Upscaled Discrete Operators for Seismic Wavefield Propagation
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Solution Overview
Problem
Current seismic data processing methods face challenges in accurately modeling the Earth's interior with complex geological structures and large datasets, particularly in reverse-time modeling, where small timesteps limit efficiency and accuracy.
Innovation Solution
A method is developed to process data by defining desired timesteps and spatial steps based on medium properties, compounding discrete seed operators, and upscaling them to achieve larger timesteps and spatial steps, allowing for efficient and accurate recreation of wavefields at earlier times.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If small timesteps are used in finite-difference methods to ensure stability, then numerical stability is improved, but processing efficiency and productivity deteriorate due to the large number of computational steps required
Solution Approach 1:
The propagation process is segmented into multiple stages: first computing fine-scale seed operators with small timesteps for stability, then compounding these operators to achieve coarse-scale operators with large timesteps. This segmentation allows the system to benefit from both small-timestep stability and large-timestep efficiency.
Solution Approach 2:
The invention transitions from the time dimension by computing operators offline and storing them for reuse. Instead of marching forward in time with small steps, the system pre-computes multi-step operators and applies them as unified operations, effectively moving the computational burden to a different temporal dimension.
2Measurement precision
If small spatial steps are used to resolve fine-scale medium structures, then modeling accuracy is improved, but device complexity and computational cost increase due to the fine mesh requirements
Solution Approach 1:
The spatial domain is segmented into fine-scale regions for computing seed operators and coarse-scale regions for application. The fine-scale details are captured in the pre-computed operators, allowing coarse-scale propagation without requiring fine-scale meshes during the actual wavefield propagation.
Solution Approach 2:
The fine-scale medium properties are incorporated into the seed operators in advance through pre-computation. This preliminary action embeds the fine-scale information into the operators themselves, eliminating the need to resolve fine-scale structures during the propagation process.
3Measurement precision
If large datasets are processed to accurately represent the Earth's interior, then measurement precision is improved, but loss of time increases due to the computational burden of processing extensive data
Solution Approach 1:
The operators are pre-computed offline incorporating all necessary medium properties and fine-scale details. This preliminary computation stores the essential information in a compact form, eliminating the need to repeatedly process large datasets during actual wavefield propagation and imaging operations.
Solution Approach 2:
Instead of processing the original large-scale medium model repeatedly, the invention creates compact operator copies that encapsulate the essential propagation characteristics. These operator copies can be applied efficiently without requiring access to or processing of the full detailed medium model.
Data Source
AI summary
Processing data representing a wavefield propagating through a medium by defining, based on one or more properties of a region of the medium and of the wavefield therein, a desired timestep and a desired spatial step for a discrete operator. Discrete seed operators having an initial timestep and an initial spatial step less than the desired timestep and the desired spatial step are then defined, and these seed operators are compounded to obtain an operator having a greater timestep and upscaled to obtain an operator having a greater spatial step. The compounding and upscaling are repeated until an operator having the desired timestep and the desired spatial step is obtained. The operator having the desired timestep and the desired spatial step may be applied to the data representing the wavefield propagating through a medium to propagate the data backwards in time to recreate the wavefield at earlier times.