Roman Pašteka

On the application of Euler deconvolution to the analytic signal

Standard Euler deconvolution is applied to potential-field functions that are homogeneous and harmonic. Homogeneity is necessary to satisfy the Euler deconvolution equation itself, whereas harmonicity is required to compute the vertical derivative from data collected on a horizontal plane, according to potential-field theory. The analytic signal modulus of a potential field is a homogeneous function but is not a harmonic function. Hence, the vertical derivative of the analytic signal is incorrect when computed by the usual techniques for harmonic functions and so also is the consequent Euler deconvolution. We show that the resulting errors primarily affect the structural index and that the estimated values are always notably lower than the correct ones. The consequences of this error in the structural index are equally important whether the structural index is given as input (as in standard Euler deconvolution) or represents an unknown to be solved for. The analysis of a case history confirms serious errors in the estimation of structural index if the vertical derivative of the analytic signal is computed as for harmonic functions. We suggest computing the first vertical derivative of the analytic signal modulus, taking into account its nonharmonicity, by using a simple finite-difference algorithm. When the vertical derivative of the analytic signal is computed by finite differences, the depth to source and the structural index consistent with known source parameters are, in fact, obtained.

Estimation of distant relief effect in gravimetry

We analyze gravitational effects of distant topographic and bathymetric relief beyond the (earth-centered) angular distance of 1° 29′ 58″ (i.e., beyond the outer limit of the Hayford-Bowie zone O, or approximately 167 km ) using a spherical earth model. Our results support current procedures that neglect distant relief effects for most local gravity surveys but show their potential importance for continental- and global-scale surveys. The distant relief can produce horizontal gradients as large as 0.3 E (0.03 mGal∕km) . In mountainous areas, the gravitational effect of the distant relief is significant, even for local surveys, although the vertical gradient of the distant relief effect never exceeds ±30 E (3 mGal∕km) on the earth’s surface.

The effect of topography in calculating the atmospheric correction in gravimetry

Although the gravitational effect of Earth’s atmosphere has relatively small values it is generally recommended to account for it in precision gravimetry. Since the effect is height-dependent, it is especially worth considering when the survey covers a broad range of gravity station heights and where the survey is performed close to a continental coast. Previously, the Earth’s topography was not considered significant when calculating the atmospheric correction for subtraction from the theoretical ellipsoidal gravity at the station. In fact the Earth’s surface is not flat over the continents and this variation in height must produce an additional influence upon the values of such a correction. We show using several examples that accounting for the Earth’s topography significantly changes the values from those calculated in the conventional way. The necessary calculations can be efficiently performed using a newly derived formula for the gravitational effect of a spherical shell with variable density.

The calculation of building corrections in microgravity surveys using close range photogrammetry

Use of the microgravity technique for cavity detection in the exploration of historical buildings requires careful data acquisition and modern processing procedures. We have developed a new method for the calculation of building effects, where geodetic measurements and special photogrammetric software are used. In our new approach, a three-dimensional polyhedral model of an historical building is created from images using Eos System’s PhotoModeler Scanner software. A comparison of equations for the calculation of the gravitational effect of polyhedral bodies is presented on a simple test model. The methodology of microgravity data processing is demonstrated on a small Slovak church, where two crypts were successfully detected using microgravity and GPR techniques in summer 2009. We have shown that close range photogrammetry methods offer a possibility to improve the microgravity data processing procedure.

The use of microgravity technique in archaeology: A case study from the St. Nicolas Church in Pukanec, Slovakia

The use of microgravity technique in archaeology: A case study from the St. Nicolas Church in Pukanec, Slovakia The detection of subsurface cavities, such as crypts, cellars and tunnels, in churches and castles belongs to successful applications of the employment of surface gravity measurement techniques in archaeo-prospecting. The old historic building exploration requires using of non-invasive methods, and hence the microgravity technique is a proper candidate for this task. On a case study from the Roman-Catholic Church of St. Nicolas in the town Pukanec the results of using microgravity for detection and delineation of local density variations caused by a near-surface void are shown. The acquired negative anomaly in the residual Bouguer anomalies field suggested the presence of a possible void feature. Euler deconvolution and 3D modelling were used to estimate the depth and shape of the anomalous source. Additionally, measurements of the vertical gravity gradient on several stations were performed. We tested how the use of a downward continuation of gravity, utilizing the real vertical gravity gradient, influences the shape and amplitude of the final Bouguer anomaly map.

Role of Near Topography and Building Effects in Vertical Gravity Gradients Approximation

Importance of precise vertical gradient of gravity (VGG) determination by means of relative gravity measurements is mainly connected with absolute gravity measurements and setting of global and local gravity reference networks. The gravitational effect of the topography and near building structures and their contribution on the vertical gradient of gravity (VGG) was studied. A strong impact of near topography on the VGG values was found in the case of the mountainous areas - deviations up to 88 percent of normal value were obtained by means of relative gravity measurements. Near building structures gravitational effect was estimated by means of simple polyhedrons - very specific nonlinear behaviour of VGG is demonstrated on two model examples. Synthetic tests for the estimation of determined VGG precision are also presented. The error of polynomial estimation of the VGG can be several times higher than the error within measured gravity. For a set of 29 real measurement points a relatively good coincidence between the measured and calculated VGG values was achieved. Application of predicted values of the VGG instead of the normal ones in cases of unknown actual values can lead to a quality improvement of gravimetric reference networks, as well as prospecting VGG measurements.

Integrated Geophysical and Geological Investiga-tions of Karst Structures in Komberek, Slovakia

A complex of geophysical methods were used to investigate a small karst area aimed at the production of detailed geological mapping, to confirm geological localization of known sinkholes, and to find possible continuations of caves and voids below the surface. The dipole electromagnetic profiling and radiometric mapping (the gamma-ray spectrometry method) were applied to determine the spatial distribution of hard carbonate rocks and weathered valley-fill sediments. Detailed high-definition magnetometry was carried out at selected sites in the studied region with the aim of distinguishing between sinkholes and man-made lime-kilns, pits where limestone was heated and transformed into lime. The microgravity and the electrical-resistivity tomography (ERT) methods were used to create high-resolution images of the underground cave. The results of ERT and the geological survey were used as an initial model for gravity modeling. Subsurface cavities of various sizes are contrasting geophysical objects, and the electrical resistivity can range from very conductive to relatively resistive depending on the composition of the filling materials. The interpretation of resistivity properties is not always straightforward. We must distinguish air-filled (high-resistivity) and loamy water-filled (low-resistivity) cavities and fractures. The combined geophysical methodology permits us to determine a more accurate near-surface geological model, in our case the parallel interpretation of a strong conductive anomaly in the ERT inversion and a predominant density decrease in the gravity modelling yield the presence of cavities at depths approximately of 50 to 60 m below the surface.

Case history: integrated geophysical survey at Katarínka Monastery (Slovakia)

Katarinka (St. Catherine) is the ruin of an abandoned Franciscan monastery from the early 17th century located in the western Small Carpathians in Slovakia. Historical sources and paintings suggest that, beside the remains of the monastery that are still visible, a circle of eight chapels, a pilgrim’s hospice, a cemetery, and garden terraces originally surrounded the main building of the monastery. From 2009 to 2012, geophysical campaigns were performed to find evidences and positions of remains of these buildings of the monastery campus. An initial magnetic overview survey revealed multiple local accumulations of disordered dipole anomalies. Since these accumulations did not allow a structural interpretation, ground penetrating radar measurements were conducted. The ground penetrating radar results clearly showed wall structures beneath almost all magnetic anomaly accumulations. In between the remains of the monastery main building, ground penetrating radar and electrical resistivity tomography were performed at different areas that were difficult to access because of a strong cover of vegetation and steep topography.

The role of near topography and building effects in vertical gravity gradients approximation

The gravitational effect of the topography and near-building structures and their contribution on the vertical gradient of gravity (VGG) was studied. The strong impact of near topography on the VGG values was found in the case of the mountainous areas – deviations of up to 88% of normal value were obtained by means of relative gravity measurements in selected parts of Slovakia. Newly developed software and a high-quality detailed digital terrain model of Slovakia was used for the evaluation of the topographical effect. The gravitational effect of near-building structures was estimated by means of simple 3D bodies approximation, i.e., rectangular or polygonal prisms. A very specific non-linear behaviour of VGG is demonstrated on model examples. A relatively good agreement between the measured and calculated (predicted) VGG values was achieved for a set of selected 32 real measurement points. The application of estimated (predicted) values of the VGG instead of the normal ones can lead to a quality improvement of global and local gravimetric reference networks, as well as prospecting VGG measurements.

Applying the regularized derivatives approach in Euler deconvolution and modeling geophysical data to estimate the deep active structures for the northern Red Sea Rift region, Egypt

Applying the regularized derivatives approach in Euler deconvolution and modeling geophysical data to estimate the deep active structures for the northern Red Sea Rift region, Egypt The Red Sea is considered to be a typical example of a newly formed ocean. Moreover the northern Red Sea region and Gulf of Suez are generally important due to their hydrocarbon resources. Estimation of higher derivatives of potential fields represents a significant role in geophysical interpretation (qualitative and/or quantitative), as has been demonstrated in many approaches. One of the most popular methods, employing higher derivatives is the well known Euler deconvolution method. In this method it is very important to stabilize the derivatives evaluation, because they are very sensitive to noise and errors in the interpreted field. One way to stabilize higher derivative evaluation is the utilization of the Tikhonov regularization. We show the influence of regularized derivatives on the properties of the classical 3D Euler deconvolution algorithm and apply it to geophysical potential field data from the Red Sea Rift and its surroundings. The solution obtained with regularized derivatives gives better focused depth-estimates, which are closer to the real position of sources; the results presented here can be used to constrain depth to active crustal structures (boundaries and volcanisms) for northern Red Sea rift. Estimated Euler solution map from Bouguer data utilizing the Tikhonov regularization reveals both the continental-oceanic crust boundary and several shallow listric normal faults spreading on the Red Sea margins having NW-SE direction, suggesting NE-SW extension in these regions. Also, generalized depth model for the structure of the Gulf of Aqaba (three pull-apart basins) was well recognized from this map. However, Euler solutions with band pass filter of magnetic data gives best depth-estimates connected with the volcanic intrusive bodies (intense magmatic activity) prevalent on and around the axial trough transform faults resulted from initiation of Red Sea Rift. This depth estimation was derived resulting different structural indexes (SI). The Majority of seismic epicenters along Red Sea rift is clustered on axial trough and on or near some active initiated transform faults of Red Sea basin which attributed to stresses from magmatic activity and rifting process.