Post-seismic deformation following large earthquakes offers insights into the rheology of the lithosphere and upper asthenosphere. The Mojave, in southern California, is one of the best studied regions on Earth, yet key questions, about fault slip rates and rheological heterogeneity, remain unanswered. Unprecedented geodetic coverage of the 2019 Ridgecrest earthquakes provides an opportunity to test whether rheological models developed for the Mojave, from the Landers, Hector Mine and El Major Cucapah earthquakes, are applicable north of the Garlock fault, and to place bounds on the effects of local rheological heterogeneties associated with the Coso volcanic field. This volcanic field, which is located to the NW of the Mw7.1 rupture trace, is a region of high heat flow and geothermal activity. The locally high temperatures in the Coso volcanic field are likely to be associated with low viscosities compared to the surrounding regions, and high pore pressures due to the hydrothermal activity. The aftershock sequence associated with the Ridgecrest earthquakes shows a notable absence of large magnitude earthquakes in this region. We use variational Bayesian independent component analysis to isolate postseismic deformation in GPS time series around the earthquakes. We present models of the possible poroelastic, afterslip and viscoelastic response driven by coseismic stress changes in the July 2019 Ridgecrest earthquakes and investigate the possible effect of the Coso volcanic field. By modelling a series of different afterslip geometries, and viscoelastic rheologies we identify features of the GPS- and InSAR-derived surface deformation which are diagnostic of different post-seismic mechanisms and rheological heterogeneities.