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Geophysics provides a multidimensional suite of investigative methods that are transforming our ability to see into the very fabric of the subsurface environment, and monitor the dynamics of its fluids and the biogeochemical reactions that occur within it. Here we document how geophysical methods have emerged as valuable tools for investigating shallow subsurface processes over the past two decades and offer a vision for future developments relevant to hydrology and also ecosystem science. The field of “hydrogeophysics” arose in the late 1990s, prompted, in part, by the wealth of studies on stochastic subsurface hydrology that argued for better field‐based investigative techniques. These new hydrogeophysical approaches benefited from the emergence of practical and robust data inversion techniques, in many cases with a view to quantify shallow subsurface heterogeneity and the associated dynamics of subsurface fluids. Furthermore, the need for quantitative characterization stimulated a wealth of new investigations into petrophysical relationships that link hydrologically relevant properties to measurable geophysical parameters. Development of time‐lapse approaches provided a new suite of tools for hydrological investigation, enhanced further with the realization that some geophysical properties may be sensitive to biogeochemical transformations in the subsurface environment, thus opening up the new field of “biogeophysics.” Early hydrogeophysical studies often concentrated on relatively small “plot‐scale” experiments. More recently, however, the translation to larger‐scale characterization has been the focus of a number of studies. Geophysical technologies continue to develop, driven, in part, by the increasing need to understand and quantify key processes controlling sustainable water resources and ecosystem services.

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[1] Appropriate regularizations of geophysical inverse problems and joint inversion of different data types improve geophysical models and increase their usefulness in hydrogeological studies. We have developed an efficient method to calculate stochastic regularization operators for given geostatistical models. The method, which combines circulant embedding and the diagonalization theorem of circulant matrices, is applicable for stationary geostatistical models when the grid discretization, in each spatial direction, is uniform in the volume of interest. We also used a structural approach to jointly invert cross-hole electrical resistance and ground-penetrating radar traveltime data in three dimensions. The two models are coupled by assuming, at all points, that the cross product of the gradients of the two models is zero. No petrophysical relationship between electrical conductivity and relative permittivity is assumed but is instead obtained as a by-product of the inversion. The approach has been applied to data collected in a U.K. sandstone aquifer in order to improve characterization of the vadose zone hydrostratigraphy. By analyzing scatterplots of electrical conductivity versus relative permittivity together with petrophysical models a zonation could be obtained with corresponding estimates of the electrical formation factor, the water content, and the effective grain radius of the sediments. The approach provides greater insight into the hydrogeological characteristics of the subsurface than by using conventional geophysical inversion methods.

[1] There is growing interest in the use of geophysical methods for hydrological model parameterization. Empirical induced polarization (IP)-hydraulic conductivity (K) relationships have been developed, but these are only applicable to sediments in which the IP response shows limited variation with electrical current frequency. Here we examine the spectral IP response of samples taken from a UK sandstone aquifer and compare measured parameters with physical and hydraulic properties. We demonstrate the limited value of existing IP-K models due to the inherent IP frequency dependence of these samples. Our results show how the mean relaxation time, t, is a more appropriate measure of IP response for these sediments. A significant inverse correlation between the surface area to pore volume ratio and t is observed, suggesting that t is a measure of a characteristic hydraulic length scale. This is supported by a measured strong positive correlation between log t and log K. Our measurements also reveal evidence of a relationship between t and a dominant pore throat size, which leads to postulations about the parallelism between the spectral IP behavior and unsaturated hydraulic characteristics. Additional experiments show how the relaxation time is affected by degree of fluid saturation, indicating that saturation levels must be accounted for if our empirical relationships are applied to vadose zone studies. Our results show clear evidence of the potential value of frequency-based IP measurements for parameterization of groundwater flow models.

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Over the last 15 years significant advancements in induced polarization (IP) research have taken place, particularly with respect to spectral IP (SIP), concerning the understanding of the mechanisms of the IP phenomenon, the conduction of accurate and broadband laboratory measurements, the modelling and inversion of IP data for imaging purposes, and the increasing application of the method in near-surface investigations. We here summarized the current state of the science of the SIP method for near-surface applications and describe which aspects still represent open issues and should be the focus of future research efforts.Significant progress has been made over the last decade in the understanding of the microscopic mechanisms of IP; however, integrated mechanistic models involving the different possible polarization processes at the grain/pore scale are still lacking. A prerequisite for the advances in the mechanistic understanding of IP was the development of improved laboratory instrumentation, which has led to a continuously growing database of SIP measurements on various soil and rock samples. We summarize the experience of numerous experimental studies by formulating key recommendations for reliable SIP laboratory measurements. To make use of the established theoretical and empirical relationships between SIP characteristics and target petrophysical properties at the field scale, sophisticated forward modelling and inversion algorithms are needed. Considerable progress has been made also in this field, in particular with the development of complex resistivity algorithms allowing the modelling and inversion of IP data in the frequency domain. The ultimate goal for the future are algorithms and codes for the integral inversion of 3-D, time-3 lapse and multi-frequency IP data, which defines a 5-D inversion problem involving the dimensions space (for imaging), time (for monitoring) and frequency (for spectroscopy). We also offer guidelines for reliable and accurate measurements of IP spectra, which are essential for improved understanding of IP mechanisms and their links to physical, chemical and biological properties of interest. We believe that the SIP method offers potential for subsurface structure and process characterization, in particular in hydrogeophysical and biogeophysical studies.