Dispersion of Love waves propagating in a heterogeneous layer of finite thickness over a semi-infinite medium has been studied. Two plausible, separate cases, namely, the lateral and vertical inhomogeneity in the upper layer have been considered. The laws of variations of shear-wave velocity and rigidity in the layer have been assumed to follow exponential functions. Based on the concept of constructive interference, the frequency equations have been deduced. The dispersion curves for all of the cases have been drawn and compared with a structure when the superficial layer is homogeneous. For the case of lateral inhomogeneity, the dispersion curves show that the phase velocity decreases in the direction of increasing shear-wave velocity (also of rigidity) and vice-versa. It is also interesting to note that the rays pile up with increasing distance until being cut off when propagating in the direction of increasing shear-wave velocity in the lateral direction—the phenomenon shows that no further propagation beyond the critical distance is possible.

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