Annals 47, 5, 2004 1581 ANNALS OF GEOPHYSICS, VOL. 47, N. 5, October 2004 Key words lithospheric flexure – differential com- paction – Triassic 1. Introduction The peculiarity of carbonate platforms is that sediments can be produced only in a few meters of water depth. This notwithstanding, in many regions of the world both past and present plat- forms commonly consist of several hundred me- ters of continuous successions of shallow-water sediments and these thick accumulations can be explained only if accommodation space is con- tinuously created, that is if subsidence of the un- derlying ‘substratum’ and/or sea level rise con- tinuously occurs for relatively long time spans. As concerns sea level variations, nowadays we have a widely accepted knowledge of the first-order global fluctuations scale (Haq et al., 1987) and therefore, for almost any geological time interval we can grossly quantify the con- tribution of this phenomenon in producing ac- commodation space. Whatever the case, be- Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy Claudia Marella (1), Riccardo Caputo (2) and Alfonso Bosellini (3) (1) Dipartimento di Scienze della Terra, Università degli Studi di Camerino, Italy (2) DiSGG, Università degli Studi della Basilicata, Potenza, Italy (3) Dipartimento di Scienze della Terra, Università degli Studi Ferrara, Italy Abstract The phenomenon of subsidence induced by the growth of carbonate platforms has been investigated with the aid of numerical modelling. The research aimed to quantify the relative contribution of this process in the creation of the accommodation space required to pile up thick neritic bodies. We analysed two end-member deformation styles, namely the elastic behaviour of the lithosphere when locally loaded and the plastic-like reaction of a sed- imentary succession underlying a growing carbonate buildup. The former process, analysed using a modified flexural model, generates a regional subsidence. In contrast, the latter process, simulated by considering the compaction occurring in soft sediments, generates a local subsidence. We attempted to quantify the amount and distribution of subsidence occurring below and surrounding an isolated platform and in the adjacent basin. The major parameters playing a role in the process are discussed in detail. The model is then applied to the Late Anisian-Early Ladinian generation of carbonate platforms of the Dolomites, Northern Italy, where they are spec- tacularly exposed. Taking also into account the Tertiary shortening that occurred in the area, both local and re- gional subsidence contributions of major platform bodies have been calculated aimed at a reconstruction of the map of the induced subsidence. A major outcome of this study is that the accommodation space, that allowed the accumulation of very thick shallow-water carbonate successions in the Dolomites, was only partially due to lithospheric stretching while the contribution given by the ‘local’ overload is as high as 20-40% of the total sub- sidence. Our results also shed some light on the water-depth problem of the Triassic basins as well as on the basin-depth to platform-thickness relationships. Mailing address: Prof. Riccardo Caputo, DiSGG, Uni- versità degli Studi della Basilicata, C.da Macchia Romana, 85100 Potenza, Italy; e-mail: rcaputo@unibas.it 1582 Claudia Marella, Riccardo Caputo and Alfonso Bosellini cause eustatic curves commonly show some tens of meters of continuous sea-level rise and, just in a few cases, up to 100-150 m, at a first glance this natural phenomenon cannot explain, at least alone, the growth of thick platforms that occurred during many geological periods. As a consequence, subsidence of the under- lying substratum must be claimed as the princi- pal mechanism for the generation of accommo- dation space during the build up of these sedi- mentary bodies. Subsidence of the Earth surface can basical- ly occur as a consequence of three major processes. Firstly, if the lithosphere is horizon- tally stretched, it becomes thinner (e.g., McKen- zie, 1978), the top and bottom interfaces be- come closer due to the occurrence of a large- scale pure shear and thus the Earth surface sub- sides. This process is mainly referred to as tec- tonic subsidence and typically occurs during a rifting stage. Secondly, if the crust and/or the lithosphere become denser, a new lithostatic equilibrium must be reached. A typical example of this process is the thermal subsidence associated with the cooling of the lithosphere in passive margins (Sclater et al., 1971). Thirdly, if the crust is locally overloaded, again new lithostatic conditions are required to keep the equilibrium. Depending on the rheo- logic and mechanical behaviour of rocks, this process can induce ‘local’ subsidence at the scale of the applied load as well as regional ef- fects at distances several times the size of the loaded area. This last case commonly occurs in regions where important topographic structures like volcanoes and oceanic islands can be gen- erated on top of the Earth surface in relatively short time intervals. Typical examples are the fore-deep basins associated with the mountain chains and the post-glacial rebound of Scandi- navia. In this paper the subsidence induced in the lithosphere and within the uppermost crust by the growth of isolated carbonate platforms is in- vestigated. One of the principal aims of this re- search is estimating the amount and the distri- bution of subsidence during the growth of a carbonate platform. To achieve this goal we set up a numerical model compiled with the Matlab software. In order to evaluate the role played by the parameters considered, we performed sever- al tests. A second important aim of this study is the application of the model to the carbonate plat- forms that grew in the Dolomites, Northern Italy, during Middle Triassic that represent a spectacular and world famous example of car- bonate build-ups. As a major outcome, we can tentatively quantify the amount of subsidence induced by the platforms’ load and its distribu- tion in the palaeo-Dolomites region. Based on the thickness of the neritic successions and con- sidering the calculated pattern of the ‘near- field’ contribution, the amount of subsidence induced by a ‘far-field’ process can be easily obtained. According to the Middle Triassic geo- dynamics of the area, the tectonically induced subsidence can be roughly estimated and con- sequently we can have some idea on the amount of stretching which occurred during that time interval. 2. The numerical model In order for subsidence to occur, the litho- sphere and/or the crust must deform either lo- cally or regionally. The deformation process can occur according to three end-member be- haviours of lithospheric rocks: elastic, plastic and viscous. To estimate the subsidence induced by the growth of carbonate platforms two effects have been considered. Firstly, the flexure of a thin elastic plate and, secondly, the plastic deforma- tion due to compaction of the underlying strati- graphic successions progressively buried. As a first approach, we did not consider the possible contribution associated with a viscous behaviour because important effects in terms of amount of deformation are negligible in rela- tively short time spans, say of the order of a few million years (e.g., Ranalli, 1987). The elastic behaviour of the lithosphere has already been recognised in several geodynamic conditions. Classical examples are the flexure induced by the Hawaiian Islands chain (Tur- cotte and Schubert, 1982), the bending occur- ring in front of oceanic trenches along subduc- 1583 Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy tion zones (Karner and Watts, 1983; Wang, 2001) or the deflection associated with conti- nental sedimentary basins (e.g. Walcott, 1970). The elastic deformation is analysed here us- ing a flexural model of bending lithosphere sup- ported by a denser substratum. The permanent volume reduction occurring in the sedimentary succession, which is progressively buried under the increasing load of a growing carbonate plat- form, has been considered and consequently modelled as a plastic deformation. The two in- dependent deformational processes are then summed up to calculate the induced subsidence. 2.1. Flexural model The flexure of the lithosphere can be analysed considering the bending of an isotrop- ic elastic plate of thickness h, much smaller than the two horizontal dimensions, subjected to a surface load located at the top and supported by a denser substratum (fig. 1). In such conditions, three forces are involved: firstly, the downward facing force exerted by the surface load; sec- ondly, the elastic force generated by the plate re- sisting bending; thirdly, the buoyant force due to the replacement of dense asthenosphere rocks with less dense lithosphere rocks. Considering the three forces acting on the plate, the general equation describing the deflection in the xy- plane is (e.g., Timoshenko and Goodier, 1951) D x w x y w y w gw L2 m i4 4 2 2 4 4 4 2 2 2 2 2 2 2 + + + - =t t_ i( 2 (2.1) where g is the gravity acceleration, ρm the den- sity of the asthenosphere, ρi the density of the replacing materials (sediments and water), L is the linear surface load and w is the deflection of the plate relative to the centre of load applica- tion. D represents the flexural rigidity that is equal to Te3E/12(1− ν 2), where Te is the elastic thickness, E is the Young modulus and ν is the Poisson coefficient. This equation can be applied to linear topo- graphic features like mountain ranges or aligned oceanic islands. Indeed, in this case, where the bending geometry is the same in any cross-section normal to the long dimension of the loading body the problem is reduced to a one-dimensional elastic bending D dx d w gw Lm i4 4 + - =t t_ i . (2.2) For a linear load along the y axis at x = 0 the gen- eral solution is (Turcotte and Schubert, 1982) cos sinw w e x x/ x x 0= +a a - a a k (2.3) where wx is the deflection at a distance x from the load, w0 is the maximum deflection at x = 0 given by Fig. 1. Simplified sketch of the numerical model used to estimate the subsidence induced by the growth of a carbonate platform: deflection and compaction processes occurring within the elastic and plastic layers, respec- tively, are indicated along with the main parameters. E: Young modulus; ν: Poisson coefficient; Te: equivalent elastic thickness; ρw: water density; ρp: platform rock density; A: platform dimensions; ρm: mantle density. 1584 Claudia Marella, Riccardo Caputo and Alfonso Bosellini w0 = Lα3/8D (2.4) and α is the flexural parameter α = [4D/(ρm + − ρi ) g]1/4. Keeping in mind that the aim of this study is to estimate the flexure of the lithosphere caused by a point load as a carbonate platform (bidi- mensional case), we also need to consider the shear stress induced in the yz-plane that obvi- ously plays an important role in reducing the maximum subsidence. According to Lowrie (1997), because a load with equal horizontal di- mensions causes a central depression that is less than a quarter the effect of the linear load a cor- rective coefficient is introduced in eq. (2.3), which thus becomes . cos sinw w e r r 0 25 /r 0= +a a - a a k; E (2.5) where r is the radial distance from the point load. We are well aware that this coefficient is an over- simplification of the mathematical aspects and it does not correspond to a rigorous solution of the differential equation. Nevertheless, we prefer to keep the mathematics to a minimum for several reasons. Firstly, because the principal aim of the paper is to assess the order of magnitude of this natural phenomenon and not to quantify it exact- ly. Secondly, the values that some of the param- eters included in the above equations can assume within their possible ranges induce an even larg- er variability in the results. Accordingly, eq. (2.5) has been used to estimate as a first attempt the amount of lithospheric flexure due to the growth of a carbonate platform. 2.2. Compaction model The plastic deformation is estimated by ap- plying a compaction model. The thickness reduc- tion of the sedimentary successions, buried under an increasing load has been calculated. The com- paction in sedimentary units commonly occurs due to the leakage of pore fluids and to a general geometric reorganisation of the particles consist- ing in the partial collapse of the grain framework, plastic deformation of soft fragments, and frac- turing and pressure solution phenomena (Rieke and Chilingarian, 1974). At greater depths even mineralogical transformations can contribute to a progressive volume (i.e. thickness) reduction. All these factors lead to a reduction in porosity. An- other important factor that influences the porosi- ty reduction is the precipitation of cement mate- rial, though this process is more an obstacle to the compaction process. If analysed in detail, diagenetic compaction of sediments is not a simple plastic deformation mechanism, but for the purposes of this re- search and particularly at the scale we consider, as a first approximation this natural process can be modelled as a plastic deformation (fig. 1). The mechanical compaction of sediments depends on the buried depth (i.e. lithostatic load) and on the differential stresses. If the compaction is the only working process, the thickness of the solid component remains con- stant and therefore the ratio between solidity (1− φ ) and the thickness reduction is linear (Baldwin and Butler, 1985). In this study we use a simple porosity-depth function as pro- posed by Athy (1930). Ruby and Hubert (1960) showed that the porosity should be an exponen- tial function of depth in the form e cz 0=z z - (2.6) where φ 0 is the initial porosity and c is the com- paction factor. In this study we follow the approach proposed by Sclater and Christie (1980), which allows esti- mation of the depositional (i.e. original) thickness of a sedimentary succession from the present-day thickness as directly measured in the field. For example, if we assume a total overburden thick- ness that caused a certain compaction, inversion of eq. (2.6) allows to ‘de-compact’ the deposits. Accordingly, we can calculate the thickness for any depth of burial and from the difference be- tween this calculated value and the present-day thickness we obtain the amount of compaction that occurred during any time interval. 3. Parameter definition A key step in any numerical modelling is the choice of the most suitable and correct val- 1585 Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy ues for each parameter and variable introduced in the calculations. Many of these values can be easily inferred from the abundant literature on the topic (e.g., Jaeger and Cook, 1979; Turcotte and Schubert, 1982; and references therein), while in some cases the choice of the numerical value is more difficult because the lack of geo- logical, mechanical and geodynamic informa- tion does not allow a tight constraint of the pa- rameter. In these cases, a more or less wide range of values has been tested. 3.1. Elastic deformation Table I lists all the numerical values and ranges attributed to the parameters used in the program. However, in the following, only the most important parameters will be discussed. As concerns elastic deformation, one of the most important parameters is the elastic thick- ness, Te, which generally does not represent the entire lithosphere but only that part behaving elastically. Indeed, one of the major problems in defining this parameter is that the lithosphere is not perfectly elastic as assumed in the theory from which eqs. (2.1) to (2.5) are derived. In fact, the possible occurrence of hotter and/or less competent volumes within the lithosphere, diffuse creeping phenomena and the possible crust-mantle decoupling de facto strongly re- duce the real elastic behaviour of the litho- sphere. In order to account for these rheological heterogeneities within the lithosphere, a per- fectly elastic but thinner lithosphere is com- monly considered, that is an ‘equivalent elastic thickness’ is introduced in the calculations. For the oceanic crust the elastic thickness is a function of age and roughly coincides with the isotherm of 600 C° (McNutt, 1988). In con- trast, the continental lithosphere does not en- tirely depend on temperature and pressure con- ditions (Burov and Diament, 1995). The thermal state of the continental litho- sphere is one important factor among others that determines the value of the equivalent elas- tic thickness. Other factors are the state of the crust-mantle interface, the thickness and pro- portions of the mechanically competent crust and mantle and the local curvature of the plate that is directly dependent on the bending stress- es (Burov and Diament, 1995). Burov and Diament (1995) document that the continental lithosphere elastic thickness has a wide range of values between 5 and 110 km. These authors also emphasise the occurrence of a bimodal distribution characterised by two peaks at 10-30 km and 70-90 km, respectively. Table I. List of parameters, their symbols and values used during numerical modelling. The values in the last column are those selected for the model application to the Late Anisian-Early Ladinian carbonate platforms of the Dolomites, Northern Italy. The selected values for the initial porosity and the compaction factor refer to the Bellerophon Formation (BEL) and the Werfen Formation (WER), respectively. Parameter Symbol Unit Value or range Selected value Young modulus E Pa 1010-1011 1010 Poisson coefficient ν - 0.22-0.25 0.25 Equivalent elastic thickness Te km 10-50 21 Mantle density ρm kg/m3 3000-3500 3500 Replacement density average of ρw-ρp kg/m3 1100 1100 Platform density ρp kg/m3 1800-2200 2200 Initial porosity φ 0 - 0.3-0.7 BEL 0.6 WER 0.5 Compaction factor c m−1 2 ⋅10− 4-7 ⋅10− 4 BEL 5 ⋅10 − 4 WER 2.7 ⋅10− 4 1586 Claudia Marella, Riccardo Caputo and Alfonso Bosellini Similarly, McNutt (1988) have compiled a data- base of elastic thickness values reported in the literature for the continental lithosphere under major mountain chains. The minimum value they collected is 15 km, the maximum 30 km. Based on the gravity anomalies of the Kr- ishna-Godavari Basin in India and the inferred load induced by the sedimentary infill, Krishna et al. (1999) suggest that the best fitting value of the equivalent elastic thickness to explain the observed gravity anomalies is about 30 km. Similar values were assumed to calculate the tectonic subsidence and the crustal flexure in the Chaco Basin, Bolivia (Coudert et al., 1994). Accordingly, though the elastic thickness strongly depends on the broader and specific ge- odynamic conditions to be numerically simulat- ed, as a first attempt for continental lithosphere we chose a range of values between 10 and 50 km. The variability of Te has a twofold effect. Firstly, by decreasing the equivalent elastic thickness the maximum deflection increases al- most proportionally and, secondly, the peripher- al bulge moves closer to the central depression and becomes more pronounced (fig. 2a). Also the Young modulus is inversely pro- portional to the maximum deflection, though its effects are less important because by varying E of one order of magnitude (from 1010 to 1011 Pa), w0 varies of about ± 25% (fig. 2b). Another influencing parameter is the mag- nitude of the point load that is directly propor- tional to the maximum deflection (eq. (2.4)). On the other hand, this parameter is a function of i) the initial distribution and extension of the neritic conditions (i.e. the growing carbonate platform), ii) the amount of aggradation, iii) the amount of progradation and iv) the selected val- ue for the density of platform rocks. All these factors will be further analysed and discussed in a later section where the numerical model is ap- plied to real examples of carbonate platforms. Elastic deformation is also influenced by the density contrast that determines the buoyant force induced by the replacement of the as- thenosphere mantle rocks with less dense mate- rials (fig. 1). Indeed, while the density of the re- placement materials is close to unity, consisting for more than 95% of water, the replaced man- tle rocks can range between 3000 and 3500 kg/m3. Whatever the case, the final result is not strongly affected. 3.2. Plastic deformation As concerns deformation associated with compaction, the most important parameters are the initial porosity and the compaction factor. Initial porosity, φ0, can strongly vary from more Fig. 2a,b. a) Influence of the equivalent elastic thickness (Te ) on the deflection. The larger the value, the stronger the layer, the less important the maximum deflection. b) Influence of the Young Modulus on the de- flection. Note the inverse proportionality between the Young modulus and the maximum deflection, the shift and the magnitude of the peripheral bulge. a b 1587 Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy than 60% to less than 15% (Pryor, 1973; Camp- bell et al., 1974). Indeed, these extremely vari- able values of porosity are associated with strong variations in the possible amount of porosity reduction and therefore in compaction and the consequent subsidence. This parameter is particularly influential during the initial bur- ial history of sediments (fig. 3a), though at depths greater than 5 km, all curves tend to con- verge to a similar value. The second important parameter playing a role during the compaction process is the so- called compaction factor, c, in eq. (2.6) (fig. 3b). In fact, although all c-curves have the com- mon tendency to a progressive reduction in porosity, at great depths, say more than 5 km, small and large values of c differ up to almost 20%. But even more important is the influence of this parameter during the burial evolution. For example, during the first 1000 m of burial, a compaction factor of 8 ⋅10−4 induces about 30% of porosity reduction, while a value of 2⋅10−4 is associated with only a 10% porosity reduction, that is of sedimentary compaction and thus of induced subsidence. This parameter strongly depends on the lithology of the sedi- ments and especially on their texture character- istics. A further influential factor as concerns the amount of induced subsidence is obviously the original thickness of the sedimentary unit un- dergoing compaction. Indeed, it is clear that whatever the compaction factor and the initial porosity are, the larger the original thickness the larger the final amount of induced subsi- dence (fig. 3c). Again with reference to the plastic deforma- tion and considering a simplified 3D truncated- conical shape for carbonate platforms, it is ob- vious that the amount of burial of the underly- ing sedimentary units varies with the position relative to the platform limits. Indeed, com- paction is nil outside the platform toe of the slope and it is maximum inside the ring defin- ing the shallow-water depositional area. There- fore, the slope angle directly influences the di- mension of the annular gradient for the amount of compaction occurring in the sediments un- derlying the carbonate build up. Carbonate plat- forms in the Dolomites commonly range be- tween 25° and 45°. 4. Applications to Triassic platforms of the Dolomites As mentioned in the introductory notes, the numerical model has been applied to some of the most spectacular and well-known examples of carbonate platforms in the world: the Dolomites of Northern Italy. Indeed, during the Middle and Upper Triassic, the whole region Fig. 3a-c. Reduction of porosity (i.e. compaction) associated to progressive burial: a) with variable ini- tial porosity and constant compaction factor (c = 4⋅10−4); b) with variable compaction factors (c) and constant initial porosity (φ 0 = 0.5). c) Subsidence induced by compaction of a ‘plastic’ layer, for differ- ent initial thicknesses and material properties, as a function of the overburden. a b c 1588 Claudia Marella, Riccardo Caputo and Alfonso Bosellini was characterised by several episodes of fast growing isolated carbonate buildups. The di- verse generations of platforms generally differ in thickness, amount of aggradation and progra- dation and their relative rates. An extensive lit- erature exists on the topic (see, for example, Bosellini et al., 1996 and references therein). In order to test the numerical model, among the several generations of platforms that can be recognised in the Triassic succession of the Dolomites, we selected the so-called pre-vol- canic Late Anisian to Early Ladinian platforms which are 400-800 m thick and show high aggradation rates and relatively simple pre- growth stratigraphic conditions. The relatively short time interval (i.e. Late Anisian-Early Ladinian) of platform growth, lasting probably less than 2 Myr (Gianolla et al., 1998), assures that the assumption of a geologi- cally restricted temporal time window is satis- fied and therefore the viscous contribution to de- formation can be neglected (e.g. Walcott, 1970; Beaumont, 1978). Due to the strong influence of the equivalent elastic thickness in the numerical modelling, we paid special attention to the selection of this parameter. As previously discussed, the elastic thickness of the continental lithosphere de- pends on numerous factors. Burov and Diament (1995) showed that the thermal state of the lith- osphere, the crust-mantle interface, the thick- ness and proportions of the mechanically com- petent crust and mantle and the local curvature of the plate, which is directly related to the bending stress, are all crucial properties in defining the equivalent elastic thickness of a re- gion. Nevertheless, following Burov and Dia- ment (1995), an estimate of the equivalent elas- tic thickness of the Dolomite region during Middle Triassic can be attempted. Based on the available data for the Hercynian orogeny that affected the area during the Devonian-Car- boniferous period, the thermal age of the litho- sphere at the time of platform growth was about 100 Myr (Del Moro et al., 1980; Zanferrari and Poli, 1992). Based on this age and if we assume a realistic value for the Triassic crustal thick- ness of about 20-25 km as an average, follow- ing Burov and Diament (1995) it is possible to estimate a Te between 20 and 22 km. As a mean value, we selected 21 km for our calculations, bearing in mind a ± 5% of variability induced by this parameter. The next step was quantifying the load pro- duced by each carbonate platform and its area of influence. It is therefore necessary to identify and locate the several buildups belonging to this Middle Triassic generation of platforms and to define the dimensions of each carbonate body. Based on literature data (Gianolla et al., 1998, and references therein), published geological maps (Leonardi et al., 1968; Caputo et al., 1999) and available unpublished data (M. Stefani and P. Gianolla, pers. comm.), we inferred the possi- ble initial dimensions of the different platforms, the amount of aggradation and that of prograda- tion which characterised the growth of the sever- al Late Anisian-Early Ladinian carbonate bodies. Due to the locally deep erosion and the tectonic deformation that occurred in the Dolomites, the reconstruction of the geometric parameters (thickness and lateral extension) has sometimes been inferred. However, due to the relatively Fig. 4. The present-day distribution of the Late Anisian-Early Ladinian carbonate platforms consid- ered for modelling in the present note. The filled cir- cles tentatively represent the size of the initial nuclei, while the external circles (radial pattern) are propor- tional to the final size (maximum progradation). The general geometry of the bodies is obviously highly simplified. Platform labels indicated in figure corre- spond to table II. Major thrusts affecting the region are also represented. 1589 Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy strong influence of these parameters on the cal- culated subsidence, we attempted a conservative interpretation keeping the inferred dimensions to the minimum values. Accordingly, in fig. 4, the nuclei of the considered platforms are highly simplified and represented as filled circles whose dimensions are roughly indicative of the possible initial size. We emphasise that in some cases the consid- ered platforms, whose corresponding values are reported in table II, merged during their growth due to convergent progradation thus forming a unique larger carbonate body. This is certainly the case, for example, of the Civetta-San Lucano- San Martino platforms (P14-P15-P16 in fig. 5; Bosellini et al., 1996) and the Gran Vernel-Mar- molada platforms (P8-P9 in fig. 5; Stefani and Caputo, 1998). However, in terms of produced load and thus of induced subsidence, our separate and simplified carbonate bodies are roughly equivalent to more realistic platform shapes. With respect to the plastic contribution to de- formation, an important aspect of numerical modelling is the selection of the parameters characterising the underlying sedimentary units that are supposed to have undergone compaction Table II. List of parameters used for modelling the 16 carbonate platforms. Label: platform label used in figs. 6 and 7; a – initial platform radius (m); b – final platform radius (m); c – final platform thickness (m); d – pres- ent-day thickness of the Bellerophon Formation underlying the platform (m); e – present-day thickness of the Werfen Formation underlying the platform (m); f – present-day thickness of the post-Werfen to pre-Late Anisian succession; g – estimated maximum overburden on top of the Werfen Formation. Label Name a b c d e f g P1 Croda dei Baranci 1800 3250 400 260 420 400 4220 P2 Tre Scarperi 1500 3100 400 310 420 400 4310 P3 Cadini di Misurina 1250 2500 400 310 410 400 4240 P4 Putia-Sass Rigai 2600 4000 650 140 200 150 2300 P5 Sassolungo 1200 1950 450 215 140 100 1750 P6 Sella 900 1600 450 220 80 100 1780 P7 Sciliar-Catinaccio 3000 5200 500 150 290 130 1780 P8 Gran Vernel 1250 2500 750 230 170 150 1700 P9 Marmolada 1300 2150 750 235 160 150 1880 P10 Ombretta 3000 4800 800 220 200 150 1750 P11 Latemar 2400 3000 750 180 320 150 1650 P12 Viezzena 2000 2950 750 210 310 150 1650 P13 Agnello 2100 3400 750 145 340 150 1600 P14 Civetta 3200 4500 500 205 220 500 2840 P15 San Lucano 2900 4300 500 190 250 500 2540 P16 San Martino 3200 5200 600 160 300 450 2330 Fig. 5. Tentative palinspastic reconstruction of the Dolomites and assumed location and distribution of the carbonate platforms during Late Anisian-Early Ladinian. Platform labels correspond to table II. The dotted pattern shows the outer limit of the coalesced platforms. 1590 Claudia Marella, Riccardo Caputo and Alfonso Bosellini during the growth of the carbonate buildups. First of all, we have to define which formations could have undergone some compaction. In- deed, the pre-Late Anisian stratigraphy of the Dolomites shows that on top of the Palaeozoic metamorphic basement the sedimentary units of some interest for our model due to their thick- ness, lithology and area distribution are the Val Gardena Sandstone (Middle Permian), the Bellerophon Formation (Late Permian) and the Werfen Formation (Schythian). Other sedimen- tary units also exist but they mainly consist of carbonate layers, like for example the Contrin Formation, or they are coarse-grained like the Sesto and Ponte Gardena Conglomerates. In the former case, diagenesis usually occurs soon af- ter deposition thus impeding any important com- paction during burial; while in the latter case, the compaction factor is generally extremely low and so not influential in our calculations. More- over, as concerns the Val Gardena Sandstone, the time elapsed between sedimentation and the growth of the platforms investigated in this pa- per was probably sufficiently long to allow an al- most complete diagenesis. Therefore their possi- ble contribution to subsidence as induced by compaction is likely to be negligible. According to geological and stratigraphic data (e.g., Bosellini, 1968), the present-day thickness of the Bellerophon and Werfen for- mations have been inferred in correspondence with the several carbonate platforms (table II). However, in order to estimate the amount of compaction suffered by these two sedimentary formations during the growth of the Late Anisian- Early Ladinian platform generation and the con- sequent amount of induced subsidence, it is also necessary to know their pre-platform burial histo- ry and particularly the thickness of the strati- graphic succession already overlying the Bel- lerophon and Werfen units just before the Late Anisian. Therefore, the amount of the post- Scythian to pre-Late Anisian overburden existing in correspondence with each considered platform has been also inferred (Assereto et al., 1977; Ma- setti and Trombetta, 1998; Gianolla et al., 1998) and used during numerical modelling (table II). There is no way to directly measure the ini- tial porosity (φ0) and the compaction factor (c) of the two above-mentioned sedimentary units. However, by considering comparable present- day sediments (e.g., Campbell et al., 1974; Scla- ter and Christie, 1980) these parameters have been tentatively assumed for the Bellerophon and Werfen units. The selected values of initial porosity are 0.6 and 0.5, respectively, while those of the compaction factor are 5⋅10− 4 and 2.7⋅10− 4, respectively (table I). Furthermore, in order to correctly calculate the amount of subsidence induced by com- paction, the total burial overlying the Permo- Scythian formations just before the occurrence of the Oligocene-Quaternary widespread ero- sion must be estimated (table II). Accordingly, following the procedure proposed by Sclater and Christie (1980), we calculated the thickness of the two modelled sedimentary units just be- fore the growth of the Late Anisian-Early La- dinian carbonate platforms. These values have been used as reference values for the calculation of the induced compaction (viz. subsidence). 5. Subsidence map It is clear that the present-day distribution of the investigated platforms does not correspond to the original pattern. It is well known that mainly during Cainozoic times the Dolomites suffered considerable deformation (e.g., Doglio- ni and Bosellini, 1987). However, in order to account for the large-scale effects of the elastic deforma- tion induced by each single carbonate body, we had to perform a palinspastic restoration to ob- tain the original distribution. We are well aware of the complex tectonic evolution that affected the region both in terms of intensity, distribution and kinematics of the different deformational events recognised in the area (e.g., Caputo, 1996). Nevertheless, as a first approximation we can assume that the bulk of shortening which oc- curred in the Dolomites has a mean N-S direc- tion (Doglioni, 1987; Doglioni and Bosellini, 1987; Castellarin et al., 1992; Caputo, 1997; Ca- puto et al., 1999). Accordingly, we firstly identi- fied the major thrusts affecting the region and the amount of shortening they caused and then we reconstructed a simplified palaeogeographic map of Middle Triassic times (fig. 5) slightly modifying that proposed by Bosellini (1996). 1591 Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy Based on this palinspastic restoration and the consequent re-location of the carbonate platforms we thus performed the calculations of the induced elastic deformation for the broader Dolomite region. As a first step, we calculated the subsidence induced by a single platform at different stages of the whole process. Figure 6a-d shows an ex- ample of subsidence evolution in four time steps, relative to the Sciliar-Catinaccio platform (P7). Both local and regional contributions are evident, while the gradient in between the two patterns is an effect of the prograding slope. The same calculations have been performed for all investigated platforms and all contribu- tions have been summed up to generate the total subsidence map represented in fig. 7. This map represents the regional distribution of the amount of subsidence induced by the growth of the Late Anisian to Early Ladinian carbonate buildups. Also in this case, both local and re- gional patterns are evident. Fig. 6a-d. Four time-steps map (a to d) represent- ing the progressive subsidence induced by the growth of a single pre-volcanic platform: the exam- ple corresponds to the Sciliar-Catinaccio (P7 in figs. 4 and 5 and in table II). The contour lines of the in- duced subsidence are in meters (see grey scale). Fig. 7. Map of the calculated subsidence induced by the growth of all Late Anisian-Early Ladinian carbon- ate platforms. Both elastic (regional) and plastic (lo- cal) contributions are evident and can be easily quan- tified. The round geometry of the local contributions is due to the simplified shape of the carbonate bodies assumed in the model. The contour lines of induced subsidence are in meters (see grey scale). The maxi- mum regionally induced subsidence is concentrated in the Central Dolomites and amounts to about 220 m, while local contributions range between 40 and 90 m. 6. Concluding remarks Due to the uncertainties in the selection of some of the parameters used in the numerical model and according to their more or less im- portant influence in the calculations as dis- cussed in a former section of the paper, it is clear that our final results should be considered as a first order approximation of the investigat- ed natural phenomenon. Nevertheless, these re- sults clearly show that the subsidence induced by the growth of the Late Anisian-Early Ladin- ian carbonate platforms in the Dolomites gave an important contribution for generating the ac- commodation space required for these thick successions of shallow-water sediments. a b c d 1592 Claudia Marella, Riccardo Caputo and Alfonso Bosellini Based on the distribution and the diverse thickness values of the platforms (table II), we can tentatively reconstruct the map of the total subsidence occurred in the Dolomites during the Middle Triassic that caused the necessary ac- commodation space (fig. 8a). According to our calculations, the subsidence induced by the growth of carbonate platforms gives an impor- tant contribution as high as 20% to 40% of the total amount of subsidence. Consequently, this contribution should not be disregarded especial- ly when dealing with stratigraphic, palaeogeo- Fig. 8a-c. a) The estimated pattern of the total sub- sidence in the Dolomites during Middle Triassic as inferred from the thickness of the carbonate bodies (table II). b) Map of the subsidence induced by the growth of the platforms (simplified from fig. 7). c) Pattern of the tectonic subsidence obtained from the former two maps and likely induced by a far field extensional stress field. The map emphasises the ex- istence of a NE-SW oriented graben affecting the Central Dolomites. Dashed lines represent the two major border faults (or fault systems). Contours lines are in metres in all three maps (see correspon- ding grey scales). a b c Fig. 9a,b. Regional (a) and local (b) subsidence of a carbonate platform (Bosellini, 1984). In the former case, the water depth of the basin roughly corre- sponds to the thickness of the carbonate platform. In the latter case, with a similar amount of aggradation, the adjacent basin is much shallower. 1: deep-water deposits; 2: platform slope deposits; 3: internal plat- form deposits. 1593 Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy 400-800 m thick overlying platforms has a mag- nitude of some tens of meters, while its gradient is distributed within the progradation zone, that is between the nucleus of the platform, where compaction is maximum, and the toe of the slope, where the compaction is nil. It is thus clear that the Middle Triassic subsidence in- duced by compaction generated a ‘very local’ effect. Therefore, the latter hypothesis for the Fig. 10. Map of the calculated subsidence occurred during Middle Triassic and reduced to its present-day distribution after considering the Tertiary contrac- tion. graphic and geodynamic reconstructions of the Dolomites. Moreover, this local overload by car- bonate platforms induces a positive feedback be- cause any increased subsidence induces further growth and consequently a larger load onto the lithosphere. The quantification for the first time of this contribution is a major result of this paper. Obviously a remote stress field, whose ori- gin is probably associated with a process of lithospheric stretching, induced the remaining 60-80% of subsidence. By combining the map of the total subsidence (fig. 8a) with that of the induced subsidence (fig. 8b) it is possible to obtain a map of the tectonic subsidence (fig. 8c). According to fig. 8c, the Central Dolo- mites are characterised by a 20 km wide NE- SW trending graben where the two border faults (or fault systems) show a vertical dis- placement of about 200 m. It is well known that immediately after the growth of the Late Anisian-Middle Ladinian carbonate platforms, the Central Dolomites were affected by a short but intense volcanic event. It is noteworthy that the two major magmatic bodies (Predazzo and Monzoni) documented in the area, partially in- truding the platforms and associated with vol- canic edifices, are located exactly along the southern border of the graben. It is likely that the rising of the magma and the emplacement of the plutons were facilitated by a crustal scale extensional structure. Further geologic and palaeogeographic im- plications of this study also regard the depth of the surrounding and/or adjacent basins. In fact, if a platform subsides solidly with the adjacent basin, the water-depth of this basin grossly corre- sponds to the thickness difference between plat- form carbonates and basin sediments. In contrast, if a platform subsides independently the former equation is not valid (fig. 9a,b). The results ob- tained from the application of the proposed nu- merical model to the Middle Triassic evolution of the Dolomites certainly gave a contribution to unravel this problem and to choose between the two hypotheses. Indeed, the approach followed allows the differential subsidence between the ar- eas with a direct overload induced by the plat- form and the adjacent basin to be quantified. According to the results presented in this pa- per, the differential subsidence induced by the a b 1594 Claudia Marella, Riccardo Caputo and Alfonso Bosellini occurrence of an ‘independent’ subsidence (fig. 9b) is supported by our numerical modelling. However, because the differential subsidence we calculated is distributed along a distance of several hundreds of metres to some kilometres, corresponding to the dimension of a prograding slope, its influence in terms of thickness varia- tions and original geometry of the sedimentary bodies is probably not detectable with geologi- cal means. These results can be easily extended to other generations of carbonate platforms of the Dolo- mites as well as elsewhere in the stratigraphic record. A second major outcome of this research is the reconstruction of the present-day distribution of the subsidence induced by the local overload, after re-considering the Tertiary shortening that affected the region (fig. 10). With the exception of the local ‘troughs’ directly caused by, and un- derlying the platforms, lateral variations in the amount of induced subsidence is generally lim- ited, being about 50 m across the whole Dolo- mite region. Consequently, also in this case, even specific and dedicated geological investiga- tions will probably not disclose any significant information in the stratigraphic record docu- menting these small variations relative to the depth of the basin surrounding the platforms or concerning the thickness of the basinal deposits. Acknowledgements We thank to M.R. Gallipoli, M. Mucciarel- li, D. Albarello for discussions on the numerical modelling and to M. Stefani and P. Gianolla for supporting unpublished data about the Triassic platforms of the Dolomites. REFERENCES ASSERETO, R., C. BRUSCA, M. GAETANI and F. JADOUL (1977): The Pb-Zn mineralization in the Triassic of the Dolomites. Geological history and genetic interpreta- tions, L’Industria Mineraria, XXVIII, 1-15. ATHY, L.F. (1930): Density, porosity and compaction of sed- imentary rocks, Bull. Am. Ass. Petrol. Geol., 14, 1-24. BALDWIN, B. and C.O. BUTLER (1985): Compaction curves, Bull. Am. Ass. Petrol. Geol., 69, 622-626. BEAUMONT, C. (1978): The evolution of sedimentary basins on a viscoelastic lithosphere: theory and examples, Geophys. J. R. Astron. Soc., 55, 471-497. BOSELLINI, A. (1968): Paleogeologia pre-anisica delle Dolomiti Centro-Settentrionali, Atti Acc. Naz. Lincei, CCCLXV, 1-33. BOSELLINI, A. (1984): Progradation geometries of carbonate platforms: example from the Triassic of the Dolomites, Northern Italy, Sedimentology, 31, 1-24. BOSELLINI, A. (1996): Geologia delle Dolomiti (Ed. Athe- sia, Bolzano), pp. 192. BOSELLINI, A., C. NERI and M. STEFANI (1996): Geologia delle Dolomiti. Introduzione geologica. Guida all’es- cursione generale, in 78a Riunione Estiva Soc. Geol. Italiana, 16-18 Settembre, San Cassiano, pp. 120. BUROV, B. and M. DIAMENT (1995): The effective elastic thickness (Te) of the continental lithosphere: what does it really mean?, J. Geophys. Res., 100, 3,905-3,927. CAMPBELL, R., F. CORTS et al. (1974): Well evaluation Con- ference – North Sea, Schlumberger, France, pp. 171. CAPUTO, R. (1996): The polyphase tectonics of Eastern Dolomites, Italy, Mem. Sci. Geol., 48, 93-106. CAPUTO, R. (1997): The puzzling regmatic system of East- ern Dolomites, Mem. Sci. Geol., 49, 1-10. CAPUTO, R., M. STEFANI and G. DAL PIAZ (1999): Contrac- tional and transcurrent tectonics in the Marmolada Group (Dolomites, Italy), Mem. Sci. Geol., 51 (1), 63-77. CASTELLARIN, A., L. CANTELLI, A.M. FESCE, J.L. MERCIER, V. PICOTTI, G.A. PINI, G. PROSSER and L. SELLI (1992): Alpine compressional tectonics in the Southern Alps. Relationships with the N-Apennines, Ann. Tectonicae, 6 (1), 62-94. COUDERT, L., M. FRAPPA, C. VIGUIER and R. ARIAS (1994): Tectonic subsidence and crustal flexure in the Neogene Chaco basin of Bolivia, Tectonophysics, 243, 277-292. DEL MORO, A., F.P. SASSI and G. ZIRPOLI (1980): Prelimi- nary results on the radiometric age of the Hercynian metamorphism in the South-Alpine basement of the Eastern Alps, N. Jb. Geol. Paläont. Mh., 707-718. DOGLIONI, C. (1987): Tectonics of the Dolomites (Southern Alps-Northern Italy). J. Struct. Geol., 9 (2) 181-193. DOGLIONI, C. and A. BOSELLINI (1987): Eoalpine and mesoalpine tectonics in the Southern Alps, Geol. Rund., 76, 735-754. GIANOLLA, P., V. DE ZANCHE and P. MIETTO (1998): Triassic sequence stratigraphy in the Southern Alps (Northern Italy): definition of sequences and basin evolution, in- Mesozoic and Cenozoic Sequence Stratigraphy of Eu- ropean Basins, SEPM Spec. Publ. 60, 719-747. HAQ, B.U., J. HARDENPOL, P.R. VAIL, R.C. WRIGHT, L.E. STOVER, G. BAUM, T. LOUTIT, A. GOMBOS, T. DAVIES, C. PFLUM, K. ROMINE, H. POSAMENTIER and R. GIAN DU CHENER (1987): Mesozoic-Cenozoic Cycle Chart, Version 3.1A. JAEGER, J.C. and N.G.W. COOK (1979): Fundamentals of Rock Mechanics (Chapman and Hall, London), 3rd edi- tion, pp. 593. KARNER, G.D. and A.B. WATTS (1983): Gravity anomaly and flexure of the lithosphere at mountain ranges, J. Geophys. Res., 88, 10,449-10,477. KRISHNA, M.R., S. CHAND and C. SUBRAHMANYAM (1999): Gravity anomalies, sediment loading and lithospheric flexure associated with the Krishna-Godavarin Basin, eastern continental margin of India, Earth Planet. Sci. 1595 Growth and subsidence of carbonate platforms: numerical modelling and application to the Dolomites, Italy Lett., 175, 223-232. LEONARDI, P. (1968): Le Dolomiti. Geologia dei Monti tra Isarco e Piave (Ed. Manfrini, Rovereto), 2 vols. LOWRIE, W. (1997): Introductory geophysics (Cambridge University Press, London), pp. 354. MASETTI, D. and G.L. TROMBETTA (1998): L’eredità anisica nella nascita ed evoluzione delle piattaforme medio-tri- assiche delle Dolomiti occidentali, Mem. Sci. Geol., 50, 213-237. MCKENZIE, D.P. (1978): Some remarks on the development of sedimentary basins, Earth Planet. Sci. Lett., 40, 25-32. MCNUTT, M.K. (1988): Variations of elastic Plate Thickness at Continental Thrust Belts, J. Geophys. Res., 93, 8,825-8,838. PRYOR, W.A. (1973): Permeability-porosity patterns and variations in some Holocene sand bodies, Am. Ass. Petrol. Geol. Bull., 57, 162-189. RANALLI, G. (1987): Rheology of the Earth. Deformation and Flow Processes in Geophysics and Geodynamics (Allen & Unwin), pp. 366. RIEKE, H.R. and G.V. CHILINGARIAN (Editors) (1974): Com- paction of Argillaceous Sediments, Dev. Sedimentol., 16, pp. 424. RUBY, W.W. and M.K. HUBERT (1960): Role of fluid pressure in mechanics overthrust faulting, II. Overthrust belt in geosynclinal area of Western Wyoming in light of fluid- pressure hypothesis, Bull. Geol. Soc. Am., 70, 167-206. SCLATER, J.G. and P.A.F. CHRISTIE (1980): Continental stretching: an explanation of post mid-Cretaceous sub- sidence of the central North Sea Basin, J. Geophys. Res., 85, 3711-3739. SCLATER, J.C., R.N. ANDERSON and M.L. BELL (1971): Ele- vation of ridges and evolution of the Central Eastern Pacific, J. Geophy. Res., 76, 7,888-7,915. STEFANI, M. and R. CAPUTO (1998): Stratigrafia triassica e tettonica Alpina nel Gruppo Marmolada-Costabella (Dolomiti Centrali), Mem. Soc. Geol. Italiana, 53, 263-293. TIMOSHENKO, S. and J.N. GOODIER (1951): Theory of Elas- ticity (McGraw-Hill, New York), pp. 506. TURCOTTE, D.L. and G. SCHUBERT (1982): Geodynamics Applications of Continuum Physics to Geological Problems (J. Wiley and Sons, New York), pp. 450. WALCOTT, R.I. (1970): Flexural rigidity, thickness and vis- cosity of the lithosphere, J. Geophys. Res., 75, 3,941- 3,954. WANG, W.H. (2001): Lithospheric flexure under a critically tapered mountain belt: a new technique to study the evolution of the Tertiary Taiwan orogeny, Earth Plan- et. Sci. Lett., 192, 571-581. ZANFERRARI, A. and M.E. POLI (1992): Il basamento su- dalpino orientale: stratigrafia, tettonica varisica e alpina, rapporti copertura-basamento, Studi Geologici Camerti, 1992/2 (spec. vol.), 299-302. (received October 6, 2003; accepted March 4, 2004)