Adaptive Lebedev Staggered Grid for TTI Seismic Simulation
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Solution Overview
Problem
Conventional methods for simulating seismic wave propagation in tilted transversely isotropic media require extremely fine grid spacings, making them computationally intractable and resource-intensive, while existing approaches fail to accurately model such media without significant computational costs.
Innovation Solution
The use of an adaptive Lebedev staggered grid, which combines features of staggered and adaptive grids, allowing for varying grid spacings based on field parameters, reduces memory usage and computation time while maintaining high numerical accuracy by splitting field variables into subsets stored at different positions within a cell and using finite-difference schemes to solve elastic wave equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional finite-difference elastic modeling approaches are used for TTI media, then accurate seismic wave simulation is achieved, but computational cost becomes intractable due to required fine grid spacing
Solution Approach 1:
The patent applies adaptive grid spacing where different regions of the computational domain use different grid resolutions. Regions with complex geological structures or high wave activity use finer spacing to maintain accuracy, while homogeneous regions use coarser spacing to reduce computational cost. This local adaptation resolves the contradiction by making grid spacing dependent on local requirements rather than using uniform fine spacing throughout.
Solution Approach 2:
The patent implements dynamic grid refinement where the grid spacing is adjusted based on wave propagation characteristics and geological complexity during simulation. The grid can be refined adaptively in regions where waves interact with complex TTI structures and coarsened in regions where waves propagate through simpler media, allowing the computational mesh to dynamically adapt to the physics being simulated.
2Reliability
If uniform fine grid spacing is used to avoid simulation artifacts in TTI media, then numerical accuracy is maintained, but memory usage and computation time increase significantly
Solution Approach 1:
The adaptive grid implementation uses local quality by assigning different grid spacings to different spatial regions based on their specific requirements. Regions requiring high fidelity (such as near sources, receivers, or complex geological interfaces) use fine spacing, while other regions use coarser spacing. This dramatically reduces the total number of grid points and associated memory requirements while maintaining simulation reliability where it matters most.
3Measurement precision
If conventional staggered grid is used for TTI media simulation, then wave propagation accuracy is improved, but device complexity and computational burden increase
Solution Approach 1:
The patent segments the computational domain into multiple zones with different grid spacing characteristics. Each zone can be independently managed with its own resolution, allowing the complex staggered grid structure to be broken down into simpler, more manageable segments. This segmentation reduces the overall complexity while maintaining the accuracy benefits of staggered grids in critical regions.
Data Source
AI summary
Disclosed are systems and methods for numerically simulating seismic-wave propagation in tilted transversely isotropic (TTI) media, using an adaptive Lebedev staggered grid. In various embodiments, the adaptive grid includes multiple horizontal zones having different associated grid spacings, which may be determined based on a vertical wave-velocity model. The numerical simulation may involve iteratively solving a set of finite-difference equations including finite-difference coefficients that vary spatially depending on the grid spacing. Additional embodiments and features are described.