We develop finite element models of the coseismic displacement field accounting for the 3D elastic structures surrounding the epicentral area of the 2019 Ridgecrest earthquake sequence containing two major events of Mw7.1 and Mw6.4. The coseismic slip distribution is inferred from the surface displacement field recorded by interferometric synthetic aperture radar. The rupture dip geometry is further optimized using a novel nonlinear-crossover-linear inversion approach. It is found that accounting for elastic heterogeneity and fault along-strike curvilinearity improves the fit to the observed displacement field and yields a more accurate estimate of geodetic moment and Coulomb stress changes. We observe spatial correlations among the locations of aftershocks and patches of high slip, and rock anomalous elastic properties, suggesting that the shallow crust's elastic structures possibly controlled the Ridgecrest earthquake sequence. Most of the coseismic slip with a peak slip of 7.4 m at 3.6 km depth occurred above a zone of reduced S-wave velocity and significant post-Mw7.1 afterslip. This implies that viscous materials or fluid presence might have contributed to the low rupture velocity of the mainshock. Moreover, the zone of high slip on the northwest-trending fault segment is laterally bounded by two aftershock clusters, whose location is characterized by intermediate rock rigidity. Notably, some minor orthogonal faults consistently end above a subsurface rigid body. Overall, these observations of structural controls improve our understandings of the seismogenesis within incipient fault systems. Plain Language Summary On July 4 and 5, 2019, a magnitude 7.1 and 6.4 earthquake occurred near the town, Ridgecrest, California. The permanent surface movements induced by these events were captured by satellite images. Here, we develop realistic numerical models and innovational optimization algorithms to investigate the displacement fields and image the distribution of the earthquake slip. These events were hosted by a pair of orthogonal faults and their resolved orientations are similar to the nearby known fault structures. We discover that the fault slip and aftershock locations could be related to the local rock materials, suggesting that the variable elastic properties of the shallow crust might have influenced the development of the Ridgecrest earthquake sequence. As also supported by other seismic and geophysical datasets, most of the coseismic slip appeared over a zone of elastic weakness where could be relevant to subsurface viscous or fluid bodies, meanwhile, aftershocks tended to cluster within a shallow rigid body. Overall, the findings of this study provide insights into potential structural controls over the seismic occurrence and help improve our understandings of the seismogenesis within the western Mojave desert.