Gravity inversion by second order approximation applied to the Styrian Basin (Austria)

An approximative second order gravity inversion scheme by a truncated power series expansion is applied to derive the thickness of the Neogene, mostly clastic, sedimentary section of the Styrian Basins in South–East Austria, which are sub‐basins of the Pannonian Basin System. These sub‐basins with a derived thickness of up to 4 km are of interest for geothermal exploitation because of the increased geothermal gradient and heat flow observed in the Pannonian Basin in general and a geothermal gradient of 4°–5°/100 m measured in some wells in the Styrian Basin. The Styrian Basin also has been an area for hydrocarbon exploration in the past 50 years, with oil and gas show encountered in several exploration wells and one sub‐commercial gas discovery. The Miocene and Plio–Pleistocene volcanism in the Styrian Basin caused by Miocene crustal thinning is discussed in terms of the influence to the gravity inversion taking the aeromagnetic field into account. The volcanism is of relevance for the geothermal prospectivity but poses problems for the single layer‐based gravity inversion scheme. Results are discussed from a computational side comparing observed and calculated gravity fields but also the match with well data is discussed. In terms of gravity inversion methodology, the presented can be viewed as an approximative fast‐track approach.


INTRODUCTION
The Tertiary basins of Eastern Styria can be viewed as the western extension of the Pannonian Basin complex (Kollmann, 1964;Kröll et al., 1988;Sachsenhofer et al., 1996;Tari et al., 2020).The area is located in the transition zone between the Eastern Alps and the Pannonian Basin and has been described as a region characterized by upper crustal extension (Tari et al., 1999(Tari et al., , 2020) ) resulting in the formation of the Miocene sub-basins in Eastern Styria as part of the Pannonian-Carpathian region.
Historically, the Styrian Basin was an area of exploration efforts for hydrocarbons with the latest hydrocarbon exploration well drilled in 1996, the well Petersdorf-1, total depth 3090 m by RAG (Rohöl Aufsuchungs Gesellschaft).Most hydrocarbon exploration activity in the Styrian Basin was carried out by RAG from the 1950s onward (Kollmann, 1964).
The Ludersdorf-1 non-commercial gas discovery, drilled by OMV in 1982, is the sole hydrocarbon discovery made in the Styrian sub-basins.Even with larger volumes, the discovery would not be suitable for development due to the restricted local development of the Miocene reefal carbonate reservoir and the associated high CO 2 and N 2 content of the encountered gas.Across the Austrian border, to the east and south, a number of small, but commercial oil and gas fields are located in Hungary and Slovenia situated in the Pannonian Basin.
The Styrian Basin as part of the Pannonian Basin System is an area of an increased geothermal gradient of 4-5˚C/100 m and a terrestrial heat flow of up to 105 mW/m 2 resulting from the thinned crust of the extensional Pannonian Basin which also resulted in Miocene and later Plio-Pleistocene volcanism, which is widespread in the Pannonian Basin complex (Kovacs & Szabo, 2008;Sachsenhofer et al., 1996).
Because of the advantageous high geothermal parameters in the area, some of the exploration wells, originally targeting hydrocarbons were subsequently converted to geothermal hot water producers for balneological usage (Blumau-1a and Waltersdorf-1).Other wells, such as the Radkersburg-1 and 2 and the Stegersbach Thermal-1 wells, were outright drilled as a geothermal balneological water producers.
Renewed interest in the utilisation of geothermal resources in Austria led to an upturn of activities particularly targeting district heating purposes, as for instance discussed by Schreilechner et al. (2022) for the Vienna Basin -which has a normal geothermal gradient of 3˚/100 m however.
In the following, an approximative fast-track gravity inversion is applied to the residual gravity to derive an estimate for the thickness of the Neogene sedimentary basin fill.The Neogene, mostly clastic sediments, is easy to drill and if deep enough may be a target for geothermal exploitation.

GEOLOGIC BACKGROUND OF THE NEOGENE STYRIAN BASIN
An overview of the Tertiary and pre-Tertiary Geology of the Styrian Basin has been given by Kollmann (1964) and Kröll et al. (1988) and later, with special emphasis on the prospectivity for hydrocarbons, by Sperl and Wagini (1994) and Sachsenhofer et al. (1996).The Styrian Basin is a subbasin of the oil and gas rich Pannonian Basin complex.It is situated south-east of the Eastern Alps some 150 km (94 mi) south of Vienna in the vicinity of Austria's second-largest city Graz.The basin is about 100 km long and 60 km wide.A couple of hydrocarbon exploration wells have been drilled in the Styrian Basin, mostly by Rohöl Aufsuchungs Gesellschaft (RAG) (originally a joint venture of Mobil and Shell under the operatorship of Mobil), the older wells based on scarce and poor-quality subsurface information as described by Sperl and Wagini (1994).Despite encountered gas and oil shows, most exploration wells were classified as dry.In 1982 OMV discovered an uncommercial gas accumulation in the Ludersdorf-1 well, close to RAG's Styrian concession.The reservoir is a Badenian (Middle Miocene) reefal limestone (Lithothamnium or Nullipora) build-up, penetrated on a small fault-bounded block.The encountered gas had significant amounts of N 2 and CO 2 and it was considered uncommercial for development at the time of the discovery.
The Styrian Basin is a Miocene wide-rift style extensional basin between the Eastern Alps and the Pannonian Basin complex.As outlined by Sachsenhofer et al. (1996) the crustal thickness in the area of the Styrian Basins decreases from 35 km in the west to less than 25 km depth in the east as a result of the extensional stretching (and due to the isostatic response due to Alpine loading to the west).This Moho relief is also in line with crustal thickness results by Granser et al. (1989) based on gravity inversion.The crustal thinning is responsible for the high present day heat flow of 55-105 mW/m 2 and increased geothermal gradient of 4-5˚C/100 m.
The stratigraphic chart of Neogene basin fill for the Styrian Basin is shown in Figure 1 according to Tari et al. (2020) and Sachsenhofer et al. (1996).The surface geology of SE Styria is shown in Figure 2.
The Tertiary basin deposition commenced during an initial moderate subsidence in the Ottnangian period (17.5 my); widespread coal-rich sediments were deposited in floodplain and lacustrine swamp environments.Accelerated subsidence during the Karpatian period (16.8 my) led to a marine ingression and relatively deep-sea environments with turbiditic sediment deposition.From the deltaic environments on the basin rims, subaqueous fans were formed due to the high sediment influx rate.Due to the proximity of the contemporaneously emerging Alps, in the northern and western parts of the Styrian sub-basin, a strong flux of coarse turbiditic clastics (sandstone and conglomerates) is observed.These Upper Karpatian (Middle Miocene) alluvial fans are considered analogues to the units that are currently under investigation for the Vienna Basin Communal Heating Geothermal Project (Schreilechner et al., 2022).
Synchronously with the increasing subsidence rate, andesitic volcanism occurred during the Miocene, causing elevated thermal gradients in the region between 18 and 16 my.Towards the end of the Karpatian (Middle Miocene) period, a major marine regression led to widespread progradation of fans directed to the basin centre (Sachsenhofer et al., 1996).This coincided with the formation of the top syn-rift unconformity marked by an angular unconformity and erosion across the entire basin (Styrian Phase).Large amounts of coarse clastic sediments were deposited over this unconformity referred to as the 'Badenian basal conglomerates'.During the Lower Badenian, a new marine transgression occurred.At times of sea-level standstill, carbonate platforms (Lithothamnium limestone) formed on the basin flanks, whereas in the central basin, a deep marine environment with turbidites prevailed.At the end of the Lower Badenian the sea reached its largest extent.The Upper Badenian (13.6 my) is characterized by another regressional phase which lasted until lower Sarmatian (Upper Miocene) time with a minor unconformity at the top of the Badenian sediments.During the Sarmatian (11.5 my) separation of the Pannonian Basin from the Mediterranean Sea led to a decrease in salinity towards brackish conditions.During the Late Miocene and Pliocene, sediments of limnic and fluvial origin predominated in the Styrian Basin.
An early Miocene volcanic phase, mainly Andesitic was initiated by crustal thinning of the Pannonian Basin or subduction along the Carpathian Front (Kovacs & Szabo, 2008;Sachsenhofer et al., 1996).A second volcanic phase occurred in the Plio-Pleistocene producing small paleo-volcanoes with tuffs and local basaltic flows.Both volcanic events are typical of the Pannonian Basin realm (Kovacs & Szabo, 2008).
As the Styrian Basin is located in the transition zone between the Eastern Alps and the Pannonian Basin, a complex pre-Neogene 'Basement' geology is encountered.
The pre-Neogene basement in the area comprises of crystalline and highly metamorphic rocks of the Austroalpine system in the western part of the AOI (area of interest), to the north the Graz Paleozoic units are outcropping and the Penninic units encountered to the east as the Eastern Alpine Nappes give way to the Pannonian Basin realm (Sachsenhofer et al., 1996).As discussed by Tari et al. (1999) and Tari et al. (2020), the Penninic basement is made up of a metamorphic core complex.In the north-east of the AOI, the Rechnitz Window with metamorphosed deep-water sediments (serpentinites and greenschists) is outcropping.To the north, the Graz Paleozoic is outcropping with rather lowgrade metamorphic Devonian dolomites and Phyllites.The pre-Tertiary basement lithology, and hence also rock density, is complex in the AOI which adds uncertainty to the assumption of a single constant density contrast between pre-Tertiary basement and Neogene sedimentary fill.Rock densities of these various pre-Tertiary units were investigated by Steinhauser et al. (1983) who published a compilation of surface rock densities in Austria based on 6000 surface rock samples.For the Eastern Alpine Crystalline Units, a density value of 2.85 g/cm 3 is reported, whereas densities of 2.70-2.75g/cm 3 for the rather low-grade metamorphic Paleozoic and Penninic units are quoted by Steinhauser et al. (1983).Further complexities for the gravity inversion arise from the Miocene and later Plio-Pleistocene volcanism in the area.This topic is also discussed by Kröll et al. (1988) and Sachsenhofer et al. (1996) and will be further explored in the discussion on the depth-to-basement gravity inversion results and the interpretation of the aeromagnetic field.The Neogene Graz Basin is subdivided into several sub-basins such as the Gnas and Fürstenfeld sub-basins and the Western Styrian Basin.Previous interpretations (e.g.Kröll et al., 1988) describe a Neogene basin fill of up to 2 km for the Gnas sub-basin.Sperl and Wagini (1994) deducted a depth-to-basement of up to 4 km from two-dimensional gravity modelling which is in line with the present gravity inversion work.
Based on the work by Sperl and Wagini (1994) and Sachsenhofer et al. ( 1996), a regional seismic survey was acquired by RAG and subsequently the exploration well Petersdorf-1 drilled in 1996 which reached total depth at 3080 mMD (metres measured depth) in the pre-Tertiary basement.The top basement was reportedly encountered around 2900 mMD relating to about 2400 m.b.s.l.(metres sub-sea) depth below sea level.The well was classified as a dry hole and has been plugged and abandoned.The predicted depth-to-basement by gravity inversion is about 2090 mSS for a density contrast of −0.2 g/cm 3 .Petersdorf-1 encountered an alluvial basalfan of about 300 m of basal, dolomitic conglomerates, the dolomitic material probably being derived from Devonian dolomite units of the Graz Paleozoic.The dolomitic strata would put the density contrast surface of the pre-Tertiary at the level of the top of the fan in a gravimetric sense -but not in a depositional age sense as the alluvial fan deposition probably occurred in the Ottnangian period.

GRAVITY DATA
For the area of interest (AOI) a subset of the BEV (Bundesamt für Eich-und Vermessungswesen, Austrian Federal Office of Metrology and Surveying) gravity database is used which is described in detail by Meurers and Ruess (2009).
All gravity data acquired in Austria during the past 50 years by different institutions have been reprocessed and homogenized by BEV to compile a new and accurate Bouguer gravity data set of the Eastern Alpine region.Reprocessing was based on modern methods of terrain correction procedures and a digital terrain model (DTM) with 50 m spacing for accurate corrections even in rough and mountainous areas.The DTM and digital cadaster also helped correcting the station coordinates that had been extracted from topographic maps in some of the early surveys.The BEV data set consists of gravity stations with an average station distance of less than 3 km, even in mountainous regions.Commonly, the Bouguer gravity is based on orthometric rather than on ellipsoidal heights.Based on the newest geoid models, the Bouguer anomaly for the new map was determined using ellipsoidal heights, and the geophysical indirect effect was estimated.Mass reduction for the Bouguer is 2.67 g/cm 3 .Austrian Gauß-Krüger M34 projection is used for the AOI in the South-Eastern Region of Austria and covers an area of 6650 km 2 .The distribution of the gravity stations is shown in Figures 3 and 4, there are about 5200 stations within the AOI.The majority of the gravity stations in South-Eastern Styria were recorded by the Montanuniversität Leoben and the remainder by the Austrian BEV.As the area is located in the transition from the Eastern Alps to the Pannonian Basin a considerable topographic relief is encountered towards the west of the AOI which is shown in Figure 3 based on the actual gravity station heights.The topography shown in Figure 3 is however not based on the much finer DTM used to calculate the terrain corrections by BEV.

GRAVITY FIELD
The Bouguer gravity field as derived from the Bundesamt für Eich-und Vermessungswesen stations is shown in Figure 4.
A strong negative regional overprint can be observed which is caused by the isostatic effect of the Alps.To remove the regional (isostatic) field a high-pass filter was applied to the Bouguer gravity, and the residual gravity is shown in Figure 5.A high-pass filter with a wavelength of 100 km was used to eliminate the isostatic long-wavelength effects caused by the mountain load of the Alps and subsequent deformation of the Moho.The isostatic gravity field of the Eastern Alps and its relation to the crustal thickness and Moho relief has been investigated by Ebbing et al. (2006), Sachsenhofer et al. (1996), Wagini et al. (1988), Zanolla et al. (2006) and others.Granser et al. (1989) used a 120 km low-pass filter to calculate a long-wavelength Moho-related regional field.A comparison of the inverted Moho relief by Granser et al. (1989) shows a good fit to the Moho relief shown by Zanolla et al. (2006) and Ebbing et al. (2006), furthermore, the long-wavelength regional field is very similar (nearly identical) to the isostatic regional field derived by Wagini et al. (1988) which is the isostatic regional field used by Wagini and Sperl (1994) and Sachsenhofer et al. (1996) for their gravity modelling.The 100 km high-pass residual gravity is here assumed to be equivalent to the isostatic residual gravity field and was subsequently used as an input for the approximative gravity inversion to calculate Neogene sedimentary fill and the top pre-Tertiary relief surface.A constant value of 10 mGal was subtracted from the residual gravity (Figure 5) prior applying the inversion algorithm to tie the residual gravity to outcropping basement regions.The rationale for this operation is illustrated in Figure 6 where the 10 mGal contour (in red) is superimposed on the top pre-Tertiary map by Kröll et al. (1988).The cropped gravity grid was then shifted by 10 mGal to generate a 0 m reference datum used for the subsequent gravity inversions as a necessary boundary condition.

SECOND ORDER GRAVITY INVERSION
The inversion routine applied is based on the inverse power series in the Fourier domain for the gravity effect of a layerbased model developed by Parker (1973).The basement relief is given by the function h(x,y), the two-dimensional (2D) Fourier Transform is given by  and the inverse by  −1 .The definitions follow Granser (1987a), f is the 2D, spatial frequency  = (  ,   ), and  = ∕2 with  being the gravitational constant and  the density contrast, here assumed to be a constant.2 will be called Bouguer plate factor.
The Parker (1973) power series expansion in the Fourier domain to calculate the gravity effect of the layer with relief h(x,y) is shown in equation ( 1).
(1) Parker's (1973) uniformly convergent operator power series suggests an approach in line of the classical theory of power series inversion (e.g.Bronstein & Semendjajew, 1976) which from the standpoint of functional analysis is the application of the Schmidt-Lichtenstein theory (Rall 1974) for an operator power series.
This inverse series of the Parker series (1) was derived by Granser (1987a) and is shown in the following equation (which is equation 13 in the aforementioned paper).
F I G U R E 5 Residual Bouguer gravity (100 km high-pass filter).Units mGal.
It has been discussed by Granser (1987a) that this series (2) is not uniformly convergent for higher frequencies in contrast to Parker's (1973) uniformly convergent forward series (1); which is intuitively clear as high frequency undulations of the gravity can not be caused by deeper parts of the layer topography ℎ.However, the theoretically derived low-pass frequency cut-off is quite severe.This low-pass frequency (Granser, 1986(Granser, , 1987a)), guaranties convergency but the series may also converge for higher frequencies which may need to be tested out.Similar observations have been made by Oldenburg (1974) for an iterative inversion procedure also based on Parker's (1973) forward method.Inverse series (2) has been used by Nagendra et al. (1996) and adapted to the magnetic case by Pustisek (1990).The issue of non-convergence for higher frequencies is also discussed by Guspi (1993).In the following, a different approach is used, and the power series (2) is restricted to the first two terms, with the first order term being the Bouguer plate term and a second order term involving a vertical gradient calculation of the squared gravity scaled by the Bouguer plate term.Convergence is no longer an issue for a finite series (but high frequency errors may occur).Obviously a two term Taylor series expansion can only be an approximative solution.
As (2| |)  is the frequency domain expression of the vertical derivative operator   of the th order for potential fields; the second order approximation for the gravity inversion can be written as follows in the space domain with  defined as above (gravity divided by Bouguer plate term 2). ℎ In the following this approximative second order approach is used to calculate the basement relief h(x,y) from the gravity field.As will be seen, uncertainties caused by the simplified constant density contrast assumption involving both the basement density and the Neogene sediment fill as well as effects of the local Tertiary volcanism outweighs the mathematical approximation errors in the inversion algorithm.

BASEMENT RELIEF BY GRAVITY INVERSION
Two realisations of the gravity inversion were calculated using the approximative second order formula (3) with density contrasts between the Neogene sedimentary fill and the F I G U R E 6 The 10 mGal contourlines in red of the high-pass gravity (Figure 6), superimposed on the georeferenced base-Tertiary map published by Kröll et al. (1988).
pre-Tertiary basement of −0.3 and −0.2 g/cm 3 .A density analysis of the Neogene cover from wells in the North-Western Pannonian Basin, Lake Neusiedl (Fertö) area (Granser 1987b, Granser et al., 1991) in comparison gave a best fitting density contrast of −0.26 g/cm 3 .The density contrast of −0.2 g/cm 3 was found to give a better match with well data in the Gnas and Fürstenfeld sub-basins in comparison with well results (Table 1), also the work of Sperl and Wagini (1994) indicates a similar density contrast, see also Sachsenhofer et al. (1996).The calculated basement relief is shown in Figure 7 for the density contrast of −0.2 g/cm 3 and in Figure 8 for a density contrast of −0.3 g/cm 3 .Subsequently, the −0.3 g/cm 3 basement surface was used as relief function for the forward gravity calculation with Parker's (1973) forward Fourier series using 10 series terms.The resulting error map of observed minus calculated gravity is shown in Figure 9 and shows an error field with a high frequency jitter of generally less than 0.5 mGal except in areas where the input gravity was clipped to zero-level basement (the clipping being a slightly un-physical procedure).As such in a mathematical sense the inversion can be regarded as successful.
The top pre-Tertiary basement map published by Kröll et al. (1988) shown in Figure 6 is in comparison to the calculated basement relief with a density contrast of −0.2 g/cm 3 (Figure 7) and −0.3 g/cm 3 (Figure 8) of similar shape.The calculated depth of the Gnas Sub-basin depocentre is 3.5-4 km b.s.l. for the inversion with a density contrast of −0.2 g/cm 3 whereas in the Map by Kröll et al. (1988) the maximum depth is only about 2 km b.s.l.Depths of up to 4 km for the Gnas Sub-basin have also been suggested by Sperl and Wagini (1994) and Sachsenhofer et al. (1996) based on two-dimensional gravity modelling.The exploration well Petersdorf-1 located in the northern part of the Gnas Basin encountered basement about 2400 m.b.s.l. which is in good accordance with the basement map given the previously mentioned basal dolomitic conglomerate layer.The shallower solution of the gravity inversion with a density contrast of −0.3 g/cm 3 (Figure 8) is closer to the map published by Kröll  (1988) but the top pre-Tertiary basement solution is too shallow in many control points such as the well Petersdorf-1 and the Fürstenfeld-1, Blumau-1a and Stegersbach Thermal-1 wells in the Fürstenfeld sub-basin (Table 1).For the Western Styrian Basin, the −0.3 g/cm 3 solution seems preferable which probably is related to the higher basement rock densities (2.85 g/cm 3 ) of the Eastern Alpine Crystalline Units in the west of the area of interest (Figure 2).

RESULTS OF GRAVITY INVERSION IN COMPARISON TO WELL RESULTS
The well locations and depths were collated from various databases and plotted by the red well symbols.It has to be noted that some uncertainties in the well locations are observed, some wells were drilled in the 1950s and 60s with poor documentation.The green circles are locations taken from the maps by Kröll et al. (1988) and Sachsenhofer et al. (1996).In red script the reported total depth (TD) from ground level is plotted, the top pre-Tertiary depth plotted in green.
These depths are given metres below sea level (TVD m.b.s.l, true vertical depth).The exploration well Petersdorf-1 located in the northern part of the Gnas Basin encountered basement about 2400 m.b.s.l. which is in good accordance with the −0.2 g/cm 3 top pre-Tertiary map (Figure 7) taking the mentioned before basal dolomitic conglomerates layer into account which would be the relevant pre-Tertiary surface as density contrast, although in sensu stricto not the pre-Tertiary in a depositional sense as the fan is assumed to have been deposited in the Ottnangian period.It has to be noted that several wells did not reach pre-Tertiary basement as for example the well Paldau-1 with TD of 1438 m TD (from Kelly Bushing -KB) and 1130 m.b.s.l.Many wells drilled a considerable section into the pre-Tertiary basement (mostly Palaeozoic or Penninic metamorphic rocks).An extreme example is the well Radochen-1 drilled by OMV in 1981 which encountered base Tertiary at 66 m.a.s.l. and TD'd at 997 m MD b.s.l.(measured depth from KB) or from ground level which is also commonly used for Austrian wells), therefor penetrating an 1065 m section of metamorphic Palaeozoic metasediments.Kröll et al. (1988) F I G U R E 9 Error field inversion -input gravity minus forward gravity calculated by 10 term Parker (1973) forward series of the inversion result −0.3 g/cm 3 (Figure 8).Units mGal.
given a comprehensive description of the wells in the area that reached the pre-Tertiary.The well locations in the top pre-Tertiary relief map in Figure 6 given by Kröll et al. (1988) differ for some wells to the plotted locations from the abovementioned database and in the author's, view these locations are more reliable.For the well Stegersbach Thermal-1 that was drilled in 1989 and hence after the publication of Kröll et al. (1988), the location and depth-to-basement were taken from the map by Sachsenhofer et al. (1996).The base Tertiary depth of 3040 m.b.s.l. is actually the deepest drilled depth within the area of interest.The well was outright drilled for balneological use for the Stegersbach Spa.A listing of wells penetrating top pre-Neogene 'Basement' in comparison to the depths of the gravity inversions is given in Table 1.Indicating in general a better fit of the −0.2 g/cm 3 inversion results.

AEROMAGNETIC DATA AND EFFECTS OF MIOCENE VOLCANISM
Austria is covered by a regional aeromagnetic survey acquired in the years 1979-1982 by the GBA -Geological Survey of Austria.The flight spacing is 2 km W-E and 10 km N-S control lines (Heinz & Blaumoser, 1994;Blaumoser, 1991) and hence of rather low resolution.Because of the topographic relief encountered in Austria various barometric flight elevations were flown; within the area of interest (AOI) the flight elevation is 1000 m above sea level (Blaumoser, 1991).The total magnetic anomaly is shown in Figure 10.The most striking feature is the strong positive anomaly north of the Burgenland Swell.This magnetic feature has been known since the 1930s from ground magnetic data and has been interpreted as result of a Miocene shield volcano made up of Andesitic material, the Bad Gleichenberg volcano (Jäger, 2004;Kröll et al., 1988;Sachsenhofer et al., 1996;Slapansky et al., 1999).Comparison with the gravity maps (Figures 4  and 5) shows no striking effect of this shield volcano in the gravity field.Kröll et al. (1988) assumed an interfingering of sedimentary layers with volcanic layers for this lack of gravity response; only the Bad Gleichenberg Kogel (46˚54′ N/15˚54′ S -467,014 mE/5195,886 mN) where the Miocene volcanics are outcropping (Figure 2) exhibits a smallish positive gravity anomaly which is also reflected in the gravity inversion (and as such not caused by basement uplift).Jäger ( 2004) reported a sample form the outcrop identified as latite (i.e.trachyandesite) with a measured rock density of 2.33 g/cm 3 , the magnetic susceptibility was reported as 470 (10 −8 ) m 3 /kg or 4.7(10 −3 ) in cgs units.
The areal extend of the Miocene volcanics in the Styrian Basin has been reported by Slapansky et al. (1999) and is shown in Figure 11.As the Miocene volcanics are largely subcropping, the distribution is mainly based on well information.The Miocene shield volcanics as reported by Slapansky et al. (1999) show a good correlation to the positive magnetic anomalies.In addition to the dominant Bad Gleichenberg shield volcano, two volcanoes are within the AOI, the Walkersdorf volcano and the Weltendorf volcano (Slapansky et al., 1999) which are partly outcropping (Figure 2) and associated by positive magnetic anomalies (Figures 10 and 11).
Notably also the area of the well Mitterlabil-1 is a centre of Miocene volcanism (in sub crop) as reported by Slapansky et al. (1999), here the calculated top basement is too high which is likely due to a positive gravity effect of the volcanics.However, in other areas, there seems little gravity response associated with the Miocene volcanics, for instance at the locations of the wells St. Nikolai-1 and 2 and St. Peter-1 were the gravimetrically derived top-basement solution is deeper than well penetration.As the reported density value of 2.33 g/cm 3 for the latite in the Gleichenberg area is quite low and in the range of densities for Neogene sediments, it may be assumed as having little effect for the gravity inversion for top basement.Volcanics were discussed but not considered by Sperl and Wagini (1994) and Sachsenhofer et al. (1996) in their two-dimensional gravity modelling.
It may be noted that the Plio-Pleistocene basaltic volcanoes (outcrops shown in Figure 2) are not picked up by the present aeromagnetic data.It has been speculated by Kröll et al. (1988) that the flight line spacing is too large and also the flight level above ground too high and therefore the magnetic signal associated with the basaltic volcanics was missed as the basalts are feeder pipes of limited areal extent.

CONCLUSIONS
The proposed inversion procedure may be considered a fasttrack approximation for a single-layer gravity inversion to facilitate tests of various density scenarios.The second order F I G U R E 1 1 Structural sketch of tectonic elements of the Styrian Basin and distribution of Miocene volcanics in pink according to Slapansky et al. (1999).Well locations indicated by circles and labelled.Red from an OMV database and in green for digitized locations.Red numbers for total depth, green numbers for depth to pre-Tertiary basement.
approximative gravity inversion resulted in a good fit of the observed gravity and the forward-modelled gravity from the inverted top pre-Tertiary relief.The two realisations calculated with density contrasts of −0.2 and −0.3 g/cm 3 result in a and a 'shallower' solution.Well control indicates a better fit of the deeper solution (−0.2 g/cm 3 ) for the Gnas and Fürstenfeld sub-basins.For the West Styrian Basin, the shallower solution (−0.3 g/cm 3 ) seems more appropriate as to the west higher density basement units occur.But the complex basement lithology in the transition area from the Eastern Alps to the Pannonian Basin needs to be considered for further assessment.Additional complications arise from the quite widespread distribution of mostly sub-cropping Miocene volcanics (outlined by aeromagnetics and well penetrations) that may influence the top pre-Tertiary gravity inversion.In general, the effect of the volcanics on the basement solution seems to be not too severe according to well control and not necessarily leading to an over-or underprediction of the sedimentary basin fill.Both, for the Gnas and Fürstenfeld subbasins a depth-to-basement of up-to 4 km is calculated which may result into geothermal temperatures in excess of 160˚C at the base of the Neogene.

A C K N O W L E D G E M E N T S
The author gratefully thanks Mag.Robert Edelmaier (BEV -Austrian Federal Office of Metrology and Surveying) for supplying and the permission to use the gravity data, and Mag.Klaus Motschka & Dr. Andreas Ahl (GBA -Geological Survey of Austria) for supplying the aeromagnetic grid.Furthermore, I thank Dr. Gabor Tari (OMV) for fruitful discussions and sharing his knowledge on the Pannonian Basin Geology.
Constructive comments by the deputy editor Prof Dr. G Florio, the associate editor and two anonymous reviewers are highly appreciated.The permission by OMV for publication is gratefully acknowledged.

D A T A AVA I L A B I L I T Y S T A T E M E N T
Research data are not shared.

F I G U R E A 3
Inverted layer topography with the second order approach -to be compared with the semi-synthetic layer topography (Figure A1).

F I G U R E A 4
Error field of the semi-synthetic test layer topography versus the inverted layer topography with the second order approach.Units km.

F
Stratigraphic chart of the Neogene.Correlation of the standard global Neogene geologic stages with the local Paratethys stages and occurrences of Plio-Pleistocene and Miocene volcanics after Tari et al. (2020) and Sachsenhofer et al. (1996).

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I G U R E 3 Topographic relief based on the actual gravity station elevations (metres above mean sea level).Gravity stations indicated by crosses.
Comparison basement depths from wells and gravity inversions with density contrasts −0.2 and −0.3 g/cm 3 .Basement encounter in the wells -TVD mSS -true vertical depth m.b.s.l.Well Mitterlaibl-1 did not reach (nr -not reached) pre-Tertiary.F I G U R E 7Inverted Gravity -top pre-Tertiary basement relief using a density contrast of −0.2 g/cm 3 -units km b.s.l.Well locations indicated by circles and labelled.Red from an OMV database and in green for digitized locations.Red numbers for total depth, green numbers for depth to pre-Tertiary basement.F I G U R E 8Inverted gravity -top pre-Tertiary basement relief using a density contrast of −0.3 g/cm 3 -units km b.s.l.Well locations indicated by circles and labelled.Red from an OMV database and in green for digitized locations.Red numbers for total depth, green numbers for depth to pre-Tertiary basement.et al.

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Aeromagnetic anomaly field -flight elevation 1000 m barometric -subset of the Austrian Aeromagnetic Survey 1977-1982.Units nT.

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Forward calculated gravity field from the semi-synthetic topography (FigureA1) with density −0.3 g/cm 3 .