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 Valask & aacute; 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. Valask & aacute; 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 Valask & aacute; 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.

During the summer of 2024, Mt. Etna was characterized by a sequence of six powerful paroxysmal events originating from the Voragine summit crater. This activity marked a significant departure from the preceding years, when paroxysms at the Southeast Crater prevailed. The high dynamicity of this period required continuous and precise monitoring, mapping, and quantification, which were achieved through frequent Unoccupied Aerial System surveys. Using the difference of digital elevation models, which compared the pre-eruptive surface of April 29, 2024, against the post-eruptive surface of September 12, we clearly demonstrated a pattern dominated by net accumulation over the Voragine, with the greatest vertical accretion reaching over 108 m. This substantial growth, attributable to repeated lava effusion and pyroclastic deposition, established Voragine as the new peak of Mt. Etna, reaching an elevation of 3403 m a.s.l. on August 14. We then analyzed the effect of topography changes on gravimetric terrain corrections, which is important for computing the complete Bouguer anomaly, and the impact of variations in the nearest topography on the prediction of vertical gravity gradients. Owing to this effect, differences up to 10 mGal in terrain corrections and up to 150 mu Gal/m in vertical gravity gradient were calculated. This interdisciplinary work provides a detailed quantification of the eruptive products from Mt. Etna's 2024 volcanic sequence and highlights the critical impact of the resulting morphological changes on high-precision gravimetric surveys, thus emphasizing the need for up-to-date digital terrain models.

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 applicability and benefits of the Growth inversion methodology in near-surface geophysics, specifically microgravimetry, is demonstrated here by three case studies from the realm of archeological prospection and sinkhole hazard detection. We use the GROWTH-23 package to arrive at heterogenous source body models and GROWTH-dg to produce homogenous models. We took existing gravity data, namely local gravity anomalies or residual complete Bouguer anomalies, from three case studies and inverted them using the Growth approach. We analyzed the choice of proper values of the individual adjustable Growth inversion parameters for the individual near-surface Growth solutions. The obtained best-recovery Growth models were compared with and validated against the existing interpretations of the same microgravimetric data sets. Lessons were learned from these comparisons regarding the settings of the individual adjustable Growth parameters. The first case study is from the field of archeological prospection and regards the microgravimetric detection of medieval tombs, crypts, and buried foundations in a church. The second case study deals with detection of surface collapse and sinkhole hazard associated with shallow underground mining. The third case study targets sinkhole hazard in an urban area stemming from unknown cavities such as cellars. All in all, the application of the Growth inversion in these cases proved successful and has demonstrated its benefits.

A long-wavelength geoidal geometry reflects mainly lateral density variations in the Earth’s mantle, with the most pronounced features of the Indian Ocean Geoid Low and the West Pacific and North Atlantic Geoid Highs. Despite this spatial pattern being clearly manifested in the global geoidal geometry determined from gravity-dedicated satellite missions, the gravitational signature of the deep mantle could be refined by modelling and subsequently removing the gravitational contribution of lithospheric geometry and density structure. Nonetheless, the expected large uncertainties in available lithospheric density models (CRUST1.0, LITHO1.0) limit, to some extent, the possibility of realistically reproducing the gravitational signature of the deep mantle. To address this issue, we inspect an alternative approach. Realizing that the gravity geopotential field (i.e., gravity potential) is smoother than its gradient (i.e., gravity), we apply the integral operator to geopotential and then investigate the spatial pattern of this functional (i.e., radially integrated geopotential). Results show that this mathematical operation enhances a long-wavelength signature of the deep mantle by filtering out the gravitational contribution of the lithosphere. This finding is explained by the fact that in the definition of this functional, spherical harmonics of geopotential are scaled by the factor 1/n (where n is the degree of spherical harmonics), thus lessening the contribution of higher-degree spherical harmonics in the radially integrated geopotential. We also demonstrate that further enhancement of the mantle signature in this functional could be achieved based on modelling and subsequent removal of the gravitational contribution of lithospheric geometry and density structure.

Gravimetry is a discipline of geophysics that deals with observation and interpretation of the earth gravity field. The acquired gravity data serve the study of the earth interior, be it the deep or the near surface one, by means of the inferred subsurface structural density distribution. The subsurface density structure is resolved by solving the gravimetric inverse problem. Diverse methods and approaches exist for solving this non-unique and ill-posed inverse problem. Here, we focused on those methods that do not pre-constrain the number or geometries of the density sources. We reviewed the historical development and the basic principles of the Growth inversion methodology, which belong to the methods based on the growth of the model density structure throughout an iterative exploration process. The process was based on testing and filling the cells of a subsurface domain partition with density contrasts through an iterative mixed weighted adjustment procedure. The procedure iteratively minimized the data misfit residuals jointly with minimizing the total anomalous mass of the model, which facilitated obtaining compact meaningful source bodies of the solution. The applicability of the Growth inversion approach in structural geophysical studies, in geodynamic studies, and in near surface gravimetric studies was reviewed and illustrated. This work also presented the first application of the Growth inversion tool to near surface microgravimetric data with the goal of seeking very shallow cavities in archeological prospection and environmental geophysics.

The knowledge of the vertical gradient of gravity (VGG) at observation points (benchmarks) in the field or at indoor pillars at observatories is needed across various earth science disciplines. The accurate value of VGG is required to reduce the precise measurements of gravity carried out by various modern gravimeters from the sensor height of the instrument to the level of the benchmark on the ground. No portable and easy to use instrumentation is available for measuring the VGG in the field, although portable quantum devices may change the situation in the future [1]. However, the average value of the VGG over a short vertical span near the surface, which approximates the point VGG value, can be observed by relative gravimeters in the so-called tower mode. Such observations call for the use of special-design (custom-made) tripods, or sturdy geodetic tripods, and repeated measurements of gravity by a relative gravimeter in the upper and lower positions, vertically separated by about one meter, or in several positions along the vertical, separated by decimeters. The in situ VGG measurements are demanding to carry out in the field, especially under harsh conditions. Particularly, strong wind can compromise or even halt the VGG observation, due to introducing high levels of background noise in the data. Therefore, the in situ VGG values are often missing, although highly needed for geophysical, geodetic or geodynamic applications.

A new code for gravity inversion is freely available. It can be used to work with data on complete Bouguer anomaly (CBA) and temporal gravity changes (dg), and is derived from several previous independent codes for CBA data inversion (GROWTH gravity inversion) and for gravity inversion of dg data (GROWTH-dg). This methodology enables the recovery of general 3D structures for anomalous density as a free aggregation of small parallelepiped cells filled with an adjusted density contrast. The non-linear problem is solved by exploration of the model space. This new code offers the following interesting advantages: (a) integrated approach for working indistinctly with CBA or dg data, (b) only one code to run, even for further graphical presentations, (c) only a limited number of necessary parameters, having all of them suggested default values, (d) ample graphical information on the running screen, and (e) can be run instantly. We describe the new code and its parameters and possibilities, together with some operational aspects. Several test cases are included. The GROWTH-23 code can be freely downloaded from the GROWTH-23_software repository at github.com, under an open source license.

Thin elongated sources, such as dykes, sills, chimneys, inclined sheets, etc., often encountered in volcano gravimetric studies, pose great challenges to gravity inversion methods based on model exploration and growing sources bodies. The Growth inversion approach tested here is based on partitioning the subsurface into right-rectangular cells and populating the cells with differential densities in an iterative weighted mixed adjustment process, in which the minimization of the data misfit is balanced by forcing the growing subsurface density distribution into compact source bodies. How the Growth inversion can cope with thin elongated sources is the subject of our study. We use synthetic spatiotemporal gravity changes caused by simulated sources placed in three real volcanic settings. Our case studies demonstrate the benefits and limitations of the Growth inversion as applied to sparse and noisy gravity change data generated by thin elongated sources. Such sources cannot be reproduced by Growth accurately. They are imaged with smaller density contrasts, as much thicker, with exaggerated volume. Despite this drawback, the Growth inversion can provide useful information on several source parameters even for thin elongated sources, such as the position (including depth), the orientation, the length, and the mass, which is a key factor in volcano gravimetry. Since the density contrast of a source is not determined by the inversion, but preset by the user to run the inversion process, it cannot be used to specify the nature of the source process. The interpretation must be assisted by external constraints such as structural or tectonic controls, or volcanological context. Synthetic modeling and Growth inversions, such as those presented here, can serve also for optimizing the volcano monitoring gravimetric network design. We conclude that the Growth inversion methodology may, in principle, prove useful even for the detection of thin elongated sources of high density contrast by providing useful information on their position, shape (except for thickness) and mass, despite the strong ambiguity in determining their differential density and volume. However, this yielded information may be severely compromised in reality by the sparsity and noise of the interpreted gravity data.

Gravimetric observations were carried out in 2015, to image the uppermost portion of the volcanic plumbing system of Mt. Etna (Italy). Gravity measurements were performed using two relative gravimeters, along a profile that crosses the summit craters area (elevations between 2,820 and 3,280 m a.s.l.). Accurate positioning of the gravity observation points was determined through GPS measurements. After applying elevation and terrain corrections, the reduced gravity data were used to build a 2D density model of the uppermost part of the volcano edifice. This model was constrained using to-date knowledge of the structural setting of the area and the available volcanological data. We highlighted the presence of low-density material below the summit craters, down to the depth of about 2.1 km, interpreted as highly altered, fumarolized and structurally weakened material. It is also likely that the close presence of the conduits feeding the summit craters of the volcano contributes to the gravity low in the SW half of the measurement profile. Conversely, the gravity low observed at the northern edge of the profile could reflect the high concentration of faults and eruptive fissures in the Pizzi Deneri area, in correspondence of the Ellittico caldera rim.

We review the current geoscientific knowledge of the volcanic unrest of 2004–2005 on Tenerife (Canary Islands) and revisit its gravimetric imprint. We revise the interpretation of the observed spatiotemporal (time-lapse) gravity changes accompanying the unrest by applying the Growth inversion approach based on model exploration and free geometry growing source bodies. We interpret the Growth solution, our new gravimetric model of the unrest, in the context of structural controls and the existing volcanological and geological knowledge of the central volcanic complex (CVC) of the island. Structural controls are inferred from the updated structural subsurface CVC density model obtained by our new Growth inversion of the available complete Bouguer anomalies (CBA data). Our gravimetric picture sees the unrest as a failed eruption, due to a stalled magma intrusion in the central position below the Teide–Pico Viejo stratocones, followed by upward and lateral migration of volcanic fluids reaching the aquifer and the SW end of the caldera wall. We thus classify the volcanic unrest of 2004–2005 as hybrid, in agreement with previous studies. The Growth inversion indicates that magma propagated along the boundary between the basaltic core of the island, the Boca Tauce volcanic body and the more permeable (less compacted) volcanic rocks with lower density. This gravimetric picture of the unrest provides new insights into the potential future reactivation of the volcanic system. Article Highlights Current geoscientific knowledge of the Tenerife volcanic unrest of 2004–2005 is reviewed New insights into the unrest are yielded by Growth inversion of observed time-lapse gravity changes Role of the freely adjustable inversion parameters in the Growth methodology is demonstrated Pros and cons of the Growth inversion approach in volcano gravimetric applications are illustrated

New gravimetric observations were carried out in the summit area of Mt. Etna in July 2021. Only the north-west half of the planned survey area was accessible to field work due to ongoing intense eruptive activity. The new gravimetric observation points (171 in number) were positioned using precise geodetic positioning based on GNSS technology. Due to rough conditions, unstable ground and wind, the gravity observations were collected with a precision of about 15 microGal using two relative gravimeters (CG5 and CG6). Complete Bouguer anomalies (CBA) were compiled. The computation of accurate topographic correction for CBA compilation poses a challenge because of the ever-changing topography around the summit craters due to intense eruptive activity. Precise topographic correction was computed using the Toposk software. The available high resolution (5 m) DEM released in 2016, and the reference constant topographic density of 2300 kg/m3, which resulted from our analysis as representative for the summit area, were adopted for the numerical evaluation of the topographic correction. These data will serve the 2D and 3D density modelling for determining the subsurface structural model of the summit area and the upper-most part of magma feeders of the summit craters on Etna.

Globally there is abundant terrestrial surface gravity data used to study the time variation of gravity related to subsurface mass and density changes in different geological, geodynamical and geotechnical environments. We present here a tool for analysing existing and newly acquired, 4D gravity data, which creates new findings from its reuse. Our method calculates in an almost automatic way the possible sources of density change responsible for the observed gravity variations. The specifics of the new methodology are: use of a low number of observation points, relatively small source structures, low signal/noise ratio in the data, and a free 3D source geometry without initial hypothesis. The process is based on the non-linear adjustment of structures defined by aggregation of small cells corresponding to a 3D section of the sub-floor volume. This methodology is implemented in a software tool, named GROWTH-dg, which can be freely downloaded for immediate use, together with a user manual and application examples.

We analyse spatiotemporal gravity changes observed on the Ischia island (Italy) accompanying the destructive earthquake of 21 August 2017. The 29 May 2016 to 22 September 2017 time-lapse gravity changes observed at 18 benchmarks of the Ischia gravimetric network are first corrected for the gravitational effect of the surface deformation using the deformation-induced topographic effect (DITE) correction. The co-seismic DITE is computed by Newtonian volumetric integration using the Toposk software, a high-resolution LiDAR DEM and the co-seismic vertical displacement field derived from Sentinel-1 InSAR data. We compare numerically the DITE field with its commonly used Bouguer approximation over the island of Ischia with the outcome that the Bouguer approximation of DITE is adequate and accurate in this case. The residual gravity changes are then computed at gravity benchmarks by correcting the observed gravity changes for the planar Bouguer effect of the elevation changes at benchmarks over the same period. The residual gravity changes are then inverted using an inversion approach based on model exploration and growing source bodies, making use of the Growth-dg inversion tool. The found inversion model, given as subsurface time-lapse density changes, is then interpreted as mainly due to a co-seismic or post-seismic disturbance of the hydrothermal system of the island. Pros and weak points of such interpretation are discussed.

The accurate deformation-induced topographic effect (DITE) should be used to account for the gravitational effect of surface deformation when analyzing residual spatiotemporal (time-lapse) gravity changes in volcano gravimetric or 4D micro-gravimetric studies, in general. Numerical realization of DITE requires the deformation field available in grid form. We compute the accurate DITE correction for gravity changes observed at the Laguna del Maule volcanic field in Chile over three nearly annual periods spanning 2013–2016 and compare it numerically with the previously used free-air effect (FAE) correction. We assess the impact of replacing the FAE by DITE on the model source parameters of analytic inversion solutions and apply a new inversion approach based on model exploration and growing source bodies. The new inversion results based on the DITE correction shift the position of the mass intrusion upwards by a few hundred meters and lower the total mass of the migrated fluids to roughly a half, compared to the inversion results based on the local-FAE correction. Our new Growth inversion results indicate that vertical dip-slip faults beneath the lake, as well as the Troncoso fault play active roles in hosting migrating liquid. We also show that for the study period, the DITE at Laguna del Maule can be accurately evaluated by the planar Bouguer approximation, which only requires the availability of elevation changes at gravity network benchmarks. We hypothesize that this finding may be generalized to all volcanic areas with flatter or less rugged terrain and may alter interpretations based on the commonly used FAE corrections.

Gravitational effect of surface deformation is in 4D microgravimetry treated as the deformation-induced topographic effect (DITE). The DITE field is computed using Newtonian volumetric integration which requires high resolution digital elevation model (DEM) and vertical displacement field in areal form. If only elevation changes on benchmarks of the gravimetric network are available, instead of the vertical displacement field, the DITE on benchmarks can be evaluated only approximately, using a planar Bouguer or a normal free-air-effect (nFAE) approximation. Here we analyse the adequacy and accuracy of these two approximations in a case study for the December 2018 fissure eruption on Etna accompanied by significant surface deformation caused primarily by a relatively shallow dyke. The outcome is that in volcanic areas of similar morphology as that over the Etna summit area, and for surface deformation fields due to relatively shallow dykes, neither the Bouguer nor the nFAE approximation of the DITE is accurate enough. In such situations the residual gravity changes should be computed with both the Bouguer and nFAE corrections and interpreted as two marginal cases. In addition we analyse also a correction for the effect of benchmark elevation change based on the topographically modelled (predicted) vertical gradient of gravity (VGG) meant to approximate the in-situ VGG values at benchmarks. This correction does not appear suitable to approximate the DITE in conditions of our case study or in broader sense.

In volcano gravimetry, when analyzing residual spatiotemporal (time-lapse) gravity changes, the accurate deformation-induced topographic effect (DITE) should be used to account for the gravitational effect of surface deformation. Numerical realization of DITE requires the deformation field available in grid form. We compute the accurate DITE correction for gravity changes observed at the Laguna del Maule volcanic field in Chile over three nearly annual periods spanning 2013–2016 and compare it numerically with the previously used free-air effect (FAE) correction. We assess the impact of replacing the FAE by DITE on the model source parameters of analytic inversion solutions and apply a new inversion approach based on model exploration and growing source bodies. The new inversion results based on the DITE correction shift the position of the mass intrusion upwards by a few hundred meters and lower the total mass of the migrated fluids to roughly a half, compared to the inversion results based on the local-FAE correction. Our new Growth inversion results indicate that vertical dip-slip faults beneath the lake, as well as the Troncoso fault play active roles in hosting migrating liquid. We also show that for the study period, the DITE at Laguna del Maule can be accurately evaluated by the planar Bouguer approximation, which only requires the availability of elevation changes at gravity network benchmarks. We hypothesize that this finding may be generalized to all volcanic areas with flatter or less rugged terrain and may modify interpretations based on the commonly used FAE corrections.

Some geophysical or geodynamic applications require the use of true vertical gradient of gravity (VGG). This demand may be associated with reductions of or corrections to observed gravity or its spatiotemporal changes. In the absence of in situ measured VGG values, the constant value of the theoretical (normal) free air gradient (FAG) is commonly used. We propose an alternative to this practice which may significantly reduce systematic errors associated with the use of constant FAG. The true VGG appears to be better approximated, in areas with prominent and rugged topography, such as alpine or some volcanic regions, by a value based on the modelled contribution of the topographic masses to the gradient. Such prediction can be carried out with a digital elevation model (DEM) of sufficient resolution and accuracy. Here we present the VGG field computed for Mt. Etna (Italy), one of the most active and best monitored volcanoes worldwide, to illustrate how strongly the VGG deviates spatially from constant FAG. The predicted (modelled) VGG field is verified by in situ observations. We also take a look at the sensitivity of the VGG prediction to the resolution and quality of used DEMs. We conclude with discussing the applicability of the topo-predicted VGG field in near surface structural and volcanological micro-gravimetric studies.

We present a comprehensive view of the origin, significance and implications of topographic effects in gravimetry. These are gravitational effects of topographic masses that are present in any observable quantity of the earth's gravitational field. In most gravimetric applications and their computational realizations, when topography is not the focus of the study, these effects need to be properly treated as corrections (reductions). Some of them might not be obvious or intuitive, and may remain misunderstood and mistreated. First, we look at topographic effects in geodesy and focus on those that affect the determination of the geoid from terrestrial gravity data. We review the origin and role of both the direct and indirect, the primary and secondary topographic effects. Then, we review the Bouguer concept in geophysical applications. Finally, we take a look at the topographic effect induced by the deformation of the topographic surface and its importance in the interpretation of observed spatiotemporal gravity changes. We illustrate the sizes and shapes (spatial properties) of these effects, discuss their relevance and impacts in the areas of geodesy, geophysical structural studies (exploration and prospection), and in geodynamics with a focus on volcano geodesy.

In situ values of vertical gradients of gravity (VGGs) are often needed when compiling residual spatiotemporal gravity changes that are interpreted in volcanic areas with the objective of drawing inferences about sources of volcanic unrest or pending eruptions. VGG values are seldom acquired by in situ observations. Their availability in 4D volcano-microgravimetric surveys and studies can be mediated by predicting the VGGs based on high resolution high accuracy DEMs and modelling the topographic component (constituent) of the VGG. Based on a modelling effort and in situ verification of VGG predicted on Etna in the summit craters area, on the north-east rift and on benchmarks of the monitoring network covering the volcano in a wider context, we learned that the VGG prediction can be improved by using drone-borne photogrammetry with GNSS ground control to produce a finer DEM in the closest vicinity of the VGG point (benchmark or field point) with resolution higher than the available high-resolution LiDAR-derived DEM, and using detailed modeling of gravity effect (on VGG) of anthropogenic objects such as walls and buildings adjacent to the VGG points. In this poster we present the methods used in the refined VGG prediction and the results of the verification of VGGs predicted on Etna.