Surface Waves in Laterally Heterogeneous Media

Surface wave methods exploit the dispersive properties of Rayleigh and Love waves to estimate the shear wave velocity profiles in vertically heterogeneous subsurfaces. Typically, they rely on a simplified one-dimensional (1D) analytical forward model where the lateral variation of the layer thickness is neglected and so is the fraction of the incident energy of the fundamental mode that is reflected or converted to higher modes. A theoretical study is presented that attempts to define an analytical model that overcomes the limitations of 1D forward models. In particular, we revisit properties of semianalytical approaches that aim at solving the dynamics of Love waves in laterally heterogeneous media made of a soft upper layer of varying thickness lying over an infinitely deep hard layer. The novel analytical model stems from a local-mode expansion of waves with laterally varying amplitudes, which allows for both reflections of the incident modes and coupling to higher modes. The best wave approximation stems from an action principle that leads to a coupled system of second-order ordinary differential equations (ODEs) for the wave amplitudes. Last, an application of this model and its validity are discussed.