In boundary element formulations, repeated evaluations of Green’s functions over large source and receiver grids and wide frequency ranges hinder the scalability of the method for application to large-scale problems. In this work, tensor decomposition formats are leveraged to obtain an a priori low-rank approximation of Green's functions. The approach is based on the Greedy Tucker Approximation, in which the Green's tensor is iteratively enriched through rank-one updates obtained from a Proper Generalized Decomposition–type alternating least-squares procedure. A Petrov-Galerkin formulation is adopted to enhance robustness and accuracy of the reduced representation. The resulting approximation decomposes the Green's functions into low-dimensional basis functions coupled through a compact core tensor, yielding substantial reductions in memory requirements. This representation allows source-receiver locations, wavenumber, frequency, material parameters, and soil depth to be treated as explicit separable dimensions. Moreover, the low-rank structure enables efficient reconstruction of the spatial-domain Green’s functions by applying inverse fast Fourier transforms to the separated wavenumber components instead of the full Green's tensor. The approach is well suited for problems involving four to five parametric dimensions, beyond which the core tensor may become limiting. To accommodate higher-dimensional parameter spaces, a hierarchical Tucker decomposition is incorporated within the same greedy framework. Unlike the standard Tucker decomposition, the hierarchical Tucker decomposition organizes the tensor dimensions through a dimension tree, factorizing the core tensor into a hierarchy of lower-dimensional tensors and thereby controlling the growth of the core tensor as the number of parameters increases. The performance of the proposed algorithms is demonstrated using an elastodynamic layered halfspace example with multiple parameter combinations treated as separable dimensions. Results are validated against those obtained from the direct stiffness method, with comparisons of computation time and memory requirements.