3D finite-difference synthetic acoustic log in cylindrical coordinates

摘要

A finite-difference method of numerical simulation of sonic logging has been developed and implemented. The very general statement is considered: the surrounding medium is allowed to be 3D heterogeneous and a source can be located at any point inside or outside the well. To provide a maximally precise description of the sharpest interface of the problem, the interface between the well and surrounding formations, we use cylindrical coordinates with the axis directed along the well. In order to avoid an excessive azimuth inflation of grid cells with an increase of radius we perform periodical refinement of the grid step in the azimuth direction. In order to truncate the area of computations, Perfectly Matched Layer (PML) for cylindrical coordinates is developed and implemented. Its main advantage in comparison with other approaches is an extremely low level of artificial reflections and the absence of necessity to perform splitting of variables in the azimuth direction.Based on this numerical method, a software oriented for the use of parallel computations is developed and implemented under Message Passing Interface Library. Results of numerical experiments for a well with completion embedded within layered elastic background with a vertical planar crack are presented and discussed.