J. van der Kruk

Soil hydrology: Recent methodological advances, challenges, and perspectives

Technological and methodological progress is essential to improve our understanding of fundamental processes in natural and engineering sciences. In this paper, we will address the potential of new technological and methodological advancements in soil hydrology to move forward our understanding of soil water related processes across a broad range of scales. We will focus on advancements made in quantifying root water uptake processes, subsurface lateral flow, and deep drainage at the field and catchment scale, respectively. We will elaborate on the value of establishing a science-driven network of hydrological observatories to test fundamental hypotheses, to study organizational principles of soil hydrologic processes at catchment scale, and to provide data for the development and validation of models. Finally, we discuss recent developments in data assimilation methods, which provide new opportunities to better integrate observations and models and to improve predictions of the short-term evolution of hydrological processes.

GPR Full-Waveform Sensitivity and Resolution Analysis Using an FDTD Adjoint Method

GPR tomography is a useful tool for mapping the conductivity and permittivity distributions in the shallow subsurface. By exploiting the full GPR waveforms it is possible to image sub-wavelength features and improve resolution relative to what is possible using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of the final result, therefore limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal resolution and information content analysis. We present here a novel method for computing the sensitivity kernels (Jacobian matrix) based on an FDTD adjoint method. We show that the column sum of absolute values of the Jacobian, often used as a proxy for model resolution, is inadequate, such that a formal resolution analysis should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of the experiment and shows the extent of the unresolved model space.

Full-waveform inversion of GPR data in frequency-domain

A new full-waveform inversion scheme is developed to obtain high-resolution images of cross-hole ground penetrating radar (GPR) data. The inversion is formulated as a non-linear least squares problem which minimizes errors between synthetic and observed data. The full-waveform modeling is implemented in frequency domain using the finite-difference (FDFD) solution of Maxwell equation. Here, we are using an iterative gradient method (Gauss-Newton) where the gradient is determined by using the forward vector wavefield and the backward-propagated vectorial residual wavefield. The algorithm inverts sequentially from low to high frequencies and permittivity and conductivity distributions can be obtained simultaneously. Preliminary inversion results of a synthetic example for a homogeneous background model with embedded high contrast parameters anomalies show that the permittivity result is comparable with time domain full-waveform inversion that uses an expanding bandwidth for increasing iterations.

Multi-component GPR imaging for different heights of source and receiver antennas

For imaging ground penetrating radar (GPR) data, three of the most important parameters are the wave speed, polarisation and amplitude. Choosing an appropriate forward model that incorporates these three parameters is a critical aspect of imaging. A new multi-component imaging algorithm that takes into account the polarisation and vectorial radiation characteristics of GPR data has recently been developed. The forward model used to calculate the imaging operators in this imaging algorithm is based on far-field expressions for the radiation characteristics of a dipole present on an interface. Here, multi-component images obtained using elevated source and receiver antennas are presented. As the height of the antennas above the surface is increased, the bandwidth of the scattered data decreases. This results in decreasing spatial resolution for increasing height of the antennas.

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.

Development and drift-analysis of a modular electromagnetic induction system for shallow ground conductivity measurements

Electromagnetic induction (EMI) is used for fast near surface mapping of the electrical conductivity (EC) for a wide range of geophysical applications. Recently, enhanced methods were developed to measure depth-dependent EC by inverting quantitative multi-configuration EMI data, which increases the demand for a suitable multi-channel EMI measurement system. We have designed a novel EMI system that enables the use of modular transmitter/receiver (TX/RX) units, which are connected to a central measurement system and are optimized for flexible setups with coil separations of up to 1.0 m. Each TX/RX-unit contains a coil, which is specifically adjusted for transmitting or receiving magnetic fields. All units enable impedance measurements at the coils, which are used to simulate its electrical circuit and analyze temperature-induced drift effects. A laboratory drift analysis at 8 kHz showed that 88% of the drift in the measured data is due to the change in the electrical transmitter coil resistance. The remaining 12% is due to changes in the transmitter coil inductance and capacitance, the receiver impedance and drifts in the amplification circuit. A measurement under field conditions proved that the new EMI system is able to detect a water-filled swimming pool with 50 mS m−1, using a coil separation of 0.3 m. In addition, the system allows in-field ambient noise spectra measurements in order to select optimal low-noise measurement frequencies.

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.

Towards 3D full-waveform inversion of crosshole GPR data

2D crosshole ground penetrating (GPR) full-1 waveform inversion (FWI) has shown superior resolution 1 compared to ray-based inversion tomograms for synthetic and experimental data. To invert measured 3D data with a 2D j model that has a reduced geometrical spreading and assumes infinite source and receiver dimensions perpendicular to the 2D inversion plane, the Bleistein transformation can be used to convert the measured 3D data to 2D. This far-field conversion consists of a phase shift and amplitude correction that is based on the first arrival travel time of each trace. In the case of late arrival and high amplitude events that 1 can occur due to low-velocity waveguides andfast propagating refracted waves, this transformation can introduce errors especially in the amplitude such that the inverted conductivity is less accurate. To overcome these problems, we have replaced the 2D finite difference time domain FDTD forward model in the FWI scheme with the well-known gprMax3D FDTD modeling program. In this way, we do not need to use the Bleistein 3D-to-2D filter with its far-field approximation, and we can deal with the correct geometrical spreading and approximate better realistic point source and receivers. Currently, the 2D FWI algorithm has been extended to 2.5D by replacing the 2D FDTD with the gprMax 3D FDTD modeling program. The first test of the 2.5D FWI is based on inversion results of a data set acquired at the Widen site in Switzerland that contained a low-velocity waveguide. The new 2.5D FWI performed well in reconstructing the models. The new 2.5D FWI enables a more reliable re-construction of the subsurface image, especially the electrical conductivity tomograms and to the full use of all the modeling possibilities of the gprMax modeling tool.

GPR full waveform sensitivity and resolution analysis using an FDTD adjoint method

Radar tomography is a useful technique for mapping the permittivity and conductivity distributions in the shallow subsurface. By exploiting the full radar waveforms, it is possible to improve resolution and, thus, image subwavelength features not resolvable using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of a final result, possibly limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal model resolution and information content analysis. We present a novel method for computing the sensitivity functions (Jacobian matrix) based on a time-domain adjoint method. Because the new scheme only computes the sensitivity values for the transmitter and receiver combinations that are used, it reduces the number of forward runs with respect to standard brute-force or other virtual-source schemes. The procedure has been implemented by using a standard finite-difference time-domain modeling method. A comparison between cumulative sensitivity (column sum of absolute values of the Jacobian) images, which is sometimes used in geoelectrical studies as a proxy for resolution in practical cases, and formal model resolution images is also presented. We show that the cumulative sensitivity supplies some valuable information about the image, but when possible, formal resolution analyses should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of an experiment and shows the extent of the unresolved model space.