The rotated Cartesian coordinate method to remove the axial singularity of cylindrical coordinates in finite‐difference schemes for elastic and viscoelastic waves

Autor: Mingwei Zhuang, Jianyang Zhou, Qing Huo Liu, Songlin Wei
Rok vydání: 2017
Předmět:
Zdroj: Geophysical Prospecting. 66:27-39
ISSN: 1365-2478
0016-8025
Popis: SUMMARY When modelling the propagation of 3-D non-axisymmetric viscoelastic waves in cylindrical coordinates using the finite-difference time-domain (FDTD) method, one encounters a mathematical singularity due to the presence of 1/r terms in the viscoelastic wave equations. For many years this issue has been impeding the accurate numerical solution near the axis. In this paper, we propose a simple but effective method for the treatment of this numerical singularity problem. By rotating the Cartesian coordinate (RCC) system around the z-axis in cylindrical coordinates, the numerical singularity problems in both 2-D and 3-D cylindrical coordinates can be removed. This algorithm has three advantages over the conventional treatment techniques: 1) the excitation source can be directly loaded at r = 0; 2) the central difference scheme with second-order accuracy is maintained; 3) the stability condition at the axis is consistent with the FDTD in Cartesian coordinates. This method is verified by several 3-D numerical examples. Results show that the method is accurate and stable at the singularity point. The improved FDTD algorithm is also applied to sonic logging simulations in non-axisymmetric formations and sources. This article is protected by copyright. All rights reserved
Databáze: OpenAIRE
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