Joint Inversion of GPR and ER Data
Authors: Domenzain Diego 
Published: June 2020

Imaging the subsurface can shed knowledge on important processes needed in a modern day
human's life such as ground-water exploration, water resource monitoring, contaminant and
hazard mitigation, geothermal energy exploration and carbon dioxide storage. As computing
power expands, it is becoming ever more feasible to increase the physical complexity of
Earth's exploration methods, and hence enhance our understanding of the subsurface.

We use non-invasive geophysical active source methods that rely on electromagnetic fields
to probe the depths of the Earth. In particular, we use Ground penetrating radar (GPR) and
Electrical resistivity (ER). Both methods are sensitive to electrical conductivity while
GPR is also sensitive to electrical permittivity. We combine both types of data and let the
different physical sensitivities of both methods cooperate in order to account for non-uniqueness
of the subsurface image.

Full-waveform inversion (FWI) of GPR is a promising technique for recovering permittivity and
conductivity of the subsurface by using the full response of the electromagnetic wave. While many
advances have been made to FWI by the seismic exploration community, using FWI on GPR surface
acquired data is a young and growing field of research. Using the full response of ER data is a
more common practice in the geophysical community. However, the spatial resolution of the recovered
conductivity lacks high spatial-frequency content due to the inherent sensitivity of the data.

Fortunately, the sensitivities of GPR and ER are complimentary. GPR is sensitive to conductivity
through reflection and attenuation while ER is directly sensitive to conductivity. GPR is sensitive
to high spatial-frequency content while ER is sensitive to low spatial-frequency content.

We present a novel non-linear joint inversion that iteratively combines the sensitivities of both
GPR and ER surface acquired data. Our algorithm uses both GPR and ER sensitivities in order to
effectively alleviate the non-uniqueness of the recovered electrical parameters. We join GPR and ER
sensitivities within the same computational grid and without the need of petrophysical relationships.
By further assuming structural similarities between permittivity and conductivity, we are able to
relax a priori assumptions about the subsurface and accurately recover parameters in regions where the
GPR data has a signal-to-noise ratio close to one. Furthermore, assuming a good initial model is
available our algorithm makes no assumption of the underlying geometry.

The demanding computing requirements of GPR-FWI entail an unfeasible amount of memory for existing ER
inversion methods. This is due to the very fine discretization of the subsurface required by GPR-FWI.
We develop a 2.5d ER adjoint method inversion that is capable of recovering accurate subsurface
conductivity from field data and relaxes the amount of required memory. We test our method on field data
from an alluvial aquifer site and find agreeable results with existing measurements in the literature.
Having feasible computational methods for both GPR and ER inversions is an important step for using our
joint inversion algorithms on field data.