A three-dimensional finite difference code for the modeling of sonic logging tools

Abstract

This paper presents a numerical program for the simulation of elastic wave propagation and scattering in three-dimensional (3-D) cylindrical coordinates based on the first-order velocity-stress finite-difference scheme on staggered grids. Both Liao’s and Lindman’s absorbing boundary conditions are implemented for the exterior boundaries to efficiently truncate the computation domain for elongated 3-D well logging problems. Symmetric and anti-symmetric boundaries in azimuthal and axial directions are also implemented in the code to further reduce the size of the problem. Included for the first time with this code are very large and complex geometrical structures such as the whole slotted sleeve housing of a sonic well-logging tool which typically involves hundreds of millions of unknowns. The calculation for such a large problem only takes a couple of days on a four-processor SGI Power Challenge machine. Different types of slotted sleeve models are studied for sonic logging tools. Simulation results show that different slotted sleeves vary widely in delaying and attenuating the pipe waves which travel along the tool housing. A new slotted sleeve structure with three horizontal slot sections for every vertical slot period is proposed for better performance. A dipole source is found to produce much cleaner waveforms than a monopole source.