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Spatially-Optimized Finite-Difference Schemes for Numerical Dispersion Suppression: an Implementation Using Symbolic Computation
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 81st EAGE Conference and Exhibition 2019, Jun 2019, Volume 2019, p.1 - 5
Abstract
Summary
In this work, a 4th order DRP 2D elastic wave formulation with free surface boundary conditions is presented, extending methods of Tam and Webb (1993 ). Staggered first-derivative stencils are derived and applied to the P-SV formulation of Virieux (1986 ). Performance is compared to the Taylor-series-derived staggered scheme of equal extent, demonstrating the versatility and universal benefits of spatial optimization. Implementation of both FD schemes is carried out using Devito, a domain-specific Python module and compiler for FD applications. Devito allows for model specification with a handful of high-level symbolic Python objects to build an FD operator, used to generate highly optimized C++ code at runtime via a series of intermediate representations, allowing for complex multi-stage optimizations. The high-level, symbolic nature of Devito ensures concise, readable model code and expedites workflow compared to model building with low-level languages, enabling rapid prototyping in hours as opposed to weeks or months without sacrificing underlying code quality. This work showcases the potential of symbolic computation for implementing non-conventional FD stencils, and the straightforwardness of doing so with Devito.
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