Ground motion models (GMMs) have historically been used as input in the development of probabilistic seismic hazard analysis (PSHA) and as an engineering tool to assess risk in building design. Generally these equations are developed from empirical analysis of observations that come from fairly complete catalogs of seismic events. One of the challenges when doing a PSHA analysis in a region where earthquakes are induced is that the catalog of observations is not complete enough to come up with a set of equations to cover all expected outcomes. This work is part of a study where we use a deterministic finite-difference wave-form modeling to compliment the traditional development of GMMs. Specifically we leverage our industry expertise in developing and applying detailed physics based subsurface models to accurately model the propagation of the wavefield from source to receiver. Of particular interest is how the source model representation scales with magnitude and how this translates to modeled ground motions at a surface. A kinematic fault rupture model is used to test the sensitivity of the GMMs to variability in the fault rupture process that is physically consistent with observations. These tests will aid in constraining the degree of variability in modeled ground motions due to a realistic range of fault parameters and properties. From this study it is our conclusion that in order to properly capture the uncertainty of the GMMs with magnitude up-scaling one needs to address the impact of uncertainty in the near field (<10km) imposed by the lack of constraint on the finite rupture model. By quantifying the uncertainty back to physical principles it is our belief that it can be better constrained and thus reduce exposure to risk. Further, by investigating and constraining the range of fault rupture scenarios and earthquake magnitudes on ground motion models, hazard and risk analysis in regions with incomplete earthquake catalogs, can be better understood.