Peter Vajda | Slovak Academy of Sciences (original) (raw)

Papers by Peter Vajda

Research paper thumbnail of Truncation Filtering Methodology: Input gravity data and pattern matching

The compilation of proper input gravity data for the Truncation Filtering Methodology (TFM) from ... more The compilation of proper input gravity data for the Truncation Filtering Methodology (TFM) from observed gravity is discussed. The aim of the TFM interpretation is to determine the anomalous density distribution, or at least some of its characteristics, below the earth's surface in a studied region. It implies that the input data must be equal to the gravity effect (attraction) of all such anomalous masses of interest. Furthermore, the TFM requires that the input gravity data be given on a level reference surface, the position of which is further constrained by the requirement to stay outside all the anomalous masses, hence above all the terrain, in order to avoid downward continuation through anomalous masses. Such a requirement is imposed by the fact, that the TFM is a pattern recognition technique and the knowledge of patterns comes from synthetic modeling on a level surface without topography. Consequently the requirements imply that the input data needed are the gravity disturbances, corrected for the effects of topography and bathymetry, harmonically upward continued to a level surface tightly enveloping the topo-surface in the area of interest. Numerical procedures and several approximations in compiling such data are discussed.

Research paper thumbnail of GROWTH-23: An integrated code for inversion of complete Bouguer gravity anomaly or temporal gravity changes

Computers & Geosciences, Dec 31, 2023

A new code for gravity inversion is freely available. It can be used to work with data on complet... more 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.

Research paper thumbnail of Observation and Local Prediction of the Vertical Gravity Gradient

IEEE IMM, 2024

The knowledge of the vertical gradient of gravity (VGG) at observation points (benchmarks) in the... more 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

Research paper thumbnail of Gravimetric inversion based on model exploration with growing source bodies (Growth) in diverse earth science disciplines

AIMS mathematics, 2024

Gravimetry is a discipline of geophysics that deals with observation and interpretation of the ea... more 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.

Research paper thumbnail of GROWTH-23: An integrated code for inversion of complete Bouguer gravity anomaly or temporal gravity changes

Computers and Geosciences, 2024

A new code for gravity inversion is freely available. It can be used to work with data on complet... more 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.

Research paper thumbnail of New insights into geological setting of the summit area of mount Etna volcano (Italy) inferred from 2D gravity data modelling

Front. Earth Sci., 2023

Gravimetric observations were carried out in 2015, to image the uppermost portion of the volcanic... more 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.

Research paper thumbnail of On Gravimetric Detection of Thin Elongated Sources Using the Growth Inversion Approach

Surveys in Geophysics

Thin elongated sources, such as dykes, sills, chimneys, inclined sheets, etc., often encountered ... more 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 reprodu...

Research paper thumbnail of Benefits and Limitations of the Growth Inversion Approach in Volcano Gravimetry Demonstrated on the Revisited 2004–2005 Tenerife Unrest

Surveys in Geophysics, 2023

We review the current geoscientific knowledge of the volcanic unrest of 2004–2005 on Tenerife (Ca... more 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 r...

Research paper thumbnail of A free-geometry geodynamic modelling of surface gravity changes using Growth-dg software

Scientific Reports

Globally there is abundant terrestrial surface gravity data used to study the time variation of g... more 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 ma...

Research paper thumbnail of Interpretation of spatiotemporal gravity changes accompanying the earthquake of 21 August 2017 on Ischia (Italy)

Contributions to Geophysics and Geodesy, 2021

We analyse spatiotemporal gravity changes observed on the Ischia island (Italy) accompanying the ... more 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...

Research paper thumbnail of Corrigendum: Interpretation of spatiotemporal gravity changes accompanying the earthquake of 21 August 2017 on Ischia (Italy)

Contributions to Geophysics and Geodesy, 2022

Research paper thumbnail of Chapter 4 Recent Developments and Trends in Volcano Gravimetry

The aim of this chapter is to take a look at some developments and new trends in volcano gravimet... more The aim of this chapter is to take a look at some developments and new trends in volcano gravimetry. First, we will review the objectives of the research work within this subfield of geophysics, discuss the data and methods it uses, and outline the outputs it strives for. Then, we will turn our attention to three areas where innovative approaches possibly can forward this field of study. The first has to do with the coupling between vertical deformations of the topographic surface (elevation changes) and the observed gravity changes or, in other words, with the removal of the deformation-induced gravimetric signal from the observed gravity changes to obtain the net gravity changes caused by volcanic signals. The second and third areas regard the inversion of the observed gravity changes and deal with two recently or newly developed inversion approaches that both are characterized by the ability to produce a suite of diverse solutions that can be analyzed and discriminated based on a...

Research paper thumbnail of Deformation-induced topographic effect due to shallow dyke: Etna December 2018 fissure eruption case study

Contributions to Geophysics and Geodesy, 2021

Gravitational effect of surface deformation is in 4D microgravimetry treated as the deformation-i... more 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 analyze 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 approximat...

Research paper thumbnail of Novel treatment of the deformation–induced topographic effect for interpretation of spatiotemporal gravity changes: Laguna del Maule (Chile)

Journal of Volcanology and Geothermal Research, 2021

Abstract In volcano gravimetry, when analyzing residual spatiotemporal (time-lapse) gravity chang... more Abstract 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.

Research paper thumbnail of Topographic gravimetric effects in earth sciences: Review of origin, significance and implications

Earth-Science Reviews, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Research paper thumbnail of On inverting gravity changes with the harmonic inversion method: Teide (Tenerife) case study

Contributions to Geophysics and Geodesy, 2015

Here we investigate the applicability of the harmonic inversion method to time-lapse gravity chan... more Here we investigate the applicability of the harmonic inversion method to time-lapse gravity changes observed in volcanic areas. We carry out our study on gravity changes occured over the period of 2004–2005 during the unrest of the Central Volcanic Complex on Tenerife, Canary Islands. The harmonic inversion method is unique in that it calculates the solution of the form of compact homogeneous source bodies via the mediating 3-harmonic function called quasigravitation. The latter is defined in the whole subsurface domain and it is a linear integral transformation of the surface gravity field. At the beginning the seeds of the future source bodies are introduced: these are quasi-spherical bodies located at the extrema of the quasigravitation (calculated from the input gravity data) and their differential densities are free parameters preselected by the interpreter. In the following automatic iterative process the source bodies change their size and shape according to the local values...

Research paper thumbnail of Topographically Predicted Vertical Gravity Gradient Field and Its Applicability in 3D and 4D Microgravimetry: Etna (Italy) Case Study

Pure and Applied Geophysics, 2020

Some geophysical or geodynamic applications require the use of true vertical gradient of gravity ... more 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.

Research paper thumbnail of High-precision local gravity survey along planned motorway tunnel in the Slovak Karst

Contributions to Geophysics and Geodesy, 2019

Results from a detailed gravity survey realized along the planned highway tunnel in the karstic a... more Results from a detailed gravity survey realized along the planned highway tunnel in the karstic area of Slovak Karst in the eastern Slovakia are presented. Detailed gravity profiles crossed an area of rugged topography, therefore the terrain corrections played a crucial role in the gravity data processing. The airborne laser scanning technique (LiDAR) was used in order to compile a high-resolution digital terrain model (DTM) of the surrounding area and to calculate terrain corrections properly. The difference between the Bouguer anomalies calculated with an available nationwide DTM and those with new LiDAR-based model can be significant in some places as it is presented in the paper. A new method for Bouguer correction density analysis based on surface data is presented. Special underground gravity measurements in the existing nearby railway tunnel were also conducted in order to determine the mean density of the topographic rocks. The Bouguer anomalies were used to interpret lithol...

Research paper thumbnail of Deformation induced topographic effects in inversion of temporal gravity changes: First look at Free Air and Bouguer terms

Contributions to Geophysics and Geodesy, 2015

We review here the gravitational effects on the temporal (time-lapse) gravity changes induced by ... more We review here the gravitational effects on the temporal (time-lapse) gravity changes induced by the surface deformation (vertical displacements). We focus on two terms, one induced by the displacement of the benchmark (gravity station) in the ambient gravity field, and the other imposed by the attraction of the masses within the topographic deformation rind. The first term, coined often the Free Air Effect (FAE), is the product of the vertical gradient of gravity (VGG) and the vertical displacement of the benchmark. We examine the use of the vertical gradient of normal gravity, typically called the theoretical or normal Free Air Gradient (normal FAG), as a replacement for the true VGG in the FAE, as well as the contribution of the topography to the VGG. We compute a topographic correction to the normal FAG, to offer a better approximation of the VGG, and evaluate its size and shape (spatial behavior) for a volcanic study area selected as the Central Volcanic Complex (CVC) on Teneri...

Research paper thumbnail of Refined prediction of vertical gradient of gravity at Etna volcano gravity network (Italy)

Contributions to Geophysics and Geodesy, 2018

Predicted values of the vertical gradient of gravity (VGG) on benchmarks of Etna’s monitoring sys... more Predicted values of the vertical gradient of gravity (VGG) on benchmarks of Etna’s monitoring system, based on calculation of the topographic contribution to the theoretical free-air gradient, are compared with VGG values observed in situ. The verification campaign indicated that improvements are required when predicting the VGGs at such networks. Our work identified the following factors to be resolved: (a) accuracy of the benchmark position; (b) gravitational effect of buildings and roadside walls adjacent to benchmarks; (c) accuracy of the digital elevation model (DEM) in the proximity of benchmarks. Benchmark positions were refined using precise geodetic methods. The gravitational effects of the benchmark-adjacent walls and buildings were modeled and accounted for in the prediction. New high-resolution DEMs were produced in the innermost zone at some benchmarks based on drone-flown photogrammetry to improve the VGG prediction at those benchmarks. The three described refinements ...

Research paper thumbnail of Truncation Filtering Methodology: Input gravity data and pattern matching

The compilation of proper input gravity data for the Truncation Filtering Methodology (TFM) from ... more The compilation of proper input gravity data for the Truncation Filtering Methodology (TFM) from observed gravity is discussed. The aim of the TFM interpretation is to determine the anomalous density distribution, or at least some of its characteristics, below the earth's surface in a studied region. It implies that the input data must be equal to the gravity effect (attraction) of all such anomalous masses of interest. Furthermore, the TFM requires that the input gravity data be given on a level reference surface, the position of which is further constrained by the requirement to stay outside all the anomalous masses, hence above all the terrain, in order to avoid downward continuation through anomalous masses. Such a requirement is imposed by the fact, that the TFM is a pattern recognition technique and the knowledge of patterns comes from synthetic modeling on a level surface without topography. Consequently the requirements imply that the input data needed are the gravity disturbances, corrected for the effects of topography and bathymetry, harmonically upward continued to a level surface tightly enveloping the topo-surface in the area of interest. Numerical procedures and several approximations in compiling such data are discussed.

Research paper thumbnail of GROWTH-23: An integrated code for inversion of complete Bouguer gravity anomaly or temporal gravity changes

Computers & Geosciences, Dec 31, 2023

A new code for gravity inversion is freely available. It can be used to work with data on complet... more 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.

Research paper thumbnail of Observation and Local Prediction of the Vertical Gravity Gradient

IEEE IMM, 2024

The knowledge of the vertical gradient of gravity (VGG) at observation points (benchmarks) in the... more 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

Research paper thumbnail of Gravimetric inversion based on model exploration with growing source bodies (Growth) in diverse earth science disciplines

AIMS mathematics, 2024

Gravimetry is a discipline of geophysics that deals with observation and interpretation of the ea... more 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.

Research paper thumbnail of GROWTH-23: An integrated code for inversion of complete Bouguer gravity anomaly or temporal gravity changes

Computers and Geosciences, 2024

A new code for gravity inversion is freely available. It can be used to work with data on complet... more 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.

Research paper thumbnail of New insights into geological setting of the summit area of mount Etna volcano (Italy) inferred from 2D gravity data modelling

Front. Earth Sci., 2023

Gravimetric observations were carried out in 2015, to image the uppermost portion of the volcanic... more 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.

Research paper thumbnail of On Gravimetric Detection of Thin Elongated Sources Using the Growth Inversion Approach

Surveys in Geophysics

Thin elongated sources, such as dykes, sills, chimneys, inclined sheets, etc., often encountered ... more 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 reprodu...

Research paper thumbnail of Benefits and Limitations of the Growth Inversion Approach in Volcano Gravimetry Demonstrated on the Revisited 2004–2005 Tenerife Unrest

Surveys in Geophysics, 2023

We review the current geoscientific knowledge of the volcanic unrest of 2004–2005 on Tenerife (Ca... more 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 r...

Research paper thumbnail of A free-geometry geodynamic modelling of surface gravity changes using Growth-dg software

Scientific Reports

Globally there is abundant terrestrial surface gravity data used to study the time variation of g... more 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 ma...

Research paper thumbnail of Interpretation of spatiotemporal gravity changes accompanying the earthquake of 21 August 2017 on Ischia (Italy)

Contributions to Geophysics and Geodesy, 2021

We analyse spatiotemporal gravity changes observed on the Ischia island (Italy) accompanying the ... more 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...

Research paper thumbnail of Corrigendum: Interpretation of spatiotemporal gravity changes accompanying the earthquake of 21 August 2017 on Ischia (Italy)

Contributions to Geophysics and Geodesy, 2022

Research paper thumbnail of Chapter 4 Recent Developments and Trends in Volcano Gravimetry

The aim of this chapter is to take a look at some developments and new trends in volcano gravimet... more The aim of this chapter is to take a look at some developments and new trends in volcano gravimetry. First, we will review the objectives of the research work within this subfield of geophysics, discuss the data and methods it uses, and outline the outputs it strives for. Then, we will turn our attention to three areas where innovative approaches possibly can forward this field of study. The first has to do with the coupling between vertical deformations of the topographic surface (elevation changes) and the observed gravity changes or, in other words, with the removal of the deformation-induced gravimetric signal from the observed gravity changes to obtain the net gravity changes caused by volcanic signals. The second and third areas regard the inversion of the observed gravity changes and deal with two recently or newly developed inversion approaches that both are characterized by the ability to produce a suite of diverse solutions that can be analyzed and discriminated based on a...

Research paper thumbnail of Deformation-induced topographic effect due to shallow dyke: Etna December 2018 fissure eruption case study

Contributions to Geophysics and Geodesy, 2021

Gravitational effect of surface deformation is in 4D microgravimetry treated as the deformation-i... more 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 analyze 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 approximat...

Research paper thumbnail of Novel treatment of the deformation–induced topographic effect for interpretation of spatiotemporal gravity changes: Laguna del Maule (Chile)

Journal of Volcanology and Geothermal Research, 2021

Abstract In volcano gravimetry, when analyzing residual spatiotemporal (time-lapse) gravity chang... more Abstract 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.

Research paper thumbnail of Topographic gravimetric effects in earth sciences: Review of origin, significance and implications

Earth-Science Reviews, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Research paper thumbnail of On inverting gravity changes with the harmonic inversion method: Teide (Tenerife) case study

Contributions to Geophysics and Geodesy, 2015

Here we investigate the applicability of the harmonic inversion method to time-lapse gravity chan... more Here we investigate the applicability of the harmonic inversion method to time-lapse gravity changes observed in volcanic areas. We carry out our study on gravity changes occured over the period of 2004–2005 during the unrest of the Central Volcanic Complex on Tenerife, Canary Islands. The harmonic inversion method is unique in that it calculates the solution of the form of compact homogeneous source bodies via the mediating 3-harmonic function called quasigravitation. The latter is defined in the whole subsurface domain and it is a linear integral transformation of the surface gravity field. At the beginning the seeds of the future source bodies are introduced: these are quasi-spherical bodies located at the extrema of the quasigravitation (calculated from the input gravity data) and their differential densities are free parameters preselected by the interpreter. In the following automatic iterative process the source bodies change their size and shape according to the local values...

Research paper thumbnail of Topographically Predicted Vertical Gravity Gradient Field and Its Applicability in 3D and 4D Microgravimetry: Etna (Italy) Case Study

Pure and Applied Geophysics, 2020

Some geophysical or geodynamic applications require the use of true vertical gradient of gravity ... more 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.

Research paper thumbnail of High-precision local gravity survey along planned motorway tunnel in the Slovak Karst

Contributions to Geophysics and Geodesy, 2019

Results from a detailed gravity survey realized along the planned highway tunnel in the karstic a... more Results from a detailed gravity survey realized along the planned highway tunnel in the karstic area of Slovak Karst in the eastern Slovakia are presented. Detailed gravity profiles crossed an area of rugged topography, therefore the terrain corrections played a crucial role in the gravity data processing. The airborne laser scanning technique (LiDAR) was used in order to compile a high-resolution digital terrain model (DTM) of the surrounding area and to calculate terrain corrections properly. The difference between the Bouguer anomalies calculated with an available nationwide DTM and those with new LiDAR-based model can be significant in some places as it is presented in the paper. A new method for Bouguer correction density analysis based on surface data is presented. Special underground gravity measurements in the existing nearby railway tunnel were also conducted in order to determine the mean density of the topographic rocks. The Bouguer anomalies were used to interpret lithol...

Research paper thumbnail of Deformation induced topographic effects in inversion of temporal gravity changes: First look at Free Air and Bouguer terms

Contributions to Geophysics and Geodesy, 2015

We review here the gravitational effects on the temporal (time-lapse) gravity changes induced by ... more We review here the gravitational effects on the temporal (time-lapse) gravity changes induced by the surface deformation (vertical displacements). We focus on two terms, one induced by the displacement of the benchmark (gravity station) in the ambient gravity field, and the other imposed by the attraction of the masses within the topographic deformation rind. The first term, coined often the Free Air Effect (FAE), is the product of the vertical gradient of gravity (VGG) and the vertical displacement of the benchmark. We examine the use of the vertical gradient of normal gravity, typically called the theoretical or normal Free Air Gradient (normal FAG), as a replacement for the true VGG in the FAE, as well as the contribution of the topography to the VGG. We compute a topographic correction to the normal FAG, to offer a better approximation of the VGG, and evaluate its size and shape (spatial behavior) for a volcanic study area selected as the Central Volcanic Complex (CVC) on Teneri...

Research paper thumbnail of Refined prediction of vertical gradient of gravity at Etna volcano gravity network (Italy)

Contributions to Geophysics and Geodesy, 2018

Predicted values of the vertical gradient of gravity (VGG) on benchmarks of Etna’s monitoring sys... more Predicted values of the vertical gradient of gravity (VGG) on benchmarks of Etna’s monitoring system, based on calculation of the topographic contribution to the theoretical free-air gradient, are compared with VGG values observed in situ. The verification campaign indicated that improvements are required when predicting the VGGs at such networks. Our work identified the following factors to be resolved: (a) accuracy of the benchmark position; (b) gravitational effect of buildings and roadside walls adjacent to benchmarks; (c) accuracy of the digital elevation model (DEM) in the proximity of benchmarks. Benchmark positions were refined using precise geodetic methods. The gravitational effects of the benchmark-adjacent walls and buildings were modeled and accounted for in the prediction. New high-resolution DEMs were produced in the innermost zone at some benchmarks based on drone-flown photogrammetry to improve the VGG prediction at those benchmarks. The three described refinements ...