The AlpArray Gravity Research Group (AAGRG), as part of the
European AlpArray program, focuses on the compilation of a homogeneous
surface-based gravity data set across the Alpine area. In 2017 10 European
countries in the Alpine realm agreed to contribute with gravity data
for a new compilation of the Alpine gravity field in an area spanning from
2 to 23

Here, the AAGRG presents the data set of the recalculated gravity fields on
a 4 km

A first interpretation of the new map shows that the resolution of the
gravity anomalies is suited for applications ranging from intra-crustal- to
crustal-scale modeling to interdisciplinary studies on the regional and
continental scales, as well as applications as joint inversion with other
data sets. The data are published with the DOI

There is a long history of geological and geophysical research on the Alpine orogen, the results of which point to two main groups of complexity. The first is the temporal evolution of the mountain belt, with plates, terrains and units of different size and level of deformation mostly investigated from the geological record (e.g., Handy et al., 2010). This inheritance directly influences the second level of complexity, which is structural and characterizes every level of the lithosphere from sedimentary basins to orogenic roots and also the upper mantle. The level of along-strike variability of the Alps exceeds what is known in other mountain belts such as the Andes and the Himalayas (Oncken et al., 2006; Hetényi et al., 2016) and explains why some of the orogenic processes operating in the Alps are still debated.

Structural complexity at depth, and thus the advancement of our understanding of orogeny, can be resolved by high-resolution 3D geophysical imaging. This is among the primary goals of the AlpArray program and its main seismological imaging tool, the AlpArray Seismic Network. This modern array has used over 628 sites for more than 39 months across the greater Alpine area such that no point on land was farther than 30 km from a broadband seismometer (Hetényi et al., 2018). While seismic imaging of the entire Alps in 3D became a reality following decades of active- and passive-source projects, imaging efforts in gravity reached 3D earlier thanks to the availability of national data sets of the Alpine neighboring countries with partly high-resolution and 3D modeling approaches among others (Ehrismann et al., 1976; Götze, 1978; Kissling, 1980; Götze and Lahmeyer, 1988; Götze et al., 1991; Ebbing, 2002; Ebbing et al., 2006; Marson and Klingelé, 1993; Kahle and Klingelé, 1979). However, these land data sets for historical reasons were acquired in national reference systems and were seldom shared, preventing high-resolution pan-Alpine gravity studies using homogeneously processed data.

With respect to the national expertise and databases available in the Alpine countries, the formation of an international research group (AlpArray Gravity Research Group; AAGRG) was decided within the framework of activities in the European AlpArray program and established at an EGU splinter meeting in 2017. In the subsequent workshops in Bratislava (Slovakia) in 2018, and two further technical meetings of the group (again in Bratislava in 2018 and in Sopron, Hungary, in 2019), the organizational, scientific, and numerical requirements for the compilation of the new pan-Alpine digital gravity database were established, which consists of Bouguer and free-air anomalies (BA and FA) and values of mass correction. Although most of the national group members were extensively involved in the processing of data, we would like to remind with gratitude that by far the most intensive part of the processing was done by the group members from Bratislava and Banská Bystrica (Slovakia).

In the following, we present our effort, omitting historical obstacles, in compiling and merging all available land and sea gravity data in the greater Alpine area, a total of more than 1 million on- and offshore data points. We committed to the exact same data processing procedures so that even proprietary point-wise data can be included at the project's initial stage and represented in the final Bouguer anomaly grids.

We emphasize that the data set is primarily a product to be used for an interdisciplinary 3D modeling of the Earth's lithosphere which requires precise mass corrections, considering topography, bathymetry and onshore lake corrections. Therefore, it differs significantly from modern gravity potential field compilations which aim at geoid and quasi-geoid modeling (e.g., Denker, 2013). Here, we focus on providing a valuable data set for numerous interdisciplinary projects in the AlpArray program and other European geo-projects that support crustal and mantle modeling in the Alpine-Mediterranean region.

We document in detail our procedures, from raw data to final high-resolution gravity maps. The referencing and quality assessment of various gravity databases and digital Earth surface models are discussed in Sect. 2. The equations and their implementations to obtain various gravity anomaly products, as well as the reprocessing of original raw data and of the related corrections, are described in Sect. 3. Section 4 presents the new, homogenized Bouguer gravity map for the Alps. In Sect. 4.3 we describe the attached Bouguer map, together with an accompanying description and interpretation of the gravity anomalies in the Alps and their surroundings. Notes on the uncertainty of the compilation are given in Sect. 5. We conclude on the listing and availability of the new gravity data (Sect. 6), which we share publicly as a contribution to further gravity studies in the region at different scales.

Additionally, information is provided in four appendices for detailed descriptions of national data sets, procedures, strategies and comparisons. Appendix A contains a list of abbreviations used; Appendix B gives a brief overview of the historical activities of the main actors and the national contributions to the pan-Alpine Bouguer gravity map; Appendix C presents and compares the digital elevation models (DEMs) used; and finally, Appendix D provides details on the mass correction (MC) software and compares MC gravity effects resulting from different DEMs.

In total, all gravity data sets used comprise 1 008 815 gravity stations. Figure 1 shows the spatial distribution of the original data sets country by country. The initial situation for the assessment and application of existing data, available publications, data density and quality description is provided country by country in Appendix B.

The distribution of more than 1 million gravity stations in the area of investigation and compilation. Colors indicate the national databases used in the compilation.

One of the key problems in the unification of gravimetric databases is the homogenization of position, height and gravimetric coordinate systems used in each database. Through its historical development, each country has used and sometimes still uses local systems and their realization (frame), which are often based on the established principles of reference systems using older ellipsoids or older geodetic reference networks and projections. These systems and their realizations thus contain several differences which are responsible for large inhomogeneities, shifts and errors in position, height and gravity. These errors are most evident in the mutual comparison of data from individual countries.

To avoid these problems in the position of gravimetric points, all position data were transformed from local systems to the European Terrestrial Reference System 1989 (ETRS89), which is accurate, homogeneous and recommended for all European countries (Altamimi, 2018). A similar situation is in the height systems in that countries use different types of physical heights, they are linked to different tide gauges, and each country has a different practical implementation of the relevant height system. The solution is again the transformation to a uniform platform in the form of ellipsoidal heights in the ETRS89 system based on the ellipsoid GRS80 (Moritz, 2000). The situation is similar in gravimetric reference systems, in which especially the gravimetric databases that have been created for decades often use old gravimetric systems linked to the Potsdam system. An important step was therefore to convert these data into gravimetric systems which are connected to absolute gravimetric points and measurements, such as IGSN71 (Morelli et al., 1972) or modern national systems connected with the recent absolute measurements, which are verified by international comparisons of absolute gravimeters (Francis et al., 2015).

For these transformations, national transformation services were used (operated by national mapping services, e.g., SAPOS, SKPOS) or transformations implemented into standard GIS tools or our own software implementations based on national standards, information and experience of individual responsible institutions. The transformation from physical heights in national vertical systems to ellipsoidal heights in the ETRS89 system, ellipsoid GRS80, was realized using available local geoid and quasi-geoid models available through transformation services or implemented in current geodetic processing programs (e.g., Trimble Business Center, Leica Infinity). If a local geoid or quasi-geoid model was not available for some areas, then the global geopotential model EIGEN-6C4 (Förste et al., 2014) was used for transformation. This model was also used for marine data, for which the height of points was not given or had zero value.

Provided data include a local identifier, horizontal coordinates in the local coordinate systems (except France and Croatia), physical height, ellipsoidal coordinates in the ETRS89 system, ellipsoidal height above the GRS80 ellipsoid (except France, the Czech Republic and Slovenia) and the gravity value. For each parameter available metadata describing, for example, coordinate system (ellipsoid, EPSG code), transformation method or transformation service used, and local geoid and quasi-geoid were also collected.

Figure 2 shows the transformation scheme. For data sets for which all information was available, an independent transformation control check was performed between the local and global coordinate systems and between physical and ellipsoidal heights using available geodetic geoid and quasi-geoid models. Differences in position were in the majority of cases less than 1 m. All larger differences were individually investigated. A similar situation was for the heights, for which differences were generally less than 50 cm. These differences were mostly caused by different transformations, its practical software realization or local specifics of the data set.

Data statistics and an overview of selected metadata are given in Table 1.

Transformation scheme for unification of the national positioning, height and gravity reference systems.

Data statistics and an overview of selected metadata. From the total of originally 1 076 871 gravity stations, 1 008 815 data points were used for the compilation of the gravity maps. Most of the points were eliminated during the post-processing of offshore data.

One of the important elements in the calculation of complete Bouguer anomaly (CBA) is the calculation of proper mass corrections. The prerequisite for the calculation of correct gravity effects of topographic masses is the use of high-resolution digital terrain models (DTMs). Further information on the availability and use of DEMs in the Alpine area is given in Appendix C.

Both the new complete Bouguer anomaly (CBA) and the free-air anomaly of the
studied region were calculated for ellipsoidal heights of calculation points
with their geographical coordinates (

The basic formula for the CBA calculation was adopted from Meurers et al. (2001):

Note: though different from the SI
units, we will use the unit mGal for gravity, which is still frequently used
in gravimetry; 1 mGal

From a methodological viewpoint, the use of ellipsoidal heights for CBA calculation is innovative. Considering the participating countries, so far this concept has only been used in Austria (Meurers and Ruess, 2009). It ensures that Bouguer anomalies, which then, in the sense of physical geodesy, actually are gravity disturbances corrected for terrain mass effects, are not disturbed by the geophysical indirect effect (GIE; e.g. Li and Götze, 2001; Hackney and Featherstone, 2003) contrary to Bouguer anomalies relying on physical heights.

One of the main problems in the homogenization of data and recompilation of
gravity fields was the use of different procedures for the calculation of
mass correction (MC) and bathymetry correction (BC) by national
operators/authorities. This meant that a complete recalculation had to be
carried out for the new compilation based on the available point data and
the best digital elevation models (DEMs) available. The proper choice of DEMs
is discussed in Appendix C. An important first step before starting the
recompilation was to test and select the available software to calculate the
mass corrections. We compared two custom software packages developed by team
members: Toposk software (Zahorec et al., 2017a) and TriTop (Holzrichter et
al., 2019). Considering the results of this comparison (refer to Appendix D),
we decided to use Toposk based on ellipsoidal heights

If the normal field in Eq. (1) is defined at the height above the surface
ellipsoid, it is necessary to define the effects of terrain and bathymetry
masses above the ellipsoid (not above the geoid). Therefore, the concept
requires the use of ellipsoidal heights of the observation points, and at the
same time it is necessary to transform the topography and bathymetry grids from
physical to ellipsoidal heights. In the AlpArray area, the situation is more
or less simple, the ellipsoid is below the geoid throughout the region
(approx. 30 to 55 m). This greatly simplifies the calculation. In the case
of continental areas, we get a slightly thicker layer of topography whose
effect is calculated in the same way as in the case of physical heights
(with the density of 2670 kg m

Schematic comparison of physical vs. ellipsoidal concept of CBA. Note that the effect of additional water masses is calculated in a two-step process.

In connection with the above calculation methods, one note is appropriate.
The difference between the two versions (physical vs. ellipsoidal heights)
of the CBA defines GIE, which has a normal gravity component (defined by the
free-air gradient) and a component defined by the gravitational attraction
of the masses between the geoid and the ellipsoid. In our case, this second
component is equal to the total gravitational effect of these masses with a
density of 2670 kg m

Figure 4 visualizes the MC values at all collected points. They reach values up to 375 mGal, while the ellipsoidal height of the points is from about 35 to 3938 m. The height dependence of the calculated MC is displayed in the lower right corner of the figure. The difference between the calculated MC and the gravitational effect of the truncated spherical layer (to the same distance) defines classic terrain corrections. They reach values of almost 100 mGal.

Map of mass correction (up to the distance of 166 730 m, density
2670 kg m

When calculating bathymetric corrections (BCs), the gravity effect is
calculated due to the difference in density between the water masses of the
offshore areas and those of the land masses. In contrast to the MC, we
calculate BC with physical heights as explained in Sect. 3.1 and Fig. 3.
Water masses above the ellipsoid level are thus considered with their real
density of 1030 kg m

Bathymetric corrections reach significant values for offshore and near
coastal points and amount to more than 200 mGal (Fig. 5). The comparison
with the frequently used planar approximation is in the upper right corner
of the figure. Unlike MC (refer to Fig. 4), these differences are not
systematic and reach about

Map of bathymetric corrections (up to the distance of 166.7 km,
density 1640 kg m

Because the DEMs used in the MC calculation also include the volumes of
water masses of Alpine lakes, these volumes are calculated with an incorrect
density (2670 instead of 1000 kg m

For many large lakes in Switzerland bathymetric surveys have been carried
out since 2007 (Urs Marti, personal communication, 2019). The resolution of these models varies
between 1 and 3 m. For all the other lakes which contain bathymetric contours
in the topographic map at a scale of

In Slovenia there are two big Alpine lakes of glacial origin located in the Julian Alps in the northwestern part of the country. For both lakes, high-resolution bathymetric data are available. Bathymetric surveys were performed in the years 2015–2017 (Harpha Sea, 2017). The maximum depths for Lake Bohinj and Lake Bled are 45 and 30 m, respectively. The bathymetric grid size of 20 m was used to compute the Alpine lake corrections for the new CBA.

No digital depth information was available for Austrian lakes. Therefore,
shorelines and bathymetric contour lines have been digitized from
topographic maps and interpolated to grids with 10 m spacing. All lakes (in
total 36) exceeding either a water volume of 25

The depth data for lakes in the German parts of the Northern Alps was
digitized from topographic maps at a scale of

The models mentioned were combined with existing detailed DEMs, and the lake
correction itself was calculated as the difference of the gravitational
effects of two topography models, one containing the level of the lakes and
the other their bottom (e.g., Fig. 6 for Lake Geneva). Calculated lake
corrections (density 1670 kg m

Examples of topography models used to calculate lake corrections
(here, Lake Geneva, Switzerland). Top shaded relief

Map of lake corrections (correction density is 1670 kg m

Although the peripheral southeastern part of the new Bouguer gravity map is not
covered by terrestrial data which were available to the project, this area
was filled by the digitization of the CBA map of the former SFR Yugoslavia
at a scale of

The reprocessing included the identification and correction of individual steps in the frame of CBA calculations to ensure a processing status which complies with that of the recalculated anomaly of the new AlpArray map. Specifically, normal gravity was corrected for the difference between the IGF 1967 and the Somigliana/GRS80 equations. Then the simple free-air correction was replaced by a more accurate approach, and the sphericity of the Earth was taken into account. However, this was neglected in cases when simple planar Bouguer corrections in the original data were used. For the last two corrections, the approximate heights at the digitization points generated from the model MERIT (multi-error-removed improved-terrain) were used. Finally, atmospheric correction was calculated, which was not considered in the original CBA. These reprocessing steps remained problematic as the uniform procedure of their calculation was not used for the original CBA map and the original values were not published. Therefore, given that MC and BC could not be recalculated and replaced by new values, we must expect more significant errors in the transformed CBA. Figure 8 shows a comparison of transformed CBA map with a map constructed from available data within the project for Croatia. Fortunately, the differences between the maps are not significantly large, the standard deviation of differences is about 1.8 mGal with a low systematic difference (the mean value of the differences is less than 0.5 mGal). We therefore assume that the replaced anomaly in the southeastern part of the map (Serbia, Bosnia and Herzegovina) is of similar quality than the main part.

Comparison of CBA maps (density 2670 kg m

As a challenge for the further development of the AlpArray CBA map, we also
estimated the global effects of the true atmosphere and distant relief.
Atmospheric correction is usually calculated based on a simple approximation
according to Wenzel (1985). By the term true atmosphere, we mean the model
of the atmosphere derived from the effect of a spherical shell with radially
dependent density using the US standard atmosphere 1976 (Karcol, 2011) with
an irregularly shaped bottom surface formed by the Earth's surface,
calculated globally (Mikuška et al., 2008). The difference between
atmospheric correction calculated by both approaches for the AlpArray region
(calculated for selected database points) is shown in Fig. 9. The
differences reach a maximum of about 0.16 mGal. As a function of height
(approx. 0.04 mGal km

Comparison of atmospheric correction at selected points covering the whole AlpArray area. The black dots represent the atmospheric correction calculated by a simple approximation according to Wenzel (1985). The red dots show the calculation using the effect of true atmosphere subtracted from the global constant value of 0.874 mGal (Mikuška et al., 2008), and the blue line is its linear approximation.

Distant relief effect (DRE) represents the combined effect of topography and bathymetry beyond a standard distance of 166.7 km around the whole Earth (refer to Mikuška et al., 2006, for more detailed information). Figure 10 shows this effect calculated at selected points in the AlpArray study area. The calculation was made in the classical concept of physical heights. The calculation for ellipsoidal heights would differ slightly (in quantitative terms), but the basic features would be retained as presented. The inclusion of this effect in the CBA is a task for future studies. DRE is dominated mainly by long-wavelength trends, superimposing also high-frequency patterns in mountainous regions due to its dependence on height. Because terrain masses are largely compensated for by isostatic compensation, distant-compensating mass distribution should be considered as well (e.g., Szwillus et al., 2016) either by applying isostatic concepts or by relying on global crust–mantle boundary models. However, these additional considerations are beyond the main objective of this publication.

The summary effect of topography and bathymetry (densities of 2670 and

AlpArray gravity data have different levels of confidentiality. In some cases, only interpolated grids are available. Therefore, well-defined interpolation procedures are required. Interpolating scattered gravity data onto regular grids is commonly done in 2D, ignoring the fact that original data are acquired at different elevations rather than at a constant level. More exact solutions would be achieved by solving a proper boundary value problem. However, those methods are very time consuming, and avoiding mathematical artifacts due to limitation of data in terms of spatial extent and resolution is not trivial at all. Hence, the AAGRG decided to provide grids based on 2D interpolation first.

For assessing the 2D interpolation error in rugged terrain, two synthetic gravity data sets have been created based on two different kinds of source representation: a polyhedron model (method by Götze and Lahmeyer, 1988) and an equivalent source model (EQS) determined by the method of Cordell (1992). The model response has been calculated at the scattered positions of a subset of Austrian gravity data, as well as at the grid nodes with 1 km spacing. The synthetic data sets almost keep the wavelength content of real-world data. The elevation at the grid nodes was interpolated by 2D-Kriging based on the scattered data information.

In the case of the polyhedron model, the differences between exact 3D prediction and 2D interpolation do not exceed the range of 1–2 mGal. Only
in small, isolated areas are the errors larger than 5 mGal. The same holds
for the equivalent source representation in which the errors are in the range
of

Interpolation error estimate (gravity difference between gravity fields predicted by the EQS model and by 2D interpolation; contour interval 0.1 mGal, color bar in milligals (mGal) and axis coordinates in meters; Gauß–Krüger projection, M31).

In large-scale 3D modeling, 3D models rarely match the data better than the errors estimated in the scenarios tested above. Therefore, 2D interpolation seems to be justified even if it is not exact from a theoretical viewpoint. In local-scale interpretation, the situation may be different. However, another problem arises when using interpolated grids. Modelers need to know the elevation to which interpolated Bouguer or free-air anomalies refer.

Assuming the interpolation operator to be linear, Bouguer anomaly (BA) and free-air anomaly (FA) interpolated at each grid node

The Bouguer anomaly at grid node

Particularly in rugged terrain, FA and MC are not smooth functions of
horizontal coordinates. Therefore, applying Eq. (9) is rather questionable.
Instead, the free-air anomaly at a grid node

Note that we implicitly also included bathymetry in the MC term appearing in
Eqs. (7) to (14). Regarding the Bouguer anomaly

Equation (15) neglects the small density difference between lake and ocean water. However, this leads to only small errors on the order of a few percent of the lake correction for reasonable crustal densities.

To conclude, in addition to the methodological procedures just described, we will now
describe another problem related to the gridding of our database. In the case
of the AAGRG compilation, interpolation of original and gridded data has
been done by an iterative procedure:

Data providers, who were not allowed to release original information, created gridded data relying initially on their own scattered data and keeping only the nodes inside their own territory on a grid the AAGRG defined in common for the whole area.

After merging all data sets from AAGRG members one common grid was interpolated.

In the next step grid nodes of the neighboring countries were merged with the provider's original data set, and a new data grid was interpolated.

This iterative procedure continued until the variation of
interpolated grid data close to the borders was well below an error threshold
defined by

We have focused on commonly used global geopotential models (GGMs) up to the degree/order of 2190, mainly on EIGEN-6C4 elaborated jointly by GFZ Potsdam and GRGS Toulouse (Förste et al., 2014) and EGM2008 (Pavlis et al., 2012). Both models are created by the combination of satellite and terrestrial gravity data. The spatial resolution of these models is roughly about 10 km.

The GGMs are usually used in connection with the so-called residual
terrain modeling (RTM) technique, which greatly improves gravity values
calculated from GGMs on the Earth's surface. The RTM technique accounts for the
difference between the gravitational effect of the real terrain masses
represented by high-resolution DEMs and smoothed mean elevation surface
represented, e.g., by the DTM2006 model (Pavlis et al., 2007). However, since
the effect of the detailed DEM would be subtracted retrospectively in the
Bouguer anomaly calculation, it means that, in order to obtain BA, we only
need to subtract the gravity effect of the DTM2006 (

We calculated the gravity values

Comparison of Bouguer anomaly maps (correction density 2670 kg m

Figure 12 shows a comparison of a BA map derived from terrestrial data with
the map derived from the EIGEN-6C4 model (calculation points were made on a
2 km

GGM data points located in gaps of the original gravity points were separated by the shortest distance criteria of 15 km using a standard database search query in QGIS. A 15 km criterion was chosen as a compromise between covering GGM data close enough to the vicinity of the terrestrial data (Fig. 19) but at the same time not filling gaps that are too small between them, which could lead to local artificial anomalies.

We here present a short overview of the features of the new Bouguer anomaly
map (Fig. 13). The most prominent feature of the complete Bouguer anomaly
(CBA) is the Alpine gravity low (AGL), which is characterized by gravity
values ranging from

New pan-Alpine Bouguer gravity anomaly map. The first order dominant regional gravity anomalies: AGL – Alpine gravity low, PoBGL – Po Basin gravity low, CAGL – the Central Apennine gravity low, IGH – Ivrea gravity high, VVGH – Verona/Vicenza gravity high, VFGL – Venetian/Friuli Plain gravity low. The second dominant regional gravity anomaly: MGHi – Mediterranean gravity high, CLGH – Corso/Ligurian gravity high, TGH – Tyrrhenian gravity high, CSGL – Corsica/Sardinia gravity low, SAGH – south Adriatic gravity high, IGH – Istria gravity high, WCGL – Western Carpathian gravity low, DGL – Dinaric gravity low, MeGH – Merdita gravity high, ADGL – pre-Adriatic depression, PBGH – Pannonian Basin gravity high, TDGH – Transdanubian gravity high, PGH – Papuk gravity high, MsGH – Mecsek gravity high, FGGH – Fruška Gora gravity high, DBGL – Danube Basin gravity low, MBGL – Makó/Békés Basin gravity low, APGL – Apuseni gravity low. The rest of the study area: PGL – Pyrenean gravity low, MCGL – Massif Central gravity low, PBGL – Paris Basin gravity low, URGGL – Upper Rhine graben gravity low, RBGH – Rhône/Bresse Graben gravity high, BFGH – Black Forest gravity high, VGH – Vosgesian gravity high, KKGL – Krušné hory (Erzgebirge)/Krkonoše gravity low, TBLGH – Tepla/Barrandian/Labe gravity high, MGL – Moldanubic gravity low, OOGL – Orlice/Opole gravity low, MSGH – Moravo/Silesian gravity high, USGH – Upper Silesian gravity high, SGH – Sudetes gravity high, KB – Krško Basin. A high resolution 600 dpi plot of the map is available in the supplement.

A second prominent low is the Po Basin gravity low (PoBGL). The gravity
values here range from about

A significant anomaly feature represented by a very narrow local gravity high
can be clearly recognized between the Western Alps and the Po Basin. This
anomaly is well known as the Ivrea gravity high (IGH). It is characterized
by maximum values of

To the northeast of the Po Basin, we can observe the Verona/Vicenza gravity high (VVGH), which has been recently modeled as being generated by increased density crustal intrusions related to the Venetian magmatic province (Tadiello and Braitenberg, 2021; Ebbing et al., 2006). The Venetian/Friuli Plain gravity low (VFGL) is located in eastern Italy, which is presumably caused by low-density sedimentary infill, also like the gravity low in the Po Basin (Braitenberg et al., 2013).

A prominent gravity high is the Mediterranean gravity high (MGHi). This
regional-scale anomaly has its maximum over the Corso/Ligurian Basin, the
Corso/Ligurian gravity high (CLGH). It is characterized by maximum values of

The Adriatic Sea region is largely characterized by a positive gravity
field, in which the south Adriatic gravity high (SAGH) dominates with values
from

In the Eastern Alps, the AGL splits towards the east into two branches of
less pronounced gravity lows: the Western Carpathian gravity low (WCGL) and
the Dinaric gravity low (DGL). In the Western Carpathians, the values vary
from 0 to

The Pannonian Basin extending between the Western Carpathians and the
Dinarides is accompanied by a relatively regional gravity high (Pannonian Basin gravity high, PBGH) whose
values range in a narrow interval from

The rest of the study area extending north of the MGHi, AGL and WCGL is
accompanied by an indistinct yet variable gravity field with the values
varying generally from

The gravity field of the Bohemian Massif can be divided into several
subparallel positive (up to

The gravity field over the Franconian Platform area north of the Molasse
Basin is quite variable, and values range from

The Rhenish Massif is distinctly asymmetric, positive (up to approx.

The newly compiled gravity database of the Alps and their surroundings is based on decades of data collection and processing experience of the AAGRG members. The national gravity data, which were recompiled here under new, modern geophysical and geodetic aspects (Sects. 2 and 3), were collected with rather different instruments at different times over the last 70 years and processed with extremely different processing methods. At the end of the data processing, we therefore asked ourselves for what purposes it can be used and how accurate the new map actually is. The first question can be answered relatively easily: with medium- to large-scale modeling of the Alpine lithosphere and/or the Alpine Earth crust, as realized in the AlpArray initiative, there should be no problems with the final accuracy of the database: these errors are small compared to the uncertainties that result from modeling and simulation. The second question about accuracy (uncertainty), which is caused by using extremely different data sets, is much more difficult to answer because in practice for all participating countries there are no exploitable metadata available for the national gravity databases.

As desirable as it would have been for the submitted pan-Alpine gravity maps to present “uncertainty maps” at the same scale, this project is hindered due to the complexity of the task and the lack of information on errors and accuracies in the field campaigns and data processing of the individual countries. However, in order to obtain an estimate of the uncertainty, we have tried in the following section to list various aspects of error analysis by way of examples. It must be reserved for a later publication to present a numerical-statistical analysis of the map (e.g., with the time consuming sequential Gaußian simulation; e.g., Shahrokh et al., 2015) or statistical evaluation compared to the GOCE (Gravity field and steady-state Ocean Circulation Explorer) gravity observations that have lower spatial resolution but homogeneous error (Bomfim et al., 2013).

In Fig. 14 we show a test calculation that demonstrates the differences
between the fields of the interpolated CBA and point stations in Slovakia.
These “test data” have not been considered for the interpolation of the
Slovakian gravity grid – thus they represent an independent test of the map
quality. First, it should be noted that no deviations are greater than

Differences between the CBA grid and independent gravity points
(not used for the Slovakian part of the gravity grid compilation). It was
calculated by SURFER's simple grid-residual procedure and
showed that no gravity differences were greater than

The sources of errors in gravimetric measurements are manifold and result directly from the definition of the Bouguer anomaly and the processing of associated reduction and correction terms (Sect. 3, Eq. 1). Instrumental readings in gravimetry depend on the instrument drift and the accuracy of the scale values and are of course dependent on the external conditions in the field. In addition, there is a correction of the Earth's tides and the air pressure. The localization of the station with longitude, latitude and altitude, as well as its geographical context (e.g., measured along profiles, areal measurements, located in valleys with extensive sedimentary filling, etc.), is also subject to errors. The density of the station distribution (Fig. 1) certainly has a great influence on the accuracy of the resulting maps. This is, however, good enough for the above-mentioned modeling of the lithosphere – very small-scale modeling on a kilometer scale is excluded.

Even the indication of the positional accuracy of the gravity stations and the DEMs used pose great problems, and most of the information is not available in digital formats. The same is true for the above-mentioned field instruments and procedures used, which have been improved often over the last 70 years, and of course for the processing techniques, which started with manual-graphic methods and still allow for digitized processing from field measurements to 3D interpretation (among many others: Cattin et al., 2015; Sabine Schmidt, personal communication, 2019).

Furthermore, different numerical approaches that can be used for the data processing provide different results. In Appendix D we reported test investigations which led to the selection of the software for the calculation of the MC (Appendix D, Fig. D1). A comparison of the standard deviations (1.95 mGal for the software TriTop and 0.39 mGal for Toposk) also gives an indication of the achieved accuracy of the database – even if this can only be a partial aspect.

Two other sources of error deserve a closer look. In Sect. 5.2 we will discuss errors that occur when calculating the mass correction with different correction densities. Notes on the accuracy of the anomalies due to a 2D (on the map projection plane) and a 3D interpolation needed have already been given in Sect. 4.1. Based on national investigations in the area of Austria, indications of the achieved numerical accuracy of the Bouguer anomalies are then given in Sect. 5.3. Finally, in Sect. 5.4 the results of an error statistic based on cross validations (CVs) are given for the entire database.

However, it should not be forgotten that CV is a purely statistical measure and in minor amounts considers point data quality, which indicates that we cannot directly represent the quality of the newly compiled gravity fields from the CV.

CV works well with dense station coverage; only then can we exclude large local anomalies, for example, due to geological causes. The less dense the coverage is, the less we can exclude the presence of local anomalies. Note that these local anomalies can easily be produced by selecting improper MC density, for example, in a station setting covering a valley and adjacent mountain flanks where densities differ from the assumed MC density remarkably.

The DEM used has a significant influence on the result. For example,
differences in MC calculations using the lidar and MERIT DEM (Appendix D, Fig. D4) resulted in values of

Consider that the calculation of MC is already part of the modeling which
has to be performed with the best possible spatial resolution. For this, the
density of the masses is constant. If this density corresponds to the real
density, then only volumes of a different density within the ellipsoid must be
recognized as additional sources. For any later modeling, this setup
simplifies the model geometry considerably.
If, however, the constant MC density differs from the natural conditions,
these masses must be addressed with a different density in the model,
resulting in substantially more complicated geometry. In addition, these
model masses must be calculated with the same spatial resolution as used in
the calculation of the MC. If one considers that resolutions of the
topography of 10 m

Here, essentially the same applies as in the normal case (A) except that the creation of the initial model is considerably more complicated. A 2D density model is used for the MC and, hence, must be considered in successive models. As the same statement as above can be made, this complicates the model setup compared to the normal case (A). However, the 2D case makes sense if it is to be used for qualitative interpretation since the 2D model represents the natural conditions much better than when using a constant MC density.

Unfortunately, this case is only applicable in theory as the real density distribution is always characterized by MC densities which are not constant and not known for data processing or modeling. A priori knowledge would be the optimal case, but in this case, 3D modeling and the MC correction for the BA have to be done simultaneously in an integrated modeling framework. In order to interpret and model gravity anomalies quantitatively, it is recommended to choose the normal case (A).

The consequences for possible errors for MC from the three cases are as follows. If we would regard incorrect MC density as an error source, these errors can
be as high as 700 kg m

When including the actual density errors in the error balance, we would observe large errors of 50 mGal and more. Using these errors as a criterion for the quality of fit in the 3D model calculation makes no sense. However, if we take the physical interpretation of the BA (as explained at the beginning) as a baseline, MC density errors are indeed not errors but objects of the model calculation.

As already discussed in Sect. 4.1, any 2D interpolation procedures for Bouguer values are not exact. However, for large-scale interpretation these errors are negligible. Instead, we use two approaches for assessing the interpolation error: interpolation residuals and cross-validation residuals. Interpolation residuals depend on the mathematical representation of the interpolation grid. We use the bilinear interpolation method for calculating the residuals at points that do not coincide with grid nodes. Interpolation residuals describe how exact the scattered data are represented by the interpolation surface. Cross-validation residuals are calculated by removing one observed station from the data set and using all remaining data to interpolate a value at its location. This procedure is repeated for all the other stations of the data set. Both methods reflect gross data errors if present. However, large residuals do not indicate data errors necessarily but hint to a possible sampling problem if a true local anomaly is not sufficiently supported by the station coverage in the surrounding area. In the following, residuals are defined by differences between interpolated and observed gravity values.

The interpolation residuals of the Austrian data set range between about

Residual statistics for the Austrian data set. Units in milligals (mGal).

Interpolation and cross-validation residuals of a subset within a
small section of the Enns valley in Austria. Background image is the topography: contour
lines: CBA anomaly (mGal) interpolated using a high-resolution grid (about
200 m spacing); colored dots: residuals (

For discussing the sampling problem, Fig. 15 shows the interpolation
residuals (Fig. 15a) and the cross-validation residuals (Fig. 15b) within a smaller
section of the Enns valley in Austria. Background colors display the
topography, and contour lines show the Bouguer anomaly interpolated to a high-resolution grid with a spacing of 0.00173

As mentioned in the previous subsection both interpolation residuals and
cross-validation methods provide some picture of data quality. At the same
time, these methods can be used as a criterion for excluding gross errors
from individual databases. Both methods give qualitatively similar results
(see Fig. 15), with cross validation giving quantitatively more significant
residuals. Since in the case of cross-validation residuals (unlike
interpolation residuals) it is possible to exchange data between grid
providers in order to comply with the conditions of confidentiality of the
original data, we show in Fig. 16 a complete map of cross-validation
residuals for the whole area. While the standard deviation of these
residuals is well below 1 mGal (comparable to Table 2), the extreme values
reach tens of milligals (about 120 points exceed 10 mGal, 9 points exceed 20 mGal). An extreme point with a residual higher than 60 mGal creates a
characteristic bull-eye anomaly in the CBA map (Fig. 17). We consider
similar points with extreme residuals to be erroneous, and it is therefore
necessary to exclude them from the database before compiling the final CBA
map. Therefore, it is necessary to choose a reasonable criterion considering
the analysis of errors, as well as the problem of inhomogeneous coverage of
the territory by the data described in the previous subsections. We decided
to use the exclusion criterion of points exceeding interpolation residuals
of

Results of cross validation of the new CBA. The point sizes are proportional to the magnitude of residuals. The grey “background” represents locations with lowest residuals.

Example of an extreme value of more than 60 mGal deviation in the
new CBA map: initial CBA version

Position of excluded points (approx. 350 points in total) based
on interpolation residuals higher than

From the outset, the AlpArray (AA) initiative was organized in several research groups that contributed to the solution of specific issues. Their main task was to organize and, where appropriate, coordinate the activities of all members within the group. Of the six AA research groups, five were concerned with the solving of seismic problems, and the sixth group had set itself the task of uniformly processing and publishing modern, homogeneous gravity anomalies of land-based gravity data. The results of this group are here presented to the public in two grid versions. In the following, we provide readers (1) with information on the coverage, the acquisition of the data sets and the quality of processed data and (2) their citation, long-term archiving in a data repository and DOI allocation for research data.

At an early stage, the AAGRG considered which gravity field anomalies in an
interdisciplinary work environment could contribute to solving the principal
questions posed in the AlpArray program. We hereby make the following
anomaly data sets available to the community:

The first is free-air anomalies, reconstructed from interpolated Bouguer anomalies according to Eq. (13).

The second is complete Bouguer anomalies.

In addition, the values of the mass/bathymetric correction will be released
in a similar format to the anomalies. Their knowledge is essential because
the specification of the values for the mass correction allows for an individual
recompilation by the user with a different correction density. This is
particularly recommended if the use of an individual density is preferable
to the standard density of 2670 kg m

Also included is the grid of ellipsoidal heights.

for the public on a grid of approx. 4 km

for the working groups of the AlpArray initiative on a grid approx. 2 km

The area covered includes not only the core Alpine regions of the Western
and Eastern Alps and the Carpathians but also parts of the Northern
Apennines, the Dinarides, the Pannonian Basin and extended Alpine forelands
and parts of the Adriatic Sea and the Ligurian Sea. The lower left map
corner is located at coordinates 41

This file contains all results organized into seven columns – Lon, Lat, EH, CBA,
FA, MC, BC – which respectively correspond to Lon

The format of the digital grids is as follows.

The five digital grid files

“Pan-Alpine_2020_Bouguer_gravity_anomaly_grid.grd”,

“Pan-Alpine_2020_free-air_gravity_anomaly_grid.grd”,

“Pan-Alpine_2020_mass_correction_grid.grd”

“Pan-Alpine_2020_bathymetric_ correction_ grid.grd” and

“Pan-Alpine_2020_ellipsoidal_ height_ grid.grd”

Summary of map-relevant information.

Although it was and is the declared objective of the AAGRG to compile digital gravity data for the Alps and their adjacent areas, a high-resolution Bouguer gravity map is also available for download in PDF format (Supplement). Besides the anomaly in the form of a “heat map”, it also contains geographic information for better orientation. Figure 19 shows the spatial distribution of all original data considered for the map compilation and all areas where GGM data have been used for filling gaps (refer to Sect. 4.2).

Despite all efforts to achieve the greatest possible homogeneity in the database and processing steps, this map is intended to show that the initial database was different due to national requirements. First, the outer areas shown in red are supplements/fillings with GGM values (Sect. 4.2). Irregular black dots indicate the use of point data, and in the offshore areas of the Ligurian Sea black lines indicate the ship tracks. In the southeast of the chart, isolines have been digitized (see also Sect. 3.3).

The publication and storage of the pan-Alpine gravity data and the accompanying Bouguer gravity map follows the standards of the Alliance of European Science Organisations, which has already declared its support for the long-term storage of open-access data in consideration of disciplinary regulations in the handling of research data in the “Principles for Handling Research Data” adopted in 2010 (DFG in Germany, SNSF in Switzerland, etc.). After the completion of the AAGRG task the group is obliged for various reasons (e.g., AAGRG “Memorandum of Collaboration” with the participating countries, long-term value of the data) to store the data permanently.

GFZ Data Services (

For the gravity data to be found worldwide on the Internet, the data must be given a description that is readable by search engines. This description is provided by metadata. The specific description of metadata for our data set is important but is not part of this publication, but refer to general information in Appendix A.

Data access and use is defined by the AAGRG. The copyrights and access rights are described in a license which is firmly attached to the data and which defines in which way the data may be used or not.

The article and corresponding preprints are distributed under a Creative Commons Attribution 4.0 license. Unless otherwise stated, associated material is distributed under the same license.

For the new data sets also a DOI was assigned. They have been published with
the DOI

The aim of this publication is to report on the activities and work of the
AlpArray Gravity Research Group (AAGRG) over more than 3 years. The
group's mission was to recompile and release digital
homogenized gravity data sets that are based on terrestrial gravity
measurements that are owned by the national Alpine neighboring countries
(in total more than 1 million data points). They can be used for high-resolution modeling, interdisciplinary studies from continental to regional
and even to local scales, and for joint inversion with other
data sets. Bouguer and free-air anomalies are available at a grid density of
4 km

Both digital data sets are compiled according to the most modern geophysical
and geodetic criteria and reference frames (both location and gravity). This
includes the concept of ellipsoidal heights and implicitly includes the
calculation of the geophysical indirect effect; atmospheric corrections are
also considered. For the calculation of station-completed Bouguer anomalies,
we used the following densities: 2670 kg m

In the future, the calculation of long-distance effects of
topography and bathymetry and their compensating masses (roots) are planned.
What is absolutely necessary is a more profound analysis of the map uncertainties. The associated research is complicated by the fact that for many of the
national data sets used, no metadata are available. The reasons for this are
manifold and do not lie with the group. To obtain an estimate of the error
size in the present compilation, cross validations were calculated both for
the entire grid and for the national grids. After an iterative improvement
by the elimination of erroneous data, a map error of max.

Appendix B provides the historical activities of the main actors at first and then the national contributions to the pan-Alpine Bouguer gravity map.

Zych (1988) reports on the first gravity measurements in Austria in the
course of hydrocarbon exploration as early as 1919, while more intensive,
regional and detailed measurements were carried out in the following years
with pendulums, torsion balances and gravimeters, concentrating mainly on
the Vienna Basin and neighboring areas. This and other measurements were
later included in the gravity map of Austria (Senftl, 1965) by the Federal
Office of Metrology and Surveying (BEV) at a scale of

An early compilation of gravity measurements and a gravity map covering the
entire country was published in 1921 based on data acquired since 1900
(Niethammer, 1921). In 2008, the Institute of Geophysics of the University
of Lausanne published the gravity map of Bouguer anomalies in Switzerland at a scale of

A detailed and systematic gravimetric coverage of the French territory was
conducted in the frame of the Carte Gravimétrique de la France 1965
(CGF65). The establishment of a reference network of 2000 base stations
originally linked to international absolute stations (Potsdam system) and
the gravity surveys carried out between 1945 and 1975 using North American,
LaCoste and Romberg, and Worden meters for mapping, mineral and oil
prospecting, or for academic purposes provided the first gravity
infrastructure at national scale. Despite incomplete coverage, it was
published in 1975 in the form of a map on a scale of

One may speculate that the history of gravity measurements worldwide and
especially in Italy began with the free fall experiments of Galileo Galilei
(1564–1642). In his honorary capacity we still use gals or milligals (10

In 1975 the late Italian Geodetic Commission decided on the compilation of a
new Bouguer anomaly map of Italy based on up-to-date correction standards
and homogeneous methodology. This map was published in 1991 by the National
Research Council (CNR; C.N.R.-P.F.G., 1992) as part of the Structural Model of
Italy at a scale of

In 1989 the Geological Survey of Italy, together with ENI-AGIP, published a
new gravity map of Italy scaled at

The first map of Bouguer anomalies which comprises the whole Slovenian
territory was compiled in 1967 (Čibej, 1967; Ravnik et al., 1995). It
was based on data measurements with a Worden gravity meter (no. 117) in the
framework of various gravity surveys conducted over the period 1952–1965 by
the Geological Survey of Slovenia (Stopar, 2016). Later in the frame of the
W–E Europe Gravity Project led by Getech from Leeds University, a new data set
was prepared in the 1990s which comprises 416 gravity points giving an average
density of 0.02 gravity stations per 1 km

With the start of the

Gravity field investigations and field observations in Hungary were already established by the pioneering work of Baron Loránd (Roland) Eötvös. The Eötvös torsion balance became the world's first geophysical tool for prospecting, and it revealed hundreds of hydrocarbon resources; see Szabó (2016) for a full narrative of the history.

A thorough overview of the practical and methodological developments of
gravimetry in the Slovak Republic can be found in

After this historical review we describe country by country the initial situation for the assessment and application of existing data, available publications, data density, and quality. The following partner and AAGRG member countries have contributed to the compilation of the new pan-Alpine gravity maps.

In the early beginning, gravity stations in Austria were mainly arranged
along leveling lines. The first areal network, which was surveyed by OMV (Österreichische Mineralölverwaltung),
focused on the Alpine Foreland, the Vienna basin and parts of the Flysch and
Calcareous zone of the Eastern Alps (Zych, 1988). Additional gravity
profiles were established across the central part of the Eastern Alps
(Ehrismann et al., 1969, 1973, 1976; Götze et al., 1978) 50 years ago.
The vertical coordinates of all stations so far were determined by precise
leveling, while horizontal coordinates were based on topographic map
digitization providing an accuracy estimate of

The Croatian national gravity database consists of approximately 16 500
free-air anomaly values covering the entire continental area. Data in the
database were mainly collected from 1945 to 1990 across the territory of the
former Socialist Federal Republic (SFR) of Yugoslavia. The data are almost
equally distributed across the wider territory of Croatia, also including
some points in Bosnia and Herzegovina and Slovenia. The average point
density is 1 point per 18 km

Equally for the Czech Republic and the Slovak Republic, most regional gravity surveys
were conducted from the 1950s till the 1990s. The prevalent sampling interval was
about 500 m, or five stations per 1 km

Further parameters of this exemplary new compilation are the use of the
Somigliana–Pizzetti formula for normal gravity, the spherical calculation of the
topography effect (density 2670 kg m

One of the most important steps of this process is the precise evaluation of the terrain corrections. For selected areas of Slovakia gravity maps were compiled and purpose-derived gravity maps, and density models were constructed along selected regional gravimetric profiles across the territory of the Western Carpathians. The first map in the Czech Republic was made accessible to the public in April 2009, was last updated in April 2013 and was turned into a world-wide-web format in 2014.

Since the early 1990s, gravity densifications have been realized using
Scintrex gravity meters (CG3, CG5 and currently CG6) and accurate GPS
positioning, mainly as part of major scientific projects such as
GéoFrance3D (“Millennium Project”). A new gravity database based on
both recalculated corrections with a density of 2670 kg m

The gravity data sets over France and the surrounding marine areas are
provided from the BGI global gravity databases (

Offshore gravity measurements in the study area were collected from shipborne surveys performed since the 1960s in the Gulf of Lyon and Ligurian Sea by the French IFREMER, CNEXO, SHOM and CGG. In addition, this area is also covered by the extensive gravity surveys carried out between 1961 and 1972 by the Italian Experimental Geophysical Observatory over the whole Mediterranean Sea, and it is known as the “Morelli dataset” (Allan and Morelli, 1971). These surveys were conducted with different generations of sea gravity meters (LaCoste and Romberg, Graf-Askania, Lake Constance) mounted on a gyro-stabilized platform. Corresponding gravity data and reports are archived by IFREMER and SHOM and transmitted to the BGI.

Offshore gravity data included in the AlpArray compilation are provided by
the GEOMED2 project (Lequentrec-Lalancette et al., 2016; Barzaghi et al.,
2018). This project was recently conducted in the frame of the International
Association of Geodesy (IAG) by the International Gravity Field Service
(IGFS) and BGI, and it aimed at providing high-resolution geoid and gravity grids
and maps of the whole Mediterranean Sea. The compilation, validation and
adjustment of the above-mentioned French and Italian marine gravity surveys
were done by SHOM and BGI considering the usual protocols applied at SHOM
(Service Hydrographique et Océanographique de la Marine) for the
qualification of marine gravity data. The final GEOMED2 product led to the
realization of a 1 arcmin

The German data used in the AlpArray project originate from three main data sets that were acquired between ca. 1930 and 2010. The AlpArray area is covered by 36 442 gravity stations. As only a few historical measurements were carried out in the frame of dense local surveys, the mean point spacing is on the order of 2 to 3 km. Regional gravity measurements were either conducted at public geodetic reference points, for which precise coordinates were available, or at prominent points that could be easily identified in maps and for which coordinates were digitized. Hence, the precision of the coordinates can vary between some centimeters and some tens of meters. The heights of the German gravity stations refer to the reference system DHHN (German main leveling network) and the version valid at the time of the measurement. This may result in deviations from the current reference system DHHN2016 on the order of some centimeters. During the reprocessing in 2010, station heights were checked for plausibility by a comparison with heights taken from the DEM25 (the best German DEM at that time). As large deviations can also result from imprecise horizontal coordinates of the stations, such stations were additionally evaluated with respect to their location by means of GIS techniques and, if necessary, by an additional comparison with georeferenced digital topographic maps and orthophotos. For 95 % of the stations covering the entire German territory the differences in height are less than 2 m. Gravity stations that exhibit differences of more than 5 m to DEM25 were not considered in the data contribution for the compilation of the new AlpArray Bouguer gravity map.

The current Bouguer anomaly map for Germany (Leibniz-Institut für
Angewandte Geophysik, 2010; Skiba, 2011), based on more than 275 000 data
points, refers to the IGSN71 and a density of 2670 kg m

For the AlpArray compilation, gravity data were provided by the Leibniz Institute for Applied Geophysics (including data from the

Hungary contributed to the unified Bouguer gravity map with gridded data of
2 km

The Hungarian gravity database consists of approximately 388 000 data points
and covers the whole country with rather heterogeneous point density.
Gravity measurements were mainly carried out between 1950 and 2010 for
different purposes, which determines the point distribution. For the oil
industry, local exploration grids were established with a few hundred meters
grid spacing; on the other hand, due to transportation requirements, early
measurements were arranged along roads. The average point density of 2.8
points per 1 km

The Italian data used in the AlpArray project originate from one main data set, which is industry data handed over by ENI, and several other minor data sets, including the Province of Bolzano, newly acquired data in the Ivrea–Verbano zone preferentially to fill earlier data gaps (Scarponi et al., 2020), data acquired in the Province of Bolzano during the INTAGRAF project, and SwissTopo data. The AlpArray area is covered by 130 905 gravity stations, of which the ENI data set has 128 479 stations on land and offshore, in the Province of Bolzano there are 1737 stations, and in the Ivrea–Verbano area there are 689 stations. The data are very dense in the Po plain and scarcer at the higher elevations, with a mean point spacing of 705 m. Gravity measurements other than ENI were conducted at cadastral geodetic reference points for which precise coordinates were available or were acquired at a position and height with parallel GNSS observations. The ENI data points were acquired with either traditional geodetic survey or the newer points with GNSS. The positions of the Italian gravity stations refer to the reference system GRS80, with the industry data having been transferred to GRS80 in the frame of a revision of the database and with the heights in normal heights. Geoidal heights were converted to ellipsoidal heights by adding the ITALGEO geoid heights. We have compared the normal heights with different terrain models, with MERIT (Yamazaki et al., 2017) and in the Region Veneto with the local high-resolution DEM. The average difference with MERIT of the entire database is 0.3 m, and the root mean square difference is 12.63 m. The criterion for using a data point for the final map was a difference with MERIT of less than 50 m. This large height difference is limited to relatively higher elevations outside the plains and is probably due rather to the sparse grid-spacing of the MERIT model than to misplacement of the stations. We find that 66.64 % and 79.57 % of the entire onshore database has a height error below 5 m and below 10 m compared to MERIT, respectively. The absolute values of the ENI database referred to the old Potsdam gravity system and were transferred to the IGSN71, correcting the values for 14.00 mGal (Morelli, 1948; Wollard, 1979). In the areas with both ENI data and modern acquired data, the systematic shift was confirmed by direct comparison of the absolute gravity values.

From the gravity map of the Geological Survey of Slovenia (Čibej, 1967)
approximately 2150 gravity points were selected for the construction of the
regional map at the scale of

In the frame of the W-E Europe Gravity Project led by Getech from Leeds a
new data set was prepared in the 1990s which comprises 416 gravity points giving an
average density of 0.02 stations per 1 km

The Swiss gravity database GRAVI-CH was collected and maintained by the University of Lausanne (Olivier et al., 2010). It consists of around 30 000 points with measurements from 1953 to 2000.

The data set used in this project is a subset of 7962 points from GRAVI-CH,
limited to the area of Switzerland and Liechtenstein and reduced to a
density of 1 point per 2 km

One of the important elements in the CBA calculation process is the determination of mass correction (MC). The key element for quality and reliable determination of MC is the use of reliable and accurate digital terrain models without canopy and buildings. Since our approaches to MC are based on calculations in different zones (see Appendix D), it is very important to provide models with the appropriate resolution and quality. The nearest zone up to 250 m is the most critical from the MC point of view. Hence, for this zone, it is best to use the highest-quality models based on lidar technology or respective digital photogrammetry with 1–10 m resolution. Each country, depending on availability, provided a model suitable for calculating the “inner zone” (Appendix D). The basic metadata summary is in Table C1. Acquired models differ in the raw data collection methods, resolution, time of creation, position and height coordinate system, and accuracy. Due to the problem of coordinate system unification (especially height system) and general approach to MC calculation, the heights in all models were transformed to ellipsoidal heights in the ETRS89 system, ellipsoid GRS80, using the appropriate local geoids and quasi-geoids of the individual countries.

List of DEMs used for test and mass correction calculations in the “most inner zone” of the TOPOSK program (Appendix D) of the individual countries; the grid spacing, sources and internet references are given. The letters stand for the techniques used in the DEM compilation: “L” for lidar, “P” for Photogrammetry, “TM” for heights from digitized topographic maps, and “MERIT” and “SRTM” for the radar data.

Each of these models was tested on a set of gravimetric points located at
least 500 m from the border of each country. This test served both to detect
possible artifacts in the DEMs (especially in high mountain areas) and also
as a primary filter of the quality of the position of gravimetric points.
These differences are illustrated in Fig. C1 and statistical findings in
Table C2. Several points exceeding the threshold of

Statistical results of test calculations of consistency of surface station heights and DEMs used of the individual countries in the “most inner zone”.

Height differences (in meters) for DEMs in the “inner zone” of the TOPOSK software (refer to Appendix D) between the used DEMs and the heights of these stations.

Histograms of height difference residuals of participating countries. The values in the different classes are given in meters.

For the calculation of MC within the middle zone (250–5240 m) it is very
suitable to use DEMs with medium resolution (1–3 arcsec) which uniformly
cover the whole territory, have the same shape representation and accuracy, and
can be converted with local geoid and quasi-geoid models to ellipsoidal heights.
Thanks to remote sensing satellite techniques, several commercial or freely
available digital elevation models are currently available
(

Basic characteristics of the global DEMs tested.

From these models the best one is MERIT due to the removal of major error components from the satellite DEMs like absolute biases, stripe, speckle noise and canopy height biases (Yamazaki et al., 2017; Hirt, 2018). This was confirmed also by an independent comparison at selected gravimetric points with new, precisely measured positions with GNSS in Switzerland, Slovenia and Slovakia (refer to Table C4 and Fig. C3), where large errors in the mountainous parts were due to canopy. The MERIT DEM was used in the original 3 arcsec resolution, and for T2 zone calculation it was resampled to the 25 m resolution.

The overall quality of the MERIT model has been tested at most gravity station heights. The differences can be seen in Fig. C4 and basic statistical data in Table C5.

Histograms of height residuals between global DEMs and 7097 selected gravity stations on the territory of Slovakia. The values in the different classes are given in meters.

Statistical results of test calculations of consistency of station heights for the territory of Slovakia (7097 points) and global DEMs tested.

Height differences (in meters) between MERIT DEM heights and heights of original surface-gravity stations; MERIT DEM heights were considered for the “middle zone” of the mass calculation software TOPOSK (refer to Appendix D).

Statistical results of test calculations of consistency of station heights and the MERIT DEM used.

Largest differences were observed in Croatia, Czech Republic, France, and Hungary most likely due to the low quality of the position of gravity stations.

The Toposk software (Zahorec et al., 2017a) is designed for the calculation
of the gravitational effect of the near-terrain masses for both “near-terrain effect” (NTE) and “mass correction” (MC), i.e., the total masses
between the topography and the zero level – geoid or ellipsoid (we point out
the difference from the terrain correction (TC), which represents only
masses exceeding the classical “Bouguer shell”). The program is suitable for
highly accurate calculations in rugged terrain using high-resolution DTMs.
Different DTMs, with increasing resolution towards the calculation point,
are used within particular zones. By default the program uses the following
zoning:

T1: inner zone (0–250 m from the calculation point),

T2: intermediate zone (250–5240 m) and

outer zones: T31 (5.24–28.8 km) and T32 (28.8–166.7 km).

The TriTop software (Holzrichter et al., 2019) is an adaptive algorithm for MC based on a triangulated polyhedral representation of the topography. The runtime of the algorithm is improved by an automatic resampling of topography. The topography is resampled in a quadtree structure. The high resolution of the topography is only considered if it has a significant influence on the gravitational effect at the station and not only by the distance to the station. Therefore, there are no default zone radius definitions, but the resolution depends only on the gravitational effect and differs for each station. In comparison to Toposk, TriTop does not consider a high-resolution zone (T1; see above) and does not interpolate topography in this zone in dependence to station height. The DTM heights are not modified.

The programs were compared to each other on different sets of points from Slovakia and Austria. Mainly the second comparison was important because of the typical Alpine terrain character of the majority of the territory in Austria. The obtained results by the Toposk and TriTop software were compared with previously computed mass corrections (NTE) from the Austrian gravity database. This comparison was realized on a set of 28 420 points with the ellipsoidal heights ranging from 158.35 to 2898.78 m. The character of the differences between mass corrections from the Austrian gravity database and NTE calculations by means of the Toposk and TriTop programs is visible from histograms in Fig. D1. Finally, the Toposk software was selected for the recalculation of MC effects due to better statistical parameters (median and standard deviations) and the absence of outliers in the calculations. The differences in MC of both algorithms are observed in areas where stations are located close to steep slopes in topography. The differences of the results in Austria are caused by the main difference of both algorithms and in particular the handling of the inner zone T1. TriTop does not change or interpolate the topography around the station. This might lead to larger correction values in areas of highly rugged terrain due to steep slopes close to the station or even in cases in which the station height is slightly below the DTM. The comparison shows that in the area of highly rugged terrain the inner zone just around a station should be handled separately from the rest. Therefore, we decided to perform mass corrections with the Toposk software.

Comparison of the differences between original mass corrections
from the Austrian gravity database and NTE calculations by means of programs

For most countries, we used the available local detailed DEMs (Appendix C)
with the resolution of 10–20 m (derived mainly from lidar data) for
calculation in the innermost Toposk zone (T1). For all other zones we chose
the best available global DEMs. We got good results with SRTM models for
outer zones. For the intermediate zone T2, we decided to use the MERIT model
based on our tests (Appendix C). MERIT was also used for the inner zone if
local models were unavailable. This model (resampled to a 1 arcsec
resolution) showed better height accuracy compared to other global models
(based on the height residues at the points of the databases tested) and
consequently minor differences in MC compared to local models (Fig. D2). The
mentioned height residues of individual points of the databases in relation
to local (or MERIT) models were subsequently used as a control criterion.
In particular, we consider points with height residues greater than

Near-terrain effect (or mass correction, density 2670 kg m

Comparison of original mass correction (or terrain corrections) values and values calculated using local DEMs. Note: there are different scales for each graph.

Differences in mass correction values (correction density 2670 kg m

There are options to verify calculated MC values and estimate their error.
For some databases, we had the original MC or TC values, which allows us to
compare and control different approaches. Figure D3 shows graphs and
statistical comparisons for some countries. The maximum differences are at
the level of several milligals, and the RMS error in most cases is below 1 mGal. Note
that the graphs do not show excluded points (above

The supplement related to this article is available online at:

While a separate page could be filled with detailed author contributions, we highlight the great joint effort that resulted in the current paper and, within that, that all authors contributed to data curation as the most crucial step.

The conceptualization stems from the AlpArray program and included authors GH, HJG, CB, RP, PZ, JP, MB, JE, GG, AG, BM, JS, PS, ES and MV.

The methodology and formal analysis rested mostly on the shoulders of PZ, JP, RP, BM, and CS for the processing of Mediterranean offshore data; there was help from many others, at least one person per country for investigating national data sets.

The original draft was written by HJG, BM, PZ, JP, MB, GH, RP, SB and CB. All co-authors have reviewed and approved the final version of the manuscript.

Funding was acquired on a national basis, as described in the acknowledgements.

HJG and GH ensured the overall project administration and supervision.

The authors declare that they have no conflict of interest.

This first compilation of gravity databases in the Alps and their surroundings has many helpers and supporters in the national administrations, state offices, national founding agencies, the academic working groups of the participating universities, the steering committee of the AlpArray program and finally in the library services of the GFZ (Potsdam, Germany). We would like to thank them all very much for their support. The group met several times for 2 d working meetings, and we gratefully thank the organizers. The results of this study contribute to the activities of EPOS (European Plate Observing System), its French component RESIF (Réseau Sismologique et Géodésique Français) and the Czech component CzechGeo. In Trieste (Italy) the research contributed to MIUR support for the Department of Mathematics and Geosciences, University of Trieste.

Finally, we would also like to thank Tomislav Bašić, Josip Stipčević (Croatia), Roland Pail, Reiner Rummel, Kirsten Elger, Christian Voigt (all from Germany), and an anonymous reviewer for supporting our work.

This research has been supported by EPOS/CzechGeo (grant no. LM-2015079), EPOS (European Plate Observing System), its French component RESIF (Réseau Sismologique et Géodésique Français), the German Research Foundation, (grant no. EB 255/7-1), the National Research, Development and Innovation Office, Hungary (grant no. 124241), the Swiss National Science Foundation (grant nos. PP00P2_157627, PP00P2_187199, and CRSII2_154434), the Slovak Research and Development Agency (grant nos. APVV 19-0150, APVV 16-0146, and APVV 16-0482), the Scientific Grant Agency VEGA, Slovakia (grant nos. 2/0006/19 and 2/0100/20), and the Slovenian Research Agency (grant no. P1-0011).

This paper was edited by Christian Voigt and reviewed by Roland Pail and one anonymous referee.