Modeling of wave propagation in multi-layered environments with rough interfaces and volume heterogeneities: A T-matrix approach

Layering or stratification, as well as volume (spatial) heterogeneity and rough boundaries between the layers (the interface roughness), are ubiquitously present in natural environments and caused by combination of many processes, for instance, by regular gravity-controlled vertical sedimentation, as well as continuous and discrete irregularity due to granular microstructure, presence of solid inclusions, gas bubbles, voids, and spatial fluctuations of their volume concentration. In this paper, we consider wave propagation, scattering, and attenuation in a stack of elastic layers with various types of irregularities (or scattering mechanisms), represented by volume heterogeneity within the layers and roughness of the interfaces in between, and given by spatial continuous and discrete variations of material parameters. A general idea of suggested here theoretical approach originates from one used in acoustics to consider underwater sound propagation for calculating the coefficient of reflection of compressional plane waves from a stack of fluid homogeneous layers with flat interfaces (modeling, for example, discretely stratified water-like sediments) using the reflection coefficients of each interface. We show that a similar, but a more general matrix approach, can be developed to include scattering mechanisms, such as interface roughness and volume heterogeneity, as well as different types of media and waves, for instance compressional and shear seismic waves (vertically and horizontally polarized) in elastic, viscoelastic, and poroelastic layers. A general full-wave solution for an arbitrary number of such layers is described in terms of transition matrix coefficients, or T-matrixes, taken from a set of simpler solutions for a plane wave transformation, reflection and scattering from, and transmission through, a single layer located between two homogeneous half-spaces and therefore isolated from interactions with other boundaries. Inside of this layer, for simplicity, scattering mechanisms are isolated as well - either a rough interface or volume heterogeneity is allowed. These simplified T-matrix solutions (found separately for each “isolated” layer and interface of the system) provide inputs to a set of integral equations which describe interactions between different layers and interfaces. Then a general solution, the scattering amplitude or T-matrix of the whole stack of layers can be obtained using an iterative procedure that starts from a simple case of two half-spaces at the basement. As an example, scattering from a heterogeneous elastic layer is considered resulting in explicit expressions for the coherent reflection loss and the incoherent scattering strength. Applications to remote sensing of underwater sediments and sea ice are discussed. [Work supported by ONR and BSF].