Seismic Interpolation via Radon Transform
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Solution Overview
Problem
Irregularly spaced geophones in seismic surveys due to physical obstructions or drift cause poor resolution and accuracy in seismic tomographic images, as conventional interpolation methods are inefficient and prone to aliasing effects.
Innovation Solution
The method employs a Radon transform to interpolate seismic data exclusively in the frequency-Radon domain, pre-computing basis function correlation factors and iteratively computing anti-leakage Radon coefficients, which reduces computational complexity and memory requirements, and simulates data as if collected from regularly spaced geophones.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional interpolation methods are used to handle irregularly spaced geophones, then the method can process seismic data, but the computational efficiency is poor and aliasing effects occur
Solution Approach 1:
The patent transforms the seismic data from the spatial domain to the frequency-Radon domain, changing the dimensionality of the data representation. This transformation allows the interpolation to be performed in a different mathematical space where irregular sampling can be handled more efficiently, reducing both computational complexity and aliasing effects while maintaining accuracy.
Solution Approach 2:
The patent changes the parameters of the data representation by using the Radon transform to convert seismic data into the frequency-Radon domain. This parameter transformation enables the use of basis function correlation factors and iterative anti-leakage Radon coefficients, which significantly improves computational efficiency and reduces aliasing compared to conventional spatial domain interpolation methods.
2Productivity
If conventional interpolation methods are used, then seismic data can be processed, but memory requirements and computational complexity are high
Solution Approach 1:
By moving the interpolation problem to the frequency-Radon domain through the Radon transform, the patent reduces the computational complexity. The transformation converts the difficult spatial interpolation problem into a simpler problem involving basis function correlation factors and iterative coefficient computation in the transformed domain, significantly reducing both time and memory requirements.
Solution Approach 2:
The patent pre-computes basis function correlation factors in the frequency-Radon domain before performing the actual interpolation. This preliminary computation allows the main interpolation process to proceed more efficiently using these pre-derived factors, reducing the overall computational burden and speeding up the interpolation process.
3Adaptability or versatility
If geophones are irregularly spaced due to physical obstructions or drift, then data collection is possible in challenging environments, but image resolution and accuracy deteriorate
Solution Approach 1:
The frequency-Radon domain serves as an intermediary space between the irregularly sampled spatial data and the desired regular grid output. By transforming the data to this intermediate domain, processing it with the anti-leakage Radon transform and basis function correlation factors, and then transforming back, the method effectively bridges the gap between irregular sampling conditions and high-resolution imaging requirements.
Solution Approach 2:
The iterative anti-leakage Radon transform process incorporates feedback mechanisms where the computed Radon coefficients are used to progressively improve the interpolation accuracy. The iterative process allows the method to adapt to the irregular sampling pattern and converge on a high-resolution image that accurately represents the subsurface despite the challenging acquisition conditions.
Data Source
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AI summary
A system and method for interpolating seismic data collected by a set of geophones arranged in an irregularly spaced grid by: transforming the collected seismic data by a Radon transform; precomputing a set of basis function correlation factors by geometrically scaling a spatial geometry of each temporal frequency slice of the transformed seismic data independently by its temporal frequency; computing, solely in the transformed domain, an anti-leakage Radon transform of the seismic data by computing each Radon coefficient independently for each temporal frequency slice using the pre-computed basis function correlation factors, until a relative error between the collected seismic data and an approximation of the collected seismic data based on the Radon coefficients is less than a predetermined convergence threshold; and simulating seismic data collected in a regularly spaced grid by interpolating the anti-leakage Radon transform of the collected seismic data in the irregularly spaced grid.