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3D finite‐difference synthetic acoustic logging in cylindrical coordinates
Author(s) -
Pissarenko D.,
Reshetova G.V.,
Tcheverda V.A.
Publication year - 2009
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.2008.00743.x
Subject(s) - computation , azimuth , computer science , grid , computational science , boundary value problem , domain decomposition methods , geometry , boundary (topology) , algorithm , mathematical analysis , finite element method , mathematics , physics , thermodynamics
On the basis of the application of a finite‐difference approximation of an initial boundary value problem for elastic wave equations (velocity/stress formulation), a numerical method and its algorithmic implementation have been developed in order to perform a computer simulation of sonic logging. A very general statement is dealt with – the surrounding medium is allowed to be 3D heterogeneous and the source can be located at any point inside or outside the well. To provide the most precise description of the sharpest interface of the problem – the interface of the well, we formulate the problem in cylindrical coordinates with a z axis directed along the well. In order to avoid excessive azimuth inflation of grid cells with radius increase, we perform periodical refinement of the grid step in the azimuth direction. This guarantees the quasi‐uniform size of the grid cells throughout the area of computation. In order to truncate area of computation, a classical version of a perfectly matched layer is developed and implemented for cylindrical coordinates. Its main advantage in comparison with other approaches is an extremely low level of artificial reflections and it is not necessary to perform splitting of variables in the azimuth direction. Implementation of parallel computations is performed via domain decomposition: the area of computation is sliced into a number of adjoining discs and each disc is assigned to its own processor unit. Data exchange between processor units is performed with the help of a message‐passing interface library. Results of numerical experiments for an elastic medium with a circular crack are presented and discussed.