  Estimating subsurface properties like hydraulic conductivity using
hydrogeological data alone is challenging in field sites with sparse wells.
Geophysical data, including Self-potential (SP) and Magnetotelluric (MT), can
improve understanding of hydrogeological structures and interpolate data
between wells. However, determining hydraulic conductivity requires a proper
petrophysical relationship between hydraulic conductivity and inferred
geophysical properties, which may not exist or be unique. In this work, we
propose a joint-inversion approach without assuming petrophysical
relationships, using self-potential data to connect groundwater flow velocity
to electrical potential differences, and MT data to estimate hydraulic
conductivity and electrical conductivity. A spectral method is employed for the
self-potential forward problem. To accelerate joint data inversion, a dimension
reduction technique through the Principal Component Geostatistical Approach is
used. The applicability and robustness of the joint-inversion method are
demonstrated through inversion tests using hydrogeophysical data sets generated
from subsurface models with and without petrophysical relationships. The joint
hydraulic head-SP-MT data inversion can reasonably estimate hydraulic
conductivity and electrical resistivity, even without knowledge of a one-to-one
petrophysical relationship. On average, joint inversion yields a 25%
improvement in hydraulic conductivity estimates compared to single data-type
inversion. Our proposed joint inversion approach, with SP-data compensating for
the absence of a known petrophysical relationship, provided close agreement
with joint inversion of head and MT data using a known petrophysical
relationship. Successful inversion tests demonstrate the usefulness of SP data
in connecting hydrogeological properties and geophysical data without requiring
a petrophysical relationship.
