Generalized Form of the Invariant Imbedding Method and Its Application to the Study of Back-Scattering in Shallow-Water Acoustics

A generalized form of the matrix-invariant imbedding method was developed to solve boundary-value problems for coupled systems of Helmholtz-type equations. Within this approach, a boundary-value problem solution can be obtained by solving evolutionary first-order imbedding equations for a matrix-valued function. The proposed method is applied to the solution of coupled equations for mode amplitudes describing the propagation of acoustic waves in a range-dependent shallow-water waveguide. The back-scattering of modes by bathymetry features is investigated, and the coefficients of the modal expansion of the wave reflected by an inhomogeneity in the bottom relief are computed. It is demonstrated that back-scattering is strongly connected with the modal interactions and that the back-scattered field consists of modes with numbers different from the number of the incident mode.

Design and Validation of the Invariant Imbedded T-Matrix Scattering Model for Atmospheric Particles with Arbitrary Shapes

Light scattering by non-spherical particles is an important factor influencing atmospheric radiative transfer. To accurately simulate the scattering properties of non-spherical particles, the Invariant Imbedded T-matrix method (IIM T-Matrix) is developed by combining the Lorenz–Mie theory and invariant imbedding technique. In this model, the non-spherical particle is regarded as an inhomogeneous sphere and discretized into multiple spherical layers in the spherical coordinate system. The T-matrix of the inscribed sphere is firstly calculated by the Lorenz–Mie theory, and then taking it as the initial value, the T-matrix is updated layer by layer by using the invariant imbedding technique. To improve the computational efficiency, the model is further parallelized by the OpenMP technique. To verify the simulation accuracy of the IIM T-Matrix method, the results of the model are compared with those of the EBCM (Extended Boundary Condition Method) T-Matrix method, DDA (Discrete Dipole Approximation) and MRTD (Multi-Resolution Time Domain). The results show that the scattering phase matrix simulated by the IIM T-Matrix method closely agrees with that of the well-tested models, indicating that the IIM T-Matrix method is a powerful tool for the light scattering simulation of non-spherical particles. Since the IIM T-Matrix method is derived from the volume integral equation, compared to the T-Matrix method which is based on surface integral principles (i.e., “EBCM” or the “null field method”), it can be applied to the scattering calculations of particle with arbitrary shapes and inhomogeneous compositions, which can greatly expand the application scope of the T-Matrix method.