Site response in sedimentary basins is influenced by complex three-dimensional (3D) features, including trapping of seismic waves, focusing of seismic energy and basin resonance. Current ground motion models (GMMs) incorporate basin effects using one-dimensional parameters like V_S30 and shear wave velocity isosurface depths, which are limited in capturing lateral and 3D effects. To address these limitations, we develop seismic site response models based on novel parameters that represent multi-dimensional properties of the Los Angeles Basin (LAB) geometry and shear wave velocity. We define a basin shape for the LAB using depth to subsurface geologic interfaces associated with the oldest sedimentary deposits (depth to a particular shear wave velocity horizon, i.e., 1.5 km/s - z_1.5) and the depth to the crystalline basement (z_cb) which are determined using geologic cross sections and community seismic velocity model profiles. We explore a suite of geometric descriptors computed for the LAB and southern California, from which three parameters with the greatest predictive potential are selected and evaluated using empirical ground motion residual analyses in combination with the Boore et al. GMM. The results demonstrate that the zonal heterogeneity index (), standard deviation of the absolute difference between z_1.5 and z_cb () and standard deviation of z_cb () each provide a reduction in site-to-site variability (ϕ_S2S) of empirical GMMs. The reduction in ϕ_S2S is period-dependent, with average decreases of 3%, 26% and 6% for , , and , respectively. Although these reductions are modest from an engineering application perspective, they are statistically significant, underscoring the inherent difficulty in fully characterising complex basin effects. Collectively, these findings indicate that the inclusion of basin-specific geometric parameters yields measurable, albeit incremental, improvements in site response prediction and establishes a framework for the progressive refinement of seismic hazard characterisation within sedimentary basins.