In this study, we present an estimate of the gravity signal of the slabs
beneath the Alpine mountain belt. Estimates of the gravity effect of the
subducting slabs are often omitted or simplified in crustal-scale models.
The related signal is calculated here for alternative slab configurations at
near-surface height and at a satellite altitude of 225 km.
We apply three different modelling approaches in order to estimate the
gravity signal from the subducting slab segments: (i) direct conversion
of upper mantle seismic velocities to density distribution, which are then
forward calculated to obtain the gravity signal; (ii) definition of slab
geometries based on seismic crustal thickness and high-resolution upper
mantle tomography for two competing slab configurations – the geometries are
then forward calculated by assigning a constant density contrast and slab
thickness; (iii) accounting for compositional and thermal variations with
depth within the predefined slab geometry.
Forward calculations predict a gravity signal of up to 40 mGal for the
Alpine slab configuration. Significant differences in the gravity anomaly
patterns are visible for different slab geometries in the near-surface
gravity field. However, different contributing slab segments are not easily
separated, especially at satellite altitude. Our results demonstrate that
future studies addressing the lithospheric structure of the Alps should have
to account for the subducting slabs in order to provide a meaningful
representation of the geodynamic complex Alpine area.
Introduction
Interpretation of gravity anomalies can reveal information on the
architecture and tectonic setting of the lithosphere (e.g. Zeyen and
Fernàndez, 1994; McKenzie and Fairhead, 1997; Holzrichter and Ebbing,
2006; Braitenberg, 2015; Spooner et al., 2019). For subduction zones, like
the Andes, several studies have shown that the gravity effect of the
subducting plates is significant and has to be considered in order to study
the feedback between the subducting lithosphere and the overriding plate
(Götze et al., 1994; Götze and Krause, 2002; Tašárová,
2007; Gutknecht et al., 2014; Götze and Pail, 2018; Mahatsente, 2019). For
lithosphere to subduct, a higher density than the surrounding mantle
material at the same depth interval is required, causing a negative buoyancy
for the slab, and therefore the slab is subducted into Earth's interior (e.g.
Kincaid and Olson, 1987; Ganguly et al., 2009). However, the gravitational
contribution of subducting material in the upper mantle to the gravity field
has so far not been systematically addressed for the Alpine system. In order
to provide an assessment, the magnitude of the gravity signal of such
subcrustal long wavelength features has to be estimated.
The Alpine mountain belt (Fig. 1a) is chosen for this sensitivity study
because firstly a large range of recent seismic tomography studies imaged
subducting slab segments in the Alpine region (e.g. Babuška et al., 1990;
Lippitsch et al., 2003; Spakman and Wortel, 2004; Mitterbauer et al., 2011;
Karousová et al., 2013; Zhao et al., 2016; Kästle et al., 2018;
El-Sharkawy et al., 2020). Those different studies suggest different
configurations of slab segments (see Sect. 1.1), allowing us to test how
sensitive the gravity field is to varying geometries of subducting slab
segments. Secondly, previous Alpine models addressing the Alpine gravity
field have considered the subcrustal mantle inhomogeneities in the form of
lithosphere thickness (e.g. Ebbing et al., 2006; Spooner et al., 2019) or in
the form of mantle density variations (Tadiello and Braitenberg, 2021) but
without identifying the isolated effect of subducting slabs segments in the
velocity or density variations. If the contribution of the mantle density
variations is not considered, a significant part of the gravity field might
be attributed to crustal thickness variations or intracrustal sources.
In addition, the Bouguer anomaly of the Alps (Fig. 1b) shows no direct sign
of subducting slabs (in contrast to the Andes subduct zone) as the field is
dominated by crustal thickness variations (Ebbing et al., 2001, 2006).
Therefore, forward modelling of the proposed slab geometries, as imaged by
high-resolution tomographic studies, is necessary to separate the gravity
signal caused by the subducting slabs from the gravity anomaly field.
(a) Topography from ETOPO1 from Amante and Eakins (2009), with faults in
red after Schmid et al. (2004). (b) Bouguer anomaly based on XGM 2019
(Zingerle et al., 2020) with a maximum spherical harmonics degree of 719 at
a station height of 6040 m above the ellipsoid, just above the surface of the
Alps. Correction density for rock: 2670 kg m-3; and for water: 1030 kg m-3.
We present three different approaches to model the gravity effect of the
slab segments and discuss the strengths and limitations of the applied
methods. In the first approach, the Alpine subcrustal density distribution
is derived by converting seismic velocities to density. This model is then
forward calculated to estimate the gravity response. In the second approach,
3-D slab geometries are derived by evaluating seismic crustal thickness
estimations and high-resolution upper mantle tomographic models. Here, two
competing slab configurations are chosen. The predefined slab geometries are
then forward calculated by assigning different density contrasts and slab
thicknesses. The third approach uses similar predefined slab configurations
to those in the second approach; however, here, we consider petrology, temperature
and density variation. The gravity response is calculated for all three
approaches at a near-surface height for the gravity disturbance and the
gravity gradients at a satellite altitude of 225 km.
Alpine setting
The formation and present geodynamics of the Alps are linked to long-lasting
tectonic processes, including Adria–Europe continent–continent collision,
subduction of the oceanic and continental lithosphere, the formation of crustal
nappes as well as extensional and shortening processes (Frisch, 1979;
Stampfli and Borel, 2002; Handy, et al., 2010, 2015). The Adriatic
microplate is a major driver of the present geodynamics in the Alpine
region, which is trapped between the converging major plates of Europe and
Africa. Adria is moving anti-clockwise with respect to Europe, as seen by
GPS observations (e.g. Nocquet and Calais, 2004; Vrabec and Fodor, 2006;
Serpelloni et al., 2016) and is subducted beneath the Apennines to the west
as well as to the east beneath the Dinarides, while colliding with Eurasia
in the Alps to the north (e.g. Channel and Horvath, 1976; Dewey et al.,
1989; Stampfli and Borel, 2002; Handy et al., 2010; Le Breton et al.,
2017). Subducting slab segments have been imaged by different seismological
body wave travel-time tomographic studies as well as surface wave
tomographic studies within the Alpine upper mantle (e.g. Babuška et al.,
1990; Lippitsch et al., 2003; Spakman and Wortel, 2004; Mitterbauer et al.
2011; Karousová et al., 2013; Zhao et al., 2016; Kästle et al.,
2018; El-Sharkawy et al., 2020). However, the configuration of subducting
slab segments remains controversial. In the Western Alps, Lippitsch et al. (2003)
propose a slab break-off at about 100 km depth, which is in line with
the findings of Beller et al. (2018), Kästle et al. (2018) and
El-Sharkawy et al. (2020). In contrast, a continuous subducting slab segment
in the Western Alps, down to at least 250 km depth, is imaged by a number of
other tomographic models (e.g. Koulakov et al., 2009; Zhao et al., 2016; Hua
et al., 2017; Lyu et al., 2017).
A continuous subduction of Eurasia beneath the Central Alps down to at least
200 km depth is imaged by different tomographic models (e.g. Lippitsch et
al., 2003; Piromallo and Morelli, 2003; Koulakov et al., 2009; Mitterbauer
et al., 2011; Hua et al., 2017; Fichtner et al., 2018; El-Sharkawy et al.,
2020). A potential slab gap with an approximate size of 2∘ is
separating the subducting slab segments in the Central Alps to the Eastern
Alps as imaged by, e.g. Lippitsch et al. (2003). The slab configuration and
subduction direction in the Eastern Alps remains unclear. According to the
classical view, Eurasia is subducting beneath Adria in a southward
subduction (Hawkesworth et al., 1975; Lüschen et al., 2004, 2006). This
idea was challenged by Lippitsch et al. (2003), Schmid et al. (2004),
Kissling et al. (2006), Handy et al. (2015) and Hetényi et al. (2018).
Instead, slab break-off in the Eastern Alps and a northward-dipping Adriatic
slab in the easternmost Alps is suggested, leading to a switch of the slab
polarity, as Adria is subducting beneath the European plate (Handy et al.,
2015). The view that Adriatic and not Eurasian lithosphere is subducting
northwards in the Eastern Alps has been opposed by Mitterbauer et al. (2011),
as their model shows a northward-dipping slab in the eastern most
Alps connected to the European plate. In an early tomographic study, Babuška
et al. (1990) proposed that both Eurasian and Adriatic lithosphere is
subducting in the Eastern Alps. In subsequent studies and interpretations,
this model was mentioned but northward subduction of Adria seems to be
favoured (e.g. Karousová et al., 2013; Hetényi et al., 2018). Recently,
subduction of both Eurasian and Adriatic lithosphere in the Eastern Alps
down to about 150 km has been suggested by Kästle et al. (2020) and
El-Sharkawy et al. (2020) based on surface wave studies. For a more in-depth
comparison and discussion of tomographic Alpine models, the reader is
referred to, e.g. Kästle et al. (2020).
Data
The Bouguer anomaly (Fig. 1b) is based on the XGM 2019 global model (Zingerle et
al., 2020) developed for spherical harmonics up to degree 719, with a
resolution of ∼ 25 km (half wavelength). The XGM 2019 model is
a global integrated gravity model, which includes satellite and terrestrial
measurements. The Bouguer anomaly is calculated from the free-air gravity
disturbance with a correction density of 2670 kg m-3 for topography
and a correction density for water of 1030 kg m-3 for the offshore areas
using Tesseroids (Uieda et al., 2016). For the Tesseroids, we use the
topography and bathymetry from ETOPO (Amante and Eakins, 2009), which was
regridded at a regular grid with a grid space of 25 km to match the
resolution of the XGM 2019 model for a maximum degree of 719. The gravity
field is defined at a constant station height of 6040 m above the ellipsoid,
just above the surface of the Alps. The resulting Bouguer anomaly shows a
gravity low on the order of -200 mGal over the high topography of the Alps,
indicating an isostatic crustal thickening in response to topography (e.g.
Ebbing et al., 2006). Additionally, we calculate the mass correction for the
gravity gradients at a station height of 225 km representing the Gravity
field and steady-state Ocean Circulation Explorer (GOCE)
satellite altitude. The topographic corrected gravity gradients after Bouman
et al. (2016) measured by the GOCE European Space Agency (ESA) satellite mission are presented in
the Appendix.
For the definition of the slab geometry, we use crustal thickness estimates
based on the receiver function study by Spada et al. (2013). The crustal
thickness map was digitized and the Moho gap in the Eastern Alps is filled
by nearest-neighbour interpolation. To avoid edge effects, surrounding areas
are supplemented by the Moho depth model of the European plate by Grad et
al. (2009); both data sets were merged using a cosine taper with a taper
width of 2∘ using Eq. (1). The overlapping areas at the grid
edges are distance weighted to obtain a smooth transition.
Gnew=Tx,y⋅G1x,y+1-Tx,y⋅G2(xy),
with Tx,y=cosD⋅π2⋅L,
with G=grids,T=taper,D=dx,L=taper length.
The merged Moho depth map is sampled at a regular grid with a cell size of
0.25∘ (Fig. 2) to be consistent with the resolution of the topographic
and gravity models.
(a) Digitized Moho depth after Spada et al. (2013) with a
0.25∘ grid spacing. (b) Moho depth estimation after Grad et al. (2009)
with a 0.25∘ grid spacing (c) merged Moho depth map from Spada et
al. (2016) and Grad et al. (2009) with a grid resolution of 0.25∘
using a cosine taper with a 2∘ width.
For the upper mantle seismic velocity, the 3-D shear-wave velocity model
(MeRE2020) by El-Sharkawy et al. (2020) is used (Fig. 3). The model covers
the upper mantle across the Alpine–Mediterranean area down to a depth of 300 km,
and absolute shear-wave velocities are given.
In this study, relative shear-wave velocities in the depth range from 70 to
200 km are calculated with respect to a 1-D average shear-wave velocity
model; the background model is described in El-Sharkawy et al. (2020). The
upper limit of 70 km is introduced because (i) we focus on the contribution
of the slab segments therefore removing crustal information from the model;
(ii) the MeRE2020 tomography model is not sensitive to shallow structures – as
a result, the slabs are not well recovered in depths shallower than 70 km;
(iii) we want to ensure a uniform upper boundary. The lower boundary of
200 km is chosen based on clear images of the Alpine slab segments to at least
200 km depth (with the exception of the Western Alpine slab), as discussed in
Sect. 1, and the assumptions that depth larger than 200 km will have a
negligible effect on the regional gravity field considered here.
The ambient noise tomography by Kästle et al. (2018) is used to define
the geometry of the Western Alpine slab segment; hence, we follow the idea of
a slab break-off in the Western Alps at 100 km depth (Kästle et al.,
2020), as suggested also by Lippitsch et al. (2003) and Beller et al. (2018).
For the Eastern Alps, we consider two alternative models. For the first
hypothesis, the P-wave tomography by Lippitsch et al. (2003) is used to
define the Eastern Alpine slab segment. The second hypothesis is based on
Kästle et al. (2020) and El-Sharkawy et al. (2020). It assumes southward
subduction of a short Eurasian slab as well as northward subduction of a
short Adriatic slab in the Eastern Alps. The slab configurations which are
incorporated in the Alpine density models are discussed in greater detail in
Sect. 4.1.
Conversion of seismic velocities into density distribution
Seismic velocity variations are dependent on temperature and pressure.
Densities in the subsurface are also temperature and pressure dependent. A
conversion factor (ζ) can describe the linear relation between
seismic velocities variations and densities variation (e.g. Tiberi et al.,
2001; Webb, 2009). We convert seismic shear-wave velocities from the
MeRE2020 tomographic model by El-Sharawy et al. (2020) in the depth range
from 70 to 200 km, as discussed in Sect. 2, to obtain a density
distribution of the upper mantle in the Alpine region based on a conversion
factor (ζ). The relationship between seismic velocities and densities
is described in Eq. (2); this assumption is a strong simplification of
reality but gives a first-order estimation of the expected relative density
structure beneath the Alps.
ρrel=Vsvabs(1+Δ%)-Vsvabs⋅ζ=Vsvabs⋅Δ%⋅ζ,
with Vsvabs the absolute velocities from MeRE2020,
Δ% the percentage deviation from the MeRE2020
background model and
ζ the conversion factor.
The result is strongly dependent on the chosen conversion factor. A range
for conversion factors has been proposed in the literature for different
rock types ranging from 0.1 to 0.45 (e.g. Isaac et al., 1989; Isaak, 1992;
Karato, 1993; Kogan and McNutt, 1993; Vacher et al., 1998). The relative
shear-wave velocity distribution in a 3-D domain from the MeRE2020 tomography model
from El-Sharkawy et al. (2020) is converted using a constant
conversion factor (ζ) of 0.3. The converted relative density
distribution varies between -240 and 350 kg m-3. High correlations
between the structural pattern in the converted density distribution and the
relative seismic velocities are observed (Fig. 3), the similarity in the
structure pattern is expected due to the linear relationship we introduced
here. The converted 3-D relative density distribution reflects the variation
of seismic velocities in the Alpine lithosphere and therefore includes the
heterogeneities of the subduction slab segments, as seen by the tomographic
models (Fig. 3). The relative density model is transferred into Tesseroids
with a horizontal expansion of 0.2∘ and a vertical expansion of 3 km.
The Tesseroid model is forward calculated in order to estimate the
gravity response of the converted density distribution of the Alpine
lithosphere in the depth interval of 70 to 200 km. No horizontal
extensions of the mantle model are introduced because relative densities are
used, and therefore edge effects are not expected to be significant and would
only affect the outer most degrees of the model. The slab segments are
located central in the model far away from possible artefact due border
effects.
(a–c) Depth slices of relative surface wave velocities
(Vsv) from
MeRE2020 (El-Sharkawy et al., 2020). (d–f) Converted relative density
distribution in different depths based on a conversion factor (ζ) of 0.3.
CA – Central Alpine slab; EA – Eastern Alpine slab; NA – Northern
Apennine slab.
Results
In the forward-calculated gravity field, a gravity high with a magnitude of
∼ 40 mGal is observed over the Alps (Fig. 4). That might be
interpreted as relating to the proposed slab segments in the Northern
Apennine and Alpine area. However, the gravity field (and gradients; see the
Appendix) is dominated by anomalies outside the Alpine realm (Fig. 4), for
instance, in the Ligurian Sea and the Dinarides–Hellenides orogen. Therefore,
in the next step, we try to concentrate on the seismic anomalies in the
Alpine realm that can be related to the slab segments.
Forward-calculated gravity signal from relative density
distribution converted from relative seismic velocities using a conversion
factor of 0.3 at a station height of 6040 m.
Slab models
To estimate the gravity contribution of independent slab segments, we
introduce different models for the subducting lithosphere. First, we use a
set of models with simple constant density distribution in the slab, where
the parameters, namely the density contrast and thickness of the slab
segment is varied (approach 2). Secondly, we create a set of slab models
accounting for compositional and thermal variations with depth (approach 3).
Those models of approach 3 are created with the LitMod3D software package
(Fullea et al., 2009), and here the slabs are strictly vertical due to
software limitations. Slab models created within LitMod will be referred to as
LitMod models in the following. For all non-LitMod models, the gravity and
gravity gradients are calculated using Tesseroids, which are spherical
prisms (Uieda et al., 2016).
Slab modelling with constant density contrast and slab thickness
We define two alternative slab configurations based on crustal thickness
model by Spada et al. (2013) and several different tomographic studies; see a
detailed description of the slab configurations below. At different depths,
isolines are picked in the Moho depth map and tomographic images, defining
the upper boundary of subducting slab segments. The isoline of the crust
mantle boundary (Moho interface) is used as an onset of the slab to the
crust and defines the upper boundary of the subduction slab segment. At
upper mantle depth, increased seismic velocity anomalies in tomographic
models beneath the Alps are interpreted as contrast between colder and
therefore denser subducting material to the surrounding mantle material. At
100, 150 and 200 km depths, the upper boundary of the slab segment is
defined at the 0 % contour line of the relative seismic velocity, marking
the transition from rocks with low velocity to high-velocity rocks. The
isolines at the Moho interface (100, 150 and 200 km depths) are
displayed upon the Alpine topography (Fig. 5a–b). Vertical interpolation
between the upper boundary isolines at different depths (Moho depths of 100,
150 and 200 km) defines a continuous surface of the upper slab boundary. The
lower boundary of the slabs, and therefore the thickness of the slab segment,
is not picked based on seismic data but assumed to have constant thicknesses
for simplifications. The thickness is varied for different models from 60 to
100 km depth.
Defined isolines based on crustal thickness estimations and
seismological tomography models for the upper slab boundary for (a) Configuration 1
and (b) Configuration 2. Black arrows indicate the
subduction direction. The fault configuration after Schmid et al. (2004) is shown in red.
Alternative slab configurations
We define two different slab configurations. Configuration 1 (Fig. 5a)
features a northeast-subducting slab segment in the Eastern Alps based on
Lippitsch et al. (2003). A Central Alpine slab segment is defined based on
Lippitsch et al. (2003) and MeRE2020 (El-Sharkawy et al., 2020) subducting
in south–southeast direction. The Eastern and Central Alpine slab segments
are separated by a slab gap and show perpendicular subduction directions.
The east–southeastward subducted slab segment in the Western Alps is
defined using the tomographic model of Kästle et al. (2018), supporting
the idea of slab break-off at about 100 km depth. Only attached slab
segments are considered, ignoring potential mantle upwelling in the
break-off zone and neglecting the potentially remaining detached slab segment in
larger depths. In addition, a southwest-subducting slab segment beneath the
northern Apennines is considered down to about 200 km depth, as imaged by
MeRE2020 (El-Sharkawy et al., 2020) because of its proximity to the Western
Alps.
Configuration 2 (Fig. 5b) considers a slab configuration mainly based on the
interpretation of the MeRE2020 model (Fig. 3) by El-Sharkawy et al. (2020).
In the Eastern Alps, both a short southward-subducting Eurasian slab segment
as well as a short northward-subducting Adriatic slab are assumed. The
Central and Western Alpine slab segments as well as the slab beneath the
northern Apennines are identical to Configuration 1.
Forward calculation
To estimate the gravity effect of the slab configurations, the geometries
are discretized into Tesseroids with a 0.2∘ extension in the
horizontal domain and a vertical size of 20 km. The Tesseroids range from 40
to 200 km depth. First, a constant density contrast is assigned to the
entire slab. We test density contrasts from 20 to 80 kg m-3.
The thickness of the Alpine slab is not well constrained. We test for three
slab volumes by assigning three slab thicknesses (60, 80 and 100 km)
based on studies of other subducting slab segments (e.g. Wang et al., 2020).
Due to the curved geometries of the proposed slab segments, rectangular
Tesseroids with a horizontal expansion of 0.2∘ will either over-
or underestimate the volume of a subducting slab at the edges of the slab.
The percentage volume share of each Tesseroid to the slab geometry is
calculated. The assigned density contrast of the Tesseroids which does not
lay fully within the slab geometry is decreased according to the percentage
volume within the slab geometry. Therefore, the density distribution
correlates to the hypothetical slab positions and volumes in the Alpine
subsurface without increasing the discretization resolution of the Tesseroid
model beyond the uncertainty of gravity measurements and seismic
tomographies. The offset between the 40 km upper Tesseroid boundary to the
slab onset at the crust at 44 km depth is corrected using the same process.
Results
Forward-calculated slab models for predefined slab geometries of
Configurations 1 and 2 with a constant density contrast of 60 kg m-3 and
a constant thickness of 80 km result in a sharp gravity signal ranging from
70 to 100 mGal (Fig. 6). Both models generate gravity signals on the
order of magnitude of 70 mGal in the Central Alpine region as well as in the
Apennines. The gravity signal in the Eastern Alps differs for the two
hypotheses (Fig. 6a, b). The Western Alpine slab segment shows the weakest
signal in both models.
Forward-calculated gravity disturbance signal at a station height
of 6040 m for predefined subcrustal slab geometries with a content density
contrast of 60 kg m-3 and a constant thickness of 80 km. (a) Predefined
slab Configuration 1. (b) Predefined slab Configuration 2.
The gravity signal ranges from 30 to 110 mGal depending on the assigned
density contrast and thickness for both slab geometry models (Fig. 7). The
highest magnitude of the forward-calculated gravity signal is on the order of
110 mGal and is observed for a slab model with a density contrast of
80 kg m-3 and a constant slab thickness of 100 km, while the lowest signal
is produced by a combination of 20 km m-3 density contrast and a slab
thickness of 60 km. Similar gravity response is produced by different
combinations of density contrast and volume. The signal pattern is
influenced by the predefined slab geometry, while the magnitude of the
gravity signal depends on the density contrast and thickness (Fig. 7).
Forward-calculated gravity disturbance signal for 12 different
combinations of density contrast and slab thickness for subcrustal slab
Configuration 1 at a station height of 6040 m.
Forward-calculated gravity gradients at satellite height show the same
dependency of signal strength (see the Appendix). The forward-calculated gravity
field of approach 2 differs significantly from the forward-calculated
gravity field of the complete mantle density inhomogeneity of approach 1
(Fig. 4), which only reaches a positive mantle effect of a maximum of 50 mGal.
Geophysical and petrological modelling with LitMod
For modelling the Alpine slab segments taking temperature and pressure
variations as well as composition of the lithosphere and sublithosphere
into account, the geophysical and petrological modelling software LitMod3D
is utilized (Fullea et al., 2009). LitMod3D is a finite difference code,
which allows the modelling of lithospheric and sublithospheric structures
down to 400 km depth by solving the heat transfer, thermodynamical,
rheological, geopotential and isostasy equations (Afonso et al., 2008;
Fullea et al., 2010).
A LitMod model consists of a set of crustal, lithospheric and
sublithospheric layers characterized by their petrophysical and thermal
properties, which are used as input data (Fullea et al., 2010). LitMod
provides as an output, i.e. the density, temperature and pressure
distribution as well as the forward-calculated gravity disturbance and
gravity gradients (Fullea et al., 2009).
The assigned composition for the different layers is calculated using a
LitMod subroutine which utilizes the Perple_X algorithm of
Connolly (2009). Perple_X calculates in the LitMod
implementation the specific bulk rock properties based on the six main
lithospheric oxides (SiO2, Al2O3, FeO, CaO, Na2O) by
minimizing Gibbs free-energy equation. The Alpine lithosphere and
sublithosphere as well as the proposed slab segments are modelled using
standard global lithospheric and sublithospheric compositions to test the
influence of compositional variations within the slab segments on the
gravitational signal. Here, we use the so-called Tecton and Proterozoic
type composition (Table 1). Those compositions were chosen for a model with
a homogeneous crust, lithosphere and sublithosphere, where the density
changes as a function of temperature and pressure based on the assigned
compositions. The different slab composition is introduced to test whether a
compositional contrast, in addition to the expected thermal difference,
results in a significant density contrast between the slab and the
surrounding material.
Mineralogical composition for the lithospheric and sublithospheric
structure.
a Classifications according to Griffin et
al. (1999b). b McDonough
and Sun (1995). c Workman and Hart (2005). DMM – depleted
mid-oceanic ridge basalt mantle; PUM – primitive upper mantle. Gnt – garnet. SCLM – subcontinental lithospheric mantle.
First, we create a reference model (M0) without a slab segment. This
model contains topography from the ETOPO1 data set (Amante and Eakins, 2009),
the Moho depth from Spada et al. (2013) and Grad et al. (2009). The
lithosphere asthenosphere boundary (LAB) is a required interface for the
LitMod3D to divide the model between the lithosphere and sublithosphere
and to assign compositions. We introduce a fixed technical LAB at a depth of
100 km throughout the model despite the presence of slabs, as the LAB is
defined as the 1300 ∘C isotherm. This setup avoids the
isotherm following the geometrical shape of the slab, which would lead to a
location in unrealistic large depths (> 200 km). In addition, we
neglect the topography of the LAB for several reasons: (i) the information of
the lithospheric thickness in the Alpine forelands is sparse and under
ongoing discussions, (ii) the fixed depth value is based on thermal isostasy
LAB estimations from Artemieva et al. (2019), which show a LAB depth in the
range of 80 to 120 km depth in the Alpine forelands. This technical LAB is
used to parameterize the model and is not meant to represent the topography
of the LAB. The modelled slab segments are extending vertically downwards.
Slab segments are introduced stepwise for the lithosphere and
sublithosphere domains into the model as well as thermal anomalies for the slab
segment beneath the technical LAB, which describes the 1300 ∘C
isotherm (Table 2). Calculating the difference with the reference model
(M0) allows us to estimate the effect a slab segments has on the density,
temperature distribution of the Alpine subsurface and therefore on the
Alpine gravity field based on slab position, slab geometry and composition.
Different LitMod models and their incorporated lithospheric and sublithospheric structures and compositions.
A positive density contrast between subducting material and the surrounding
mantle material results in a negative buoyancy force. A density contrast is
introduced into the LitMod model by a difference in composition between the
subducting denser slab and the surrounding mantle (Fig. 9). Here, we use
Tecton-like compositions for the lithosphere and the subducting slab
segments since the Alpine slab segments result from continent–continent
collision (Tables 1 and 2). A later model features a Proterozoic slab
composition (M8). Depleted mid-oceanic ridge basalt mantle (DMM) and
primitive upper mantle (PUM) are used for the sublithospheric domain.
In addition to the density contrast within the sublithosphere, a temperature
anomaly of -100 K is introduced for the sublithospheric part. Later
models include a variation of temperature anomalies (M5, M6,
M7). Note those compositions are used as a first-order test and serve
as a starting point for synthetic slab models to illustrate the
compositional and thermal effect on the gravity signal by influencing the
density distribution. They do not necessarily represent the compositional
mantle environment in the Alpine region.
(a) 3-D model set up using LitMod3D. Topography, Moho and LAB depth
as well as the vertical incorporated slab models are used as input layers
with assigned petrophysical and thermal properties. (b) Profile along
11∘ longitude through a LitMod model containing topography,
crustal and lithospheric thickness as well as a slab segment. ρ1-5
indicate petrophysical and thermal property variations for each layer.
Results
The gravity signal of the predefined slab segments is forward calculated as
well as the background model without incorporation of slab segments. The
residual between both forward calculations gives the gravitational
contribution of the slab segments, while other gravitational effects, like
the topography or crustal thickness variation and mantle variations outside
the slab, are not considered.
A slab segment with an average Tecton Gnt. composition (M1, M2)
results in a slightly denser material compared to the surrounding mantle
(M0), while a slab segment with a Proterozoic composition (M8)
shows a less dense lithospheric structure compared to the reference model
(M0); this composition results in less dense slab segment, which would
not be subducted due to the positive buoyancy (Fig. 10). However, we aim to
illustrate the effect composition has on the density distribution within the
slab and to the surrounding mantle and show the importance of correct
compositional information; therefore, we focus on the difference in density
contrast between slab and surrounding mantle and neglecting the sign of the
density contrast.
(a) Density profile at 11∘ longitude and 45∘
latitude for the full vertical model space of 400 km depth. Density profiles
for three different models (M0, M1, M9) with different
compositional properties are shown. (b) Zoomed-in profile at the depth range
of present slab segments.
The difference in density distribution (density contrast) within the slab
segments with a Tecton composition (M1, M3) to the reference
model (M0) is on the order of 5 kg m-3 for the lithosphere and on
the order of 10 kg m-3 for the sublithospheric domain (Fig. 10a). The
density variations within the lithospheric and sublithospheric slab domain
are less than 1 kg m-3 resulting from both depth-dependent variations in
pressure and temperature. Between lithosphere and sublithosphere, a rapid
increase in density contrast is observed (Fig. 10a). The density contrast of
a lithospheric Proterozoic slab composition (M9) to the reference model
(M0) is on the order of -30 kg m-3 (Fig. 10b).
(a) Residual density contrast for lithospheric and
sublithospheric slab segments of model (M3) with Tecton-like composition
within the lithosphere and PUM and DMM composition in the sublithosphere
with an additional thermal anomaly of -100 K
for the sublithospheric slab segment to the background model (M0). (b) Residual
lithospheric density contrast of a Proterozoic lithospheric slab segment
(M8) to a Tecton compositional surrounding mantle (M0). Residual
density contrast is limited to the technical LAB as the sublithospheric
part is identical to the reference model (see also Fig. 9b).
The gravity signal caused by the proposed slab segment configurations is
estimated for lithosphere and sublithosphere separately. The
forward-calculated gravity effect, at topographic surface level, for the slab
Configuration 1 for the lithospheric part is on the order of 4 mGal, while
the sublithospheric gravity signal is in the range of 7 mGal (Fig. 12a, b).
The combined gravity signal is on the order of 12 mGal (Fig. 12c). The
gravity signal in the Eastern Alps for Configuration 2 is significantly
larger on the order of 17 mGal for the combined model (Fig. 12f).
Residual of the forward-calculated gz gravity signal of
lithospheric slabs at surface station height based on LitMod models with
Tecton-like compositions in the lithosphere and PUM and DMM compositions in
the sublithosphere (M1, M2, M3, M4) with an
additional thermal anomaly of -100 K for the sublithospheric
slab segment, for predefined slab configurations to the background model
(M0). (a–c) Configuration 1. (d–f) Configuration 2. Crustal and
topographic contribution are nullified.
The calculated gravitational effect of a slab segment with Proterozoic
composition and a Tecton surrounding mantle composition is on the order of
-40 mGal for the gz component (Fig. 12a).
(a) Forward-calculated gravity effect of a Proterozoic
lithospheric slab segment to a Tecton compositional surrounding mantle for
Configuration 2, obtained by calculating the residual between M8 and
M0. (b) Gravity signal produced by purely compositional effect in the
sublithosphere between a PUM and DMM composition, obtained by calculating
the residual between M5 and M6. (c) Gravity signal produced by
purely thermal anomaly of -100 K for a sublithospheric slab
segment, obtained by calculating the residual between M3 and M6.
(d) Gravity signal produced by purely thermal anomaly of -200 K for a
sublithospheric slab segment obtained by calculating the residual between
M6 and M7.
The gravity response to a compositional variation within the sublithosphere
between the incorporated slab segment (DMM composition) and the surrounding
mantle (PUM composition) is on the order of 4 mGal (Fig. 12b). The gravity
response for a pure thermal anomaly of -100 K within the sublithospheric
slab segment is on the order of 16 mGal (Fig. 12c), while a pure thermal
anomaly of -200 K within the sublithospheric slab segment is on the order
of 21 mGal.
Discussion
The imprint of the gravity response caused by the density distribution based
on direct conversion of seismic velocities (approach 1) is visible; however,
individual and independent slab segments cannot be identified (Fig. 4). The
strength of this approach is that it is fast to implement and can provide a
first-order characterization of the gravity signal and slab geometries of
subducting lithosphere. However, a clear characterization of subducting slab
segments is not possible. First of all, the density model depends on the
resolution and regularization of the seismological model, which can lead to
distortions in the gravity response (e.g. Root, 2020). The method is
dependent on the choice of the conversion factor and might overestimate the
density (see the large negative anomaly in the Ligurian Sea). The conversion
factor is a strong simplification of nature and for such a geodynamic
complex area, a constant conversion factor is not adequate.
The forward-calculated gravity field with competing predefined slab
geometries (approach 2) shows a clear gravity signal, where the individual
slab segments are distinguishable (Fig. 6).
A relative gravity low related to the slab gap in the Eastern Alps is a
prominent feature in the gravity signal of Configuration 1 (Fig. 6a). The
Eastern Alpine slab segment of Configuration 1, due to its relatively small
volume, results in a lower signal compared to the Central Alpine slab
segment.
Configuration 2 shows a larger gravity signal in the Eastern Alps up to
100 mGal (Fig. 6b) compared to Configuration 1. The increase of the gravity
signal is attributed to the subduction of both Eurasian and Adriatic
lithosphere in the Eastern Alps. The gravity signal shows a continuous
transition from the Central Alps to the Eastern Alps, where the contribution
of the destined slab segment cannot be distinguished in the resulting
gravity field (Fig. 6b). In the Western Alps, Configurations 1 and 2 show a
lower gravity signal compared to the Central Alps. This is attributed to the
much shallower Western Alpine slab segment that penetrates down to 100 km
depth.
The gravity signal is influenced by both the assigned density contrast and
thickness of the slab. A trade-off between both parameters is clearly
observable, as the same gravity response of the slab configuration can be
achieved with different values of density contrast and slab thickness,
therefore making it impossible to derive slab properties in the form of density
contrast and slab thickness from the gravity field (Fig. 7).
The calculated densities in LitMod3D models (approach 3) are estimated by
taking temperature and pressure variations into account based on an assigned
composition. The composition has a strong influence on the resulting density
contrast. In the case that the compositional contrast between slab segment
and surrounding mantle is small, the density contrast is consequently small
as well (Figs. 9 and 10a). With increasing compositional differences, the
density contrast increases as well. A strong density contrast within the
slab segment is recognizable between lithospheric and sublithospheric
domains (Fig. 10a and b), while the variations between the slab and
surrounding mantle remain small.
The gravity signal in the Eastern Alps shows a significantly larger signal from
the lithosphere and sublithosphere domains for Configuration 2 (Fig. 11d–f)
compared to Configuration 1 (Fig. 11a–c). The different slab
segments are distinguishable with the exception of the two slab segments in
the Eastern Alps in Configuration 2 (Fig. 11). The contribution from the
lithospheric domain to the gravity signal is smaller than that from the
sublithospheric domain (Fig. 11b and e). However, the slab gap and the eastern
slab segment feature can be recognized in the lithospheric part in
Configuration 1 but not in the gravity signal of the full model.
The Proterozoic slab segment has a larger gravity response compared to the
Tecton-like composition. This gravitational signal is negative due to the
less dense Proterozoic composition in comparison to the reference model
(M0) (Fig. 12a).
Sublithospheric composition has only a small influence on the gravity
field, on the order of 4 mGal (Fig. 12b). However, a thermal anomaly within
the sublithospheric slab on the order of -100 K results in a gravitational
response of 16 mGal (Fig. 12c) and for a -200 K anomaly on the order of
21 mGal (Fig. 12d). Both the composition and the thermal variation influence
the density and consequently the gravity response. However, the thermal
component is a much larger contributor.
For the three approaches (Sects. 3, 4.1 and 4.2), a measurable gravity
effect of the subducting slab segments is observable. The independent slab
segments are distinguishable to a certain degree with the exception of the
bivergent slab configuration in the Eastern Alps (Figs. 6, 11) and the
model containing converted density from seismic velocities (Fig. 4), while
the slab configurations cannot be separated at satellite altitude
(see the Appendix). Forward-calculated gravity anomalies from converted density
distribution suggest a gravitational signal of the slab segments on the
order of 40 mGal, which corresponds to a density contrast of 20 to 40 kg m-3
in the models with predefined slab geometry. The models with a
Tecton-like composition suggest a gravity effect of the slab segments on the
order of only 16 mGal, corresponding to a density contrast of 20 kg m-3
in the simple model. Increasing the compositional difference with a Tecton
composition suggests a gravity signal on the order of 30 mGal and is in line
with the converted density model.
All three methods show a positive gravity signal contribution, which can be
related to subcrustal density variations for approach 1 and to predefined
subcrustal slab segments for approaches 2 and 3, up to 40 mGal to the Alpine
gravity field. That is significant in comparison to the observed Bouguer
anomaly with a minimum of ∼-200 mGal. If this contribution is
not considered, a significant part of the gravity signal is attributed to
crustal thickness or intracrustal sources. Due to the long-wavelength
appearance of the gravity effect which might not be relevant for small-scale
or local studies, the effect is only seen as a shift. For gravity models of
larger areas (e.g. Eastern Alps) or even entire regions, this should not
be neglected. For one, estimates of crustal thickness or the mass
distribution are significantly biased, and placing the Alps in the
geodynamic context of the surroundings requires a careful and complete
consideration of all sources in order to provide the realistic density
distribution required for geodynamic models (e.g. Reuber et al., 2019).
Conclusions
We have addressed the potential gravity effect of proposed slab segments in
the Alpine region using three different modelling approaches.
One approach is converted density from seismic tomography. In the resulting gravity signal,
the imprint of slab segments is visible; however, distinguishing between the
different and independent slab segments is not possible.
Models with predefined slab segments are dependent on the assigned density
contrast and volume as well as on the predefined positions of the slab
segments. The gravity signal caused by the slab segments is sharp and can
be separated for the different slab segments for the gravity field at the
surface. Significant gravity contributions to the Alpine gravity from slab segments below 200–250 km are unlikely.
Another approach involves combining petrophysical–geophysical modelling results in the most complex
models. The calculated density variation within the slab is rather small
compared to the density contrast between lithosphere and sublithosphere.
The density distribution within the slabs, and consequently the gravity
field, is highly influenced by the slab composition and thermal structure.
Subcrustal density variation (approach 1) and predefined slab segments
(approaches 2 and 3) suggest a positive subcrustal gravity contribution of
up to 40 mGal. Even though this might be considered as a maximum gravity
estimation of slabs, this value is significant, even compared to the
observed Bouguer anomaly low of -200 mGal along the Alps. The interpretation
of density variation in the mantle in terms of subducting slab structures is
a means to provide a meaningful representation of the geodynamic complex
Alpine area. For future studies, correct slab density structure is crucial
to provide a representation of the Alpine geodynamic setting. Precise
estimations of the slab density structure require a correct crustal density
and crustal thickness model. With the integration of further observables, it
might be possible to judge the correct slab configuration beneath the
Alps. Furthermore, future studies based on the AlpArray network will be of
high interest in better defining slab geometries as well as their
properties.
Gravity gradients at satellite height
For all Alpine density models presented above (Sects. 3, 4.1 and 4.2), we
have also calculated gravity gradients at a station height of 225 km. This
station height corresponds to the second mission phase of GOCE carried out by ESA.
We anticipated that gravity gradients measured by the GOCE satellite mission
are sensitive to the slab segments in the Alpine region. Our result show
that the long wavelength signal of the different present slab segments
contributes to a large-scale gravity response where the different
contributors cannot be separated. Therefore, we conclude that against our
anticipation gravity gradients at satellite height are in fact not sensitive
to the Alpine slab configuration. We show the gravity gradients here
(mainly the gzz component) for completeness.
Measured gravity gradients from the GOCE mission (Bouman et al., 2016),
which were corrected for topography and bathymetry, range from 2.5 to -2.5 E
at a satellite altitude of 225 km (Fig. A1). A negative gravity anomaly
of -2.5 E in the gzz component is observed equivalent to the vertical gz component (Fig. A2).
However, no clear sign for subducting lithosphere can
be observed in any component of the gravity gradient tensor.
The forward-calculated gzz component at 225 km station height from a density
model (Sect. 3) with converted densities ranges from -3.5 to 0.7 E (Fig. A2).
A positive gravity signal of about 0.5 E in the Apennine and Alpine
regions is observed, which could be linked to subducting slab segments.
However, it is impossible to separate specific slab segments.
Forward-calculated Tesseroid models (Sect. 4.1) for slab Configurations 1
and 2 with a constant density contrast of 60 kg m-3 and a constant
thickness of 80 km result in a less sharp gravity signal for the gzz
component at a station height of 225 km (Fig. A3) compared to the gz
component at station height of 6040 m (Fig. 6). The gravity signal for the
gzz component is in the range of 0.8 to 1 E. At satellite altitude, the
gravity signal is observed as a large area with a positive gravity effect
for Configurations 1 and 2. The contribution of the different slab segments
to this positive gravity effect is not distinguishable. The only
recognizable difference is the size of this positive gravity signal.
Configuration 1 shows a smaller anomaly due to a lower volume of subducting
material in the Eastern Alps.
In addition, the signal strength for the forward-calculated gzz component
shows the same dependency of signal strength to the density contrast and slab
thickness (Fig. A4) as the gz component (Fig. 7). The signal strength of the
gzz component ranges for the 12 different combinations from 0.3 to 2 E
(Fig. A4). The gravity signal cannot be separated and affiliated with a
certain slab segment. The gzz gradient signal shows a large blurry gravity
high over the Alps, which thins out to the edges.
The gravity effect for the LitMod models (Sect. 4.2) with the slab
Configuration 1 shows in the lithosphere domain a signal strength of about
0.05 E, while the sublithospheric gravity signal is in the range of 0.1 E
for the gzz component at a satellite altitude of 225 km. The combined
gravity signal is on the order of 0.14 E (Fig. A5). A Proterozoic slab
produces a larger amplitude in signal strength; however, the different slab
segments cannot be separated again (Fig. A6).
GOCE gradients at 225 km after Bouman et al. (2016)
corrected for topography and bathymetry with a 5∘ extension to
remove far-field effects. The gravity gradients are presented in a
north–east–up coordinate system.
Forward-calculated gzz gravity signal from relative density
distribution converted from relative seismic velocities using a conversion
factor of 0.3 for the 225 km station height.
Forward-calculated gzz gravity signal at a station height of 225 km
from predefined subcrustal slab geometries with a content density
contrast of 60 kg m-3 and a constant thickness of 80 km. (a) Slab configuration of Configuration 1.
(b) Slab configuration of Configuration 2.
Forward-calculated gzz gravity signal for 12 different combinations
of density contrast and slab thickness at a station height of 225 km for
subcrustal slab Configuration 1.
Forward-calculated gzz gravity signal at satellite altitude of 225 km
based on LitMod models with Tecton-like compositions in the lithosphere
and PUM and DMM compositions in the sublithosphere (M1, M2, M3,
M4) with an additional thermal anomaly of -100 K
for the sublithospheric slab segment, for predefined slab configuration to
the background model M0. (a–c) Configuration 1.
(d–f) Configuration 2. Topographic and crustal effects are nullified.
Forward-calculated gravity effect for the gzz component at
satellite height of a Proterozoic lithospheric slab segment to a Tecton
compositional surrounding mantle for Configuration 2 obtained by calculating
the residual between M8 and M0.
Code availability
Tesseroids is available at https://tesseroids.readthedocs.io/en/stable/ (Uieda et al., 2016).
LitMod3D is available at https://github.com/javfurchu/litmod (Fullea et al., 2009).
The generic mapping tools (GMT) is available at https://github.com/GenericMappingTools/gmt/releases/tag/5.4.5 (Wessel and Luis, 2013).
Data availability
The forward-calculated gravity signal models are publicly available through https://nextcloud.ifg.uni-kiel.de/index.php/s/BeRgpioKgAMkZbE, last access: 8 March 2021.
ETOPO1 is available from the National Centers for Environmental Information (https://www.ngdc.noaa.gov/mgg/global/, Amante and Eakins, 2009).
XGM2019 is available through the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/tom_longtime, Zingerle et al., 2020).
MeRE2020 is available from the website of the IRIS Earth models repository (EMC; https://ds.iris.edu/ds/products/emc-mere2020/, El-Sharkawy et al., 2020).
European Moho map can be accessed from https://www.seismo.helsinki.fi/mohomap/ (Grad et al., 2009).
GOCE gravity gradients are available from https://earth.esa.int/eogateway/catalog/goce-global-gravity-field-models-and-grids (Bouman et al., 2016).
Author contributions
ML carried out the gravity modelling, visualized and interpreted the results
and prepared the first manuscript draft. JE supervised the gravity modelling
and interpretation, designed the original research project and handled acquisition of
the financial support for the project leading to this publication and was responsible for
writing (reviewing and editing). TM defined the slab configurations based on
tectonic and seismological knowledge and was responsible for writing (reviewing and editing). AES
created and provided the surface wave tomography model MeRE2020 and was responsible for writing
(reviewing and editing).
Competing interests
The authors declare that they have no conflict of interest.
Special issue statement
This article is part of the special issue “New insights on the
tectonic evolution of the Alps and the adjacent orogens”. It is not associated with a conference.
Acknowledgements
The authors thank the reviewers, Carla Braitenberg and an anonymous referee,
for their valuable suggestions, which helped to improve the manuscript
significantly.
This study is part of the projects “Integrierte 3D Modellierung des Schwere-
und Temperaturfelds zum Verständnis von Rheologie und Deformation der
Alpen und ihrer Vorlandbecken – INTEGRATE” and “Surface Wavefield Tomography
of the Alpine Region to Constrain Slab Geometries, Lithospheric Deformation
and Asthenospheric Flow in the Alpine Region” funded by German Research
Foundation (DFG) in the “Mountain Building Processes in Four Dimensions” SPP.
We thank the developers of open scientific software products which were utilized in
this study: Tesseroids (Uieda et al., 2016), LitMod3D (Fullea et al., 2009;
Afonso et al., 2008) and Generic Mapping Tools (GMT) (Wessel et al.,
2013; Wessel and Luis, 2017).
Financial support
This research has been supported by the Deutsche Forschungsgemeinschaft (grant nos. EB255/7-1 and EB 255/6-1).
Review statement
This paper was edited by Giancarlo Molli and reviewed by Carla Braitenberg and one anonymous referee.
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