Soil-structure-interaction (SSI) effects are typically non-negligible for structures that possess one or more of the following attributes: a massive super-structure and/or foundation elements, a large uninterrupted footprint or interface with the soil domain, and a soft, supporting soil medium. The SSI effects comprise the dynamic interaction between: (1) the far-field soil domain; (2) the (potentially inelastically behaving) near-field soil domain; and (3) the structure. The far-field domain is semi-infinite unless the bedrock or a rock outcrop is very near and, thus, it can be represented with a reduced-order model in the form of impedance functions. The use of impedance functions in SSI analyses allows the computational cost to be reduced by several orders of magnitude without compromising the solution accuracy. Moreover, it is now possible to obtain time-domain representations of the inherently frequency-dependent impedance functions. As such, accurate nonlinear time-history analyses of problems that involve SSI effects can be now carried out in a computationally efficient manner. However, the current catalogue of impedance functions is limited to simple foundation shapes and soil profiles. In the present study, we provide a systematic approach with which impedance functions for arbitrarily shaped foundations resting on (or embedded in) heterogeneous soil domains can be obtained. In order to obtain the impedance functions, forward wave propagation analyses are carried out on a high-performance computing platform. The finite element method is employed to account for the arbitrary heterogeneity of soil and for different foundation types and geometries. In the forward analyses, the semi infinite remote boundaries are treated with Perfectly Matched Layers (PML) which, to date, are considered to offer the best Wave-Absorbing Boundary Condition (WABC) representation. Practical examples are provided that display pronounced variations in impedance functions with respect to frequency, which illustrate and quantify the importance of using frequency-dependent impedance functions in SSI analyses.