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.

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.

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.

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 hE of the calculation points and ellipsoidal digital elevation models (using in the majority of cases local geoids for the transformation). On the other hand, the bathymetric and simplified atmospheric corrections were calculated for physical heights H of the calculation points. Bathymetric corrections were also calculated by means of the Toposk software but in a slightly adjusted mode (see below and Fig. 3).

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-3). In the case of marine areas, the situation is somewhat more complicated as the ocean masses are partly above the ellipsoid level. If we want to take these into account with their real density (1030 kg m-3), it is necessary to separate their effect from terrain masses. Numerically, this can be done by taking these water masses into account first as topographic masses (i.e., with a density of 2670 kg m-3) and then also as part of the bathymetric correction (i.e., with a density of -1640 kg m-3). As a result, we assign a density ρ of 1030 kg m-3 to these water masses (ρ=2670–1640 kg m-3).

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-3 (no difference in density at sea and on land). This is in apparent contradiction to published papers which state that the GIE should be calculated with different densities for land and sea (offshore with a density of 1030 kg m-3). This apparent discrepancy is due to different approaches to bathymetric correction. The approach of Chapman and Bodine (1979) is based on free-air anomalies which do not include bathymetric corrections, unlike our CBA. The GIE is thus easier to define in our case (for a constant density of 2670 kg m-3 in the whole space considered between the geoid and the ellipsoid) thanks to the consideration of the rock–water density contrast in this space as part of the bathymetric correction.

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.

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 1:500 000 (Bilibajkič et al., 1979). The CBA map (with a correction density of 2670 kg m-3) was published in 1972 and covers the whole area of the former SFR Yugoslavia. Its northern part was converted into an electronic form in the diploma thesis of Grand (2019). For the needs of the AlpArray project, a map was used especially for the territory of Serbia and Bosnia and Herzegovina. The gravity data of Slovenia and Croatia were also originally part of the Yugoslavian gravity map (refer to Appendix B – Croatia). In contrast to the digitization for the AAGRG described here, the Slovenian and Croatian database contains new data.

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.

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-1) it mainly depends on the topography and to a much lesser extent also on the density model. Using a linear approximation instead of a time-consuming calculation at specific points would lead to maximum errors of about 0.02 mGal. Note that in order to maintain the real situation regarding the distribution of atmospheric masses, we used physical heights, not ellipsoidal heights.

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.

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 ±1 mGal and exceed ±2 mGal only at a few spots (Fig. 11).

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 (xi,yj) read as 7BAint(xi,yj)=gint(xi,yj)-γint(xi,yj)-MCint(xi,yj),8FAint(xi,yj)=gint(xi,yj)-γint(xi,yj), where the suffix “int” denotes interpolated quantities and MC is the gravitational effect of surplus and deficit mass with respect to the reference ellipsoid. By transforming Eq. (7) and using Eq. (8) we get 9FAint(xi,yj)=BAint(xi,yj)+MCint(xi,yj). Assuming the Bouguer anomaly to be a sufficiently smooth function of horizontal coordinates, true gravity at the position (xi,yj) of a grid node and at the true elevation htopo(xi,yj) can be approximated by 10g(xi,yj,htopo)≈grec(xi,yj,htopo)=BAint(xi,yj)+γ(xi,yj,htopo)+MC(xi,yj,htopo), where the suffix “rec” denotes approximated (reconstructed) quantities.

The Bouguer anomaly at grid node (xi,yj) and at true elevation htopo(xi,yj) is 11BA(xi,yj,htopo)=g(xi,yj,htopo)-γ(xi,yj,htopo)-MC(xi,yj,htopo). Approximating g(xi,yj,htopo) by Eq. (10) and inserting it into Eq. (11) results in BA(xi,yj,htopo)≈BAint(xi,yj)+γ(xi,yj,htopo)+MC(xi,yj,htopo)-γ(xi,yj,htopo)-MC(xi,yj,htopo) or 12BA(xi,yj,htopo)≈BAint(xi,yj). However, this approach neglects the fact that the Bouguer anomaly is the gravity effect of all sources at the true location of a station and therefore depends on the station heights as well. We would get the same result as in Eq. (12) for any arbitrary elevation h used in Eqs. (10) to (12), also for hint. Hence, we can interpret the interpolated Bouguer anomaly as being valid at the true elevation htopo(xi,yj) of a grid node (xi,yj) but also at elevation hint. Because interpolation is always associated with smoothing, we can argue that the best location for referencing the Bouguer anomaly is hint. If modelers use true elevations for the grid nodes, then models based on polyhedron approaches suffer from an aliasing problem because the topography is not well represented by the grid. A smoothed (interpolated) topography would work better because interpolation includes a kind of filtering.

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 (xi,yj) and at true elevation htopo(xi,yj) can be better approximated by 13FA(xi,yj,htopo)≈FArec(xi,yj,htopo)=grec(xi,yj,htopo)-γ(xi,yj,htopo)=BAint(xi,yj)+MC(xi,yj,htopo). Inserting Eq. (7) into Eq. (13) results in FA(xi,yj,htopo)≈gint(xi,yj),-γint(xi,yj)-MCint(xi,yj)+MC(xi,yj,htopo) or with Eq. (8) 14FA(xi,yj,htopo)≈FAint(xi,yj)-MCint(xi,yj)+MC(xi,yj,htopo). The free-air anomaly at the true elevation htopo(xi,yj) of a grid node (xi,yj) can be reconstructed either by Eq. (13) or (14). However, also in this case we have to keep in mind that we actually do not overcome the problem of the height dependence of Bouguer anomalies. When we use hint instead of htopo, Eqs. (13) and (14) hold accordingly.

Note that we implicitly also included bathymetry in the MC term appearing in Eqs. (7) to (14). Regarding the Bouguer anomaly BAρ calculated with density ρ differing from density ρ0 used in the mass correction (MC) term in Eqs. (7) to (14), we have to separate liquid from solid parts, which leads to the following equation: 15BAρ(xi,yj)=BAint(xi,yj)+1-ρρ0δgM(xi,yj)1-ρ-ρocρ0-ρocδgB(xi,yj), where ρoc is the density of ocean water (1030 kg m-3).

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: a.

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.

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 (δgDTM2006(λ, φ, hE)) directly from the free-air anomaly calculated from GGM-derived gravity by the standard procedure of Eq. (16). Compared to Eq. (1), Eq. (16) lacks the term for the atmospheric correction because it is already included in the GGM: 16BAGGM(λ,φ,hE)=gGGM(λ,φ,hE)-γ(φ,hE)-δgDTM2006(λ,φ,hE), where gGGM is the gravity calculated from a particular GGM at the Earth's surface (to be directly comparable with the terrestrial data) at elevations derived from the MERIT model, γ is the normal gravity, and δgDTM2006 is the gravitational (terrain and bathymetry) effect related to the model DTM2006 (of the corresponding degree of 2190) up to the distance of 166.7 km. The DTM2006 model was selected due to its close relationship with the creation of the model EGM2008. This model was originally compiled in a grid of 30 arcsec × 30 arcsec. For the purposes of our calculations, the model was transformed and resampled into a format corresponding to the calculation of the standard mass/bathymetric correction using Toposk.

We calculated the gravity values gGGM using the software GrafLab (Bucha and Janák, 2013) using the maximum degree of spherical harmonic coefficients for a specific GGM. Calculations were performed in GRS80 ellipsoidal coordinates.

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 × 2 km grid) in the area covered by terrestrial data. The maximum differences between grids are at the level of tens of milligals (RMS error is about 4 mGal) but without any systematic error. It follows that the GGM-derived map can be used to fill in gaps (marginal parts) in the terrestrial data.

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 -100 to -170 mGal. The AGL corresponds with the Alpine mountain chain and is explained by the isostatic crustal thickening, as demonstrated by the good anticorrelation with topography (Braitenberg et al., 2013; Pivetta and Braitenberg, 2020) and the isostatic compensation and gravity forward models (e.g., Ebbing et al., 2006; Braitenberg et al., 2002). It could be divided into local gravity lows that correlate with the Western, Central and Eastern Alps. Among all of them the Central Alps (the easternmost part of Switzerland) are accompanied by the highest amplitude: -170 mGal.

A second prominent low is the Po Basin gravity low (PoBGL). The gravity values here range from about -80 to -140 mGal. The PoBGL continues in the southeastern direction to the Central Apennine gravity low (CAGL), whose amplitude (-40 mGal) is significantly smaller in comparison with the Northern Apennine gravity low. In the southeasternmost part of the Central Apennines the CAGL thins out gradually.

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 +40 mGal caused by dense, lower crustal and mantle rocks that are exposed and in the near subsurface and that are planned to be drilled in the forthcoming DIVE project (Pistone et al., 2017; http://dive.icdp-online.org/, last access: 15 May 2021). It is important to note that its relative amplitude compared to the gravity lows in the Western Alps and the Po Basin reaches up to 160 mGal. It is the highest horizontal gravity gradient in the study region.

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 +200 mGal. The regional MGHi also includes the Tyrrhenian gravity high (TGH). The study covers only the northern part. Gravity values do not exceed +140 mGal. The Corso/Ligurian gravity high and the Tyrrhenian gravity high are separated from the relative Corsica/Sardinia gravity low (CSGL). The values vary from +20 to +60 mGal.

The Adriatic Sea region is largely characterized by a positive gravity field, in which the south Adriatic gravity high (SAGH) dominates with values from +20 to +100 mGal. Its maximum is located over the Gargano promontory. In the northwestern part of the Adriatic Sea, negative gravity values up to -80 mGal are observed, which belong to the easternmost part of the Po Basin gravity low. West of the Istrian peninsula the center of the residual Istria gravity high (IGH) is present, with maximum values of +30 mGal.

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 -60 mGal, while the Dinaric values range from 0 to -120 mGal (Bielik et al., 2006). The lower amplitude of the gravity field of both the WCGL and the DGL in comparison with the AGL most likely reflects a weaker continental collision resulting in thinner crust under the Carpathians and Dinarides. In the Adriatic region we can also recognize the Merdita gravity high (MeGH) and the pre-Adriatic gravity low (ADGL).

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 -10 to +20 mGal. The PBGH consists of several local positive (the Transdanubian gravity high, TDGH, the Papuk gravity high, PGH, the Mecsek gravity high, MsGH, the Fruška Gora gravity high, FGGH) and negative anomalies (the Danube Basin gravity low, DBGL, the Makó-Békés Basin gravity low, MBGL). The gravity effect of the Apuseni Mountains is negative (as low as -80 mGal).

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 -80 to +40 mGal. Based on the analysis of the gravity field in this area, we recognize the following anomalies: the Pyrenean gravity low (PGL), the Massif Central gravity low (MCGL), the Paris Basin gravity low (PBGL), the Upper Rhine graben gravity low (URGGL), the Rhône/Bresse Graben gravity high (RBGH), the Black Forest gravity high (BFGH) and the Vosgesian gravity high (VGH).

The gravity field of the Bohemian Massif can be divided into several subparallel positive (up to +20 mGal) and negative (0 to -60 mGal) belts with predominantly northeast–southwest orientation: the Krušné hory (Erzgebirge)/Krkonoše gravity low (KKGL), the Teplá/Barrandian/Labe gravity high (TBLGH), the Moldanubian gravity low (MGL), the Orlice/Opole gravity low (OOGL), the Moravo/Silesian gravity high (MSGH), the Upper Silesian gravity high (USGH) and the Sudetes gravity high (SGH).

The gravity field over the Franconian Platform area north of the Molasse Basin is quite variable, and values range from -40 to +15 mGal. The eastern part of the Franconian Platform is characterized predominantly by negative values, while the western part is characterized by positive values.

The Rhenish Massif is distinctly asymmetric, positive (up to approx. +20 mGal) over the eastern massif and negative (to approx. -20 mGal) over the western massif. The Ardennes are accompanied by the gravity low of -20 mGal. The Brabant Massif is manifested by a gravity high with an amplitude of +20 mGal.

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 ±5 mGal. The mean is 6 µGal and the standard deviation is 0.88 mGal. This is an ideal example for visualizing “mapping errors” which are expected in the case of a dense and widely homogeneous data coverage. However, in areas of less dense and less homogeneous coverage like along the Alpine crests or in the offshore areas, the number of errors increases.

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 ±5 mGal. In addition to the errors arising from the use of inexact models of the topography, additional errors can result from the varying density distribution of the masses outside the reference ellipsoid. According to Eq. (1), the Bouguer anomaly has an exact physical meaning (Meurers, 2017): it is the integral gravity effect of all sources which differ in density from (a) the rock densities outside the ellipsoid as used in the MC and from (b) the density inside the reference ellipsoid. Three cases will be discussed in more detail here, according to their significance.

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.

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 ±10 mGal. A total of approx. 350 points were excluded (Fig. 18). Except for a few points, almost all excluded points cover marine data, which confirms the naturally lower quality of marine 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 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 (http://pmd.gfz-potsdam.de/portal/about.htm, last access: 12 May 2021) is the cooperation partner for data publication via the special information service (FID GEO; https://www.gfz-potsdam.de/zentrum/bibliothek-und-informationsdienste/projekte/fid-geo/, last access: 12 May 2021). The German Research Centre for Geosciences, GFZ, the operator of GFZ Data Services, has been issuing digital object identifiers (DOI) to data sets since 2004 in accordance with the principles of the International DOI Foundation (https://www.doi.org/, last access: 12 May 2021). These data sets are archived and published by GFZ Data Services and cover the entire range of geoscientific activities.

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.