Seismic Data Interpolation via Pairwise Hankel Tensor Completion
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Solution Overview
Problem
Conventional interpolation techniques struggle with noisy and sparse seismic data, particularly in multi-dimensional grids, leading to poor performance in 5D interpolation for 3D seismic surveys.
Innovation Solution
The method employs pairwise Hankel tensors to interpolate seismic data by forming tensors from acquired seismic data, performing tensor completion on each tensor to recover interpolated frequency slices, and combining these with original data to form complete trace data, utilizing a processor to streamline the process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional interpolation techniques are used for 5D interpolation in 3D seismic surveys, then the method is simple to implement, but the processing speed is slow and performance is poor with noisy and sparse data
Solution Approach 1:
The patent segments the seismic data interpolation problem into multiple frequency slices, processing each slice independently through tensor completion. This division allows parallel processing of different frequency components, significantly improving overall processing speed while maintaining manageable complexity for each individual slice.
Solution Approach 2:
The patent transforms the interpolation problem from conventional spatial domain methods to the frequency domain by creating pairwise Hankel tensors from frequency slices. This dimensional transformation enables more efficient tensor completion algorithms to be applied, achieving three-fold improvement in processing speed for 5D interpolation.
2Measurement precision
If conventional interpolation techniques are used, then the implementation is straightforward, but accuracy is poor with noisy and sparse seismic data
Solution Approach 1:
The patent changes the parameter representation by transforming seismic data into the frequency domain and representing it as pairwise Hankel tensors. This parameter transformation enables the application of tensor completion techniques that are more robust to noise and sparsity, significantly improving interpolation accuracy for 5D seismic data.
Solution Approach 2:
The patent replaces conventional interpolation algorithms with tensor completion methods operating on Hankel tensors. This substitution introduces a more sophisticated mathematical framework that better handles the complexities of noisy and sparse seismic data, achieving superior accuracy despite increased processing complexity.
3Productivity
If pairwise Hankel tensor completion is used for 5D interpolation, then processing speed improves three-fold, but the method complexity increases
Solution Approach 1:
The patent performs preliminary actions by pre-organizing seismic data into frequency slices and constructing pairwise Hankel tensors before applying completion algorithms. This preparatory structuring of data enables the subsequent tensor completion to proceed more efficiently, achieving three-fold speed improvement while making the complex method more manageable through systematic data organization.
Data Source
AI summary
A system and method of interpolating seismic data is provided. The system and method form a plurality of pairwise Hankel tensors from acquired seismic data, and a respective pairwise Hankel tensor for each of a plurality of originally collected frequency slices, perform tensor completion on each of said pairwise Hankel tensors to recover a plurality of interpolated frequency slices, and combine said plurality of interpolated frequency slices with said originally collected frequency slices to form a set of trace data of a geographical area of interest.