Numerical generation of transparent boundary conditions on the side surface of a vertical transverse isotropic layer

We consider elastodynamics in transversely isotropic media with vertical symmetry axis. The governing equations are the two-dimensional second-order system for displacements. A numerical method for generating transparent boundary conditions on the cylindrical surface is proposed. The correspondent operator is non-local in both z-direction and time: it handles low-frequency spatial harmonics of the solution convolving their Fourier coefficients with sums-of-exponentials kernels with respect to time. Test calculations show high accuracy, efficiency, and stability of the proposed non-reflecting conditions even for those media parameters where PML fails.