Roman Pašteka

The differentiations of potential fields play an important role in their interpretations, as they are included in many of the enhanced transformations and edge detectors (Analytical Signal Amplitude, Tilt derivatives, Total Differentiation and others). However, the evaluation of horizontal and vertical differentiation is an unstable process. This instability was partially solved in the past by, e.g. Tikhonov regularisation for the first-order differentiations. Here, we present and compare several regularised stabilisations of higher-orders of differentiations. The methods are tested on synthetic and real data sets, where results indicate the usefulness of the presented method in the potential fields' processing and interpretation. Good properties of higher order regularised derivatives are demonstrated on selected edge-detection operator: in this case, on the modified balanced horizontal gradient operator.

Magnetic surveying is widely used for unexploded ordnance (UXO) detection. However, reliable target localization and characterization remain challenging because of noise, orientation‐dependent magnetic responses, elongated target geometries and inversion non‐uniqueness. In this context, we present an enhancement‐constrained stochastic magnetic inversion workflow that uses anomaly‐enhancement results as spatial prior information to restrict the admissible model space before optimization. First, magnetic anomalies are denoised using a modified non‐local means approach to suppress high‐frequency noise that would otherwise be amplified during derivative‐based processing. Modified local‐phase filters are then used to delineate laterally confined target zones, whereas approximate depth estimates constrain the vertical search range. The resulting spatial bounds are incorporated into a parsimonious stochastic inversion based on the Hunger Games Search algorithm, in which UXO responses are approximated by uniformly magnetized equivalent spheres for computational efficiency. The workflow is tested using noisy synthetic data generated from elongated UXO‐like sphero‐cylinders. The intentional mismatch between the forward‐model geometry and the equivalent‐sphere inversion model provides a more demanding assessment of robustness to geometric simplification. Normalized source strength (NSS)‐based Euler deconvolution (NSS‐Euler) is evaluated as an independent localization benchmark and is not incorporated into the proposed inversion workflow. The proposed framework is then applied to magnetic data acquired over targets with known positions and orientations at a controlled test site in Slovakia. Compared with otherwise identical unconstrained inversions, the derived spatial constraints improve target localization, reduce solution ambiguity and increase the consistency of the recovered models. NSS‐Euler provides an independent estimate of target location and depth, whereas the constrained stochastic inversion yields more accurate localization and depth estimates while additionally recovering effective‐magnetization and other source‐related parameters. Although this simplified representation cannot reproduce all geometric details of real UXO bodies, it offers a practical and computationally efficient framework for localization‐oriented interpretation. The proposed strategy may also be applicable to other compact‐target‐detection problems in which enhancement‐derived spatial information can guide inversion.

Underground water flow in karst areas and changing water levels due to extreme rain can lead to the creation of caverns and sinkhole hazards. Such is the historical experience of the Valaská village in central Slovakia. To better understand the current sinkhole threat in the village, we aim to detect shallow caverns using microgravimetry. Our broader objective is to examine the capabilities of the Growth inversion methodology to detect and characterize shallow cave space. In our study, we focus on the benefits and weak points of the Growth inversion approach, which is a free-geometry inversion method based on model exploration and growing source bodies. Since a sole gravimetric inversion produces ambiguous results, we pay attention to the role and setup of the several free user-adjustable inversion parameters of Growth. We examine tuning these parameters for the specific needs of shallow cavity detection. Valaská experienced sinkholes in 1964, 1968 and 2019. That of 1964 is known for a curious loss of a horse sunk into a karst chimney. Our gravimetric work shows that the sinkhole hazard at the exposed lot in Valaská is ongoing despite the mitigation construction measures. The Growth approach proved to be applicable and useful in microgravimetric identification of sinkhole threat and detection of shallow caverns in karst.

Underground water flow in karst areas and changing water levels due to extreme rain can lead to creation of caverns and sinkhole hazard. Such is the historical experience of the Valaská village in central Slovakia. To better understand the current sinkhole threat in the village, we aim at detecting shallow caverns using microgravimetry. Our broader objective is to examine the capabilities of the Growth inversion methodology to detect and characterize shallow cave space. In our study we focus on the benefits and weak points of the Growth inversion approach, which is a free-geometry inversion method based on model exploration and growing source bodies. Since a sole gravimetric inversion produces ambiguous results, we pay attention to the role and setup of the several free user-adjustable inversion parameters of Growth. We examine tuning these parameters for specific needs of shallow cavities detection. Valaská experienced sinkholes in 1964, 1968 and 2019. That of 1964 is known for a curious loss of a horse sunk into a karst chimney. Our gravimetric work shows that the sinkhole hazard at the exposed lot in Valaská is ongoing despite the taken mitigation construction measures. The Growth approach proved to be applicable and useful in microgravimetric identification of sinkhole threat and detection of shallow caverns in karst.

Microgravimetry has been used in near surface investigations for detecting cavities. It has already proven its success in revealing unknown crypts and tombs in archaeological prospection. It was involved in searching for new cave spaces in karst. It was also employed in detecting void spaces in shallow-mining areas to mitigate sinkhole hazard. In our study we focus on the applicability, benefits and limitations of using the 3D Growth inversion approach for inverting the high-resolution high-precision micro-gravity data observed in undermined areas with the purpose of detecting shallow void space that could lead to sinkhole development, slow surface subsidence or collapses. Growth inversion has several free, user-specified inversion parameters that shape the Growth solution. Our case study presented here is related to sinkhole hazard due to abandoned shallow brown-coal mining under fields with agricultural activities. We pay attention to tuning these parameters for specific needs of cavity detection in terms of long and narrow shallow mining shafts.

The search for the correct value of the regularization parameter is the crucial step in the concept of the Tikhonov regularization. The present sequential methods are using the specialized curves (L _p norms or L curves) on which the points with given properties are searched and tested as desired values of the regularization parameter. Here, we extended one of those methods into two dimensions for the regularized downward continuation operator, while there are situations where the noise shows some directional dependence. The two regularization parameters—one for the each direction ( x and y ), could be the partial answer to these problems. The method is tested on the synthetic and two real data sets from detailed and regional magnetometry to demonstrate its possibilities.

This study applies a Tikhonov regularization framework to aeromagnetic data from parts of northeastern Nigeria to enhance the resolution of magnetic anomalies and suppress geological and cultural noise. The dataset, covering twelve geological map sheets acquired by Fugro Airborne Surveys (2004–2009), was processed using a range of derivative-based edge-detection filters, including the Horizontal Gradient (HG), Analytic Signal (AS) amplitude, Tilt, Horizontal Gradient of Tilt (HG_Tilt), Theta, Normalized HG (TDX), TDXAS, Tilt Angle of the Total Horizontal Gradient (TAHG), Enhanced Tilt (ETilt), Enhanced Total Horizontal Derivative of the Tilt Angle (ETHDR), and Modified Horizontal Gradient Amplitude (MHGA). The MHGA method was further optimized by varying a constant offset (often a fraction or multiplication of π in its computation to evaluate its sensitivity and performance. Results show that regularized derivatives effectively minimize noise amplification while preserving structural integrity, with a revisited algorithm (published by Karcol and Pašteka in year 2025) providing the most stable differentiation. The ETHDR and MHGA (−π/3) filters delineated low-magnetic anomaly zones associated with the Bima, Yolde, Pindiga, Gombe, and Kerri-Kerri Formations, indicating promising geothermal potential. High-gradient zones correspond to granitic intrusions and fault intersections that may act as heat sources and hydrothermal conduits. These results demonstrate that integrating regularized derivatives with advanced edge-detection filters significantly enhances geothermal prospectivity mapping in complex crustal settings.

We present software for calculating gravity acceleration at points of levelling networks in Slovakia. The chosen approach uses an existing detailed gravimetric database and a back-calculation (reconstruction) of the gravity acceleration from the Bouguer anomaly map. We analyse the accuracy of this approach on a sample of independent geodetic points as well as in-situ control measurements.

The present study describes results from synthetic modelling of 2D GPR constant-offset radargrams (B-scans) for air-filled cavities with different shapes. The primary objective of these simulations was to enhance the understanding of actual GPR data when subsurface cavities are present. Three different numerical methods are used, based on the Finite-Difference Time Domain approach. During processing of received synthetic radargrams, migration plays a crucial role. When designing the final depth-sections, it proved to be extremely important the application of the so-called Combined Time–Depth Conversion transformation method. Final results showed with good precision the geometry and depth extent of studied cavities in the absolute majority of the calculated models. The verified processing steps sequence was also successfully applied to a real-world dataset from GPR survey data from St. Catherine's church in Banská Štiavnica.

The vertical differentiation of a nonharmonic quantity derived from a potential field — such as the horizontal gradient, analytic signal modulus, or tilt angle — using conventional wavenumber-domain filters designed for harmonic functions does not yield the true vertical derivative (VD) of the original quantity. Instead, it produces a pseudoderivative. However, this pseudoderivative shows characteristics similar to those of the true VD, so distinguishing between the two can be challenging in practice. Pseudoderivatives are commonly used in qualitative interpretation because they perform well in several tasks (e.g., edge analysis). This good performance stems from the fact that pseudoderivatives correspond to the Hilbert transform of the horizontal derivative of the original function. Nevertheless, analytical expressions exist, enabling the computation of true VDs for nonharmonic functions. Our analysis demonstrates that true VDs provide superior delineation of structural boundaries, particularly in geologically complex settings with interfering anomalies. Based on these results, we recommend the use of true VDs when analyzing transformed nonharmonic fields.