Jan van der Kruk

A New Vector Waveform Inversion Algorithm for Simultaneous Updating of Conductivity and Permittivity Parameters From Combination Crosshole/Borehole-to-Surface GPR Data

We have developed a new full-waveform groundpenetrating radar (GPR) multicomponent inversion scheme for imaging the shallow subsurface using arbitrary recording configurations. It yields significantly higher resolution images than conventional tomographic techniques based on first-arrival times and pulse amplitudes. The inversion is formulated as a nonlinear least squares problem in which the misfit between observed and modeled data is minimized. The full-waveform modeling is implemented by means of a finite-difference time-domain solution of Maxwells equations. We derive here an iterative gradient method in which the steepest descent direction, used to update iteratively the permittivity and conductivity distributions in an optimal way, is found by cross-correlating the forward vector wavefield and the backward-propagated vectorial residual wavefield. The formulation of the solution is given in a very general, albeit compact and elegant, fashion. Each iteration step of our inversion scheme requires several calculations of propagating wavefields. Novel features of the scheme compared to previous full-waveform GPR inversions are as follows: 1) The permittivity and conductivity distributions are updated simultaneously (rather than consecutively) at each iterative step using improved gradient and step length formulations; 2) the scheme is able to exploit the full vector wavefield; and 3) various data sets/survey types (e.g., crosshole and borehole-to-surface) can be individually or jointly inverted. Several synthetic examples involving both homogeneous and layered stochastic background models with embedded anomalous inclusions demonstrate the superiority of the new scheme over previous approaches.

Properties of surface waveguides derived from separate and joint inversion of dispersive TE and TM GPR data

Pronounced dispersion of ground-penetrating radar (GPR) waves is observed at locations distinguished by thin surface layers of high-permittivity material (e.g., water-saturated soil). The dispersion characteristics depend on the permittivity and thickness of the effective surface waveguide and the permittivity of the material below it. We introduce a scheme for estimating the values of these parameters from dispersed transverse-electric (TE) and transverse-magnetic (TM) GPR data that is analogous to recently developed methods for analyzing dispersed Rayleigh waves recorded on multichannel seismic data. Our scheme involves calculating phase-velocity spectra, picking dispersion curves from the spectra, and then inverting the dispersion curves for the subsurface material properties by using a combined local- and global-minimization procedure. Application of this new scheme to synthetic and field data demonstrates its efficacy in providing the required physical property information. Where the surface layer is relatively distinct and uniform, inversions of the resulting high-quality dispersed TE data provide all required parameters. In more heterogeneous environments, joint inversions of the TE and TM data, which usually include information in different frequency ranges, may be required.

Full-waveform inversion of cross-hole ground-penetrating radar data to characterize a gravel aquifer close to the Thur River, Switzerland

Cross-hole radar tomography is a useful tool for mapping shallow subsurface electrical properties viz. dielectric permittivity and electrical conductivity. Common practice is to invert cross-hole radar data with ray-based tomographic algorithms using first arrival traveltimes and first cycle amplitudes. However, the resolution of conventional standard ray-based inversion schemes for cross-hole ground-penetrating radar (GPR) is limited because only a fraction of the information contained in the radar data is used. The resolution can be improved significantly by using a full-waveform inversion that considers the entire waveform, or significant parts thereof. A recently developed 2D time-domain vectorial full-waveform cross-hole radar inversion code has been modified in the present study by allowing optimized acquisition setups that reduce the acquisition time and computational costs significantly. This is achieved by minimizing the number of transmitter points and maximizing the number of receiver positions. The improved algorithm was employed to invert cross-hole GPR data acquired within a gravel aquifer (4–10 m depth) in the Thur valley, Switzerland. The simulated traces of the final model obtained by the full-waveform inversion fit the observed traces very well in the lower part of the section and reasonably well in the upper part of the section. Compared to the ray-based inversion, the results from the full-waveform inversion show significantly higher resolution images. At either side, 2.5 m distance away from the cross-hole plane, borehole logs were acquired. There is a good correspondence between the conductivity tomograms and the natural gamma logs at the boundary of the gravel layer and the underlying lacustrine clay deposits. Using existing petrophysical models, the inversion results and neutron-neutron logs are converted to porosity. Without any additional calibration, the values obtained for the converted neutron-neutron logs and permittivity results are very close and similar vertical variations can be observed. The full-waveform inversion provides in both cases additional information about the subsurface. Due to the presence of the water table and associated refracted/reflected waves, the upper traces are not well fitted and the upper 2 m in the permittivity and conductivity tomograms are not reliably reconstructed because the unsaturated zone is not incorporated into the inversion domain.

Three‐dimensional imaging of subsurface structural patterns using quantitative large‐scale multiconfiguration electromagnetic induction data

Electromagnetic induction (EMI) systems measure the soil apparent electrical conductivity (ECa), which is related to the soil water content, texture, and salinity changes. Large-scale EMI measurements often show relevant areal ECa patterns, but only few researchers have attempted to resolve vertical changes in electrical conductivity that in principle can be obtained using multiconfiguration EMI devices. In this work, we show that EMI measurements can be used to determine the lateral and vertical distribution of the electrical conductivity at the field scale and beyond. Processed ECa data for six coil configurations measured at the Selhausen (Germany) test site were calibrated using inverted electrical resistivity tomography (ERT) data from a short transect with a high ECa range, and regridded using a nearest neighbor interpolation. The quantitative ECa data at each grid node were inverted using a novel three-layer inversion that uses the shuffled complex evolution (SCE) optimization and a Maxwell-based electromagnetic forward model. The obtained 1-D results were stitched together to form a 3-D subsurface electrical conductivity model that showed smoothly varying electrical conductivities and layer thicknesses, indicating the stability of the inversion. The obtained electrical conductivity distributions were validated with low-resolution grain size distribution maps and two 120 m long ERT transects that confirmed the obtained lateral and vertical large-scale electrical conductivity patterns. Observed differences in the EMI and ERT inversion results were attributed to differences in soil water content between acquisition days. These findings indicate that EMI inversions can be used to infer hydrologically active layers.

Monitoring and Modeling the Terrestrial System from Pores to Catchments: The Transregional Collaborative Research Center on Patterns in the Soil–Vegetation–Atmosphere System

AbstractMost activities of humankind take place in the transition zone between four compartments of the terrestrial system: the unconfined aquifer, including the unsaturated zone; surface water; vegetation; and atmosphere. The mass, momentum, and heat energy fluxes between these compartments drive their mutual state evolution. Improved understanding of the processes that drive these fluxes is important for climate projections, weather prediction, flood forecasting, water and soil resources management, agriculture, and water quality control. The different transport mechanisms and flow rates within the compartments result in complex patterns on different temporal and spatial scales that make predictions of the terrestrial system challenging for scientists and policy makers. The Transregional Collaborative Research Centre 32 (TR32) was formed in 2007 to integrate monitoring with modeling and data assimilation in order to develop a holistic view of the terrestrial system. TR32 is a long-term research program ...

Vector-migration of standard copolarized 3D GPR data

The derivation of ground-penetrating radar GPR images in which the amplitudes of reflections and diffractions are consistent with subsurface electromagnetic property contrasts requires migration algorithms that correctly account for the antenna radiation patterns and the vectorial character of electromagnetic wavefields.Mostexistingvector-migrationtechniquesarebased onfar-fieldapproximationsofGreen’sfunctions,whichareinappropriateforthemajorityofGPRapplications.Wehaverecently developedamethodforrapidlycomputingpracticallyexact-field Green’sfunctionsinamulticomponentvectormigrationscheme. Asignificantdisadvantageofthisschemeistheextraeffortneeded to record, process, and migrate at least two components of GPRdata.Bymakingstraightforwardmodificationstothemulticomponent algorithm, we derive an equivalent exact-field single-component vector-migration scheme that can be applied to most standard GPR data acquired using a single copolarized antenna pair. Our new formulation is valid for polarization-independent features e.g., most point scatterers, spheres, and planar objects, but not for polarization-dependent ones e.g., most underground public utilities. A variety of tests demonstrates the stability of the exact-field single-component operators.Applicationsofthenewschemetosyntheticandfield-recordedGPRdata containingdippingplanarreflectionsproduceimagesthatarevirtuallyidenticaltothecorrespondingmulticomponentvector-migratedimagesandarealmostinvarianttotherelativeorientations of antennas and reflectors. The new single-component vectormigration scheme is appropriate for migrating the majority of GPRdataacquiredbyresearchersandpractitioners.

Detection of spatially limited high‐porosity layers using crosshole GPR signal analysis and full‐waveform inversion

High-permittivity layers, related to high-porosity layers or impermeable clay lenses, can act as low-velocity electromagnetic waveguides. Electromagnetic wave phenomena associated with these features are complicated, not well known and not easy to interpret in borehole GPR data. Recently, a novel amplitude analysis approach was developed that is able to detect continuous low-velocity waveguides and their boundaries between boreholes by using maximum and minimum positions of the trace energy profiles in measured GPR data. By analyzing waveguide models of different thickness, dip, extent, permittivity, and conductivity parameters, we extend the amplitude analysis to detect spatially limited or terminated waveguides. Waveguides that show high-amplitude elongated wave trains are most probably caused by a change in porosity rather than a change in clay content. In a crosshole GPR data set from the Boise Hydrogeophysical Research Site, two terminated wave-guiding structures were detected using the extended amplitude analysis. Information gained from the amplitude analysis improved the starting model for full-waveform inversion which imaged the lateral extent and thickness of terminated waveguides with high resolution. Synthetic data calculated using the inverted permittivity and conductivity models show similar amplitudes and phases, as observed in the measured data, which indicates the reliability of the obtained models. Neutron-Neutron logging data from three boreholes confirm the changes in porosity and indicate that these layers were high-porosity sand units within low-porosity, poorly sorted sand, and gravel units.

Improved Characterization of Fine-Texture Soils Using On-Ground GPR Full-Waveform Inversion

Ground-penetrating radar (GPR) uses the recording of electromagnetic waves and is increasingly applied for a wide range of applications. Traditionally, the main focus was on the analysis of the medium permittivity since estimates of the conductivity using the far-field approximation contain relatively large errors and cannot be interpreted quantitatively. Recently, a full-waveform inversion (FWI) scheme has been developed that is able to reliably estimate permittivity and conductivity values by analyzing reflected waves present in on-ground GPR data. It is based on a frequency-domain solution of Maxwells equations including far, intermediate, and near fields assuming a 3-D subsurface. Here, we adapt the FWI scheme for on-ground GPR to invert the direct ground wave traveling through the shallow subsurface. Due to possible interference with the airwaves and other reflections, an automated time-domain filter needed to be included in the inversion. In addition to the obtained permittivity and conductivity values, also the wavelet center frequency and amplitude return valuable information that can be used for soil characterization. Combined geophysical measurements were carried out over a silty loam with significant variability in the soil texture. The obtained medium properties are consistent with Theta probe, electromagnetic resistivity tomography, and electromagnetic induction results and enable the formulation of an empirical relationship between soil texture and soil properties. The permittivities and conductivities increase with increasing clay and silt and decreasing skeleton content. Moreover, with increasing permittivities and conductivities, the wavelet center frequency decreases, whereas the wavelet amplitude increases, which is consistent with the radiation pattern and the antenna coupling characteristics.

Characterizing a GPR antenna system by near-field electric field measurements

Amethod to determine current distributions on resistively loaded Wu-King-type antennas from sparse near-field measurements of the electric field is introduced. We use a parametric formulation of current flow and invert the measured data to determine the characteristic antenna parameters and input voltage wavelets that best explain the measured electric-field data. We compare modeled and measured electricfield data to show that our inversion method yields reasonable results and that our antenna model provides a means to correct for the effects of an antenna’s finite length in migration/imagingalgorithms.Bymodifyingthedescriptionofthe current distribution, our method may be adapted for various antennatypes.

High resolution aquifer characterization using crosshole GPR full‐waveform tomography: Comparison with direct‐push and tracer test data

Limited knowledge about the spatial distribution of aquifer properties typically constrains our ability to predict subsurface flow and transport. Here we investigate the value of using high resolution full-waveform inversion of cross-borehole ground penetrating radar (GPR) data for aquifer characterization. By stitching together GPR tomograms from multiple adjacent crosshole planes, we are able to image, with a decimeter scale resolution, the dielectric permittivity and electrical conductivity of an alluvial aquifer along cross sections of 50 m length and 10 m depth. A logistic regression model is employed to predict the spatial distribution of lithological facies on the basis of the GPR results. Vertical profiles of porosity and hydraulic conductivity from direct-push, flowmeter and grain size data suggest that the GPR predicted facies classification is meaningful with regard to porosity and hydraulic conductivity, even though the distributions of individual facies show some overlap and the absolute hydraulic conductivities from the different methods (direct-push, flowmeter, grain size) differ up to approximately one order of magnitude. Comparison of the GPR predicted facies architecture with tracer test data suggests that the plume splitting observed in a tracer experiment was caused by a hydraulically low-conductive sand layer with a thickness of only a few decimeters. Because this sand layer is identified by GPR full-waveform inversion but not by conventional GPR ray-based inversion we conclude that the improvement in spatial resolution due to full-waveform inversion is crucial to detect small-scale aquifer structures that are highly relevant for solute transport.