Dynamic Green’s functions for a liquid layer overlying a transversely isotropic solid half-space due to an arbitrary source excitation within the liquid

In this paper, the axisymmetric dynamic response of a finite thickness liquid layer overlying a transversely isotropic solid half-space is developed. The use of potential functions accompanied by the integral transform method is applied to handle the equations of motion of the two media. Closed form expressions are derived for stress and displacement Green’s functions due to time-harmonic source excitations of arbitrary shape, including point and disk sources. For the numerical computation of the resultant complex integrals, a robust and effective procedure is utilized using the Residue Theorem and adaptive integration. Numerical examples are carried out for a uniformly distributed circular source. Curves of stress and particle displacement along both vertical and radial directions are presented to demonstrate the effect of the liquid layer thickness, frequency of excitation, position of the source, and the elasticity of the underlying solid material on the wavefield distribution within the entire medium. Comparisons with existing analytical and numerical solutions for simpler (special) cases are made to confirm both the validity of the expressions and the accuracy of the numerical results. •Dynamic response of an anisotropic solid underlying a liquid layer is studied.•The formulation is developed for any kind of axisymmetric excitations.•Green’s functions for point and disk sources are especially considered.•Light is shed on the roles of the layer thickness, bed material, and source depth.•Simpler cases are studied as special cases of the main problem.