize parameters such as amplitude, phase, and frequency, allowing for improved signal representation and interpolation on irregularly sampled data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional interpolation methods (Yen's Interpolator, ALFT) are used for irregular sampling grids, then the processing can be performed, but significant errors are introduced especially for high-wavenumber content and aliased signals
Solution Approach 1:
The patent employs an iterative optimization process that dynamically adjusts basis function parameters (amplitude, phase, frequency) to minimize residual error between measured and represented signals. This dynamic adaptation allows the method to converge toward the optimal representation, progressively reducing interpolation errors and improving accuracy for complex signal characteristics including high-wavenumber content and aliased signals.
Solution Approach 2:
The method changes the parameters of basis functions (amplitude, phase, frequency) through iterative optimization to achieve the best possible representation of the signal. By adjusting these parameters dynamically during the optimization process, the method adapts to the specific characteristics of the input signal and minimizes reconstruction error, thereby improving interpolation accuracy compared to fixed-parameter conventional methods.
2Measurement precision
If iterative basis function selection is used to improve interpolation accuracy, then measurement precision improves, but computational complexity increases
Solution Approach 1:
The patent implements a feedback mechanism where the residual between the measured signal and the basis function representation is continuously evaluated and used to guide the optimization process. This feedback loop allows the algorithm to iteratively adjust basis function parameters to minimize error, achieving accurate signal representation while maintaining controlled computational complexity through systematic optimization.
Solution Approach 2:
The method replaces conventional mechanical interpolation approaches with an iterative optimization system that uses mathematical basis functions and computational algorithms. This substitution enables more accurate signal representation through flexible mathematical modeling rather than rigid conventional methods, achieving improved precision while managing computational requirements through efficient optimization techniques.
Data Source
AI summary
There is provided a method of interpolating wave signals, particularly seismic signals acquired through a seismic survey, using the steps of obtaining time series of measured wave signals; and selecting iteratively basis functions to represent said measured signals with a basis function being fully defined by n parameters, wherein in each iteration one or more basis functions are combined with the selected basis functions such that the residual between the measured signals and a representation of the measured signal by the combined basis functions is minimized at the locations of the measurement at each iteration.