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The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport simulators have, in the last decade, played important roles in pushing applications towards increasingly challenging targets. Joint inversion of geophysical data that is based on structural constraints is often favored over model coupling based on explicit petrophysical relationships. More specifically, cross-gradient joint inversion has been applied to a wide range of near-surface applications and geophysical data types. To infer hydrological subsurface properties, the most appropriate approach is often to use temporal changes in geophysical data that can be related to hydrological state variables. This allows using geophysical data as indirect hydrological observables, while the coupling with a flow- and transport simulator ensures physical consistency. Future research avenues include investigating the validity of different coupling strategies at various scales, the spatial statistics of near-surface petrophysical relationships, the influence of the model conceptualization, fully probabilistic joint inversions, and how to include complex prior information in the joint inversion.

In groundwater hydrology, geophysical imaging holds considerable promise for improving parameter estimation, due to the generally high resolution and spatial coverage of geophysical data. However, inversion of geophysical data alone cannot unveil the distribution of hydraulic conductivity. Jointly inverting geophysical and hydrological data allows us to benefit from the advantages of geophysical imaging and, at the same time, recover the hydrological parameters of interest. We have applied a coupling strategy between geophysical and hydrological models that is based on structural similarity constraints. Model combinations, for which the spatial gradients of the inferred parameter fields are not aligned in parallel, are penalized in the inversion. This structural coupling does not require introducing a potentially weak, unknown, and nonstationary petrophysical relation to link the models. The method was first tested on synthetic data sets and then applied to two combinations of geophysical/hydrological data sets from a saturated gravel aquifer in northern Switzerland. Crosshole ground-penetrating radar (GPR) traveltimes were jointly inverted with hydraulic tomography data, as well as with tracer mean arrival times, to retrieve the 2D distribution of GPR velocities and hydraulic conductivities. In the synthetic case, incorporating the GPR data through a joint inversion framework improved the resolution and localization properties of the estimated hydraulic conductivity field. For the field study, recovered hydraulic conductivities were in general agreement with flowmeter data.

The sparsely spaced highly permeable fractures of the granitic rock aquifer at Stang-er-Brune (Brittany, France) form a well-connected fracture network of high permeability but unknown geometry. Previous work based on optical and acoustic logging together with single-hole and cross-hole flowmeter data acquired in 3 neighboring boreholes (70-100 m deep) have identified the most important permeable fractures crossing the boreholes and their hydraulic connections. To constrain possible flow paths by estimating the geometries of known and previously unknown fractures, we have acquired, processed and interpreted multifold, single- and cross-hole GPR data using 100 and 250 MHz antennas. The GPR data processing scheme consisting of time-zero corrections, scaling, bandpass filtering and F-X deconvolution, eigenvector filtering, muting, pre-stack Kirchhoff depth migration and stacking was used to differentiate fluid-filled fracture reflections from source-generated noise. The final stacked and pre-stack depth-migrated GPR sections provide high-resolution images of individual fractures (dipping 30-90{\deg}) in the surroundings (2-20 m for the 100 MHz antennas; 2-12 m for the 250 MHz antennas) of each borehole in a 2D plane projection that are of superior quality to those obtained from single-offset sections. Most fractures previously identified from hydraulic testing can be correlated to reflections in the single-hole data. Several previously unknown major near vertical fractures have also been identified away from the boreholes.