FFT Vectorization for 3D Elastic Wave Propagation
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Solution Overview
Problem
Current methods for processing marine seismic signals are inefficient, particularly in three-dimensional elastic wave propagation, due to limitations in conventional Fast Fourier Transform (FFT) algorithms, which affect the accuracy and speed of seismic data interpretation for hydrocarbon deposit detection.
Innovation Solution
The implementation of a vectorization scheme for high-dimensional FFTs optimizes the processing of elastic wave propagation data, improving efficiency by more than a factor of two compared to standard FFT algorithms, enabling faster and more accurate simulation and display of wave propagation underground geographical features.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional FFT algorithms are used for processing marine seismic signals, then the processing method is simple and easy to implement, but the processing speed is slow and efficiency is low
Solution Approach 1:
The patent applies segmentation by dividing the high-dimensional FFT processing into multiple one-dimensional FFT operations along different dimensions. The 3D elastic wave propagation data is processed by sequentially applying FFT along the x, y, and z dimensions, breaking down the complex high-dimensional transformation into manageable 1D operations that can be efficiently computed
Solution Approach 2:
The patent utilizes dimensionality change by transforming the processing approach from direct high-dimensional FFT to a series of 1D FFT operations across multiple dimensions. This allows the algorithm to leverage the structure of multi-dimensional data and apply efficient 1D FFT routines repeatedly, achieving O(N log N) complexity for each dimension while maintaining overall efficiency
2Measurement precision
If conventional FFT algorithms are used for three-dimensional elastic wave propagation, then the implementation is straightforward, but the processing efficiency is insufficient and accuracy is affected
Solution Approach 1:
The patent segments the 3D elastic wave propagation calculation into separate 1D FFT operations along each spatial dimension. This segmentation allows for more precise control over the transformation process in each dimension, maintaining numerical accuracy while enabling parallel computation and optimization of each 1D FFT stage
Solution Approach 2:
The patent maintains continuity of useful action by performing FFT operations along all three dimensions (x, y, z) of the elastic wave propagation data. This ensures that the full 3D spatial frequency information is captured and processed, preserving the accuracy of the wave propagation simulation while enabling efficient computation through the systematic application of 1D FFTs
Data Source
AI summary
Numerical simulations of elastic wave propagation algorithms are critical components for seismic imaging and inversion. Finite-difference schemes yield good efficiency but cannot ensure the accuracy of the high frequency component. Pseudo-spectral algorithms are accurate up to the Nyquist frequency, but its efficiency depends on the optimization of the fast Fourier transform (FFT) algorithm. The conventional FFT algorithms are optimized for signal processing, in which problems are generally one dimensional time series. For 3D wave propagation, FFT algorithms have the potential to be further optimized. Under current computer hardware architecture, a vectorization scheme for high dimensional FFTs is presented. Compared to conventional numerical scheme implementations, the systems and methods disclose herein has the best performance on the slowest or higher dimensions of data. For elastic wave propagation, vectorization improves the efficiency by more than a factor of two when compared to standard FFT algorithms.