Love waves in multilayered media with irregular interfaces: I. Modal solutions and excitation formulation

Abstract In this article, we present a new formulation of Love waves in arbitrarily irregular multilayered media by using the global generalized reflection/transmission matrices method (abbreviated to GGRTM; Chen, 1990, 1995, 1996). From the basic principle that the modal solutions are the nontrivial solutions of the free elastodynamic equation under appropriate boundary conditions, we naturally derived the characteristic frequencies and the corresponding distorted modes of Love wave in irregular multilayered media. The basic principle used here for defining modal solutions is a general one. It is identical to that used for defining normal mode solutions in laterally homogeneous-layered media (Chen, 1993) and that used for determining the resonant modes in finite-scatters case (e.g., sedimentary basin structure; see Zhou and Dravinski, 1994) and is independent of any particular mathematical technique. We found that the distorted mode in 2D structure is nonseparable in (x, z) coordinates, that is, wn,v(x,z)=∑m{a(z,ωn,v)}meikmx; whereas the normal mode for 1D structure is separable in (x,z) coordinates: un,v(x,z) = l(z,ωn,v)eiknx. Based on the formulation of GGRTM and the modal solutions, we also analytically derive the excitation formula of Love waves in irregular multilayered media, that is, the formulation of synthetic Love waves due to an arbitrarily seismic point source in such lateral heterogeneous media. We found that the synthetic Love wave in time domain can be expressed as a superposition of a series of distorted modes that is similar to the excitation formula of classic Love waves. Since the structure model used here is quite arbitrary, the new formulation of Love waves derived in this article can be applied to study a variety of seismological problems ranging from resonated motion in a sedimentary basin structure to excitation of Love waves in irregular multilayered media. It offers an alternative mean to understand the nature of Love waves in laterally heterogeneous media.