Anja Klotzsche

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.

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.

Optimization of acquisition setup for cross-hole GPR full-waveform inversion using checkerboard analysis

Tomographic inversions of cross-hole ground-penetrating radar provide images of electromagnetic properties of the shallow subsurface and are used in a wide range of applications. Whereas the resolutions of ray-based methods like first-arrival traveltime and first-cycle amplitude tomography are limited to the scale of the first Fresnel zone, full-waveform inversions incorporate precise forward modelling using the full recorded signal for a solution of Maxwell’s equation, which results in sub-wavelength resolutions. In practice, the method can be time-consuming in data acquisition and expensive in computational costs. To overcome these expenses, a semi-reciprocal acquisition setup with a reduced number of transmitters and an interchange of transmitter and receiver boreholes instead of a one-sided equidistant setup in either borehole yielded promising results. Here, this optimized, semi-reciprocal acquisition setup is compared to a dense, equidistant, one-sided acquisition setup measured at the field site Krauthausen, Germany. The full-waveform inversion results are evaluated using the checkerboard test as a capable resolution analysis tool to determine resolvabilities. We introduced also a new method of time-zero correction by a cross-correlation of a zerooffset profile with corresponding horizontal traces of each multi-offset gather. The obtained experimental results from Krauthausen combined with the checkerboard analysis indicate the main threepermittivity layers that correspond with different porosities. Also fine-layered structures within these main layers were reliably imaged. We conclude that the use of the semi-reciprocal setup is optimum for acquisition speed, inversion speed and obtained permittivity inversion results. Our results indicate that conductivity results are better for denser transmitter-receiver setups.

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

Imaging results of crosshole GPR can be significantly improved by using full-waveform inversion compared to conventional ray-based inversion schemes. A recently developed 2D finite difference time domain (FDTD) vectorial full-waveform crosshole radar inversion method was made more flexible to allow using an optimized acquisition setup that reduces the measurement speed and the computational cost. This improved algorithm was used to invert crosshole GPR data acquired within a gravel aquifer in northern Switzerland. Compared to the ray-based inversion, the results from the full-waveform inversion show significantly higher resolution images in the depth range of 6m - 10m. Comparison of the inversion results with borehole logs shows that porosity estimates obtained from Neutron-Neutron data correspond well with the GPR porosities derived from the permittivity distribution in the depth range 6 m - 10 m and that the trends are in good qualitative agreement. Furthermore, there is a good correspondence between the conductivity tomograms and natural Gamma logs at the boundary between the gravel layer and the underlying lacustrine clay sediments.

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.

Quantitative multi-layer electromagnetic induction inversion and full-waveform inversion of crosshole ground penetrating radar data

Due to the recent system developments for the electromagnetic characterization of the subsurface, fast and easy acquisition is made feasible due to the fast measurement speed, easy coupling with GPS systems, and the availability of multi-channel electromagnetic induction (EMI) and ground penetrating radar (GPR) systems. Moreover, the increasing computer power enables the use of accurate forward modeling programs in advanced inversion algorithms where no approximations are used and the full information content of the measured data can be exploited. Here, recent developments of large-scale quantitative EMI inversion and full-waveform GPR inversion are discussed that yield higher resolution of quantitative medium properties compared to conventional approaches. In both cases a detailed forward model is used in the inversion procedure that is based on Maxwell’s equations. The multi-channel EMI data that have different sensing depths for the different source-receiver offset are calibrated using a short electrical resistivity tomography (ERT) calibration line which makes it possible to invert for electrical conductivity changes with depth over large areas. The crosshole GPR full-waveform inversion yields significant higher resolution of the permittivity and conductivity images compared to ray-based inversion results.

Characterizing a low-velocity waveguide using crosshole GPR full-waveform inversion

For accurate prediction of flow and contaminant transport a detailed quantification of the local spatial hydraulic conductivity is necessary. In particular, decimeter-scale high contrast layers caused by increased porosity or clay content are important because they can have a dominant effect on solute transport. Such embedded layers when characterized by high dielectric permittivity can act as low-velocity electromagnetic waveguides and be readily identified and characterized using high-frequency crosshole GPR. We show by means of a GPR field example from a hydrological test site in Switzerland that the full-waveform inversion, which exploits the full information content of the data, is able to image a sub-wavelength thickness dipping low-velocity wave-guiding layer. Further, we show an approach to identify low-velocity waveguides from the measured data by analyzing the amplitude and energy behavior within the data. For transmitters present within the waveguide, high amplitude elongated wave-trains are detected for receivers straddling the waveguide depth range, with significantly larger amplitudes than on receivers outside the low-velocity layer, whereas transmitters outside the waveguide show an energy minimum for receivers within the waveguide.

Crosshole GPR full-waveform inversion and waveguide amplitude analysis: Recent developments and new challenges

Over the last years, crosshole GPR full-waveform inversion has proved to be a powerful tool to map and characterize aquifers with a decimeter-scale resolution. Especially the detection of small-scale high contrast layers that can be related to zones of high porosity and zones of preferential flow improved our understanding of the propagation of the electromagnetic waves related to these features. Here, we give an overview of the potential and challenges of applying the full-waveform inversion to experimental data and discuss the obtained results for crosshole GPR data acquired at different test sites. Thereby, we also demonstrate the theoretical developments and illustrate the necessary steps that are required to achieve reliable full-waveform inversion results, which are not only indicated by a good fit of the measured and modelled traces, but also by the absence of a remaining gradient for the final models. One requirement and important step is to obtain good starting models. Whereas ray-based approaches sometimes cannot provide sufficient good starting models, the waveguide amplitude analysis can help to improve these starting models.

High resolution imaging of the unsaturated and saturated zones of a gravel aquifer using full-waveform inversion

Full-waveform inversion can significantly improve imaging results of cross-hole GPR data compared to conventional ray-based inversion schemes. Recently, a 2D full-waveform finite difference time domain (FDTD) approach was used to invert cross-hole GPR data measured in the saturated zone of a gravel aquifer. Due to water table refractions and reflections, the upper part of the aquifer was not reliably imaged. Here, we reconstruct the upper part of the aquifer by imaging both the saturated and unsaturated zones. Estimating one effective wavelet, as was done for the saturated zone inversion alone, is insufficient because the effective wavelet strongly depends on the location of both the transmitter and receiver antennas. Therefore, four different source wavelets were estimated for the different combinations of antennas placement in the two zones, and the full-waveform inversion algorithm adapted accordingly. This resulted in improved images of the aquifer. In general, the observed and the synthetic traces show a good correspondence in both shape and amplitude. For the transmitters in the unsaturated domain, the amplitude fit was not optimum and can probably be improved by adjusting the conductivity starting model.

Estimation of subsurface cylindrical object properties from GPR full-waveform inversion

Precise radius estimation is of high interest for rebar and pipe characterization but very challenging. In this work, we present a novel 3D frequency-domain full-waveform inversion (FWI) approach with which the geometrical information of subsurface cylindrical objects and the dielectric properties of the penetrating medium are simultaneously extracted from ground penetrating radar (GPR) data. The presented FWI strategy optimizes and updates phase- and amplitude-related model parameters sequentially. The forward modeling step in FWI is accomplished by using gprMax3D. The Shuffled Complex Evolution (SCE) strategy is employed for the optimization procedure. The experiment with synthetic data has provided a precise reconstruction of the initial model.