Back-propagating modes in elastic logging-while-drilling collars and their effect on PML stability

The Perfectly Matched Layer (PML) approach is widely used to implement the absorbing boundary conditions for coupled multi-physics wave propagation problems. However, it has been recognized that the solution in the PML absorbing layer can become unstable in the presence of back-propagating modes. This paper analyzes the spectral location of those modes excited by monopole acoustic sources in logging-while-drilling cylindrical tools. To recover the stability of the solution for such a class of problems involving the modeling of elastic cylindrical waveguides, we propose the implementation of artificial attenuation in the waveguide to dampen undesirable modes, thereby making their amplitude negligible in the PML absorbing layer due to the limited numerical accuracy and round-off errors.