Overdeepenings in the Swiss plateau: U‑shaped geometries underlain by inner gorges

Abstract

We investigated the mechanisms leading to the formation of tunnel valleys in the Swiss foreland near Bern. We proceeded through producing 3D maps of the bedrock topography based on drillhole information and a new gravimetric survey combined with modelling. In this context, the combination of information about the densities
of the sedimentary fill and of the bedrock, together with published borehole data and the results of gravity surveys along 11 profiles across the valleys, served as input for the application of our 3D gravity modelling software referred to as PRISMA. This ultimately allowed us to model the gravity effect of the Quaternary fill of the overdeepenings and to produce cross-sectional geometries of these troughs. The results show that 2–3 km upstream of the city of Bern, the overdeepenings are approximately 3 km wide. They are characterized by steep to oversteepened lateral
flanks and a wide flat base, which we consider as a U-shaped cross-sectional geometry. There, the maximum residual gravity anomaly ranges between − 3 to − 4 mGal for the Aare valley, which is the main overdeepening of the region. Modelling shows that this corresponds to a depression, which reaches a depth of c. 300 m a.s.l. Farther downstream approaching Bern, the erosional trough narrows by c. 1 km, and the base gets shallower by c. 100 m as revealed by drillings. This is supported by the results of our gravity surveys, which disclose a lower maximum gravity effect of c. − 0.8 to − 1.3 mGal. Interestingly, in the Bern city area, these shallow troughs with maximum gravity anomalies ranging from − 1.4 to − 1.8 mGal are underlain by one or multiple inner gorges, which are at least 100 m deep (based on drilling information) and only a few tens of meters wide (disclosed by gravity modelling). At the downstream end of the Bern area, we observe that the trough widens from 2 km at the northern border of Bern to c. 4 km approximately 2 km farther downstream, while the bottom still reaches c. 300 to 200 m a.s.l. Our gravity survey implies that this change is associated with an increase in the maximum residual anomaly, reaching values of − 2.5 mGal. Interestingly, the overdeepening’s cross-sectional geometry in this area has steeply dipping flanks converging to a narrow base, which we consider as V-shaped. We attribute this shape to erosion by water either underneath or at the snout of a glacier, forming a gorge. This narrow bedrock depression was subsequently widened by glacial carving. In this context, strong glacial erosion upstream of the Bern area appears to have overprinted these traces. In contrast, beneath the city of Bern and farther downstream these V-shaped features have been preserved. Available chronological data suggest that the formation of this gorge occurred prior to MIS 8 and possibly during the aftermath of one of the largest glaciations when large fluxes of meltwater resulted in the fluvial carving into the bedrock.

Full text

Bandou etal. Swiss Journal of Geosciences (2023) 116:19
https://doi.org/10.1186/s00015-023-00447-y
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Swiss Journal of Geosciences
Overdeepenings intheSwiss plateau:
U-shaped geometries underlain byinner gorges
Dimitri Bandou1* , Fritz Schlunegger1 , Edi Kissling2 , Urs Marti3 , Regina Reber1 and Jonathan Pfander1
Abstract
We investigated the mechanisms leading to the formation of tunnel valleys in the Swiss foreland near Bern. We
proceeded through producing 3D maps of the bedrock topography based on drillhole information and a new
gravimetric survey combined with modelling. In this context, the combination of information about the densities
of the sedimentary fill and of the bedrock, together with published borehole data and the results of gravity surveys
along 11 profiles across the valleys, served as input for the application of our 3D gravity modelling software referred
to as PRISMA. This ultimately allowed us to model the gravity effect of the Quaternary fill of the overdeepenings
and to produce cross-sectional geometries of these troughs. The results show that 2–3 km upstream of the city
of Bern, the overdeepenings are approximately 3 km wide. They are characterized by steep to oversteepened lateral
flanks and a wide flat base, which we consider as a U-shaped cross-sectional geometry. There, the maximum residual
gravity anomaly ranges between − 3 to − 4 mGal for the Aare valley, which is the main overdeepening of the region.
Modelling shows that this corresponds to a depression, which reaches a depth of c. 300 m a.s.l. Farther downstream
approaching Bern, the erosional trough narrows by c. 1 km, and the base gets shallower by c. 100 m as revealed
by drillings. This is supported by the results of our gravity surveys, which disclose a lower maximum gravity effect
of c. − 0.8 to − 1.3 mGal. Interestingly, in the Bern city area, these shallow troughs with maximum gravity anomalies
ranging from − 1.4 to − 1.8 mGal are underlain by one or multiple inner gorges, which are at least 100 m deep (based
on drilling information) and only a few tens of meters wide (disclosed by gravity modelling). At the downstream end
of the Bern area, we observe that the trough widens from 2 km at the northern border of Bern to c. 4 km approxi-
mately 2 km farther downstream, while the bottom still reaches c. 300 to 200 m a.s.l. Our gravity survey implies
that this change is associated with an increase in the maximum residual anomaly, reaching values of − 2.5 mGal. Inter-
estingly, the overdeepening’s cross-sectional geometry in this area has steeply dipping flanks converging to a narrow
base, which we consider as V-shaped. We attribute this shape to erosion by water either underneath or at the snout
of a glacier, forming a gorge. This narrow bedrock depression was subsequently widened by glacial carving. In this
context, strong glacial erosion upstream of the Bern area appears to have overprinted these traces. In contrast,
beneath the city of Bern and farther downstream these V-shaped features have been preserved. Available chronologi-
cal data suggest that the formation of this gorge occurred prior to MIS 8 and possibly during the aftermath of one
of the largest glaciations when large fluxes of meltwater resulted in the fluvial carving into the bedrock.
1 Introduction
1.1 Overdeepenings
Overdeepenings are bedrock depressions with a thal-
weg that is below the base level in the region. Such ero-
sional features have been observed in mountainous areas
and their lowlands that have experienced one or multi-
ple glaciations (Preusser et al., 2010, 2011; Fischer and
Häberli, 2012; Linsbauer etal., 2016; Häberli etal., 2016).
Handling editor: György Hetényi
*Correspondence:
Dimitri Bandou
Dimitri.bandou@unibe.ch
1 Institute of Geological Sciences, University of Bern, Bern, Switzerland
2 Department of Earth Sciences, ETH Zurich, Zurich, Switzerland
3 Landesgeologie Swisstopo, Bern, Switzerland

19 Page 2 of 34
D.Bandou et al.
Overdeepenings, however, have also been reported from
flat areas such as the Midwest of North America (Wright,
1973), northern continental Europe (e.g., Piotrowski,
1997; Krohn etal., 2009), Scandinavia (Clark and Wal-
der, 1994), the North Sea (Moreau etal., 2012; Lohrberg
et al., 2022), and beneath the Greenland and Antarctic
ice sheets (Patton etal., 2016). Most authors have con-
sidered a formation beneath a glacier (e.g., Wright,
1973; Schlüchter, 1989; Preusser et al., 2011; Kehew
et al., 2012; Dürst Stucki and Schlunegger, 2013; Liebl
etal., 2023; Kirkham etal., 2021; 2023), mainly because
these depressions occur below the regional base level,
are closed depressions, and are situated in mountainous
regions far from the influence of sea-level fluctuations.
Although overdeepenings or tunnel valleys have been
reported from a large variety of settings, interpretations
of the processes through which they were carved are still
being contested (e.g., Cook and Swift, 2012; Kirkham
etal., 2022). is is the case because the analysis of the
overdeepenings’ shapes, which potentially contain diag-
nostic information for interpreting the related erosional
processes (Magrani et al., 2020; Gegg and Preusser,
2023), is thwarted as these troughs are buried by sedi-
ments. erefore, the geometries of these troughs have
to be determined indirectly by geophysical surveys or
through drillings. Nevertheless, interpretations range
from the view where overdeepenings were carved by gla-
cial processes with support by englacial and subglacial
meltwater (Egholm etal., 2009; 2012; Herman and Braun,
2008; Herman etal., 2011; Beaud etal., 2014; Liebl etal.,
2023) particularly for cases where they have a U-shaped
cross-sectional geometry characterized by a flat base and
steep lateral flanks (Kehew etal., 2012). Alternative inter-
pretations point to the importance of overpressurized
subglacial meltwater as erosional process, where a con-
tinuous (Smed, 1998; Huuse and Lykke-Andersen, 2000;
Praeg, 2003; Cohen et al., 2023) or episodic outburst of
water from beneath the snout of glaciers (Wright, 1973;
Piotrowski, 1994; Björnsson, 1996; Clayton etal., 1999;
Beaney, 2002; Shaw, 2002; Jørgensen and Sandersen,
2006) could contribute to the carving into the bedrock.
e result is a cross-sectional geometry that is V-shaped,
where the flanks are steep and converge at depth to a
narrow, approximately < 20 m wide base. e meltwa-
ter origin hypothesis bases on Bernoulli’s principle (e.g.,
Batchelor, 1967), where at the glacier’s snout a decrease
in the ice thickness leads to large drops in hydrostatic
pressures, which translates into hydrodynamic pres-
sures and thus into erosional work, under the condition
that the subglacial channel network is a closed system.
In either cases, most studies converge to the notion
where glacial carving yields tunnel valleys with U-shaped
cross-sectional geometries, whereas erosion through
overpressurized subglacial meltwater preferentially
returns V-shaped incisions.
1.2 Overdeepenings intheSwiss plateau andaim ofpaper
e Swiss Plateau, which is located on the northern side
of the Alps, hosts several well-studied tunnel valleys and
overdeepenings (Moscariello etal., 1998; Preusser etal.,
2010; Horstmeyer etal., 2012; Dürst Stucki and Schluneg-
ger, 2013; Schnellmann and Madrisch, 2014; Magrani
etal., 2020; Anselmetti etal., 2022; Gegg and Preusser,
2023), which have been analysed through seismic and
gravity surveys and sedimentary archives encountered in
drillings (Kissling and Schwendener, 1990; Rosselli and
Raymond, 2003; Dehnert etal., 2012, Buechi etal., 2017a,
b; Jordan, 2010; Dürst Stucki etal., 2010; Schnellman and
Madritsch, 2014; Reber and Schlunegger, 2016; Gegg
etal., 2021; Schwenk etal., 2022a, 2022b; Bandou etal.,
2022). In this context, three hypotheses have been pro-
posed to explain the origin of these troughs in the Alpine
region. As a first mechanism, it was considered that flu-
vial erosion could have caused the formation of narrow
gorges, which were subsequently widened by glacial
carving (Kissling and Schwendener, 1990). As a second
origin, it has been proposed that the tunnel valleys were
carved with support by overpressurized meltwater (Dürst
Stucki and Schlunegger, 2013; Cohen etal., 2023). How-
ever, as noted above, this mechanism requires a hydro-
logically closed system, which might be challenged by the
relatively large permeabilities usually measured for the
Molasse bedrock (Keller etal., 1990) that underlies these
troughs, at least in the Swiss Plateau. Finally, glacial carv-
ing through bedrock abrasion or quarrying could offer
a third mechanisms to explain the formation of these
troughs (Herman etal., 2011, Sternai etal., 2013). e
resulting erosional shapes are usually U-shaped, because
the glaciers’ viscosities result in the translation of some
of the vertical pressure gradients towards the lateral sides
through dislocation creep, thereby widening the incisions
(Cuffey and Paterson, 2010; Alley etal., 2019).
In this contribution, we aim at assessing the ero-
sional processes resulting in the formation of the over-
deepenings with a focus on the system in the Bern area
situated on the northern margin of the Swiss Alps.
Admittedly, the geometry of the overdeepenings in the
Bern region has already been reconstructed by Reber
and Schlunegger (2016) at a high level of details based
on thousands of drillings. Yet due to a lack of deep
drillings in the center of the channels, the accuracy
of the existing bedrock topography model is limited
particularly for the deeper levels. Therefore, given the
success in applying gravity surveys for disclosing the

Page 3 of 34 19 Geometry of Overdeepenings in the Alps
geometry of overdeepenings in previous contributions
(Kissling and Schwendener, 1990; Rosselli and Ray-
mond, 2003; Perrouty etal., 2016; Bandou etal., 2022),
we collected additional gravity data from the over-
deepening system in the Bern area to retrieve more
information particularly on the geometry of the lateral
flanks and the basal parts of this trough. We then com-
plemented the results of our gravity survey with a syn-
thesis on existing chronological data about the valley
fill to reconstruct the history of overdeepening forma-
tion in this area, and to infer the mechanisms through
which these troughs were formed.
2 Setting
e overdeepening system of the Bern area (Fig. 1),
which is the focus of the study, was previously uncov-
ered by thousands of shallow drillings that were sunk
into the subsurface for engineering purposes (Reber
and Schlunegger, 2016; Fig.2). is resulted in a level of
details that has been unprecedented so far for an over-
deepening system. e available bedrock topography
map (Reber and Schlunegger, 2016) shows that in the
upstream area south of Bern, the tunnel valley system
consists of two overdeepenings referred to as the Gürbe
and the Aare overdeepening (Fig.2). ey are separated
Fig. 1 Geological map taken from Swisstopo (Gerber, 1927), showing the pattern of the surface geology and the location of the drillings
and sections (stars on the figure), which provided key information for this work. These are the Brunnenbohrung Münsingen (Kellerhals
and Häfeli, 1984), the Rehhag Drilling (Schwenk et al., 2022a, b) and the Neubrügg section (Lüthy et al. (1963), for which limited information
about the chronological framework for the Quaternary sediments is available. We also used constraints offered by the Forstschotter gravel pit,
the drilling RB 9201 (Kellerhals and Isler, 1983; Geotest, 1995) and that of the Hunzigebrügg (Zwahlen et al., 2021). Modified after Beck and Rutsch
(1949), Spicher (1972) and Bandou et al. (2022). The map also shows the various sections we analysed through a gravimetric survey only (dashed
blue lines) and through a combination of a gravity survey and modelling (blue lines). These are the following profiles: (1) Bümpliz, (2) Bremgarten,
(3) Bern1, (4) Bern2, (5) Bern3, (6) Bern4, (7) Wabern1, (8) Wabern2, (9) Kehrsatz and (10) Airport. The Gürbe valley—Belpberg—Aare valley profile (11)
was already published in a previous contribution (Bandou et al., 2022)

19 Page 4 of 34
D.Bandou et al.
by a bedrock ridge made up of Early Miocene Upper
Molasse sandstones (Fig. 1). ese two troughs, which
are c. 1.5 km (Gürbe) and approximately 2.5 km-wide
(Aare overdeepening or Aare channel) and c. 160 m
(Gürbe) and 270 m deep (Aare), converge c. 10 km south
of Bern to one single depression that is c. 3 km wide and
that strikes SE-NW (Figs.1 and 2). is single depression,
which is still > 1 km wide beneath Bern, transitions into
a wider basin with side channels striking SW-NE that
connect to the main basin c. 2km NW of Bern (Reber
and Schlunegger, 2016; see Fig.2). e largest of these
side troughs was referred as the Bümpliz channel (Fig.2)
and was explored through the Rehhag scientific drill-
ing (Figs.1, 2) by Schwenk etal., (2022a, b). is drill-
ing reached the bedrock at 362 m a.s.l. (Schwenk etal.,
2022a), which corresponds to a drilling depth of 210m.
Age constraints on the overdeepening fill are provided
by three sections. ese are the deposits encountered in
Fig. 2 Map showing the bedrock topography of the Bern area with 10 m-contour lines. The map was reproduced using the openly accessible
digital dataset for the bedrock topography of the canton Bern (https://www.geo.apps.be.ch/de/;Karten;Felsrelief), and it is also available
from the openly accessible database of swisstopo (© swisstopo). This dataset was originally produced by Reber and Schlunegger (2016). The
map also displays the drillings that reached the bedrock (red dots). Most of the drillings, however, did not reach the bedrock and yield minimum
constraints on the depths of the overdeepening contour lines (green dots). The blue dots illustrate the location of the gravity stations that are
used in this study. The map also shows the profiles (in yellow) that were analyzed for the measured gravity signals (see legend of Fig. 1 for labels).
Modified after Bandou et al. (2022)

Page 5 of 34 19 Geometry of Overdeepenings in the Alps
the Aare overdeepening (Brunnenbohrung Münsingen,
Fig.1) providing an age between MIS 6 and 2 (Kellerhals
and Isler, 1983; Kellerhals and Häfeli, 1984; Zwahlen etal.,
2021; Bandou etal., 2022). Another age constraint was
established for a temporary outcrop on the downstream
end of the main overdeepening where a cliff on the SW
margin of the Aare River (Neubrügg section, Fig. 1)
exposes a suite of Quaternary sediments. is succession
consists of a till at the base and the top of the section,
which were referred to as ‘Riss’ and ‘Würm’ moraines by
Lüthy etal. (1963). e succession also includes a sand
and a gravellayer with pollen fragments in the sand layer.
Lüthy etal. (1963) did not assign a precise age to this lat-
ter unit, but they considered that the pollen fragments
(mainly from spruce and beech)couldrecord the end of
awarm period (end ofMIS 5e?). Recently, age constraints
were presented by Schwenk etal. (2022a) for the Quater-
nary infill of the Bümpliz tributary trough (Fig.1; Rehhag
drilling) based on optically stimulated luminesce (OSL)
data measured for quartz minerals (Schwenk, 2022,
Schwenk etal., 2022a). is information points towards
a minimum age of MIS 8 approximately between 300′000
and 250′000 years before present. To the SW of the
Rehhag drilling, a thick gravel referred to as Forstschotter
(Figs.1, 2 and 3), forms a cap unit, which was tentatively
assigned to the MIS 6 by Schwenk etal. (2022a) based on
its morphostratigraphic and lithostratigraphic position.
South of the Bern region the bedrock comprises several
100m-thick packages of Late Miocene sandstones, which
have been referred to as the Upper Marine Molasse
(OMM; German abbreviation) in the regional litera-
ture (Beck and Rutsch, 1949) and which also constitute
an important sediment source for the overdeepening fill
(Schwenk etal., 2022b). In the area of the city of Bern and
farther north, the bedrock consists of an alternation of
sandstones and mudstones. ese deposits are part of the
Lower Freshwater Molasse (USM; German abbreviation)
and underlie the OMM (Isenschmid, 2019). In the city of
Bern, the Molasse bedrock is dissected by transtensional
NW–SE striking faults (Isenschmid, 2019).
3 Methods
Following Kissling and Schwendener (1990) and Ban-
dou etal. (2022) we determined the change of the shape
of the overdeepenings along a series of profiles where
gravity data was acquired in the field (Sect.3.1), because
such information is most diagnostic for the erosional
mechanism at work (Preusser etal., 2011; Magrani etal.,
2020). In this context, the reconstruction of the cross-
sectional bedrock topography requires that for each
profile, the Bouguer gravity values (Sect. 3.2) and par-
ticularly the gravity contribution of the overdeepening
fill (the so-called residual anomaly values, Sect.3.3) will
be determined. Such information is then used to deter-
mine the wavelength of the main trough, and it will be
employed to identify the gravity effect of secondary over-
deepenings and/or geological structures either at the
lateral flanks of the profiles or beneath them. As a sub-
sequent step, we used a forward modelling approach to
compute the gravity effect (Sect.3.4) of the overdeepen-
ing fill thereby approximating the geometry of these bed-
rock troughs by prisms (Kissling and Schwendener, 1992;
Bandou etal., 2022). e modelling and the subsequent
visualization of the modelling results requires that coor-
dinates have to be transformed from the Swiss to a local
coordinate system (LCS, Sect.3.3).
3.1 Collection ofgravity data intheeld
We collected gravity data along 10 new sections (Figs.1,
2), which are between 2 and 6 km long and have a spac-
ing that ranges between 2 and 1km. e gravity data of
Sect.11 (Fig.2) was already processed and discussed by
Bandou etal. (2022), the results of which we include in
this paper. We particularly place our sections where the
lateral boundary of the target overdeepening is con-
strained by shallow Molasse bedrock (< 5m according to
Reber and Schlunegger, 2016) on either profile end and
where thus no significant gravity effect of the overdeep-
ening fill is expected. Upon collecting gravity data, we
selected a spacing between the newMPs (measurement
points) that ranges from 50 to 200 m. Yet some MPs were
separated by a longer distance (c. 400 to 600m) particu-
larly where the terrain (e.g., dense forest, cliffs, private
properties, train stations, tracks, highways etc.) precludes
a more densely-spaced survey. For each site, we locally
selected a point where the coordinates are placed exactly
between the cells of the 2m SwissAlti3D DEM (Digital
Elevation Model; see Fig.3). is allowed us to measure
the elevation in the middle of the four cells surround-
ing the station (Bandou, 2023a). At these sites, we meas-
ured the GNSS coordinates including the elevations that
were taken in the Swiss LV95 system. is was done to
best account for the effect of the near field topography on
the gravity signal while also taking advantage of the 2m
DEM.
For the gravity measurements, we employed the
Swisstopo Scintrex CG5 gravimeter, which has a pre-
cision of 0.001 mGal. At each location, we measured
the gravity signal through 8 cycles of 45 s each. e
instrument was then taking a total of 1000 measure-
ments per cycle. We deemed the measurements stable
and yielding an acceptable result if the gravity values
of the last four cycles were within the uncertainty of
±0.001 mGal, which is the reading resolution of the
gravimeter. We then used the average value of the 4
last cycles for further processing. Before and after each

19 Page 6 of 34
D.Bandou et al.
day of measurement, we measured the gravity values
at either the gravity station of Metas that we used as
a base (2′601′930.5, 1′197′018.2, Swiss coordinates)
or in the basement of the Institute of Geological Sci-
ences (2′599′200, 1′200′060, Swiss coordinates) to
correct the instrumental drifts. A drift rate per hour
was calculated linearly (Scintrex, 2012; see discussion
in Yu etal. (2015), and Meurers, 2018), which was used
to correct the daily measurements. Outliers caused by
earthquakes, motorized and pedestrian traffics, bikes,
and the gravimeter’s instability after transport were
identified in the field. e related information was
taken from the live gravity readings and the difference
between the average values of each cycle (including
jumps of a few mGal between them and trends in the
collected gravity data). e resulting average drift rate
was c. 0.011 mGal/h with a maximum and a minimum
drift rate of c. 0.015 and 0.005 mGal/h, respectively.
Fig. 3 Modern topography from the SwissAlti 3D DEM ( © swisstopo) with gravity profiles and gravity data from the Gravity Atlas of Switzerland,
modified from Bandou et al. (2022). The map also shows the Bouguer anomaly contour lines and the locations of our stations (blue dots) and those
of key drillings (stars). The map and the contour lines are from the openly accessible database of swisstopo (‘Carte gravimétrique de la Suisse
(Anomalies de Bouguer) 1: 500,000, © swisstopo; Olivier et al., 2008; 2011). The yellow line shows the locations of our profiles (yellow lines, see
legend of Fig. 1 for explanation of labels). The gravity values at the green and brown stations are available from the swisstopo database. The data
of the brown stations were collected in the framework of various projects, and they are now integrated in the Gravity Atlas of Switzerland. Note
that the contour lines were derived from the green stations only

Page 7 of 34 19 Geometry of Overdeepenings in the Alps
3.2 Calculation oftheBouguer gravity values
We used the swisstopo software Quawirk (available
from swisstopo upon request and described in Bandou,
2023a) and a standard density of 2670 kg/m3 (LaFehr,
1991; Bernabini et al., 1994; Holom and Oldow, 2007)
to correct the measured gravity data for gravity signals
related to elevation, tides (Hinze etal., 2005) and for the
effect of the topography on the gravity values (Bandou,
2023a). We also considered the gravity signal related
to the near-field topography using the high-precision
GNSS data and the SwissAlti3D DEM with a resolution
of 2 m as a basis (protocol available in Bandou, 2023a).
We then obtained the Bouguer anomaly value at each
MP (measurement point, Additional file1: Appendix A)
upon subtracting these contributions and the normal
gravity (according to international reference gravity for-
mula; Hinze etal., 2005) from the measured gravity data.
Bandou etal. (2022) estimated a maximum uncertainty
of ±0.13mGal through repeated gravity and GNSS meas-
urements, which we generally employed in this work (to
be on the conservative side). However, our average grav-
ity uncertainty including the contribution of the gravity
signal related to the near-field topography is ±0.04 mGal,
estimated again through repeated measurements of the
same station (Additional file 1: Appendix A and Ban-
dou, 2023a). We always show both values either through
the size of the error bars or that of the blue circles (e.g.,
Fig.4).
3.3 Projection ofdata anddetermination oftheresidual
anomalies
As mentioned above, the measured gravity stations fol-
low as much as possible the course of the profiles though
due to logistic conditions some deviations could not be
avoided. For interpretation purposes (derivation of resid-
ual anomalies and gravity modelling) the Bouguer gravity
values of all stations belonging to a profile were projected
perpendicularly onto the profile (Additional file 3:
Appendix C). We deviated from this strategy for the
profile across the Bümpliz channel where due to logistic
reasons the gravity profile had to be placed obliquely to
the orientation of the overdeepening’s long axis (Sect.4.1
and Additional file3: Appendix C and Additional file4:
Appendix D). Note that for the derivation of residual
anomalies and subsequent modelling we ignored stations
that are several hundreds of meters off the target profiles.
e residual anomaly corresponds to the effect caused
by the mass of a local structure, which, in our case, is the
fill of an overdeepening or the effect of a mountain ridge
where the bedrock density is different from the standard
2670 kg/m3 used for the Bouguer anomaly calculations
(Fig.4). Note that while principally the Bouguer gravity
effect may show the signal of a local excess or a deficit of
mass, in our study region we only expect negative anom-
alies from the overdeepenings as the densities of their
infill is lower than that of the Molasse bedrock (Ban-
dou etal., 2022). In this context, Schwenk etal. (2022a)
reported differences in the densities between the over-
deepening fill and the Molasse bedrock that range from
−300 to –400kg/m3, whereas Bandou etal. (2022) used
the Nettleton method to determine a density difference
of –500kg/m3. ese values are in excellent agreement
with the results obtained by Kissling and Schwendener
(1990) for the sedimentary fill of an overdeepening in the
Ticino valley.
e residual gravity anomaly is obtained by calculating
the difference between the gravity gradient of the region
of interest and the local Bouguer anomaly values along
the profile. erefore, as a first step, we determined the
general regional gravity gradient based on the data of the
Gravimetric Atlas of Switzerland. We complemented this
data by using the results of our own survey, which has a
higher spatial resolution along the profiles (Fig.3). Fig-
ure4 shows the procedure from a conceptual point of
view. In this example, an overdeepening with a lake infill
and a flat surface is laterally bordered by two mounds
Fig. 4 Example of how the residual anomalies were determined, using the Bümpliz profile as an example. a The target overdeepening
with a Quaternary fill occurs beneath a generally flat surface. It is flanked by a surface topography on either side, which is underlain by Molasse
bedrock on the SSE margin, and by a glacial till on the NNW side. b We determined the regional gravity gradient using the measured gravity
values (blue dots, where the size of a dot corresponds to an estimated average error of ±0.04 mGal while the maximum uncertainty of ±0.13
mGal is shown by error bars, see text) on the lateral boundaries of our target overdeepening. c The residual gravity anomalies are determined
through calculating the difference between the regional gravity gradient and the measured Bouguer anomalies. Because the Bouguer anomalies
were calculated with a standard density of 2670 kg/m3, a positive surface topography made up of Molasse bedrock with a density of 2500 kg/m3
will yield negative residual anomaly values. Such a signal would disappear if a correction with a density difference of − 170 kg/m3 would be applied
(difference between the standard Bouguer density of 2670 kg/m3 and that of the Molasse bedrock according to Bandou et al., 2022). On the NNW
boundary, the positive topography underlain by Quaternary sediments with a density of 2000 kg/m3 also yields a negative residual anomaly signal,
which could be removed if a correction with a density of − 670 kg/m3 would be applied (difference between the standard Bouguer density of 2670
kg/m3 and that of Quaternary sediments). If the overdeepening fill would be replaced by Molasse bedrock, then the residual gravity anomaly signals
would also disappear. Accordingly the mass of the Quaternary fill causing the negative gravity anomaly signals can be estimated through modelling
thereby using information about the density difference between the Molasse bedrock and the Quaternary fill
(See figure on next page.)

19 Page 8 of 34
D.Bandou et al.
Fig. 4 (See legend on previous page.)

Page 9 of 34 19 Geometry of Overdeepenings in the Alps
underlain either by Molasse bedrock or by a Quaternary
till (Fig.4a). e gravity values measured at the lateral
borders of the overdeepening were then used to constrain
the course of the regional gravity gradient (Fig.4b). e
consolidated Molasse sediments (either Lower Fresh-
water Molasse or Upper Marine Molasse, Isenschmid,
2019) has a bulk rock density of 2500 kg/m3 (Bandou
etal., 2022) that is smaller than the standard 2670 kg/m3
value used for Bouguer corrections. erefore, a positive
topography underlain by Molasse sediments will have
a negative residual signal. e same is also valid for a
positive topography, which is underlain by Quaternary
sediments with density values where the contrast to the
standard density is even higher (−670 kg/m3 according
to Bandou etal., 2022). Accordingly, a negative residual
anomaly can either be related to a signal caused by the
overdeepening fill and/or by a hill made up of Molasse
bedrock and/or Quaternary sediments (Fig. 4c). Such
patterns will be considered upon designing the modelling
strategy (see Sect.3.4).
3.4 Gravity modelling using PRISMA
All of our modelling of the residual anomalies has been
accomplished using the PRISMA routine (Bandou,
2023b) that was developed and tested in Bandou et al.
(2022). is program allows for the forward modelling of
the gravity effects of subsurface objects at freely distrib-
uted points (e.g., Nagy, 1966). e routine uses a series
of right-angled prisms (they appear as rectangles in the
cross-sections, Fig. 5) to approximate the geometry of
the structures of interest (Nagy, 1966; Banerjee and Das-
Gupta, 1977; Kissling, 1980; Karcol and Pašteka, 2019),
and it calculates the related gravity effects in a right-
handed local Cartesian coordinate system (LCS) with the
z-axis towards the Earth’s centre. For a successful applica-
tion of the PRISMA routine, we thus had to define a LCS
(see Additional file3: Appendix C for transformation of
coordinates for the case of the Bümpliz profile, which is
Sect.1 on Fig.1) where the LCS y-axis follows the gen-
eral direction of the overdeepening and where the x-axis
crosses the valley at a right angle. Note that the gravity
profiles running more or less perpendicularly to the val-
ley will normally show small angles to the direction of the
LCS x-axis (see examples in Additional file4: Appendix
D). We then projected the location of the station with
the maximum residual anomaly onto the profile to define
the origin of the LCS to facilitate the subsequent forward
modelling steps. Note that this site will also represent the
origin in the cross sections (point zero) where we present
the modelling results (e.g., Fig.6c). Note also that the cal-
culation of the gravity effect is fully 3D, yet for illustra-
tion purposes we projected the results onto the profile.
Prior to modelling, we positioned the prisms parallel
to the overdeepenings’ flanks using the contour lines of
the Reber and Schlunegger (2016) bedrock model and the
cross-sectional shape of the residual anomalies to organ-
ize and place the prisms at greater depths. In the same
sense, the lengths of the prisms are defined using apri-
ori information offered by the existing bedrock topog-
raphy model and drillings (Additional file 2: Appendix
B). Bandou etal. (2022) documented that prisms with a
distance > 1.5km from the profile will not increase the
modelled gravity signal beyond the uncertainty of our
field surveys. We therefore used prisms with such a maxi-
mum length upon modelling. Note that this is only the
case if the prism can be freely extended in the valley (e.g.,
the Bremgarten profile, see below). In the case where the
overdeepening is meandering, as is the case for the Büm-
pliz channel (Sect.5.1), we set a limit to the prism where
the bedrock turns.
Upon modelling, we started with a series of first prisms
using the a priori information offered by the bedrock
(See figure on next page.)
Fig. 5 Example (Bremgarten profile, Sect. 2 on Fig. 1), illustrating of how we proceeded upon modelling. a The first models were accomplished
considering all drilling information and assigning a bulk density of 2000 kg/m3 to the Quaternary fill of the main overdeepening and to the
positive topography on the lateral margin of the overdeepening, particularly if these topographies are overlain by Quaternary sediments.
For the Bremgarten profile, such a first model shows that the residual anomaly on the NE margin is well reproduced by the model, whereas
the model largely overestimates the residual anomaly signal of the main overdeepening. b The use of a bulk density of 2000 kg/m3
for the uppermost part of the Quaternary fill (constrained by the good fit between the modelling results and the measured residual anomalies
on the NE margin) and a slightly higher density of 2150 kg/m3 for the lower part of the section (constrained by the data from the Rehhag
drilling in Schwenk et al., 2022a) improves the fit between the modelling results and the measured residual anomaly values. However,
the model still overestimates the gravity signal related to the Quaternary fill of the overdeepenings. Note that we also assigned a density
of 2000 kg/m3 for the Quaternary masses forming the topographies on either side of the trough. c Improvements upon fitting the modelled
signal with the measured values were only possible if the widths of the prisms were reduced. We did not further increase the bulk density
of the Quaternary fill because this would not be consistent with the density values measured for the Rehhag core by Schwenk et al. (2022a). In
addition, such a model would predict a maximum depth for the Molasse bedrock, which would be much lower than the constraints offered
by drilling information. The red broken line illustrates the bedrock topography of the model by Reber and Schlunegger (2016). The blue dots are
the gravity stations, the red diamonds indicate drillings that reached the bedrock. The black rectangles show the cross sections of the prisms used
for modelling. The red star denotes the projected location of the Forsthaus drilling (see Figure D.3.1 for location) Additional file 4:

19 Page 10 of 34
D.Bandou et al.
Fig. 5 (See legend on previous page.)

Page 11 of 34 19 Geometry of Overdeepenings in the Alps
topography model of Reber and Schlunegger (2016) and
the drillings close to the section. We also considered pub-
lished data on the density contrasts between the Quater-
nary fill and the Molasse bedrock in the region (Bandou
etal., 2022; Schwenk etal., 2022a). e subsequent steps
included adding more prisms and adjusting their geom-
etries to better approximate a more complex geometry.
For the Bremgarten profile, for instance, the use of a
Fig. 6 The Bümpliz profile. a Bouguer anomalies and regional trend of the gravity field along the profile. The blue dots represent the stations
where gravity data was collected for this study. See Additional file 4: Figure D.2.1 for location of stations, Additional file 1: Appendix A for gravity
data and Additional file 2: Appendix B for information on the drillings. b Results of the final model for the Bümpliz profile, made with a total of 8
prisms with a density contrast of − 500 kg/m3 for the top prism and − 350 kg/m.3 for the rest of the prisms. The blue dots represent the observed
residual anomaly (the dot size corresponds to the average uncertainty of ± 0.04 mGal), and the orange dots are the modelled residual anomaly
values for model 8. The black bars indicate our maximum uncertainty of ± 0.13 mGal. The light blue line highlights the main anomaly. c Elevation
(SwissAlti3D 2 m DEM (© swisstopo)) along the profile (blue solid line). The red broken line illustrates the bedrock topography of the model
by Reber and Schlunegger (2016). The blue dots mark the locations of the gravity stations, the red diamonds indicate drillings that reached
the bedrock. The black rectangles show the cross sections of the 8 prisms used for modelling. The red star is the projected location of the Rehhag
drilling (see Additional file 4: Figure D.2.1 for location)

19 Page 12 of 34
D.Bandou et al.
bulk density of 2000kg/m3 for the Quaternary sediments
(which corresponds to a density contrast to the Molasse
bedrock of –500kg/m3) and the full consideration of all
drilling information allows to reproduce the measured
gravity signal along the NE margin of the profile where
the topography is underlain by Quaternary sediments.
Yet this strategy yields a gravity signal where the wave-
lengths and amplitudes are too large particularly in the
middle of the overdeepening (model 2 on Fig. 5a). e
assignment of a larger bulk density of 2170 kg/m3 to the
lower part of the overdeepening fill (following Schwenk
et al., 2022a) in combination with the consideration of
all drilling information (model 3 on Fig.5b) reduces the
wavelengths and amplitudes of the resulting gravity val-
ues, but the modelled signals are still too large. A fur-
ther increase in the bulk density of the Quaternary fill
would reduce the maximum amplitude of the modelled
gravity signal, but the wavelength of the gravity signal
particularly for the deepest part would still be too large
compared to the observed residual anomalies. Subse-
quent adjustments where the widths of the prisms were
continuously decreased particularly at greater depths,
and where the maximum thickness of the overdeepening
fill was maintained (as constrained by a drilling, red star
on Fig.5) resulted in an acceptable fit of the modelling
results with the observed residual anomalies (Fig.5c). We
already mention here that some drilling information will
not fit with the results of the model that best reproduces
the measured gravity. is is because drilling provide
very local information, while gravity records the effect of
the total mass of the Quaternary infill, as documented in
Fig.5. Moreover, due to the complex geometries of the
troughs (such as meanders and V-shaped deep incisions),
the cross-sectional solutions that we will present below
illustrate the general architecture of the troughs on either
side of the profiles rather than the local details. All mod-
elling results can be found in Bandou (2023a)and Ban-
dou etal. (2023).
4 Results andInterpretation
4.1 The Bümpliz prole (Sect.1 onFig.1)
e gravity data along the Bümpliz profile is charac-
terized by a negative main anomaly with a maximum
amplitude of –1.7 mGal between the profile distances
of 1800m and 3400m (Figs.6a, b) where the estimated
regional gravity gradient matches with the locally
observed gravity (Additional file4: Appendix D.2). is
main anomaly documents an asymmetric V-shaped
bedrock depression. e SSE flank of the depression is
steeper (> 55°) than its NNW counterpart (< 20°) where
the bedrock reaches nearly the surface at a distance
of c. 800m from the deepest point of the depression
(Fig.6c). Near the profile distance 2500m the depth of
the bedrock is apriori known from the results of the
Rehhag drillhole (Schwenk etal., 2022a). On the SSE
side, the main gravity anomaly is bordered by a side
anomaly (Fig.6b), which is most likely caused by the
surface topography and the effect of the Lower Fresh-
water Molasse bedrock forming a positive topography
at the SSE margin of the profile (e.g., Fig.4). In addi-
tion, possible effects related to the Quaternary fill of a
bedrock channel aside of the targeted cross section (see
Reber and Schlunegger, 2016) could also contribute to
this secondary anomaly.
For the first model, we employed a set-up that cor-
responds to a U-shape geometry thereby incorporating
the geometry from the existing bedrock model (Reber
and Schlunegger, 2016, red broken line in Fig.6c), and
we considered an asymmetry that is characterized by
a much steeper SSE flank compared to the NNW side.
Schwenk etal. (2022a) inferred density contrasts rang-
ing from c. –270kg/m3 to c. −420kg/m3 between the
overdeepening fill and the Lower Freshwater Molasse
bedrock based on the results of measurements with
a Multi Sensor Core Logger (MSCL; Geotek Ltd.).
Accordingly, we started with a model where we used
a value of −300 kg/m3 as a first estimate for charac-
terizing the density contrast between the Quaternary
deposits and the Lower Freshwater Molasse bedrock.
ese initial results show that the wavelength of the
modelled main anomaly is too wide and extends too
far towards the flanks compared to what the grav-
ity the data implies (Additional file4: Appendix D.2).
Subsequent improvements included a shift towards a
V-shaped cross-sectional geometry and density con-
trasts of −500 kg/m3 and −350kg/m3 (average den-
sity value taken from Schwenk etal., 2022a) between
the Molasse bedrock and the uppermost few meters
of the overdeepening fill, and for the Quaternary suite
at deeper levels, respectively. Note that according to
Schenk et al. (2022a), the material with a bulk den-
sity of 2150kg/m3 (material with a density contrast of
−350kg/m3 to the Molasse bedrock) has a depositional
age of MIS 8 and thus experienced the compaction
due to several 100m-thick ice bodies during at least 2
major glaciations.
We iteratively adjusted the model geometry on the
lateral flanks (Additional file 4: Appendix D.2) until a
best-fit between the modelled and measured residual
anomalies was reached. e final model (Fig.6c) is char-
acterized by a V-shaped cross-sectional geometry with
a > 60° steep flank on the SSE margin and a gently dip-
ping flank (< 15°) on the opposite side. In addition, the
overdeepening reaches a depth level of c. 350m a.s.l. See
Sect.5.1 for more information.

Page 13 of 34 19 Geometry of Overdeepenings in the Alps
4.2 The Bremgarten prole (Sect.2 onFig.1)
For the Bremgarten profile, we observe a main wave-
length anomaly with a maximum amplitude of c. −2.5
mGal that is most likely caused by the sedimentary fill
of the tunnel valley, and two short-wavelength and low-
amplitude local anomalies on either side of the main
residual gravity anomaly (Fig.7). In the main trough, the
residual anomalies point towards a strong asymmetry
between the NE and SW valley flanks, with the latter also
having a more complex geometry. e base of the over-
deepening seems to be narrow and V-shaped, steeper
on the SW side than on the NE. Further up, the through
widens with both flanks now seemingly having a simi-
lar slope, before the occurrence of a plateau on the SW
side creating a much wider upper part. On the other side,
the NE flank seems to keep a more uniform slope until
the near surface. Figure7 thus clearly defines the tunnel
valley residual anomaly wavelength along the profile of
approximately 3.8km.
Upon modelling the gravity signal of the main anomaly
(Fig.5), we found that the residual anomalies along the
Bremgarten profile can best be explained by the sedi-
mentary fill where the upper part has a lower density
than the basal part. is confirms the asymmetry of the
two flanks: e NE flank is wide and U-shaped, while the
SW flank has multiple steps and apparently a large pla-
teau in the shallower part of the trough (Figs.5c, 7b). e
geometry documents at least three main storeys, a wide
U-shaped upper section and a narrower and steeper mid-
dle storey especially on the SW flank. In addition, the
lowermost part is narrow and V-shaped (Fig.7c). All sto-
reys appear to be separated by a kink in the pattern of
the residual gravity anomalies. Note that because of the
complex geometry of the overdeepening network (con-
vergence between main and the Bümpliz channel), and
since the main channel might be shallowing-up and nar-
rowing towards the NW (Fig.2, Reber and Schlunegger,
2016), the drillings on the SW flank are not fully repre-
sentative of the general architecture of the overdeepen-
ing in the vicinity of the profile that is captured by gravity
information.
4.3 The Bern1 prole (Sect.3 onFig.1)
e gravity data along the Bern1 profile is character-
ized by a negative main anomaly between the profile
distances of 650m and 3100 m (Fig.8) where the esti-
mated regional gravity gradient matches with the locally
observed gravity (Additional file4: Appendix D.4). It has
a maximum amplitude of −2.5 mGal and a wavelength of
c. 2450m is main anomaly documents an asymmetric
bedrock depression where the upper part has a U-shaped
cross-sectional geometry characterized by a relatively
wide and shallow depression with a residual anomaly of
c. −0.9 mGal, while the lower part is narrow and deep
and displays a residual anomaly contriubution of c.
−1.6 mGal. e U-shaped cross-sectional geometry for
the upper part mainly becomes visible when consider-
ing the residual anomaly pattern of the SW flank, where
the values display a distinct break-in-slope at c. 1500m
profile distance (kink-1), after which the anomaly shows
a trend towards increasingly negative values farther to
the NE. Obviously, for this deeper part, the SW flank of
the depression is steeper than its NE counterpart where
the data implies the occurrence of a bedrock flank that
continuously dips at a shallow angle towards the site with
the largest residual anomaly amplitude, which is situ-
ated at c. 1800m profile distance. It is only at profile dis-
tance 2000m that the residual anomalies of the NE flank
steeply dip towards the centre of the bedrock depres-
sion (Fig.8b), marking a second break-in-slope (kink-2
on Fig.8b). On the SW side, the main gravity anomaly is
bordered by a side anomaly (Fig.8). It has a wavelength of
about 700m and an amplitude of −0.5 mGal. Apparently,
this local anomaly is caused by the effect related to the
density of the Molasse bedrock underlying the Könizberg
(see Fig.4 for explanation). In addition, the Quaternary
fill of the side channel farther south could also contribute
to this negative residual anomaly signal (Additional file4:
Figure D.1). is is the case for the stations located on
the SE side of the Könizberg mountain ridge (Fig.8 and
Additional file4: Figure D.1).
Upon modelling the gravity response of the Quater-
nary fill, we first explored the effects of different den-
sity contrasts between the bedrock and the sedimentary
infill of the tunnel valley. e results show that although
a higher density contrast of −500kg/m3 yields a maxi-
mum gravity response that is nearly twice the maximum
amplitude of the observed residual anomaly (Additional
file4: Appendix D.4), the anomaly of the NE upper flank
is perfectly reproduced by the model. is indicates that
this density contrast might be applicable for the top part
of the overdeepening, while a lower density contrast of
-350kg/m3 is likely appropriate for the lower part of the
overdeepening fill (Additional file4: Appendix D.4). e
further modelling steps finally ended with a cross-sec-
tional geometry that has a U-shaped top part where the
material is likely to have a density contrast of −500kg/
m3, and a deeper V-shaped segment filled with Quater-
nary material that has a density contrast of −350kg/m3
(in comparison to the density of the Molasse bedrock).
e upper part reaches a depth level of c. 480 m a.s.l.,
while the base of lower part is situated at > 250 m a.s.l.
and is bordered by flanks that are nearly vertical (Fig.8c).
We note, however, that at some stations the residual
anomaly values cannot fully be reproduced with the
model (e.g., at 1100 m and 1550 m profile distance),

19 Page 14 of 34
D.Bandou et al.
Fig. 7 The Bremgarten profile. a Bouguer anomalies and regional trend of the gravity field along the profile. The blue dots represent the stations
where gravity data was collected for this study. The blue line highlights the main anomaly, while the green and orange broken lines indicate
the side anomalies. See Additional file 4: Figure D.3.1 for location of stations, Additional file 1: Appendix A for gravity data and Additional file 2:
Appendix B for information on the drillings. b Final model for the Bremgarten profile, made with a total of 7 prisms with a density contrast
of − 500 kg/m3 for the uppermost three prisms and − 350 kg/m3 for the rest of the prisms (see also Fig. 5). The blue dots represent the observed
residual anomaly (the dot size corresponds to the average uncertainty of ± 0.04 mGal), and the orange dots are the modelled residual anomaly
values for model 10. The black bars indicate our maximum uncertainty of ± 0.13 mGal. The light blue line highlights the main anomaly. The effect
of the side anomalies was modelled, and the results were subtracted from the residual anomalies. c Elevation (SwissAlti3D 2 m DEM (© swisstopo))
along the profile (blue solid line). The red broken line illustrates the bedrock topography of the model by Reber and Schlunegger (2016). The
blue dots mark the locations of the gravity stations, the red diamonds indicate drillings that reached the bedrock. The black rectangles show
the cross sections of the 7 prisms used for modelling. The red star is the projected location of the Forsthaus drilling (see Additional file 4: Figure D.3.1
for location), though it is quite far off the profile (c. 500 m, see Additional file 4: Figure D.3.1). Figure 7c also shows the intersections of the prisms
with the profile that were used to correct the gravity residual anomaly for the side topography effects. This was done using a density contrast
of − 650 kg/m3 (see Fig. 4 for explanation)

Page 15 of 34 19 Geometry of Overdeepenings in the Alps
which we explain by the fact that side channels and
meanders introduce a complexity that cannot be con-
sidered by prisms alone. Furthermore, we also note that
the depths of some drillings are far off the modelled
solution, particularly for the deeper V-shaped part of
the overdeepening. As outlined below, we explain this
Fig. 8 The Bern1 profile. a Bouguer anomalies and regional trend of the gravity field along the profile. The blue dots represent the stations
where gravity data was collected for this study. The blue line highlights the main anomaly, while the orange broken line indicates the side
anomaly on the SW. See Additional file 4: Figure D.4.1 for location of stations, Additional file 1: Appendix A for gravity data and B for information
on the drillings. b Final model for the Bern1 profile, made with a total of 7 prisms with a density contrast of − 500 kg/m3 for the top two prisms
and − 350 kg/m3 for the rest of the prisms. The blue dots represent the observed residual anomaly (the dot size corresponds to the average
uncertainty of ± 0.04 mGal), and the orange dots are the modelled residual anomaly values for model 10. The black bars indicate our maximum
uncertainty of ± 0.13 mGal. The light blue line highlights the main anomaly. c Elevation (SwissAlti3D 2 m DEM (© swisstopo)) along the profile (blue
solid line). The red broken line illustrates the bedrock topography of the model by Reber and Schlunegger (2016). The blue dots mark the locations
of the gravity stations, the red diamonds indicate drillings that reached the bedrock. The drillings labelled with 1 and 2 are discussed in Sect. 5.1. The
black rectangles show the cross sections of the 7 prisms used for modelling

19 Page 16 of 34
D.Bandou et al.
misfit by the erosional mechanism, which was most likely
accomplished with water (due to the V-shaped charac-
ter). Bedrock incision by water results in the formation
of meanders, deep and narrow gorges, and sharp turns
at short downstream distances, which cannot be repro-
duced by prisms simply following the longitudinal trend
of the main channel’s depression. erefore, while our
gravity models perfectly reproduce the overall character
of the overdeepening’s geometry for the cross section (i.e.
wide and U-shaped top and a narrow V-shaped, and deep
base), it fails to reproduce meanders, side channels and
local features that occur over a short down-stream dis-
tance. While such features can accidently be hit by a drill-
ing, in most cases their gravity effects are of too low an
amplitude and too short a wavelength to be assessed by
gravity data particularly if they occur at > 100m depths
beneath the surface (see Sect.5.1 in discussion).
4.4 The Bern2 prole (Sect.4 onFig.1)
For the Bern2 profile, we determine a local residual grav-
ity anomaly that has a wavelength of about 2100m and
is approximately U-shaped. We additionally identify two
locations separated by about 700 m that show a maxi-
mum amplitude of −1.6 mGal (Additional file4: Appen-
dix D.5 and Fig.9a). In addition, the SSW flank of the
anomaly is less uniform (i.e., there are kinks and a pla-
teau) than the NNE flank, where Bouguer gravity values
change in steps.
On a closer inspection of the gravity field, we con-
clude that there probably exist two gravity anomalies of
significantly different wavelengths that overlap (Fig.9a).
e longer wavelength anomaly (blue solid line) suggests
the occurrence of a wide somewhat asymmetric trough
reaching a maximum depth at around 1700m profile dis-
tance. e shape of this long-wavelength anomaly on the
NNE flank well corresponds to the geometry proposed
by Reber and Schlunegger (2016). e short wavelength
(width of approximately 350m) local anomaly (solid red
line) reaching an additional −0.5 mGal (relative to the
longer wavelength anomaly, see Fig.9a) near profile dis-
tance 1000m suggests that there exists a significant (deep
and narrow) local bedrock depression underneath the
otherwise rather smoothly and gently dipping SSW flank
of the main trough.
Upon modelling (Additional file4: Appendix D.5), we
first considered the gravity signal exerted by the positive
topography on either side of the valley (Bandou, 2023a),
where the surface is underlain by Quaternary sediments
as disclosed by drillings (Reber et al., 2016). After sub-
traction of this topography signal from the residual
anomalies (Bandou, 2023a), we received the anomaly
values that most likely resulted from the sedimentary
fill of the overdeepening. For this correction, we used a
density contrast of −500kg/m3, because the sediments
are part of the overdeepening fill, therefore contributing
to the main anomaly effect (see Fig.4 for explanation of
the modelling concept). Note that in Fig.9, we illustrate
the combined effect of the overdeepening fill and the
contribution of the surface topography. Yet these results
are also shown in the Additional file 4: Appendix D.5
where the topographic signal was removed. Upon mod-
elling, we found that the main wavelength and ampli-
tude of the remaining signal can be explained by the fill
of an overdeepening that has a general U-shaped cross-
sectional geometry with a deepest location situated at
1700m distance from the start of the profile (Fig.9b) or
at 0m if the LCS is used as reference (Fig.9c). e gen-
eral shape of the overdeepening corresponds well with
the model by Reber and Schlunegger (2016) yet the maxi-
mum depth reached by this U-shaped depression is just
half of it (Fig.9c). In addition, the fill of this main trough
reveals two storeys where the material of the upper part
has a lower density than the sediments at the bottom of
the overdeepening. However, the local gravity anomaly of
about –0.3 mGal (after removal of the topography signal,
Additional file4: Figure D.5.5) and about 350 m wave-
length remains unexplained by the sedimentary infill of
the main trough. is signal could likely be caused by a
sedimentary fill of an inner gorge structure in the bed-
rock. In order to model such a feature, we introduced a
new prism, which we placed along the axis of the main
channel. is prism has a length of c. 200 m in both
directions from the profile (red prism on Fig.9c). We first
selected a width of 40m, a value which is based on the
largest width of the Aare inner gorge between Innert-
kirchen and Meiringen (measured on the LiDAR-based
DEM of Swisstopo and described in Hantke and Schei-
degger (1993)), and we used a thickness of 20m (equiva-
lent to the deepest prism of the main trough) as a first
very conservative estimate. We then adjusted the width
and thickness of the prism until a best-fit was reached
between the model results and observations (Bandou,
2023a). is finally yielded model 13 (Figs.9b, c), which
would be a reasonable estimate for the geometry of the
inner gorge. However, drilling data (e.g., at the Marzili c.
600m farther to the SE, see Fig.1) shows that the inner
gorge could possibly be deeper. Indeed, further model-
ling considering a narrower but deeper inner gorge yields
the same results. is shows the ambiguity of the grav-
ity method and that we reached the limit offered by the
selected approach (i.e., using prisms to approximate 3D
structures).
4.5 The Kehrsatz prole (Sect.9 onFig.1)
e 30 gravity stations of the Kehrsatz gravity profile pro-
vided us with a residual anomaly consisting of two parts

Page 17 of 34 19 Geometry of Overdeepenings in the Alps
Fig. 9 The Bern2 profile. a Bouguer anomalies and regional trend of the gravity field along the profile. The blue dots represent the stations
where gravity data was collected for this study. The blue line hightlights the main anomaly, and the red line indicates the gravity effect of the inner
gorge. See Additional file 4: Figure D.5.1 for location of stations, Additional file 1: Appendix A for gravity data and B for information on the drillings.
b Final model for the Bern2 profile (including the topographic signal), made with multiple prisms with a density contrast of − 500 kg/m3
for the top prisms and − 350 kg/m3 for the rest of the prisms. The blue dots represent the observed residual anomaly (the dot size corresponds
to the average uncertainty of ± 0.04 mGal), and the orange dots are the modelled residual anomaly values for model 13. The black bars indicate
our maximum uncertainty of ± 0.13 mGal. The light blue line highlights the main anomaly, the red line shows the secondary anomaly of the inner
gorge. c Elevation (SwissAlti3D 2 m DEM ( © swisstopo)) along the profile (blue solid line). The red broken line illustrates the bedrock topography
of the model by Reber and Schlunegger (2016). The blue dots mark the locations of the gravity stations, the red diamonds indicate drillings
that reached the bedrock. The black rectangles show the cross sections of the prisms used for modelling. Please refer to Additional file 4: Appendix
D.5 for more information

19 Page 18 of 34
D.Bandou et al.
(Additional file4: Appendix D.6 and Fig.10a): A shorter
wavelength and lower amplitude anomaly of about −0.8
mGal on the SW side between c. 500m and c. 1150m
profile distance (side anomaly with dark blue colour on
Fig.10a), and a main anomaly between c. 1150m to c.
2600 m profile distance reaching a maximum ampli-
tude of − 1.7 mGal (pale blue line on Fig. 10a). is
main anomaly shows a nearly U-shaped geometry with
a pronounced asymmetry as the NE flank appears to be
steeper.
Upon modelling (Additional file4: Appendix D.6), we
first considered the gravity effect exerted by Quaternary
sediments underlying the topography on the SW mar-
gin of our profile (topography anomaly indicated with
the green line on Fig.10a, and Figs.4 and 5 for meth-
odological approach). We then iteratively modified the
cross-sectional widths of our model prisms and adjusted
the density contrast between the Quaternary fill and the
Molasse bedrock until we found a best fit between the
model results and our observations (Additional file 4:
Appendix D.6, and Bandou, 2023a). We ended with
model 6 (Figs.10b, c), which consists of two depressions
separated by a local bedrock ridge c. 15m beneath the
surface. e side depression on the SW side is shallow
with a depth of 40m, and it shows a U-shaped cross-
sectional geometry. e cross-sectional geometry of the
main depression is also U-shaped with a wide and flat
bottom. It has an asymmetry with a flank that is steeper
on the NE than on the SW side. Please note that similar
to Bern2, the model results displayed in Fig.10 include
both the topography signal and that of the main and
side channels (see also Additional file4: Figure D.6.4 for
the results where the topographic signal was removed).
is final model 6 (and also the residual anomaly pat-
tern) shows significant differences to the bedrock model
of Reber and Schlunegger (2016), where the lack of deep
borehole data at this locality leads these authors to pro-
pose a much wider and deeper overdeepening, with a
maximum depth located farther to the SW. Note that
similar to the other profiles farther downstream, the bot-
tom part of the overdeepening hosts material that has
most likely a lower density contrast than the upper part.
Moreover, the thickness of the upper part with a higher
density contrast (c. 30m) is nearly the same as in Bern2
(c. 30m as well). Note also that upon modelling, we could
not exclude that the bedrock depressions at Kehrsatz are
underlain and thus cut by a deep inner gorge.
4.6 The Airport prole (Sect.10 onFig.1)
e Bouguer anomaly pattern of the Airport profile
shows a wide U-shaped geometry, which is additionally
asymmetric with a steeper NE flank. Two local grav-
ity anomalies are identifiable along the Airport profile
(Fig.11). e first one, situated on the SW side, has an
amplitude of c. −1.2 mGal and is caused by the Molasse
bedrock of the Längenberg (topography anomaly),
which is a mountain ridge to the West (see also Fig.4).
A second anomaly with a maximum amplitude of −3.3
mGal, which we consider as the main anomaly, docu-
ments the effect of the sedimentary infill of the valley’s
overdeepening. is large local anomaly extends from c.
1500m to c. 3900m distance along the profile, and the
maximum amplitude is measured at the MP 6008 situ-
ated at c. 3100m distance (Additional file4: Figure D.7.3
and Fig.11a). is main anomaly has a relatively steep
NE flank and a flatter but almost concave SW flank. e
gravity data additionally suggest that the deepest part
of the overdeepening is situated farther to the NE than
what is proposed by the bedrock model of Reber and
Schlunegger (2016). Moreover, contrarily to the bedrock
topography model of Reber and Schlunegger (2016), the
Bouguer anomaly shows that the flank of the overdeep-
ened valley dips much more steeply on the NE side, and
that the flank is not uniformly dipping towards the centre
on the SW side.
e PRISMA modelling was conducted to reproduce
an overall U-shaped geometry of the main anomaly with
bedrock flanks that differ in their dip angles. As an initial
model, consisting of 4 prisms with a cumulative thickness
of 200m as given by the drilling information, we selected
a setup with a constant density contrast of −500kg/m3
between the Molasse bedrock and the overdeepening
fill following Bandou etal. (2022). e results disclosed
that the bedrock depth as encountered by the drillings
could be reproduced upon modelling (Figs.11d, e), but
the models failed to reproduce the width of the trough
at greater depths as inferred by the Rb9202 (white star)
drilling (Fig.11c). Subsequent modelling revealed that a
slightly better fit between modelled and observed grav-
ity is possible by using a density contrast of −350kg/m3
for the lower three prisms (Additional file 4: Figure
D.7.7b; Fig.11e). Apparently, this alternative solution for
the geometry of the lower part of the Airport profile also
correlates with the width as constrained by the Rb9202
drilling (Additional file4: Appendix D.7).
We finally found two solutions (model 4 and model 7,
Fig.11c and e, respectively), where the calculated residual
anomalies adequately fit the observed ones. Both model
solutions show the same geometry for the upper section
of the overdeepening pointing towards an asymmetrical
U-shaped geometry for the bedrock topography under-
neath the overdeepening fill. is upper part reaches a
depth level of c. 400m a.s.l. However, the two modelled
geometries differ regarding the lower sections. e first
solution with one single density contrast of −500kg/m3
infers the occurrence of a flat and wide U-shaped deeper

Page 19 of 34 19 Geometry of Overdeepenings in the Alps
Fig. 10 The Kehrsatz profile. a Bouguer anomalies and regional trend of the gravity field along the profile. The blue dots represent the stations
where gravity data was collected for this study. See Additional file 4: Figure D.6.1 for location of stations, Additional file 1: Appendix A for gravity
data and B for information on the drillings. Three MPs at c. 300 m profile distance show a zig-zag-pattern in the gravity signals (denoted
with a question mark), which might be caused by local effects that we cannot fully explain. The green line indicates the topography effect, the dark
blue line the gravity signal of the side anomaly, the pale blue line denotes the signal of the main trough, and the orange dashed line on the NE
margin denotes the effect of a further side anomaly. b Final model for the Kehrsatz profile (including the topographic signal), made with seven
prisms with a density contrast of -500 kg/m3 for the top four prisms and − 350 kg/m3 for the three remaining prisms. The blue dots represent
the observed residual anomaly (the dot size corresponds to the average uncertainty of ± 0.04 mGal), and the orange dots are the modelled residual
anomaly values for model 6. The black bars indicate our maximum uncertainty of ± 0.13 mGal. c Elevation (SwissAlti3D 2 m DEM (© swisstopo))
along the profile (blue solid line). The red broken line illustrates the bedrock topography of the model by Reber and Schlunegger (2016). The
blue dots mark the locations of the gravity stations, the red diamonds indicate drillings that reached the bedrock. The red and white stars
(both are > 900 m to the SE of the profile) indicate locations of two deep drillings, projected onto the profile. The red one reached the bedrock,
the white one ended in the Quaternary sediments (see Figure D.6.1 for locations). The black rectangles show the cross sections of the prisms used
for modelling. Please refer to Additional file 4: Appendix D.6 for more information

19 Page 20 of 34
D.Bandou et al.
part with a maximum depth level of c. 320 m a.sl.. In
contrast, the second model solution with a density con-
trast of −350kg/m3 for the lower part returns a geom-
etry where the bedrock shape is narrow and V-shaped in
the deepest part, reaching a depth level of c. 280m a.s.l.
Here, we preferred the second model because it is more
consistent with that of the nearby Kehrsatz profile.
4.7 The Bern3, Bern4, Wabern1 andWabern2 proles
(Sect.5, 6, 7 and8 onFig.1)
e complexity of the bedrock topography beneath the
city of Bern, which is characterized by multiple side
channels and inner gorges (Reber and Schlunegger,
2016) prevented us from modelling the residual anoma-
lies of the Bern3, Bern4, Wabern1 and Wabern2 profiles
(Fig. 12). We therefore present the residual anomalies
of these profiles only (see Additional file 4: Appendix
D.8 and Fig.1 for location of profiles). Along the Bern3
profile (Fig.12a), the residual anomalies show the occur-
rence of a typical U-shaped overdeepening. e anomaly
wavelength is approximately 2 km, and we estimate a
maximum amplitude of c. −1.8 mGal. In addition, on the
SSW flank, the signal of the overdeepening appears to be
continuously dipping towards the base, which appears to
be flat. e anomaly signal of the NNE flank, however,
has a concave shape, suggesting a steeper middle sec-
tion, which transitions into a flat base. In addition to this
main anomaly with an amplitude of −1.8 mGal, we also
identified a possibly secondary short wavelength anomaly
on the SW side, which is similar to the Bern2 profile. In
comparison to the existing bedrock topography model
of Reber and Schlunegger (2016), the residual anomalies
suggest the occurrence of a wider trough with a deepest
part that is shifted more towards the SSW.
e Bern4 profile (Fig.12b) discloses a residual anom-
aly that has a U-shaped cross-sectional geometry and
that is asymmetric. Similar to Bern3, the SSW flank of
the overdeepening appears to be continuously dipping
towards the base albeit in a less uniform way than at
Bern3. e base appears to be generally flat, but locally
with a possibly complex bedrock topography. e anom-
aly signal of the NNE flank, however, points towards a
steeper side, which gradually tapers towards the base.
Apparently, there is a short plateau at c. −0.8 mGal on
both flanks. e main anomaly has a wavelength of
1.7km and a maximum amplitude of −1.4 mGal, which is
slightly less than at Bern3. Compared to the existing bed-
rock topography model of Reber and Schlunegger (2016),
the residual anomaly suggests a wider and U-shaped
trough. Because of this shape, the information offered
by the Marzili drilling (bedrock encountered at 266 m
depth) points towards the occurrence of a very narrow
and possibly deep inner gorge, as suggested by the bed-
rock model of Reber and Schlunegger (2016). It appears
that the inferred gorge is too narrow to be detected on a
gravity profile or too complex to be resolved with a pro-
file- and prism-approach.
e residual anomaly of the Wabern1 profile (Fig.12c)
point towards an overdeepening that has roughly a
U-shaped cross-sectional geometry and that is asymmet-
ric. e maximum amplitude is only c. −0.8 mGal and
measured at two locations. In comparison with all other
profiles this denotes the shallowest trough encountered
in this study. We suggest that on the SSW side, the bed-
rock is steeply dipping towards the base, which itself is
generally flat. On the other side, the flank appears flatter,
thereby gradually transitioning towards the basal part.
e bedrock topography model of Reber and Schluneg-
ger (2016) points towards the occurrence of multiple side
channels in this area. Accordingly, we cannot exclude
that one or several bedrock ridges occur underneath the
Wabern1 profile, which would correspond to the zig-
zagging shape of the residual gravity anomaly around
1000m profile distance.
Finally, the Wabern2 profile (Fig.12d) shows a residual
anomaly pattern that is roughly U-shaped and asymmet-
ric. e maximum amplitude is c. −1.3 mGal and meas-
ured at two locations, similar to Wabern1. We suggest
(See figure on next page.)
Fig. 11 The Airport profile. a Bouguer anomalies and regional trend of the gravity field along the profile. The blue dots represent the stations
where gravity data was collected for this study. The blue line indicates the main anomaly; the orange broken line refers to the side effect on the SW.
See Additional file 4: Figure D.7.1 for location of stations, Additional file 1: Appendix A for gravity data and B for information on the drillings. b and c
Model 4 for the Airport profile, made with seven prisms with a uniform density contrast of − 500 kg/m3. d and e Model 7 for the Airport profile,
made with eight prisms with a density contrast of − 500 kg/m3 for the top five prisms and − 350 kg/m3 for the three bottom prisms. For all figures:
The blue dots represent the observed residual anomaly (the dot size corresponds to the average uncertainty of ± 0.04 mGal), and the orange dots
are the modelled residual anomaly values. The black bars indicate our maximum uncertainty of ± 0.13 mGal. The light blue line highlights the main
anomaly. The figures also show the elevation (SwissAlti3D 2 m DEM (© swisstopo)) along the profile (blue solid line). The red broken line illustrates
the bedrock topography of the model by Reber and Schlunegger (2016). The blue dots mark the locations of the gravity stations, the red diamonds
indicate drillings that reached the bedrock. The red and white stars indicate locations of two deep drillings, projected onto the profile. The red one
reached the bedrock, the white one ended in the Quaternary sediments (see Additional file 4: Figure D.7.1 for locations). The black rectangles show
the cross sections of the prisms used for modelling. Please refer to Additional file 4: Appendix D.7 for more information

Page 21 of 34 19 Geometry of Overdeepenings in the Alps
Fig. 11 (See legend on previous page.)

19 Page 22 of 34
D.Bandou et al.
that on the SSW side, the bedrock is steeply dipping
towards the base, which itself is generally flat and possibly
shallow. On the NE side, the flank appears flatter, and its
limit is difficult to define because of the occurrence of a
side channel (see also Reber and Schlunegger, 2016). e
main channel is c. 2.6km wide, whereas the side channel
is much narrower (1.2km) and has a maximum anomaly
of c. −0.7 mGal. e inferred bedrock ridge at c. 2700m
distance is several hundred meters wide. In addition, the
main channel could actually be split into two channels by
a narrow ridge around 1200m profile distance.
5 Discussion
5.1 Modelling framework: density contrasts, spacing
ofstations andresolution
Our revision of the existing bedrock topography model
(Reber and Schlunegger, 2016) crucially depends on the
constraints by the gravity values assigned to the Molasse
bedrock and the Quaternary fill of overdeepenings, and
on the spatial resolution of our gravity survey. We discuss
these points in the following section together with the
strengths and weaknesses of the modelling framework
used in this paper.
5.1.1 Strength andlimitations ofour modelling framework
Our examples show that the strength of the selected
strategy (determination of the residual gravity anoma-
lies in combination with the application of the PRISMA
model) lies in the precise geometric reconstruction of
the overdeepenings’ flanks, particularly where these are
steep (> 60°). However, our setup also has some limita-
tions mainly where the overdeepening is not straight and
displays meanders. We encountered such conditions for
those profiles where the troughs are narrow and V-shaped
and where the residual anomaly showed evidence for an
inner gorge (see the Bern2 profile in Sect.4.4, and discus-
sion below). In such cases, the modelling with PRISMA
fails to properly consider the constraints offered by drill-
ings. For the Bümpliz profile, as another example, the
deepest drilling in the region (Schwenk et al, 2022a, b;
see the red star in Fig.6c) is located in a bend within the
trough and c. 200m away from our gravity profile (Addi-
tional file4: Figure D.2.4). In such cases where we have to
combine local constraints offered by drillings with infor-
mation about the overdeepenings over a larger scale such
as gravity data, we preferentially based our interpretation
on the gravity data because in a cross-section the drillings
are likely not to document features that are representa-
tive at the wavelength scale of the overdeepened trough.
Indeed, it was not the scope of our modelling exercise to
reproduce geometric details such as meanders. We rather
aimed at constraining the overall cross-sectional shape of
this particular channel (e.g., at Bümpliz) and also that of
the Aare main overdeepening, and we designed the field
campaign and the modelling strategy accordingly.
5.1.2 Comparison betweenbedrock model based ondrillings
andour gravity survey
e comparison between the bedrock topography model
that is based on drillings and our profiles, which we
reconstructed using gravity data, shows substantial dif-
ferences for nearly all profiles. is mainly concerns
the size of the deepest channel, which in many places
is much narrower according to our model than what
was proposed in Reber and Schlunegger (2016) where
the troughs appear much larger and wider. e reason
for this difference can be explained by the lack of drill-
hole data to constrain the details of the overdeepenings’
flanks, as explained by Reber and Schlunegger (2016).
In fact, while these authors had sufficient informa-
tion to reconstruct the shallow parts of the overdeep-
ened troughs at a high level of details, they did not have
enough drilling information to determine the dip angle of
the overdeepening’s flanks. erefore, they inferred dip
angles that continuously increase and then decrease with
depth, with the consequence that the resulting cross-
sectional width became larger and more concave towards
the bottom than what we suggest based on gravity data.
Deviations from the bedrock topography model of
Reber and Schlunegger (2016) and our solutions are not
only visible at the scale of an entire profile, but also at
the local scale. For the Bern1 profile, for instance, two
drillings are situated either close to our profile with a
distance < 100m (drilling labelled with 1 on Fig.8c) or
slightly further away (> 200m, drilling labelled with 2 on
Fig.8c). Both of them reached the bedrock at deep levels
Fig. 12 Residual anomalies of the a the Bern3, b the Bern4, c the Wabern1 and d the Wabern2 profiles. On the top plots, the blue dots represent
the station locations where gravity data was collected for this study. For all profiles, the blue line highlights the main anomaly, whereas for Bern3,
the red line indicates the inner gorge effect. For Wabern1, the broken orange lines on both sides denote the side anomalies. For the bottom plots,
the elevation (SwissAlti3D 2 m DEM (© swisstopo)) along the profile is represented by the blue solid line. The red broken line illustrates the bedrock
topography of the model by Reber and Schlunegger (2016). The blue dots mark the locations of the gravity stations, the red diamonds indicate
drillings that reached the bedrock. Note that for the Bern3 and Bern4 profiles, the red star indicates the location of the Marzili drilling. Please see
Figs. 3 and Figures D.8 for location of profiles and stations, Additional file 1: Appendix A for gravity data and B for information on the drillings
(See figure on next page.)

Page 23 of 34 19 Geometry of Overdeepenings in the Alps
Fig. 12 (See legend on previous page.)

19 Page 24 of 34
D.Bandou et al.
but we could not model a corresponding gravity signal.
Indeed, the application of the PRISMA routine suggests
that at a broader scale the bedrock is much shallower in
this area (Fig.8). While our modelling approach is not
capable of fully solving this conflicting information, we
tentatively consider (similar to the Marzili case, Bern4
profile in Fig. 12b) an interpretation where the shal-
low and flat bedrock shoulder inferred from our gravity
survey reflects the occurrence of a bedrock ridge that is
dissected by an inner gorge, which is too narrow to be
detected by our survey but was obviously penetrated by
a drilling.
5.1.3 Assignments ofdensities totheMolasse bedrock
andtheQuaternary ll ofoverdeepenings
Because gravity values provide information on the total
mass of an object such as an overdeepening fill, we used
bulk density values of the target sediments without litho-
facies-specific density variations as presented by e.g.,
Schwenk etal. (2022a). In a sensitivity analysis, accom-
plished to assess the bulk density of the Quaternary fill
of the Gürbe and the Aare overdeepenings (Sect.11 on
Fig.1), Bandou etal. (2022) showed that the variations
in the gravity signals measured directly above the struc-
ture in question depends on the volume and on the bulk
density, and that such relationships are non-linear: For
a small volume of sediments (e.g. expressed by a thick-
ness of 50m), a difference of 100kg/m3 in the bulk den-
sity assigned to the sediments would yield a gravity signal
of 0.2 mGal (Figure S4b in Bandou etal., 2022). A simi-
lar difference but with a 300m-thick fill would yield a 1
mGal gravity signal. If these bodies would be placed at
greater depths, then the signals would be lower as grav-
ity decreases exponentially with distance (Li and Götze,
2001). Because the maximum depth of the target over-
deepenings are in the range of several hundred meters
(Preusser etal., 2011), we constrained the bulk density
values to both the bedrock and the Quaternary sedi-
ments as precisely as possible either through (i) Nettleton
profiling along the Gürbe-Belpberg-Aare profile (Figure
S2 in Bandou etal. (2022), (ii) modelling the maximum
gravity values of an overdeepening fill (see Figure S4b
in Bandou etal., 2022), (iii) modelling well constrained
structures underlain by Quaternary sediments of known
ages (e.g., NE margin of the Bremgarten profile, Figs.5,
7), and (iv) considering published information on litho-
facies-specific density values (Schwenk et al., 2022a),
but using an average value of such data. We converged
such information to characterize sedimentary packages
tens to hundred meters thick with bulk density values,
which appears as a suitable approach to reconstruct the
overarching architecture (e.g., the stacking of multiple
storeys) as documented in Kissling and Schwendener
(1990), Bandou etal. (2022) and in this contribution.
5.1.4 Eects related tothespatial resolution ofthegravity
survey
Most of the main anomalies disclose wavelengths that
are several hundred meters to a few kilometres long.
Such signals can be easily identified by a few gravity sta-
tions (e.g., ten). At locations where we aimed at obtaining
more details about smaller-scale features such as plateaus
and knickpoints, we had to reduce the spacing between
the stations to < 100 m. In order to identify short-wave-
length structures at greater depths (such as inner gorges),
the signals of such features have to be recorded by several
stations mainly in order to differentiate them from effects
caused by shallow structures (such as a underground
garage, cellars etc.). Yet in cases where the volumes of
deep structures are not large enough, our method will
not be able to conclusively detect them. is is docu-
mented with the Bern2 profile, where the identification
of such a gorge has mainly been motivated through drill-
ing information.
5.2 Multi‑storey cross‑sectional architecture
e residual anomalies and the modelling results show
the occurrence of plateaus or break-in-slopes along
nearly all profiles. is is visible, for instance, along the
Bremgarten profile where a plateau and break-in-slopes
in the residual anomaly patterns occur at −1.0 and −2.0
mGal on the SW side (break-in-slope denoted as kink-1
and kink-2 on Fig.7b). Modelling shows that these cor-
respond to depth levels where the cross-sectional shape
of the overdeepenings change from a plateau towards
a steeply dipping flank along the profile, and where in
some cases the bulk density of the overdeepening fill
increases (e.g., Fig. 7c). For the Gürbe-Belpberg-Aare
profile (Sect. 11 on Fig. 1), Bandou et al. (2022) could
document that such plateaus and kinks in the residual
anomaly and modelling results correspond to depth lev-
els where drillings (e.g., Brunnenbohrung and RB 9201,
Fig. 1) document the occurrence of a till. is then
allowed Bandou etal. (2022) to propose that such a pla-
teau could have been formed by glacial carving, thereby
marking the base of a storey that is overlain by a sedi-
mentary sequence. Following this logic, we categorize
the cross-sectional geometries of our profiles into sto-
reys. We place the base of such a storey where a ‘plateau’
or a flat segment in a cross-section abruptly ends, giv-
ing way to a steeply dipping lateral boundary, such as at
locations indicated with 1 and 2 in Fig.13a. is allows
us to categorize each profile into a succession of at least
2–3 storeys (Table1), where the upper levels have larger
width/depth ratios than the lower ones. Accordingly, we

Page 25 of 34 19 Geometry of Overdeepenings in the Alps
Fig. 13 Proposed architecture of a the Airport profile, b the Kehrsatz profile, c the Bern2 profile, d the Bern1 profile, e the Bremgarten profile, and f
the Bümpliz profile. The profiles can be categorized into 2–3 storeys, each of which have a flat base and steep lateral flanks. See text for further
explanations

19 Page 26 of 34
D.Bandou et al.
Table 1 Amplitudes of residual anomalies and morphometric properties of the overdeepening along the various profiles
See Fig.13 and text for further information
Prole Name Bümpliz Bremgarten Bern1 Bern2 Bern3 Bern4 Wabern1 Wabern2 Kehrsatz Airport
Profile Nr. on Fig. 11 2 3 3 5 6 7 8 9 10
Width of main trough (m) 1250 3860 2450 2080 2000 1700 1600 3900 2380 2500
Maximum residual anomarly of main trough (mGal) − 1.7 − 2.5 − 2.5 − 1.6 − 1.8 − 1.4 − 0.8 − 1.3 − 1.7 − 3.3
Base of storey 1 (m a.s.l.) 550 500 500 500 – – – – 500 350–400
Base of storey 2 (m a.s.l.) 450–550 400 400 400 – – – – 350 300
Base of storey 3 or inner gorge (m a.s.l.) 330–450 300–350 200–250 < 300 – – – – 300? 250–300
Width/Depth ratio of storey 1 30 > 30 > 40 20 – – – – > 15 > 15
Width/Depth ratio of storey 2 8 15 15 15 – – – – 6 10
Width/Depth ratio of storey 3 2 6 1 < 0.5 – – – – – 4
With/Depth of entire trough 5 19 7 8 – – – – 12 10
Maximum thickness of the fill (m) 218 205 300 200 – – – – 130 240
Density of fill, storey 1 (kg/m3) 2000 2000 2000 2000 – – – – 2000 2000
Density of fill, storey 2 (kg/m3) 2150 2150 2150 2150 – – – – 2150 2150
Density of fill, storey 3 (kg/m3) 2150 2150 2150 2150 – – – – – 2150
Slope angle of eastern margin storey 1 (°) 38.7 7.6 4.6 16.7 – – – – 13 10.7
Slope angle of western margin storey 1 (°) 8.4 7.5 26.6 11.3 – – – – 13.8 18.4
Slope angle of eastern margin storey 2 (°) 82.4 17.5 35.5 13.5 – – – – 15.5 74.1
Slope angle of western margin storey 2 (°) 15.5 13.5 14 24.8 – – – – 37.6 54.5
Slope angle of eastern margin storey 3 (°) 76 83.9 65.8 2.8 – – – – – 5.1
Slope angle of western margin storey 3 (°) 20 11.4 87.1 11.3 – – – – – 29.7

Page 27 of 34 19 Geometry of Overdeepenings in the Alps
place the base of storey 1 at an elevation between 350 and
400 m a.s.l. along the Airport profile (Fig.13a). Towards
Kehrsatz, the elevation of this base rises to c. 500 m
a.s.l. and remains at this altitude farther north (Fig. 13;
Table1). Likewise, the base of the inferred storey 2 is sit-
uated slightly above 300 m a.s.l. along the Airport profile
(Fig.13a), from where it rises to c. 350 m a.s.l. at Kehrsatz
and then finally to an elevation of 400 m a.sl. in the pro-
files farther north (Fig.13). A third unit (storey 3) with
low width/depth ratios < 6 could be identified in nearly all
profiles. is lowermost storey reaches a depth level of c.
300 m a.s.l. and appears to form a several tens of meters-
to a few hundred meters-wide structure mainly beneath
the Bern2 and Bern1 and possibly also at the base of
the Bremgarten and Bümpliz profiles. e modelling
results additionally show that the sedimentary infill of
the uppermost storey 1 has a bulk density of 2000kg/m3,
whereas the underlying sedimentary sequences have a
higher bulk density of 2150kg/m3.
5.3 Change ofcross‑sectional geometries
ofoverdeepenings fromupstream todownstream
5.3.1 Upstream ofBern: U‑shaped anddeep trough
withamulti‑storey architecture
Along the Gürbe-Belpberg-Aare profile (Sect. 11 on
Fig.1), Bandou etal. (2022) inferred the occurrence of
overdeepenings (Gürbe and Aare) with a two-storey
architecture where each storey has a typical U-shaped
cross-sectional geometry with steep lateral flanks and a
flat base (width/depth ratios between 5 and 12). Whereas
the Aare overdeepening reaches a depth of c. 300 m a.s.l.,
the Gürbe trough is apparently much shallower (c. 360 m
a.s.l.).
Approximately 4 km farther downstream, the over-
deepening’s geometry is still wide (c. 3 km), asymmetric
and mainly U-shaped (Fig.13a; Table1) as disclosed by
the Airport profile, and a two- to possibly three-storey
structure can additionally be identified. According to the
modelling results, the depth of the valley at the Airport
site reaches a level between c. 270–310 m a.s.l. (depend-
ing on the assignment of bulk densities to the over-
deepening fill, see Fig. 11). is is slightly deeper than
upstream in the Aare valley. e Kehrsatz profile (Sect.9
on Fig.1), which is situated an additional 1.8 km farther
downstream, shares similarities to the Airport profile
(Fig.13b; Table1). It it is made up of two storeys, each
of which are U-shaped, asymmetric, but narrower than
farther upstream, and we additionally identified a shal-
low (40m deep) side channel on the SW side. Although
our modelling infers the occurrence of a flat base situated
at 390 m a.s.l. and thus at much shallower levels than at
the Airport, we cannot exclude that one or multiple deep
and narrow channels (storey 3?) occur at deeper levels
(Fig.13b).
5.3.2 City area ofBern: U‑shaped, shallow trough
withamulti‑storey architecture ontop andinner
gorges below
e situation then changes between the Wabern2
(Sect.8 on Fig.1) and the Bern2 profiles (Sect.4, Fig.1)
c. 1.6 kms farther downstream of Kehrsatz. ere, we
observe a much wider and shallower trough such as at
Wabern2, where the main depression is characterized
by a maximum residual anomaly of only − 1.3 mGal.
is indicates that the bedrock reaches shallower levels
than farther South such as at the Airport and Kehrsatz
sites where the maximum residual anomalies are − 3.3
mGal and then − 1.7 mGal, respectively (Figs. 10, 11;
Table 1). Downstream of Wabern2, the bedrock appar-
ently becomes even shallower and the valley gets nar-
rower at Wabern1, and then starts getting deeper again
towards Bern4 (profile 6 on Fig.1) and farther North, yet
the overall U-shaped cross-sectional geometry is main-
tained. However, the Bern4 section crosses the site of the
Marzili drilling (Fig.12b) where the bedrock was encoun-
tered at a depth of 237 m a.s.l. We were not able to detect
a clear corresponding gravity signal above the Marzili
drilling site. is is the main reason why we suggest that
the overdeepening beneath the Bern city area is charac-
terized by a shallow bedrock ridge situated several tens
of meters beneath the current surface, dissected by one
or possible multiple inner gorges where the Quaternary
mass was too small to be detected by our gravity survey.
Yet, we propose that the occurrence of such an inner
gorge can be confirmed by the Bern3 profile (Sect.4 on
Fig. 1, and Fig. 12a) and particularly along the Bern2
profile (Sect.3 on Fig.1, and Figs.9 and 13c) where we
detected secondary anomalies beneath the main wave-
length depression. At Bern2, for instance, we observe
two storeys with U-shaped cross-sectional geometries
(width to depth ratios > 15) similar to the other profiles
in the Bern area. ese storeys have steep flanks and
a flat base that slightly dips towards the NE. In addi-
tion, also at Bern2, we do observe a secondary anomaly
on the SW flank that has a short wavelength, for which
the maximum amplitude is the same as the main trough
(Fig.9). Modelling shows that such a condition can only
be reached if this secondary anomaly is caused by a nar-
row and deep structure.
5.3.3 Downstream ofBern: U‑shaped trough
withamulti‑storey architecture ontop andaV‑shaped
channel below
North of Bern at a c. 1 km downstream distance of the
Bern2 profile, the main overdeepening maintains the

19 Page 28 of 34
D.Bandou et al.
two-storey architecture. In particular, the upper part
of the Bern1 and Bern2 profiles share a similar over-
all U-shaped, two-storey geometry in cross-section
(Fig.13c, d). e lowermost part (storey 3), however, is
narrow and V-shaped with a width/depth ratio that is
lower than 1. Interestingly, if we consider the main direc-
tion of the overdeepening as reference, then the location
of the deepest site at Bern1 is aligned with the location
where we identified the inner gorge farther upstream. If
such a spatial correlation is appropriate, then it is possi-
ble that the lower V-shaped part of Bern1 is the down-
stream continuation of the inner gorge. Interestingly, the
model predicts a base at an elevation of c. 230 m a.s.l.,
which is nearly equivalent to the depth at which the Mar-
zili drilling reached the bedrock (Figs.8c and 12b). Yet a
PRISMA model of the residual anomaly pattern implies
that a bedrock at a deeper level would also be possi-
ble (Additional file4: Appendix D.4). However, such an
interpretation conflicts with the information offered by a
drilling situated at < 20 m distance of our gravity station,
for which we measured the maximum anomaly. ere the
bedrock is apparently shallower (274 m a.s.l) than what
the modelling implies. We use this observation to infer a
complex pattern for the V-shaped part of the inner gorge,
which includes the occurrence of meanders and side
channels (please see Sect.5.1).
Along the Bremgarten profile (Fig. 13e) and upon
approaching the distal termination of the main Aare
overdeepening, the uppermost part (storey 1) has a Qua-
ternary fill with a similar thickness and shape as the cor-
responding part farther upstream, but it is wider. e
bottom part appears as a composite of an upper storey
that tends to be more U-shaped (storey 2), and a basal
section which is much narrower (Fig.13e). Upon model-
ling, we assigned a minimum depth of 340 m a.s.l. to the
base of the Bremgarten section. is depth is shallower
than farther upstream, but we cannot exclude the pos-
sibility where the inner gorge, which we identified based
on gravity data (Bern2 profile, Fig.9) and drilling infor-
mation (Marzili drillhole in the Bern4 profile, Fig.12b)
continues as far north as Bremgarten. Finally, the Büm-
pliz side channel has a similar architecture in the sense
that the upper part (storey 1) is wide and U-shaped, while
the lower part displays a V-shaped cross-sectional geom-
etry (width to depth ratio of c. 2), reaching a depth level
of 340 m a.s.l.
5.3.4 Bedrock ridge withone ormultiple inner gorges buried
beneathBern, andamodern analogue
As outlined above, the main Aare overdeepening evolves
from a U-shaped cross-sectional geometry farther
upstream towards a setting where the basal part is domi-
nated by a V-shaped structure upon approaching Bern
(Figs.13, 14a). is latter structure appears to narrow to
the extent that mass is getting so small that a correspond-
ing gravity signal cannot be identified with our approach.
However, we note that drillings might eventually pene-
trate such structures as documented by the Marzili bore-
hole. Modern analogues of such a bedrock feature could
eventually be found between Innertkirchen and Meir-
ingen c. 75 km upstream of Bern (Fig. 14b). ere the
Aare River cuts through a bedrock riegel and flows in a
V-shaped inner-gorge where the width ranges from 40 m
to < 2 m in some locations (Fig.14b) and where the depth
of incision is > 140m (Hantke and Scheidegger, 1993). If
translated to the Bern situation, then the equivalent of
the bedrock ridge is situated right beneath the city area of
Bern below c. 50m of the modern surface (Fig.15; north
of Kehrsatz). Furthermore, the stoss-side of the bedrock
ridge is likely to be situated between the Wabern2 and
Wabern1 profiles, and the lee-side gives way towards the
Bremgarten profile. Similar to the current Aare gorge
at Meiringen, we infer that the thalweg was most likely
connected from upstream to downstream. We propose
this interpretation because the maximum depths, both
encountered by drillings and recovered through model-
ling, are situated at nearly the same elevation. Whether
the thalweg will shallow upwards approaching the Brem-
garten profile (Fig.15) is still the topic of further ongoing
research (see also above). Moreover, own field inspec-
tions showed that the Aare gorge south of Meiringen dis-
plays features such as glacial mills, which point towards
an origin beneath a glacier. In addition, the current
depth of the bedrock beneath the Aare gorge in Meirin-
gen is not known. erefore, we suggest that the inner
gorge system beneath Bern was also formed in a glacial
environment.
5.4 Inferred chronological framework
North of Bern, published chronological constraints were
presented for the Neubrügg section situated on the NE
end of the Bremgarten profile (Fig. 13e). For this sec-
tion, Lüthy etal. (1963) proposed a stratigraphic frame-
work with what they considered as a ‘Riss’ moraine
at the base, followed by the Karlsruhe Schotter, and a
‘Würm’ moraine on top. e ‘Riss’ moraine is addition-
ally overlain by fine-grained sediments and a gravellayer.
Pollenfragments in the sand layercouldsuggest a tran-
sition from a possibly warm to a cool-mountainous cli-
mate, which we tentatively consider as pointing towards
the end ofMIS 5ethereby following Lüthy etal. (1963).
Given this information, we assign the ‘Riss’ moraine of
Lüthy etal. (1963) to MIS 6, and the ‘Würm’ moraine to
MIS 2, but we acknowledge that such age interpretations
need to be constrained by absolute dating methods in the

Page 29 of 34 19 Geometry of Overdeepenings in the Alps
future. Accordingly, the base of storey 1 on the NE mar-
gin of the Bremgarten profile might have an age of MIS 6.
For the Bümpliz profile (Fig. 13f), Schwenk et al.
(2022a) used OSL (optically stimulated luminescence)
signals to date the topmost sediments encountered
in the Rehhag drilling to a minimum age of 250′000–
300′000yrs, which could correspond to MIS 8 (Hagen-
holz glaciation) and possibly older. As illustrated in
Fig. 14 a Perspective view looking downstream along the thalweg of the Aare main overdeepening. Note that the valley is U-shaped upstream
and then transitions in a cross-section characterized by a bedrock riegel (currently buried by several tens of m-thick Quaternary sediments),
which is dissected by one (or multiple) V-shaped inner gorges. Contour lines are shown for every 20 m elevation. The elevation of c. 500 m a.s.l.
corresponds to the lowest surface elevation encountered in this survey. b LidarDEM of the region surrounding the current Aare gorge downstream
of Innertkirchen at c. 2′658′000/1′174′000 (Swiss coordinate system), which is situated approximately 75 km upstream of Bern. The bedrock ridge
is c. 160 m high and dissected by multiple inner gorges. Most of them are filled with glacial till. Currently, the Aare River flows through an inner
gorge on the NE margin of the bedrock ridge. We consider the area surrounding the Aare gorge between Innertkirchen and Meiringen as a modern
example of the bedrock topography beneath the city of Bern

19 Page 30 of 34
D.Bandou et al.
Fig.13f and disclosed by gravity modelling, the drilled
sequence is most likely part of storey 2 and possibly 3.
In addition, this sedimentary sequence has a bulk den-
sity of c. 2150 kg/m3, which is the average of the density
values measured along the Rehhag drillcore (Schwenk
et al., 2022a). Because this sequence was deposited
during MIS 8 or possibly before, it experienced a gla-
cial loading and thus a compaction during at least two
major glaciations (i.e., during MIS 6 and MIS 2). Appar-
ently, the material encountered in the Rehhag drilling
appears to be denser than the sedimentary fill of storey
1 in the Bremgarten profile. Indeed, these sediments
were most likely deposited between MIS 6 and MIS 2
and thus experienced a compaction (Bini etal., 2009)
during one major glaciation only (i.e., during MIS 2).
Approximately 10 km farther South, wood fragments
were encountered in the Brunnenbohrung (site illus-
trated in Fig.1) at drilling depths between 200 and 230 m
and thus a few tens of meters above the base of the
Aare main overdeepening (Bandou etal., 2022; Fig.15).
e material, which was embedded in lacustrine sedi-
ments, was 14C-dated to c. 40′000 years BP (Kellerh-
als and Häfeli, 1984), which is MIS 3. e lacustrine
sequence itself is overlain and underlain by a glacial
till at c. 100 and > 250 m drilling depths, respectively
(Fig. 15). Bandou etal. (2022) used these constraints
to assign a depositional age between MIS 6 and the
Holocene to the fill of the main Aare overdeepening
along the Belpberg-Aare profile (Sect.11 on Fig.1), and
they assigned a bulk density of the 2000 kg/m3 to the
entire sedimentary fill. ese constraints allow us to
tentatively correlate the sequence along the Belpberg-
Aare profile to the fill of storey 1 farther downstream
(Fig.15).
5.5 Implications forunderstanding theformation
ofoverdeepenings intheregion
If our tentative age assignments are correct, then the
main overdeepened trough in the Aare valley (but also
in the Gürbe valley according to Bandou etal., 2022) is
filled with Quaternary sediments of which the majority of
the material has an age that is MIS 6 and younger. ese
sediments rest on a depression that is mainly U-shaped
in cross-section, and they are mainly found south of
Bern where they fill nearly the entire trough (Bandou
et al., 2022). Suites for which we assigned ages of MIS
8 and older are the fill of incisions that are encountered
beneath Bern as inner gorges and in the V-shaped lower
sections farther downstream. Such a morphology indi-
cates that upstream of Bern, glacial carving was the dom-
inating mechanism to shape the bedrock depression (e.g.,
Moreau etal., 2012), and that could have overprinted a
presumably V-shaped topography. We suggest that this
possibly original and older topography is still preserved
underneath the city area of Bern and farther down-
stream, and that it was formed through erosion by water.
is water could have originated from glacial melt and
circulated underneath a glacier during a glacial period,
thereby causing the incision (e.g., Herman etal., 2011).
Alternatively, a large supply of glacial meltwater towards
Fig. 15 Schematic section from upstream to downstream showing the modern surface topography as black dashed line, the thalweg
of the modern Aare River (pale blue), the base of storeys 1 and 2, and the age of the Quaternary fill at the Brunnenbohrung drillsite (see Fig. 1
for location of drilling). The figure also shows the bedrock ridge beneath the city of Bern (grey area) and the inferred thalweg at some time
before the MIS 8. The black rectangles indicate the uncertainty associated with the assignment of the corresponding depth. This uncertainty
is derived from modelling

Page 31 of 34 19 Geometry of Overdeepenings in the Alps
the end of a glacial period (Cohen etal., 2023) could also
have promoted a rapid downwearing of the Molasse bed-
rock, particularly at the ice margin (e.g., van der Vegt,
2012). Such a mechanism was invoked, for instance, to
explain the breaching of the bedrock ridge at the Dover
Strait and the carving of deep channels on the floor of the
eastern English Channel (e.g., Collier, 2015; Benvenuti
etal., 2017; Gupta etal., 2017; Lohrberg etal., 2022). We
consider such a scenario not unlikely given the nearly
continuous paleo-thalweg at the base of the overdeep-
ening system beneath the city of Bern (Fig.15). Accord-
ingly, while large water fluxes during the aftermath of a
major glaciation (Möhlin glaciation?) could have resulted
in the V-shaped carving of the bedrock, the subsequent
glaciations mainly resulted in the widening of the trough
but not necessarily in a further deepening, at least in the
Bern area.
6 Conclusions
Our study shows that the framework developed in this
paper, consisting of a gravity survey paired with high-
precision elevation data (such as the GNSS and the Swis-
sAlti3D 2 m-DEM) allows for a reconstruction of the
cross-sectional geometry of overdeepened valleys. is
data served as input for our 3D gravity modelling soft-
ware PRISMA, the results of which allowed us to inves-
tigate the erosional mechanisms leading to the formation
of these bedrock depressions. We presented a setup
consisting of: (i) measuring gravity data along profiles
perpendicularly to the overdeepening’s flanks and far
beyond the limits of the overdeepenings to link with the
regional gravity field; (ii) extracting the residual gravity
anomalies from these profiles, and (iii) gravity modelling.
We documented that such a strategy yielded information
on the general cross-sectional shape of the depression.
Yet an imaging of very narrow and deep structures such
as inner gorges and side channels can be very challeng-
ing or nearly impossible in some situations. is is the
case because the gravimetric signals of such structures
are pushing the entire workflow and thus the method to
its limits. Despite these hurdles, we were able to docu-
ment how the cross-sectional geometry of the Aare main
overdeepening changes downstream from a U-shaped
morphology to V-shaped structures in the deeper part.
We consider the U-shaped geometry as a response to the
glacial carving during the most recent glaciations (MIS
6 and MIS 2), whereas available stratigraphic data imply
that the age of the material filling the V-shaped lower
sections could be MIS 8 or older. is has implications
for our understanding of the erosional processes lead-
ing to the formation of these troughs. We thus envisage
an origin by water dissection either underneath a glacier
or during the aftermath of a major glaciation when large
meltwater supply contributed to the fluvial downcut-
ting into the Molasse bedrock. Strong evidence for the
inferred water control on erosion is offered by the occur-
rence of inner gorges underneath the city of Bern, which
underlie the main overdeepening. Subsequent glacia-
tions resulted in a widening of the already existing trough
without further deepening them particularly downstream
of the Bern area.
Supplementary Information
The online version contains supplementary material available at https:// doi.
org/ 10. 1186/ s00015- 023- 00447-y.
Additional le1: Appendix A. Gravity data used as initial input for each
profile upon modelling with the PRISMA routine. Gravity data used to
calculate the Bouguer anomaly, and gravity stations that we considered
to determine the uncertainties associated with the measurements of the
gravity. Elevation and bedrock data for each gravity profile. This data was
used as constraint for the modelling with the PRISMA routine.
Additional le2: Appendix B. Drilling information, regional gravity sta-
tions and isolines used for each gravity profile.
Additional le3: Appendix C. Projection of the data onto the profiles
and rotation of the coordinates’ axes so that the PRISM modelling could
be performed.
Additional le4: Appendix D. Profiles that were measured and
modelled for this paper, and details on the modelling procedure that we
applied to each profile.
Acknowledgements
Guilhem Douillet, David Mair, Patrick Schläfli, Michael Schwenk, Fabio Magrani,
Ariel do Prado, Philippos Garefalakis, and Elena Serra supported the work in
the field. Many thanks for this! We greatly acknowledge the detailed reviews
by P. Valla and an anonymous reviewer. The comments by P. Zahorec moti-
vated us to better explain our methodological approach. We thank G. Hetényi
for handling our paper as Associate Editor. And finally, we thank D. Marty for
guiding the review process as Editor.
Author contributions
FS and EK designed the study, together with DB. UM calculated the Bouguer
anomalies. RRT updated the bedrock topography model, and JP and DB con-
ducted the field survey. DB, FS and EK wrote the text and drafted the figures.
Funding
This work was financially supported by the Swiss National Science Foundation
(project No. 200021_175555) with contributions from the Stiftung Landschaft
und Kies, Swisstopo and the Gebäudeversicherung Bern GVB.
Availability of data and materials
All data used for this paper can be downloaded from the appendices. DEMs
are available from swisstopo. The bedrock and drilling information is avail-
able from the openly accessible database of the Canton Bern. The datasets
generated and/or analysed during the current study are available in the BORIS
repository, https:// boris- portal. unibe. ch/.
Declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors have no competing interests.

19 Page 32 of 34
D.Bandou et al.
Received: 8 June 2023 Accepted: 30 October 2023
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