Simulation of 2.5-dimensional borehole acoustic waves with convolutional perfectly matched layer

A 2.5-dimensional method using the PDE package of the commercial finite element software COMSOL Multiphysics is developed to simulate wave propagation in a borehole. The computation is conducted in the frequency wave-number domain. A convolutional perfectly matched layer is implemented to eliminate the reflections from artificial truncation boundaries. Waveforms obtained in time domain are in good agreement with analytic solutions in a special model, which proves the validity of the method. A numerical modeling example is presented to illustrate the capabilities of the method. It is shown that this method can be used to solve a variety of non-axisymmetric borehole acoustic wave propagation problems.