Fourier-Series Imaging for RTM Angle Gather Resolution
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Solution Overview
Problem
The imaging condition phase in reverse time migration (RTM) is incomplete, particularly in addressing issues of backscattering and wavefield separation, limiting the application of acoustic and elastic RTM (ARTM/ERTM) to a single image via basic cross-correlation, restricting their imaging capabilities.
Innovation Solution
A Fourier-series imaging condition is introduced to enhance RTM/ERTM imaging, generating an angle gather with multiple images of different reflection angles by constructing Fourier-series terms and applying rotation or reciprocity, improving image quality through Born modeling and least-square reverse time migration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If basic cross-correlation imaging condition is used, then the imaging process is simple and fast, but the angle resolution and imaging capability are limited to a single image
Solution Approach 1:
The imaging condition is segmented into multiple Fourier-series terms (cosine and sine components) with different orders (N=0, 1, 2, ...), each term handling specific angular information. This segmentation allows the system to achieve high angle resolution by processing angular components separately through different Fourier terms while maintaining computational efficiency.
Solution Approach 2:
The patent introduces a new mathematical dimension by transforming the imaging condition into the Fourier series domain. Instead of processing images directly in spatial domain, the method transforms wavefields into Fourier space where angular information is explicitly represented, enabling simultaneous computation of multiple angle images through a unified mathematical framework.
2Reliability
If temporal derivative/integration and spatial derivatives are applied, then backscattering and wavefield separation are improved, but the imaging capability remains restricted to basic cross-correlation
Solution Approach 1:
The Fourier-series imaging condition creates a universal framework that can handle multiple imaging tasks simultaneously. By using a single mathematical formulation with variable N (series order), the system can generate images for different reflection angles, handle both acoustic and elastic wavefields, and accommodate various geological conditions without requiring separate specialized algorithms for each case.
Solution Approach 2:
The imaging condition is made dynamic through the parameter N (series order), which can be adjusted to optimize performance for different imaging scenarios. Higher N values provide better angular resolution and backscattering suppression, while lower N values compute faster. This dynamic adaptability allows the same algorithm to serve multiple imaging needs without requiring separate static algorithms for each case.
3Measurement precision
If higher-order Fourier-series terms are used, then angle resolution and backscattering reduction are improved, but computational complexity increases
Solution Approach 1:
The patent applies partial action by using only the necessary number of Fourier-series terms (up to order N) required for the specific imaging task. Rather than computing all possible Fourier terms, the system determines the optimal N based on the desired angle resolution and computational resources. This partial computation approach achieves sufficient angle resolution while avoiding the excessive computational cost of computing all higher-order terms.
Data Source
AI summary
A method for performing seismic imaging of a subsurface formation includes receiving input data. The method also includes generating a simulated source-side wavefield and a simulated receiver-side wavefield based upon the input data. The method also includes producing an angle gather based upon the simulated source-side wavefield and the simulated receiver-side wavefield. The method also includes utilizing the angle gather in a virtual source term in Born modeling to improve an image quality of the angle gather.