Thrust‐fault earthquakes are particularly hazardous in that they produce stronger ground motion than normal or strike‐slip events of the same magnitude due to a combination of hanging‐wall effects, vertical asymmetry, and higher stress drop due to compression. In addition, vertical surface displacement occurs in both blind‐thrust and emergent thrust ruptures, and can potentially damage lifelines and infrastructure. Our 3D dynamic rupture modeling parameter study focuses on planar thrust faults of varying dip angles, and burial depth establishes a physics‐based understanding of how ground motion and permanent ground surface displacement depend on these geometrical parameters. We vary dip angles from 20° to 70° and burial depths from 0 to 5 km. We conduct rupture models on these geometries embedded in a homogeneous half‐space, using different stress drops but fixed frictional parameters, and with homogeneous initial stresses versus stresses tapered toward the ground surface. Ground motions decrease as we bury the fault under homogeneous initial stresses. In contrast, under tapered initial stresses, ground motions increase in blind‐thrust faults as we bury the fault, but are still the highest in emergent faults. As we steepen dip angle, peak particle velocities in the homogeneous stress case generally increase in emergent faults but decrease in blind‐thrust faults. Meanwhile, ground motion consistently increases with steepening dip angle under the stress gradient. We find that varying stress drop has a considerable scalar effect on both ground motion and permanent surface displacement, whereas changing fault strength has a negligible effect. Because of the simple geometry of a planar fault, our results can be applied to understanding basic behavior of specific real‐world thrust faults.