Seismic Data Reconstruction via Frequency Domain Transformation
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Solution Overview
Problem
Seismic imaging faces challenges in efficiently reconstructing data from irregularly acquired seismic data due to issues like dead or corrupted traces, surface obstacles, and economic limitations, where existing methods require a predefined nominal grid and are computationally expensive, especially when prior information is lacking.
Innovation Solution
The implementation of an analysis-based optimization model using the SeisADM algorithm, which adapts the alternating direction method with variable-splitting techniques, and an interpolated compressive sensing method that allows data reconstruction on any specified nominal grid, along with a mutual coherence proxy for optimizing sampling grids, reducing computational costs and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional seismic data reconstruction methods are used with predefined nominal grids, then data can be reconstructed on a regular grid, but the computational cost becomes excessively high and prior information is required
Solution Approach 1:
The patent transforms the reconstruction problem by changing the parameter representation from spatial domain to frequency domain (k-domain). By applying the Fourier transform and working with the wavenumber spectrum, the method enables efficient reconstruction without requiring iterative optimization on the spatial grid, thereby reducing computational time while maintaining accuracy
Solution Approach 2:
The patent replaces the traditional iterative optimization mechanical process with a direct spectral method. Instead of repeatedly adjusting spatial parameters through optimization algorithms, the method substitutes this with a single Fourier transform operation in the frequency domain, dramatically reducing computational steps and time
2Quantity of substance
If irregular sampling grids are used to reduce acquisition costs, then fewer measurements are needed, but the data reconstruction becomes more difficult and requires advanced processing techniques
Solution Approach 1:
The patent moves the processing from the spatial dimension to the frequency dimension. By transforming irregularly spaced spatial measurements into the wavenumber domain via Fourier transform, the method exploits the periodicity and structure in the frequency domain to simplify reconstruction, turning a complex spatial interpolation problem into a more manageable spectral analysis problem
Solution Approach 2:
The patent changes the representation parameters from spatial coordinates to wavenumber frequencies. This parameter transformation allows the use of spectral estimation techniques that are computationally efficient and naturally handle irregular sampling patterns, reducing processing complexity compared to spatial domain methods
3Loss of information
If compressive sensing with l1 norm optimization is applied, then sparse representation of seismic data is achieved, but the computational burden increases due to solving convex optimization problems
Solution Approach 1:
The patent substitutes the iterative convex optimization mechanism with a direct spectral method. Instead of solving the l1 minimization problem through repeated optimization iterations, the method uses Fourier transform and spectral analysis to directly obtain the sparse representation, eliminating the computational burden of optimization while preserving sparsity
Solution Approach 2:
The patent creates a spectral copy of the spatial domain data through Fourier transform. By working with this frequency domain copy rather than the original spatial data, the method achieves sparse representation through spectral concentration rather than optimization, significantly reducing computational time
4Measurement precision
If a fine nominal grid is used for reconstruction, then higher resolution data is obtained, but the cost and time savings of irregular versus regular survey design become insignificant
Solution Approach 1:
The patent resolves this contradiction by moving to the frequency domain where resolution is determined by spectral sampling density rather than spatial grid density. In the wavenumber domain, one can achieve high resolution with fewer measurements by exploiting the concentrated energy in specific frequency bands, maintaining fine effective resolution while preserving the cost benefits of irregular sampling
Data Source
AI summary
A method for 2D seismic data acquisition includes determining source-point seismic survey positions for a combined deep profile seismic data acquisition with a shallow profile seismic data acquisition wherein the source-point positions are based on non-uniform optimal sampling. A seismic data set is acquired with a first set of air-guns optimized for a deep-data seismic profile and the data set is acquired with a second set of air-guns optimized for a shallow-data seismic profile. The data are de-blended to obtain a deep 2D seismic dataset and a shallow 2D seismic dataset.