ALBERT

Description: Often in geophysical monitoring experiments time-lapse inversion models vary too smoothly with time, owing to the strong imprint of regularization. Several methods have been proposed for focusing the spatiotemporal changes of the model parameters. In this study, we present two generalizations of the minimum support norm, which favour compact time-lapse changes and can be adapted to the specific problem requirements. Inversion results from synthetic direct current resistivity models that mimic developing plumes show that the focusing scheme significantly improves size, shape and magnitude estimates of the time-lapse changes. Inversions of the synthetic data also illustrate that the focused inversion gives robust results and that the focusing settings are easily chosen. Inversions of full-decay time-domain induced polarization (IP) field data from a CO 2 monitoring injection experiment show that the focusing scheme performs well for field data and inversions for all four Cole–Cole polarization parameters. Our tests show that the generalized minimum support norms react in an intuitive and predictable way to the norm settings, implying that they can be used in time-lapse experiments for obtaining reliable and robust results.

Description: 〈span〉〈div〉SUMMARY〈/div〉Geophysical methods provide remotely sensed data that are sensitive to subsurface properties and interfaces. Knowledge about discontinuities is important throughout the Earth sciences: for example, the saltwater/freshwater interface in coastal areas drive mixing processes; the temporal development of the discontinuity between frozen and unfrozen ground is indicative of permafrost development; and the regolith-bedrock interface often plays a predominant role in both landslide and critical-zone investigations. Accurate detection of subsurface boundaries and their geometry is challenging when using common inversion routines that rely on smoothness constraints that smear out any naturally occurring interfaces. Moreover, uncertainty quantification of interface geometry based on such inversions is very difficult. In this paper, we present a probabilistic formulation and solution to the geophysical inverse problem of inferring interfaces in the presence of significant subsurface heterogeneity. We implement an empirical-Bayes-within-Gibbs formulation that separates the interface and physical property updates within a Markov chain Monte Carlo scheme. Both the interface and the physical properties of the two sub-domains are constrained to favour smooth spatial transitions and pre-defined property bounds. Our methodology is demonstrated on synthetic and actual surface-based electrical resistivity tomography data sets, with the aim of inferring regolith-bedrock interfaces. Even if we are unable to achieve formal convergence of the Markov chains for all model parameters, we demonstrate that the proposed algorithm offers distinct advantages compared to manual- or algorithm-based interface detection using deterministic geophysical tomograms. Moreover, we obtain more reliable estimates of bedrock resistivity and its spatial variations.〈/span〉

Description: Reliable high-resolution 3-D characterization of aquifers helps to improve our understanding of flow and transport processes when small-scale structures have a strong influence. Crosshole ground penetrating radar (GPR) is a powerful tool for characterizing aquifers due to the method's high-resolution and sensitivity to porosity and soil water content. Recently, a novel GPR full-waveform inversion algorithm was introduced, which is here applied and used for 3-D characterization by inverting six crosshole GPR cross-sections collected between four wells arranged in a square configuration close to the Thur River in Switzerland. The inversion results in the saturated part of this gravel aquifer reveals a significant improvement in resolution for the dielectric permittivity and electrical conductivity images compared to ray-based methods. Consistent structures where acquisition planes intersect indicate the robustness of the inversion process. A decimetre-scale layer with high dielectric permittivity was revealed at a depth of 5–6 m in all six cross-sections analysed here, and a less prominent zone with high dielectric permittivity was found at a depth of 7.5–9 m. These high-permittivity layers act as low-velocity waveguides and they are interpreted as high-porosity layers and possible zones of preferential flow. Porosity estimates from the permittivity models agree well with estimates from Neutron–Neutron logging data at the intersecting diagonal planes. Moreover, estimates of hydraulic permeability based on flowmeter logs confirm the presence of zones of preferential flow in these depth intervals. A detailed analysis of the measured data for transmitters located within the waveguides, revealed increased trace energy due to late-arrival elongated wave trains, which were observed for receiver positions straddling this zone. For the same receiver positions within the waveguide, a distinct minimum in the trace energy was visible when the transmitter was located outside the waveguide. A novel amplitude analysis was proposed to explore these maxima and minima of the trace energy. Laterally continuous low-velocity waveguides and their boundaries were identified in the measured data alone. In contrast to the full-waveform inversion, this method follows a simple workflow and needs no detailed and time consuming processing or inversion of the data. Comparison with the full-waveform inversion results confirmed the presence of the waveguides illustrating that full-waveform inversion return reliable results at the highest resolution currently possible at these scales. We envision that full-waveform inversion of GPR data will play an important role in a wide range of geological, hydrological, glacial and periglacial studies in the critical zone.

Description: Electrical resistivity tomography (ERT) is based on solving a Poisson equation for the electrical potential and is characterized by a good sensitivity only in the vicinity of the electrodes used to gather the data. To provide more information to ERT, we propose an image-guided or structure-constrained inversion of the apparent resistivity data. This approach uses structural information obtained directly from a guiding image. This guiding image can be drawn from a high resolution geophysical method based on the propagation equation (e.g. migrated seismic or ground penetrating radar images) or possibly from a geological cross-section of the subsurface based on some prior geological expertise. The locations and orientations of the structural features can be extracted by image processing methods to determine the structure tensor and the semblances of the guiding image at a set of pixel. Then, we introduce these structural constraints into the inversion of the apparent resistivity data by weighting the four-direction smoothing matrix to smooth along, but not across, structural features. This approach allows preserving both discontinuities and coherences in the inversion of the resistivity data. The image-guided inversion is also combined with an image-guided interpolation approach used to focus a smooth resistivity image. This yields structurally-appealing resistivity tomograms, while the whole process remains computationally efficient. Such a procedure generates a more realistic resistivity distribution (closer to the true ones), which can be, in turn, used quantitatively using appropriate petrophysical transforms, to obtain parameters of interest such as porosity and saturation. We check the validity of this approach using two synthetic case studies as well as two real datasets. For the field data, the image used to guide the inversion of the electrical resistivity data is a GPR section in the first case and a combination of seismic and structural information in the second case, which corresponds to a geothermal site at Pagosa Springs, in Colorado.

Description: 〈span〉〈div〉Summary〈/div〉Geophysical methods provide remotely sensed data that are sensitive to subsurface properties and interfaces. Knowledge about discontinuities is important throughout the Earth sciences: for example, the saltwater/freshwater interface in coastal areas drive mixing processes; the temporal development of the discontinuity between frozen and unfrozen ground is indicative of permafrost development; and the regolith-bedrock interface often plays a predominant role in both landslide and critical-zone investigations. Accurate detection of subsurface boundaries and their geometry is challenging when using common inversion routines that rely on smoothness constraints that smear out any naturally-occurring interfaces. Moreover, uncertainty quantification of interface geometry based on such inversions is very difficult. In this paper, we present a probabilistic formulation and solution to the geophysical inverse problem of inferring interfaces in the presence of significant subsurface heterogeneity. We implement an empirical-Bayes-within-Gibbs formulation that separates the interface and physical property updates within a Markov chain Monte Carlo scheme. Both the interface and the physical properties of the two sub-domains are constrained to favor smooth spatial transitions and pre-defined property bounds. Our methodology is demonstrated on synthetic and actual surface-based electrical resistivity tomography datasets, with the aim of inferring regolith-bedrock interfaces. Even if we are unable to achieve formal convergence of the Markov chains for all model parameters, we demonstrate that the proposed algorithm offers distinct advantages compared to manual or algorithm-based interface detection using deterministic geophysical tomograms. Moreover, we obtain more reliable estimates of bedrock resistivity and its spatial variations.〈/span〉

Description: 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.

Description: Determining groundwater flow paths of infiltrated river water is necessary for studying biochemical processes in the riparian zone, but their characterization is complicated by strong temporal and spatial heterogeneity. We investigated to what extent repeat 3D surface electrical resistance tomography (ERT) can be used to monitor transport of a salt-tracer plume under close to natural gradient conditions. The aim is to estimate groundwater flow velocities and pathways at a site located within a riparian groundwater system adjacent to the perialpine Thur River in northeastern Switzerland. Our ERT time-lapse images provide constraints on the plume’s shape, flow direction, and velocity. These images allow the movement of the plume to be followed for 35 m. Although the hydraulic gradient is only 1.43, the ERT time-lapse images demonstrate that the plume’s center of mass and its front propagate with velocities of $$2\times {10}^{-4}\hbox{ \hspace{0.17em} }\hbox{ \hspace{0.17em} }\mathrm{m}/\mathrm{s}$$ and $$5\times {10}^{-4}\hbox{ \hspace{0.17em} }\hbox{ \hspace{0.17em} }\mathrm{m}/\mathrm{s}$$ , respectively. These velocities are compatible with groundwater resistivity monitoring data in two observation wells 5 m from the injection well. Five additional sensors in the 5–30 m distance range did not detect the plume. Comparison of the ERT time-lapse images with a groundwater transport model and time-lapse inversions of synthetic ERT data indicate that the movement of the plume can be described for the first 6 h after injection by a uniform transport model. Subsurface heterogeneity causes a change of the plume’s direction and velocity at later times. Our results demonstrate the effectiveness of using time-lapse 3D surface ERT to monitor flow pathways in a challenging perialpine environment over larger scales than is practically possible with crosshole 3D ERT.