Subsurface electrical conductivity models from frequency-domain electromagnetic (FDEM) induction measurements are often derived using computationally efficient one-dimensional piecewise inversion (PWI) approaches. However, PWI does not account for lateral conductivity variations or the measurement overlap between adjacent soundings, which can limit model estimation accuracy. Laterally constrained inversion (LCI) introduces smoothness constraints to reduce lateral variability between neighbouring models, potentially improving continuity. In this study, both PWI and LCI use a 1D forward function, assuming a horizontally layered earth, and a horizontally laying rigid boom instrument, to perform the estimations This study presents a detailed analysis of how various 2.5D and 3D conductivity distributions, including topographic variations and instrument pitch angle, affect FDEM measurements. We examine how these measurement distortions propagate into PWI and LCI inversion results. Under ideal conditions, such as flat terrain, no instrument tilt, and simple two-layer models, both methods recover accurate conductivity structures, with LCI offering little advantage in accuracy. When topography is introduced, however, distortions occur even at slopes as small as 2°, and both methods show degraded performance, particularly in 3D scenarios. In the field example, LCI produces smoother and more stable results than PWI in the presence of noise, but its assumption of lateral smoothness can be restrictive in geologically complex settings. Our findings show that both inversion strategies are sensitive to topographic and 3D effects, and that error propagation significantly influences inversion reliability. These results highlight the need for improved methodologies capable of handling realistic acquisition conditions and measurement uncertainties in FDEM surveys.

Large areas behind the historic quay walls and bridges in Amsterdam city center are prone to soil mobilization and cavity (sinkhole) formation due to intensified infrastructure developments and extreme groundwater level fluctuations caused by climate change. We carried out a geophysical survey to investigate a sinkhole formed under the Muntplein (Amsterdam, The Netherlands). The surface trace (hole) of the sinkhole was triggered by a heavy vehicle passing over the street which lies in the vicinity of a quay wall and behind the abutment of the Muntsluis bridge. The application of ground penetrating radar (GPR) and electric resistivity tomography (ERT) provided continuous data of the shallow subsurface which enabled the detection of the backfilled cavity, its southwest (SW) extension, the bridge abutment-to-soil transition, key utility lines and the presence of two potential targets for further investigation. A follow-up geotechnical assessment supported by hydrographic survey in the canal validated our findings and substantiated our first interpretation (i.e., sinkhole in development). The paper demonstrates the applicability of non-invasive electromagnetic (EM) methods to rapidly detect cavities in critical urban areas, and, thus, to de-risk climate-smart infrastructure developments.

Electromagnetic induction measurements from multi-coil configuration instruments are used to obtain information about the electrical conductivity distribution in the subsurface. The resulting inverse problem might not have a unique and stable solution. In that case, a local inversion method can be trapped in a local minimum and lead to an incorrect solution. In this study, we evaluate the well-posedness of the inverse problem for two and three-layered electrical conductivity models. We show that for a two-layered model, uniqueness is ensured only when both in-phase and quadrature data are available from the measurements. Results from a Gauss–Newton inversion and a lookup table demonstrate that the solution space is convex. Furthermore, we demonstrate that for even a simple three-layered model, the data contained in such measurements are insufficient to reach a correct or stable solution. For models with more than 2 layers, independent prior information is necessary to solve the inverse problem. The insights from the numerical examples are applied in a field case.

Modeling ground penetrating radar (GPR) reflection data on glaciers with methods that require the discretization of the full subsurface domain is extremely computationally expensive because of the combination of a large domain size and the comparatively short wavelength of the signal. To address this issue, we build on and extend a previously proposed approach based on the assumption of a homogeneous background medium (ice) in which various scattering objects (e.g., crevasses, channels, boulders) are embedded far from each other such that multiple scattering can be ignored. The glacier bed, below which no scatterers are assumed to exist, represents the lower limit of the modeling domain. With this method, the two-way propagation of the radar waves through the ice is simulated in a semi-analytical way, whereby scattering surfaces are represented with a set of planar elements of different electric and reflective properties, allowing a wide range of objects to be simulated. As we also take the antenna radiation pattern at the air-ice interface into account, this simple algorithm is able to produce realistic 3D GPR data in a fast and memory efficient way. In this study, we validate the presented algorithm with an analytical solution for a layered model, and we simulate radar data for a model of the Otemma glacier in Switzerland featuring a realistic topography of the glacier bed and a subglacial channel.

It is not practical to obtain a large number of labeled data to train a supervised learning network in tunnel lining nondestructive testing with ground-penetrating radar (GPR). To decrease the dependence of supervised learning on the number of labeled data, an improved self-supervised learning algorithm—self-attention dense contrastive learning (SA-DenseCL)—is proposed and incorporated with a mask region-convolution neural network (Mask R-CNN), which is trained by unlabeled and labeled GPR data. The proposed SA-DenseCL adds a self-attention-based relevant projection head to the DenseCL architecture of self-supervised learning, capturing the spatially continuing information between adjacent GPR traces. In the workflow, some unlabeled GPR images are used to pre-train the SA-DenseCL network for feature extraction and obtaining the backbone weights, which is superior to the conventional pre-training methods of supervised learning pre-trained by ImageNet images. The weights of the pre-trained backbone are then used to initialize the Mask R-CNN through transfer learning. Subsequently, a limited number of labeled GPR images are used to fine-tune the Mask R-CNN for automatically identifying the locations of the reinforcement bars and voids and estimating the secondary lining thickness. The experimental results show that the average precision reaches 96.70%, 81.04%, and 94.67% in identifying reinforcement bar locations, detecting void defects, and estimating secondary lining thickness, respectively, which outperform the conventional methods that use ImageNet-based supervised learning or GPR image-based DenseCL for initializing the Mask R-CNN backbone weights. It is observed that the improved self-supervised learning-based framework can improve the detection and estimation accuracy in GPR tunnel lining inspection.

We conducted ground penetrating radar (GPR) surveys to detect the presence of simulated clandestine burials at the Amsterdam Research Initiative for Subsurface Taphonomy and Anthropology (ARISTA) test facility. Our aim is to determine the characteristic responses of the simulated clandestine burials in this man-made sandy environment (reclaimed land) and use them to provide recommendations for forensic investigations. We performed GPR surveys over three simulated clandestine burials at ARISTA during four non-consecutive days. The acquired data represent common-offset data to investigate changes to burial detectability depending on central antenna frequency (250 MHz and 500 MHz), different GPR instruments (NOGGIN or pulseEKKO), changes to survey grid orientation relative to burials, and increased soil moisture content in the survey area. In common-offset radargrams the burial anomalies take on many forms, appearing as disruptions to existing features (direct-wave arrivals and soil horizons) and as isolated reflection events (hyperbolic events and burial-length horizontal anomalies). In time slices, the burials are characterized by high- or low-amplitude rectangular anomalies. When used in conjunction, the radargrams and time slices produce characteristic responses consistent with the locations of the burials, regardless of the survey grid orientation. Increased soil moisture at the site improves the detectability of the burials.

In hydrocarbon drilling, mud filtrate penetrates permeable formations and alters the pore fluid characteristics in the immediate vicinity of the borehole. Typically, the prevailing in situ pore fluids are displaced by the invading mud filtrate, which leads to gradually changing distributions of the fluid and electrical properties. Understanding this invasion process is crucial for the interpretation of logging data and associated reservoir evaluations. Conventional logging methods tend to be inadequate for this purpose as their resolution is too low. We find that invasion depth can be determined from borehole radar data using an optimized antenna configuration and time-lapse measurements. A series of parametric sensitivity analyses provide information about the effects of variations of the rock and fluid properties on the identification and extraction of borehole radar signals reflected from the invasion front. Our results suggest that by embedding the radar antennas in cavities filled with an absorbing dielectric material, it is possible to minimize the interference arising from the metal components of the logging tool. In the simulated reservoir scenario, a time-lapse measurement mode with a time interval of at least 6 h can reliably extract the radar signals reflected from the invasion front, and the proposed borehole radar has a lateral detection range from 0.15 to 1 m. A comprehensive range of parametric sensitivity analyses indicates that the signals reflected from the invasion front are principally influenced by oil viscosity, porosity, and mud and formation water salinity, as well as by molecular diffusion coefficient and cementation exponent. These properties and parameters should be carefully explored and assessed when applying borehole radar to evaluate mud invasion information in a reservoir environment.

Marchenko-type integrals typically relate so-called focusing functions and Green's functions via the reflection response measured on the open surface of a volume of interest. Originating from one dimensional inverse scattering theory, the extension to two and three dimensions set in motion various new developments regarding imaging in complex materials. This extension, however, is based on wavefield decomposition inside the volume and a truncated medium state, i.e. a version of the medium that is reflection-free underneath the focusing location, suggesting that evanescent, refracted and diving waves cannot be included in the representation. We elaborate on a new derivation for Marchenko-like integrals that (i) extends the concept of wavefield focusing by using a generalised homogeneous Green's function, (ii) is based on partial differential equations and thereby allows for additional insights and a new physical intuition for Marchenko equations, (iii) unifies wavefield focusing for open and closed boundary systems, (iv) does not require wavefield decomposition or a truncated medium state, thus including the full wavefield Green's function, (v) enables using forward modelling to obtain, e.g., Marchenko-type, time-compact focusing functions. We place a particular focus on the latter point, illustrating and investigating how to solve the underlying partial differential equations for various types of focusing functions. This paves the way for a deeper understanding of focusing functions as well as advanced full wavefield Marchenko schemes. While the derivations are generally presented for the 3D case, we show numerical examples in 1D.