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Spatially-Optimized Finite-Difference Schemes for Numerical Dispersion Suppression: an Implementation Using Symbolic ComputationNormal access

Author: E. Caunt
Event name: 81st EAGE Conference and Exhibition 2019
Session: Poster: Seismic Modelling B
Publication date: 03 June 2019
DOI: 10.3997/2214-4609.201900660
Organisations: EAGE
Language: English
Info: Extended abstract, PDF ( 953.5Kb )
Price: € 20

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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