3D Angle Gathers via Anti-Leakage Fourier Transform
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Solution Overview
Problem
Current seismic imaging methods face challenges in accurately generating high-resolution subsurface images, particularly in complex areas with poor seismic illumination and velocity model uncertainties, leading to inefficient algorithms and artifacts in common image gathers (CIGs).
Innovation Solution
The method involves calculating angle domain common image gathers (ADCIGs) using wavefield forward and back propagation, anti-leakage Fourier transform (ALFT), and inverse fast Fourier transform (FFT) to transform wavefields into the wavenumber domain, determining reflection and azimuth angles, and converting them back to the space domain, which enhances imaging accuracy and reduces computational costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional Kirchhoff migration is used for prestack depth imaging, then the algorithm is efficient when the number of input traces is small, but the manufacturing precision and reliability of subsurface imaging deteriorates in complex areas with poor seismic illumination
Solution Approach 1:
The patent transforms the imaging problem from the space domain to the wavenumber domain by applying Fourier transforms. This parameter change allows the migration algorithm to handle complex subsurface structures more effectively while maintaining computational efficiency. The wavenumber domain representation enables better handling of wave propagation characteristics in areas with poor seismic illumination.
Solution Approach 2:
The patent introduces an intermediary Fourier transform step that acts as a bridge between the input seismic data and the final migrated image. By working in the wavenumber domain and then transforming back, the method mediates between the conflicting requirements of efficiency and accuracy, particularly for wide azimuth surveys with large numbers of input traces.
2Manufacturing precision
If the number of input traces is increased to improve imaging coverage in complex areas, then the manufacturing precision improves, but the device complexity and computational cost increase significantly
Solution Approach 1:
The patent replaces the direct spatial domain convolution operation with an equivalent operation in the wavenumber domain. This substitution transforms a computationally intensive process that scales poorly with the number of traces into a more efficient frequency-domain operation, reducing the computational complexity growth rate as more input traces are incorporated.
3Ease of manufacture
If traditional Fourier transform is used for wavenumber domain transformation, then the transformation is straightforward, but spectral leakage occurs that degrades the manufacturing precision of angle domain common image gathers
Solution Approach 1:
The patent extracts and removes the harmful spectral leakage effect by applying a window function to the spatial domain data before performing the Fourier transform. This extraction of the leakage problem allows for cleaner transformation to the wavenumber domain and more accurate calculation of angle domain common image gathers.
Solution Approach 2:
The patent applies preprocessing steps including windowing and apodization before the Fourier transformation. These preliminary actions prepare the data to minimize spectral leakage effects, ensuring that the subsequent wavenumber domain operations produce accurate ADCIGs without contamination from leakage artifacts.
Data Source
AI summary
A method for calculating angle domain common image gathers (ADCIGs). The method includes calculating a source wavefield pF of a seismic source; calculating a receiver wavefield pB of a seismic receiver; applying an algorithm of anti-leakage Fourier transform (ALFT) to transform the source wavefield pF to a wavenumber domain; applying the ALFT algorithm to the receiver wavefield to transform the receiver wavefield in the wavenumber domain; determining an imaging condition to the ALFT source and receiver wavefields in the wavenumber domain; computing a reflection angle θ and an azimuth angle φ of the source wavefield pF and receiver wavefield pB in the wavenumber domain; calculating the ADCIGs in the wavenumber domain; and applying an inverse fast Fourier transform (FFT) to determine the ADCIGs in the space domain.