<p>Estimating subsurface hydraulic conductivity with sparse hydrogeological data is challenging. Geophysical data, such as Self-potential (SP) and Magnetotelluric (MT), can be acquired additionally to improve our understanding of the underlying hydrogeological structure. However, in order to use both hydrogeological and geophysics data sets, it is necessary to identify a proper petrophysical relationship, which may not be unique or even not exist. In this work, we propose a joint-inversion approach without petrophysical relationship assumptions, using SP data, connecting groundwater flow velocity to electrical potential differences, and MT data to simultaneously estimate hydraulic and electrical conductivity. To accelerate the joint data inversion, high-dimensional hydraulic conductivity and electric resistivity fields are estimated by using a dimension reduction technique through the Principal Component Geostatistical Approach. The approach assures that the estimated parameters and their uncertainties are quantified within only a few hundred coupled forward model runs. To demonstrate the applicability and robustness of the proposed method, several tests are performed, using hydrogeophysical data sets generated from subsurface models of hydraulic conductivity and electrical conductivity. The findings demonstrate that the joint hydraulic head-SP-MT data inversion can be reasonably used to estimate hydraulic conductivity and electrical resistivity, even in the absence of knowledge of a one-to-one petrophysical relationship. On average, the proposed joint inversion yields 25% improvement in the hydraulic conductivity estimates relative to a single data-type inversion, i.e., using only of hydraulic head and core data from wells; the single data-type inversion approach can only identify the subsurface structure near the observation wells.</p>