To show the problems and methodology in 3D modelling a case example is presented, which was done regarding the lithospheric structure of the Eastern Alps. First the motivation to do the modelling is shown, thereafter which kind of information are available and how to introduce this information into the modelling process. The discussion of the modelling results will lead to the exercise, to construct and optimise a simple model.

1. Introduction
In recent years renewed interest has been given to the understanding of the structure of the Eastern Alps due to the efforts of the multidisciplinary TRANSALP research project. The TRANSALP-Traverse extends from Freising (GER) in the north to Treviso (ITA) in the south and is carried out by the TRANSALP working group, with members from Italy, Austria, Switzerland and Germany. During 1998 and 1999 a seismic reflection profile was investigated over a length of 340 km, covering the Eastern Alps and parts of the northern and southern molasse basins. The new results, stemming from the seismic profile and from the numerous interdisciplinary projects that accompany the seismic survey, make a new 3D gravity modelling necessary.

One of the problems addressed by the TRANSALP research group, was the investigation of orogenic processes driven by the collision of continental lithospheric plates in the area of the Eastern Alps. Structures and orogenic processes of the Eastern Alps are considered paradigmatic for testing plate-tectonic models of continent-continent collision by reflection seismic methods. The new image of the crust e.g. by near vertical reflections and other seismic experiments will also foster interdisciplinary interpretations by different disciplines through reduction of ambiguity which was typical in former studies.

In the present example the lithospheric density structure is investigated by matching both observed gravity fields and geoidal undulations. In this connection, we employ constraining information from newly published results of the TRANSALP group.

In our study the 3D forward modelling of near surface structures in the upper 10 km of the crust, provides an interpretation of short wavelengths and combines reflection seismic data with geological models, cross sections and surface observations. In contrast one should reckon with greater ambiguities in the velocity distribution and geometry of crustal domains which base on seismic surveys for the lower crust, e.g. the TRANSALP survey did not reveal the depth of the Moho along the profile along the central section of the profile which is superimposed by strong effects of crustal anisotropy.

Blending all available geometry and velocity information with the density model by the aid of the 3D information system supported 3D modelling of the lower crustal parts. From this we constructed the initial model that based in its deeper parts on pre-existing Moho models. In the course of the modelling process this starting density model was interactively modified in order to match the observed Bouguer gravity.
 

2. Geological setting

The Alps are an orogenic belt extending from the French-Mediterranean area to Switzerland and Austria. The present geologic structure can be understood as a result of tectonic processes, which include both extensional and compressional strain regimes, subduction of oceanic crust and collision of continental blocks due to plate motions. In the following the evolution of Alpine orogeny will be described briefly:

In the late Palaeozoic the Pangea continent was built by the Variscan orogeny, partly overlain by the shelf area of the Tethys ocean bordering in the SE. Three main regions of sedimentation can be distinguished from north to south: the Helvetic, Penninic and Austroalpine realm. In the early Jurassic the southern Penninic ocean was created due to the opening of the Pangea continent, isolating the Austroalpine realm. Between the Helvetic and the Penninic zones a further relatively small basin developed in the lower Cretaceous creating the small Middle Penninic continent, while in the south subduction of the southern Penninic oceanic crust began. During Mid-Cretaceous the collision process began with an overthrust of Austroalpine units onto Penninic.
 
 

Figure 1 Location of the 340 km long TRANSALP reflection seismic profile through the Eastern and Southern Alps. Accompanying investigations will be carried out in a strip around TRANSALP. Geology after Berthelsen et al. (1992).
 
 

Compression continued up to the lower Tertiary, when the northern Penninic ocean was closed and the nappe structure was overthrusted to the north onto the European continental margin, accompanied by folding and faulting of the rocks into thrust sheets. These movements stopped during Quaternary ages.

The resulting pronounced nappe tectonics of the Eastern Alps is shown here:

In the so-called Tauern window the Penninic base has been uncovered by cutting the overlying Austroalpine nappes due to erosion and tectonic uplift processes. The molasse zone in the north of the Alps consists of sediments in a deep geosyncline in front of the nappe pile and is overthrusted. This is supported by deep borehole drillings within the northern Calcareous Alps. To the south of the Alps, in the Po basin, a foredeep evolved where syntectonic sediments could accumulate, linked to south vergent thrusting in the Southern Alps. Besides, some rocks of magmatic/plutonic origin occur at the Po-Basin-Dolomites transition.

3. Database

The first step before the beginning of the actual density modelling is the evaluation of the data. In this example, the density modelling was done due to the Bouguer anomaly and the geoid.

Bouguer anomaly

The Bouguer gravity field used for modelling purposes was taken from three different gravity data sets. The German northern part is covered by approx. 5500 points, released by the GGA (Hannover), the Austrian central part by approx. 3700 sites (B. Meurers, University of Vienna), and the Italian southern part and the Adriatic Sea by ~3800 data points by the Bureau Gravimetrique International (BGI, Toulouse), which is thankfully acknowledged.The density for the station complete Bouguer reduction was 2670 kg/m³ for all continental masses and 1030 kg/m³ for the water of the Mediterranean Sea.
 
 

The topographic data used for the reduction are based on the GTOPO30 data with additional data for offshore areas by Sandwell.
 

Geoidal undulations

To complement the modelling of shorter and middle wavelengths by matching the Bouguer anomaly field we focussed on geoidal undulation to model long wavelengths in the gravity field. These data were published in the EGT-atlas by Lelgemann and Kuckuck (1992).

The geoid data are affected by topography and density structures as well. For matching "geoidal undulations" and the Bouguer anomaly within the same 3D density model, the effect of the topography on the geoid has to be subtracted first. This necessary topographic reduction has been done analogously to the reduction of measured gravity data which led to a station complete Bouguer anomaly.

We calculated the topographic effect by the IGMAS software. A reduction density of 2670 kg/m³ was used for land masses and 1030 kg/m³ for water within a reduction radius of 170 km (167km = Hayford O₂).
 

Figure 3 The geoidal undulations (left, after Lelgemann and Kuckuck, 1992), the part of the geoid produced by the topography (centre) and the resulting terrain reduced geoidal undulations.

To compare the trend of the Bouguer anomaly with that of the terrain reduced geoid, one sustains that gravity is superimposed by different sources in different depths of the lithosphere. In comparison to the terrain reduced geoid, the alpine Bouguer field is characterized by variations of shorter wavelengths. Therefore, we have to match two independently "observed" potential field data to modelled ones in different windows of spectrum. This will restrict model solutions and serve as additional constraint.

The concept of the reference model
Since Bouguer anomalies express relative gravity data only, density contrasts of all lateral inhomogeneities must cause the modelled field. Therefore and to avoid edge effects, a reference density model has to be considered for the use of absolute densities, which on top provides better opportunities to compare the density model with petrologic or seismic velocity models.

Figure 4 The concept of the reference model illustrated in the example of the Andean subduction zone (Kirchner, 1997). Geological model (upper left), reference model (upper right) and the resulting density model.
 
 

The used density model consists of a reference model for the background of our model. This reference model considers at least theoretically the layered density structure of a "normal earth" and should result in the expression of the earth's "normal gravity field", which is always subtracted from the absolute value of measured gravity while calculating Bouguer anomalies. In this study we used the IASPEI layered velocity model, which was converted to a local reference density model by applying relations published by Christensen and Mooney (1995). The resulting reference model is divided into three layers: the upper crust (0-10 km: 2670 kg/m³), the lower crust (10-32 km: 2900 kg/m³) and the upper mantle (32-180 km: 3350 kg/m³).
 

Constraining information

Long before the TRANSALP fieldwork has been conducted seismic profiles have been investigated in the Eastern Alps. The most prominent seismic lines are from the 1970s, like ALP'75 (Alpine Explosions Seismology Group 1976, Miller et al. 1982), SudALP1977 (Italian Explosions Seismology Group 1978, 1981, Deichmann et al, 1986), among others.
 
 

Mostly we followed the seismic image which stems from recently done TRANSALP processing for the upper model layers, and a more or less free design in the deeper model parts which was guided by several surveys. However, we always tried to compromise the findings of former interpretations with the modern seismic data, where it was advisable. E.g. the completed velocity model "Eschen-38" was used in this study as one of the main constraints for densities and geometric boundaries. This profile was modified and completed by the TRANSALP Working Group considering the new results.
 
 

In order to calculate the densities of the 3D model this velocity model was interpolated in east-west direction and velocities were converted into densities by using velocity-density relationships after Sobolev and Babeyko (1994). Their approach is sensitive to local variations of the heat and pressure conditions in the lithosphere and provides rather "realistic" densities. How it's done?

The densities of shallow geological bodies were taken from published data by Granser et al. (1989) and surface density model (Austrian Federal Office for Measurement Uncertainty, Surveying and Mapping). These density values are well constrained due to the analysis of many rock samples.

The deeper geometry of theses shallow geological bodies was inspired by seismic findings (especially in areas of the molasse basins where industry data were available), maps of the sedimentary cover (Berthelsen et al., 1992), and other geological information (e.g. structural model of Munich TRANSALP working group).
 

Figure 6 3D view of selected upper crustal structures. Gneiss (dark blue) and schist (light blue) related to the Tauern window and basement nappes (red). 3D view by IVIS-3D.

Furthermore, this 3D model was modified by geometry information of the crust-mantle boundary following an interpretation of Giese and Buness (1992).

Constraining the lithosphere-asthenosphere model boundary the velocity model of Suhadolc et al. (1990) was adopted, even when regarding the lithosphere-asthenosphere boundary big doubts of the reliability exist. We have to emphasize that for Bouguer gravity modelling the influence of these particular models is not very significant, due to the long wavelengths involved and the low density contrast at the lithosphere/asthenosphere boundary (20 kg/m³).
 
 

In addition we used the seismic line-drawing from the recent TRANSALP measurements to constrain the geometry of the crust and results of the analysis of receiver functions to constrain the geometry of the Moho along the TRANSALP profile.

The study area covers the TRANSALP-Traverse and a 260 km wide strip, 130 km to both east and west, along the traverse, covering a total area of 260 to 380 km.

The 3D density modelling is made along 27 north-south oriented parallel cross sections. The spacing between the planes is 10 km. These distances were used to ensure that the model approximates the size and location of the principal features of geological and geophysical bodies and domains well enough.

The 3D density models consists of an upper part, where the results of the reflection seismic correspond to geologic models, and a lower part, where only seismic investigations provide constraining information on geometry and density.

Depending on the weighting of the information two models haven been generated. One, which is closer to the Eschen-38 geometry and the results of the 1970's seismics (Model A), and one which features the new suggestions and ideas initiated by TRANSALP and the analysis of receiver functions (Model B).
 

MODEL A

In the course of interactive model matching the initial 3D density model has been modified and adjusted to the Bouguer anomaly. From north to south we define three domains of each crustal layer: the northern Pre-Alps, the central Eastern Alps, and the Southern Alps, forming the European plate, the melange of European and Adriatic plate, and the Adriatic plate, respectively. Generally we obtained for the Adriatic crust slightly lower density values than for the European crust. The central region with the melange of Adriatic and European crust and high compression is generally characterized by relatively high densities. However, domains of extreme density lows are located at the top of the central Tauern Window and in the area of the crustal root in the seismic inversion zone.
 
 

Figure 9 The vertical profiles through the 3D density model and the related Bouguer anomaly. Along the TRANSALP profile for the upper part (upper left) and for the whole model depth (upper right). Below a west east orientated cross-section nearly along ALP'75 is shown. The coloured dots denote the velocity model Eschen-38.

The main difference between the gravity Moho, defined on density, in respect to the seismic Moho, defined on velocity, is, that the Moho trend is less smooth in the transition zone between the European and Adriatic crust. The depth of the Moho boundary is increasing steeper to the Adriatic domain and lies in the southern part higher than in the velocity model.
 

Figure 11 The observed and modelled Bouguer gravity and the residuals.

Figure 12 The observed and modelled terrain reduced geoidal undulations and the residuals.

The comparison of the modelled and the observed fields shows, that the model is able to fit to reality. The misfits in the Bouguer anomaly are rather local and are hard to model within the resolution of the model. The misfits in the geoid seem to indicate a regional misfit, but the amount of the misfit is rather small compared to the actual fields.

MODEL B

The second model is based on the same constraining information, but in here the seismic Line-Drawing of Vibroseis und explosion seismics was used as the main constraint in constructing the geometry of the deeper crustal structures. Additionally a geological model was used in constructing the transition of the European and Adriatic crust. The main difference between this model and the previous one is the depth of the crust-mantle boundary and according to this the thickness of the lower crust in the Adriatic domain.
 
 

In a comparison to Model A it can be seen that the Adriatic crust-mantle boundary is some 10 km deeper in this model and that therefore a big lower crustal layer is introduced with a relatively high crustal density (3100 kg/m³) . Another difference to Model A that there a mainly two domains distinguished, the European and the Adriatic crust, and not three as in the previous model.
 
 

The different model lead to the question of the definition of the crust-mantle boundary. Is the seismic velocity step directly related to a density step? Or have other petrologic effects to be considered?
 
 

Exercise: Fit a simple 3D density model of the Eastern Alps to the potential fields. The densities in the Configuration-file have been calculated by the formulas of Sobolev-Babeyko (and should be the same in the model (+/- 100 kg/m³). Furthermore the geometry along TRANSALP, a Moho map and a lithosphere/asthenosphere-boundary map are available.
 

6. Final words

To understand the collision process of the Adriatic and the European plate by investigating the shape of the Moho interface remains one of the major key problems. As various seismic experiments differ in their structural results, the presented gravity modelling can help to minimize existing uncertainties and help to extrapolate information from seismic studies, which normally exist along seismic profiles only.

But as along as there are doubts in the interpretation of the seismic results, neither one of the presented models can be regarded as wrong or right. The modelling of potential fields and the quality of the model is always directly connected to the quality of the constraining data. In the cases of insecurities in the constraining data, the interpreter/modeller has to decide how to weight the information and which to consider.

Further reading:

• 3D density modelling along the TRANSALP - Project Homepage
• Ebbing, J. and Götze, H.-J., 2001.  Preliminary 3D density modeling along the TRANSALP-profile. Österreichische Beiträge zu Meteorologie und Geophysik, in press. Abstract
• Ebbing, J., Braitenberg, C. and Götze, H.-J., 2001. Forward and inverse modelling of gravity revealing insight into crustal structures of the Eastern Alps. Tectonophysics, in press.

References:

1. Alpine Explosion Seismology Group, Reporter: H. Miller, 1976. A lithospheric seismic profile along the axis of the Alps, 1975 - First Results, Pageophys, 114: 1109-1130.
2. Berthelsen, A., Burrolet, P., Dal Piaz, G.V., Franke, W. and Trümpy, R., 1992. Tectonics. In: D. Blundell, R. Freeman and St. Mueller (eds), A Continent Revealed: The European Geotraverse, Cambridge University Press.
3. Christensen, N.I. and Mooney, W.D., 1995. Seismic velocity structure and compositions of the continental crust: A global view. J. Geophys. Res, 100(B7): 9761-9788.
4. Deichmann, N., Ansorge, A. and Mueller, St., 1986. Crustal structure of the southern Alps beneath the intersection with the European Geotraverse. Tectonophysics, 126: 57-83.
5. Giese, P. and Buness, H., 1992. Moho Depth. In: D. Blundell, R. Freeman and St. Mueller (eds.), A Continent Revealed: The European Geotraverse, Cambridge University Press.
6. Granser, H., Meurers, B. and Steinhauser, P., 1989. Apparent density mapping and 3D gravity inversion in the Eastern Alps. Geoph. Prospecting, 37: 279-292.
7. Italian Explosion Seismology Group 1978. Preliminary Interpretation of the Profile HD across the eastern Alps. Boll. Teor. Appl. 20/79: 287-301.
8. Italian Explosion Seismology Group and Institute of Geophysics and ETH Zurich 1981. Crust and upper mantle structures in the Southern Alps from deep seismic sounding (1977-8) and surface wave dispersion analysis. Boll. Teor. Appl. 3/92: 297-330.
9. Kirchner, A., 1997. 3D-Dichtemodellierung zur Anpassung des Schwere- und Schwerepotentialfeldes der zentralen Anden. Berliner Geowissenschaftliche Abhandlungen, B 25, Selbstverlag Fachbereich Geowissenschaften, FU Berlin.
10. Lammerer, B. and Weger, M., 1998. Footwall uplift in an orogenic wedge: the Tauern Window in the Eastern Alps of Europe, Tectonophysics, 285(3-4): 213-230.
11. Lelgemann, D. and Kuckuck, H., 1992. Geoid undulations and horizontal gravity disturbance components. In: D. Blundell, R. Freeman and St. Mueller (eds), A Continent Revealed: The European Geotraverse, Cambridge University Press.
12. Miller, H., Gebrande, H. and Schmedes, E., 1977. Ein verbessertes Strukturmodell für die Ostalpen, abgeleitet aus refraktionsseismischen Daten unter Berücksichtigung des Alpen-Längsprofils. Geologische Rundschau, 98: 77-93.
13. Scarascia, S. and Cassinis, R., 1997. Crustal structures in the central-eastern Alpine sector: a revision of the available DSS data. Tectonophysics, 271: 157-188.
14. Sobolev, S. and Babeyko, A., 1994. Modeling of mineralogical composition , density and elastic wave velocities in anhydrous magmatic rocks. Surveys in Geophysics, 15: 515-544.
15. Suhadolc, P., Panza, G.F. and Mueller, S., 1990. Physical properties of the lithosphere-asthenosphere system in Europe. Tectonophysics, 176: 123-135.