The 3-D structure of the Somma-Vesuvius volcanic complex (Italy) inferred from new and historic gravimetric data

Abstract

Existing 3-D density models of the Somma-Vesuvius volcanic complex (SVVC), Italy, largely disagree. Despite the scientific and socioeconomic importance of Vesuvius, there is no reliable 3-D density model of the SVVC. A considerable uncertainty prevails concerning the presence (or absence) of a dense body underlying the Vesuvius crater (1944 eruption) that is implied from extensive seismic investigations. We have acquired relative gravity measurements at 297 stations, including measurements in difficult-to-access areas (e.g., the first-ever measurements in the crater). In agreement with seismic investigations, the simultaneous inversion of these and historic data resolves a high-density body that extends from the surface of the Vesuvius crater down to depths that exceed 2 km. A 1.5-km radius horseshoe-shaped dense feature (open in the southwestern sector) enforces the existing model of groundwater circulation within the SVVC. Based on its volcano-tectonic evolution, we interpret volcanic structures that have never been imaged before.

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SCieNtifiC REPORts | 7: 8434 | DOI:10.1038/s41598-017-07496-y
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The 3-D structure of the Somma-
Vesuvius volcanic complex (Italy)
inferred from new and historic
gravimetric data
Niklas Linde
1, Tullio Ricci
2, Ludovic Baron1, Alexis Shakas1 & Giovanna Berrino
3
Existing 3-D density models of the Somma-Vesuvius volcanic complex (SVVC), Italy, largely disagree.
Despite the scientic and socioeconomic importance of Vesuvius, there is no reliable 3-D density model
of the SVVC. A considerable uncertainty prevails concerning the presence (or absence) of a dense body
underlying the Vesuvius crater (1944 eruption) that is implied from extensive seismic investigations. We
have acquired relative gravity measurements at 297 stations, including measurements in dicult-to-
access areas (e.g., the rst-ever measurements in the crater). In agreement with seismic investigations,
the simultaneous inversion of these and historic data resolves a high-density body that extends from
the surface of the Vesuvius crater down to depths that exceed 2 km. A 1.5-km radius horseshoe-shaped
dense feature (open in the southwestern sector) enforces the existing model of groundwater circulation
within the SVVC. Based on its volcano-tectonic evolution, we interpret volcanic structures that have
never been imaged before.
e Somma-Vesuvius volcanic complex (SVVC) is one of the volcanoes with the highest volcanic risk worldwide
(it threatens 800,000 residents living on its slopes)1–4. e main volcanic hazards are pyroclastic ows and fallout,
earthquakes, lahars, lava ows and oods. According to recent studies, the total economic impact of a subplinian
eruption in the Vesuvian area, representing the reference scenario for the emergency plan5, 6, is estimated to 90
billion Euro7. e SVVC is a Quaternary composite stratovolcano located 15 km southeast of Naples (southern
Italy) in the Piana Campana semi-graben structure. It is bordered by Mesozoic carbonate shelves at the intersec-
tion of northwest-southeast and northeast-southwest trending oblique-slip faults and east-west trending normal
fault systems8–11. e history of the SVVC began 0.3–0.5 million years ago12 and is characterized by periods of
closed conduit rest lasting up to 1000 years that are interrupted by plinian and subplinian explosive eruptions13.
ese eruptions display the same eruptive and syn-eruptive phenomena, but they dier in terms of the volume
of emitted magma and the energy of the eruption13. e SVVC is composed of a multistage and older summit
caldera (Mt. Somma, 1132 m a.s.l.) and a nested younger cone (Mt. Vesuvius, 1281 m a.s.l.) (Fig.1). In the last
22 ka, four plinian caldera-forming eruptions (22 ka Pomici di Base, 9.7 ka Mercato, 4.3 ka Avellino, and AD 79
Pompei) and at least three major subplinian eruptions occurred (17.6 ka Pomici Verdoline, AD 472 Pollena, and
AD 1631)14. Each plinian eruption produced a summit collapse that modied the dimensions and shape of the
Mt. Somma caldera, presently characterized by steep walls in the northern sector and a gentle morphology in the
southern one15. SVVC products include lava ows and pyroclastics emitted from summit craters and calderas,
as well as from parasitic lateral vents, eruptive ssures and exogenous tholoids that are related to both explosive
and eusive eruptions. Pyroclastic deposits of plinian and subplinian eruptions blanket the northeastern sector of
Mt. Somma with thicknesses up to 70 m in topographic depressions on the lower slopes, while the southwestern
sector of the SVVC is mainly covered by historic lava ows16. Since the AD 1631 subplinian eruption, preceded
by about 500 years of rest17, Vesuvius entered in an open conduit phase that lasted until March 1944 when, aer a
violent Strombolian eruption, the volcano entered in a new close conduit quiescence.
1Applied and Environmental Geophysics Group, Institute of Earth Sciences, University of Lausanne, Géopolis, 1015,
Lausanne, Switzerland. 2Istituto Nazionale di Geosica e Vulcanologia, Via di Vigna Murata 605, 00143, Rome, Italy.
3Istituto Nazionale di Geosica e Vulcanologia, Osservatorio Vesuviano, Via Diocleziano 328, 80124, Naples, Italy.
Correspondence and requests for materials should be addressed to N.L. (email: niklas.linde@unil.ch)
Received: 3 March 2017
Accepted: 29 June 2017
Published: xx xx xxxx
OPEN

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Geophysical 3-D imaging may oer important insights about the history of the SVVC and provide geometric
constraints on past magma feeding systems. Several 3-D gravimetric inversion studies have been performed in
the surroundings of the SVVC18–22, but they strongly disagree among each other and some of them are inconsist-
ent with respect to other geophysical ndings. For example, it is expected that the high-velocity zone underlying
the Vesuvius crater that is prominent in seismic investigations23–25 should correspond to a high-density body with
a clear and unambiguous gravimetric signature. A central anomalous body is also evidenced by aeromagnetic
data and can be explained by a central highly magnetized body that extends from the surface down to at least 2 km
below the sea level26. Nevertheless, the highest resolution 3-D gravimetric inversion study to date20 largely dis-
misses the seismic ndings based on a density model that features a low-density body below the Vesuvius crater.
is result contrasts with another 3-D density model21 that indicates a central high-density body, but the sparse
station distribution used in the latter study yields a poor model resolution. It is important to better constrain and
understand the origin of this central anomalous body as most of the present-day seismicity is confounded along
its boundaries27, 28. Magnetic studies26 suggest that its top is located at shallow depths below the crater, while
seismic studies disagree about its upper limit (e.g., 1.5 km depth29 or in the near subsurface18). It is recognized
that the top interface is poorly dened by available seismic data and that the absence of a high-velocity body at
shallow depths might simply be an artifact of the initial model used in the inversion29. e actual geometry of
this high-velocity body, its origin and constitution is still uncertain. It is well-established that it takes its origin at
depths that are considerably larger than the depth to the underlying carbonate basement23, which strongly sug-
gests that it has an intrusive magmatic origin. A survey of seismic and seismological studies at other volcanoes
worldwide reveals that central high-velocity bodies are commonly interpreted as magmatic intrusions23. Initially,
it was suggested that the high-velocity body was made up of slowly cooled magmatic dikes30, while later work has
Figure 1. e main volcanic features of the SVVC14, 44, 45 with geographical names and topography produced
from a digital elevation model57 using Surfer (version 14; http://www.goldensoware.com/). Dashed lines refer
to sectors of inferred plinian calderas that would have been removed by subsequent caldera forming events. e
trajectories of the vertical sections shown in Fig.3 are indicated by blue lines.

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argued that such an interpretation is incompatible with the time-scales associated with the magma cooling pro-
cess25. Instead, an alternative explanation was proposed in terms of very fast solidication by magma quenching25.
Using new (and old) gravimetric data and a recent inversion algorithm conceived for volcanic targets31, we
present the most detailed density model of the SVVC to date. We have acquired and processed gravimetric data
from 297 new stations (precisely positioned using dierential Global Positioning System (DGPS)) with locations
chosen to complement previous studies. Furthermore, we cover the summit area in much more detail than previ-
ously (the data set include the rst gravimetric data within the Vesuvius crater). In the inversion, we account for
the topography by incorporating a modern digital elevation model (DEM) based on light detection and ranging
(LIDAR) data at a resolution of 5 m. We present this detailed 3-D density from the surface down to depths of
1–2 km. e main objectives of this study are to (1) provide a denite answer concerning the presence or not of
a dense body underlying the Vesuvius crater and (2) interpret our high-resolution 3-D density model in terms of
the evolution and present structure of the SVVC.
Results
Local Bouguer anomalies provide a rst visualization of the available gravimetric data (Fig.2). In agreement with
previous work32, we used a density of 2200 kg m−3 for topographic and Bouguer plate corrections. We referenced
the local Bouguer anomalies to a base station that was located close to the historical building of the Osservatorio
Vesuviano (Fig.1). From these data, we removed a regional trend that was inferred as part of the inversion pro-
cess. Figure2a presents the distribution of the historic data in a square of size 20 km × 20 km that is centered on
the Vesuvius crater. ese data (and additional data outside this region) have been used in previous 3-D inver-
sions21. Our new data set was acquired within the central 10 km × 10 km square region shown in Fig.2a. It is clear
that the coverage of the historic data is poor in this central region, partly because of the dicult access. e cov-
erage of our new data set (Fig.2b) is comparatively homogeneous with a renement in the summit area. is new
data set also includes the rst-ever gravity measurements in the Vesuvius crater. e new local Bouguer anomalies
(Fig.2b) clearly highlight that the central area of the SVVC is denser than 2200 kg m−3.
To better appreciate the resolution of the gravimetric inversion results, we calculate the depth of investigation
(DOI)33 based on inversion results with a 2000 kg m−3 and 2400 kg m−3 reference model, respectively. Two vertical
slices (see Fig.1) that cross in the Vesuvius crater demonstrate that the best-resolved region corresponds to the
Figure 2. Local Bouguer anomaly of the (a) historic data and (b) new data set constructed using a density of
2200 kg m−3. e region in (b) is represented by a black square in (a). e values are given with respect to the
reference station of the new data set (indicated with a ×-sign). e maps were created using Matlab (version
R2013b; www.mathworks.com).

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central part of the SVVC (Fig.3a,b). In this region, the DOI is below 0.6, while the resolution is poor at deeper
depths and increasing horizontal distances. Consequently, we mainly limit our discussion and interpretation to
model features from the sea level and upwards.
Two vertical sections (Fig.3c,d) highlight some of the main features of the density model obtained from the
gravity inversion. e region below the Vesuvius crater is markedly denser (>2450 kg m−3) than the surrounding
anks of the volcano (<2350 kg m−3). is central dense region appears continuous from the surface down to at
least 2 km depth from the land surface, aer which the model resolution is too poor to allow for denite state-
ments about its continuation. Another prevalent feature is the dense body (>2400 kg m−3) that is found 1.5 km
to the east (Fig.3c) and to the north (Fig.3d) of the Vesuvius crater. is dense body appears to be connected
with the central dense body at depth, even if this cannot be conrmed given the poor model resolution at depth
(Fig.3c,d). e geometry of this central dense body is in strong agreement with seismic results (e.g., published
gures: Fig. 724, Fig. 1023 and Fig. 325), as well as with aeromagnetic investigations (e.g., published gure: Fig.
1026). Its presence is also suggested by certain 3D gravity inversion results (published gures: Figs 621 and 721). A
3-D rendering of the dense regions (Fig.4) highlights the geometry of the two dense bodies and the comparatively
low densities below the anks of the Gran Cono (Fig.1).
Discussion
e geological interpretation is based on representative horizontal slices at decreasing altitudes. e slice at 950 m
(Fig.5a) displays a central roughly circular high-density feature corresponding to the inner part of Gran Cono
(Fig.1) and is delimited by the 1906 crater. We attribute the high-density values to the feeder conduit and to dense
(low porosity) lava layers emitted at the beginning of the 20th century (1906–191534; Fig. 119 in ref. 35) that over-
lap in correspondence to the buried rim. e porosity increases (density decreases) outside of the buried crater as
lava ows are more scoriaceous and light ash, lapilli and scoriae deposits become more common. Moving to the
north, a high-density feature is found that we attribute to the presence of abundant radial dikes and dense lava
ows outcropping on the south wall in this sector of Mt. Somma36, 37.
At an altitude of 750 m (Fig.5b), the high-density body is still positioned below the 1906–1944 tangent cra-
ters. It is surrounded by a roughly circular low-density body that hosts the shallow hydrothermal system of Mt.
Vesuvius38–40. It consists of more porous material lling the depression created by the 1631 caldera-forming erup-
tion, and in older times by the 79 AD Pompei eruption. Outside of this low-density region is a horseshoe-shaped
high-density body that is partially open in the southwestern sector (this is also clearly seen in the 450 m slice in
Fig.5c). is denser body is related to the presence of dikes and old lavas belonging to the Mt. Somma edice,
whose upper part, reaching 1900 m a.s.l.15, was destroyed by two plinian caldera-forming eruptions (the Mercato
eruption in the northwest to northeastern sector and the Pompei eruption in the northeast to southeastern sec-
tor)14, 15. South of the Mt. Somma scar, the persistent high density (showing up as a plateau in Fig.4) is likely a
manifestation of the accumulation of lava ows in the up to 400 m deep and originally narrow Atrio del Cavallo
and Valle dell’Inferno valleys41 (Fig.1). Outside of the horseshoe-shaped high-density body, the inferred densities
Figure 3. Depth of investigation (DOI) and vertical sections of the 3-D density model obtained with model
regularization in terms of an isotropic roughness and damping constraints around 2200 kg m−3: (a) DOI for the
west-east section at a latitude of 4519050 m and (b) the south-north section at a longitude of 451580 m; (c,d)
corresponding density models. In (c,d), the DOI values are used to provide a qualitative (using transparency)
assessment of how the model resolution decreases with depth. ese sections also highlight how the inversion
grid cells adapt to conform to the topography of the land surface at a resolution of 5 m. e locations of the
two transects are highlighted in Fig.1. e vertical sections were created using Matlab (version R2013b; www.
mathworks.com).

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decrease due to the increasing thickness of more porous products downslope16. Many of the parasitic vents
located on the southeastern limit of the Mercato caldera are characterized by high-density values. In contrast to
the general model of shallow and low-angle dike propagation at Vesuvius42, 43, our results rather suggest for most
of those parasitic vents, as well as for the 1937 exogenous tholoid (Fig.1), a deep and sub-vertical migration of
magma from the source to the surface (c.f., Fig.3c,d).
In the slice at 450 m (Fig.5c), we still nd the central conduit and the horseshoe-shaped dense body that
marks the buried structures of the Mercato and Pompei calderas. On the northwestern rims of the Pompei and
Mercato calderas, there is no clear high-density evidence of the conduits feeding the Pomici Verdoline vent,
the 472 AD subplinian eruption14 or the 1895–1899 eruption of the Colle Umberto exogenous tholoid (Fig.1).
e lack of denser structures delimiting the Avellino caldera is explained by the fact that the remnants of that
eruption are low-density tus originating from a giant tu cone15. Within the Avellino caldera center, a denser
body is seen that might be related to the shallow dike intrusion feeding the 1794 and 1861 eruptive parasitic vents
located downslope and aligned along east-west striking ssures16, 44, 45. e high-density body located north of the
Avellino caldera is explained by the accumulation, in a topographic depression, of thick layers of lavas erupted
during 4 eruptions between 1855 and 194446 and possibly in previous eruptive events. In the northern and eastern
sectors of Mt. Somma, several radial higher-density bodies could indicate the presence of sub-horizontal radial
dikes feeding presently buried parasitic vents developed more than 16.1 ka ago47.
e shape of the high and moderately high density region (green, yellow and red) in the −50 m slice (Fig.5d)
highlights the complex tectonic setting of the SVVC. e most pronounced feature is associated with an elonga-
tion in the northwest-southeast direction that corresponds to a major regional fault system (see. Fig. 2 in ref. 10).
A similar elongation in the northeast-southwest direction coincides with another major regional fault system (see.
Fig. 2 in ref. 10). ese results underline how the development of the SVVC has been inuenced by the tectonic
Plio-Quaternary Campanian Plain depression that is buried 2 km below a polygenic lling39. Part of this lling
surrounding the high-density body and laying on top of the Mesozoic carbonate basement15, 48 is represented by
the 37 ka old deposit of Campi Flegrei Campanian Ignimbrite49. At this depth, the remnants of the ring structures
produced by the four Plinian eruptions are either absent or unresolved.
We now discuss our results in terms of the hydrogeological setting of the SVVC, notably to provide constraints
indicating if the SVVC is hydrogeologically connected to its surroundings or if it is closed by impervious caldera
rims. is has important consequences in terms of groundwater geochemistry and ow. A hydrogeochemical
study50 suggests that groundwater circulation within the SVVC is largely dependent on the volcano-tectonic
structures10, 48 and the asymmetric topography of Mt. Somma16, 51. In the south-southwestern sector of Mt.
Vesuvius, their sampled groundwater suggests strong interaction between volcanic aquifers and the main degas-
sing system of the volcano, while no such intense interaction appears in groundwater samples from the Mt.
Somma sector. is suggests that Mt. Somma acts as a barrier to groundwater ow in the northwestern sector. Mt.
Vesuvius groundwater receives only a negligible contribution from Tyrrhenian seawater and thermal water, indi-
cating an essentially meteoric origin and a predominant south-southwest ow direction. e proposed model of
Figure 4. 3D representation using Blender (version 2.78c; www.blender.org) of the comparatively low densities
found between the Vesuvius cone and Mt. Somma. e rendered orange surface indicates a body with a density
above 2370 kg m−3 and the denser red body a density above 2440 kg m−3. e present surface topography is
represented by a black mesh and a satellite image from the same point of view is provided in the inset (Imagery
©2017, Map data ©2017 Google).

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groundwater circulation (their Fig. 1350) is fully consistent with our horseshoe-shaped anomaly (Figs4 and 5c,d)
that suggests more porous and permeable subsurface deposits in the southwestern sector of the SVVC.
We now attempt to explain the main underlying reasons for the strong dierences between our 3-D density
model and previously published 3-D density models. A previous 3-D study20 at a similar scale and resolution as
in our study led to a completely dierent density model. In that model, the region below the Vesuvius crater is
comparatively light and the anks of Gran Cono are comparatively dense. Given the expected positive relation
between density and seismic velocity, these results were used to question seismic evidence23–25 of a high-velocity
central quasi-spherical body below the crater surrounded by rocks of lower seismic velocities. We suggest that
this discrepancy is rather explained by the use of a far too coarse DEM in this gravimetric study20. For example,
by comparing our vertical proles (Fig.3c,d) with their corresponding gures (their Figs 1220 and 1320), it appears
as if they do not account for the topography of the 300 m deep crater (i.e., the crater is absent in their proles).
is omission will inevitably force the smoothness-constrained inversion to compensate by introducing a large
region of articially low densities. It is also likely to introduce a surrounding halo of comparatively higher den-
sities (in accordance with their results)20. Another illustration of the coarseness of their DEM is that they do not
account for the strong topography of the Mt. Somma ank (compare the topography of their Fig. 1220 with the
one in our Fig.3d). Based on these arguments (and given that the results are inconsistent with extensive seismic
investigations), we argue that this model20 is unreliable in regions aected by strong topography (i.e., throughout
the SVVC).
Another study21 used a similar-sized model domain as in our study based on 400 of the historic data presented
in Fig.2a. e resulting density model is partly consistent with our results (e.g., a central high-density body and a
structure that appears to be related with our horseshoe shaped dense body are found; see the slice at −1000 m in
their Fig. 621), but the results suer from a low model resolution due to the very coarse station distribution in the
central part of the SVVC (see Fig.2a). If one would use their inversion approach with a ner discretization (pos-
sible today due to increased computing capabilities) and our new data, this would most likely make their results
more comparable with our results. Nevertheless, their inversion cells do not conform to the surface topography,
which leads to very limited information about the density distribution above the sea level (their presented depth
slices are given from the sea level and downwards, while the peak of Mt. Vesuvius is at 1281 m a.s.l.). We stress
that the focus of ref. 21 was placed on deeper structures and that it is largely complementary to our present study.
Figure 5. Horizontal slices of the 3-D density model at dierent altitudes with respect to the sea level: (a)
950 m, (b) 750 m, (c) 450 m and (d) −50 m. e overlain geological features are detailed in Fig.1. e maps were
created using Matlab (version R2013b; www.mathworks.com).

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A more recent study22 resolves two dense bodies with locations that coincide with the northern and southern
parts of the horse-shaped dense body. Unfortunately, this model appears to be adversely aected by the coarse
model discretization used (815 m × 800 m in the horizontal dimensions compared to 100 m × 100 m with lo cal
adaptation to account for surface topography at a resolution of 5 m in our model). Such a coarse discretization will
inevitably lead to a poor model resolution and the risk of introducing inversion artifacts. is may also explain
the corresponding data mist that is 7 times larger than for our inversion model.
An integrated modeling and inversion study that considered both seismic and gravimetric data18 constituted
the rst 3-D density model of the SVVC. e emphasis of that study was large-scale structures (e.g., they use inter-
polated gravity data every 2.5 km) and their 3-D model is based on the interpolation of 2-D results. Furthermore,
their algorithm relies on the assumption of a strong and known relationship between seismic P-wave velocity
and density. Despite these caveats, their model (their Fig. 818) seems to indicate a denser body below the crater
and lighter material on the sides. ese results were improved by considering full 3-D modeling and inversion19
(albeit with a very coarse discretization of 2 km × 2 km × 0.5 km). e results conrm the presence of a thick and
dense intrusion beneath the Vesuvius crater that they attribute to solidied dikes. An underlying assumed rela-
tionship between seismic velocity and density implies that this structure is not resolved by the gravity data alone.
Methods
Modeling and inversion framework. Our gravimetric data consist of relative variations of the vertical
acceleration of gravity with respect to a base station (see Fig.2b). ese relative gravimetric data are mainly
sensitive to the density distribution below the survey area. Aer appropriate data processing, it is possible to use
them to obtain (by inversion) a 3-D density model. Traditionally, gravimetric data are interpreted in terms of
density variations around a pre-dened background model. is is a sound approach for at topography given
that the acquired gravimetric data will then not carry any information about the mean density of the subsurface.
Luckily, the pronounced topography of most volcanoes can be used to infer realistic density values (not only
density variations). is was recently demonstrated at Stromboli volcano, Italy, in which a targeted processing
ow and inversion provided, without any prior assumptions on density values, a density distribution that was in
good agreement with density measurements on representative rock samples31. In this work, we largely follow this
methodology31.
We discretize the SVVC and the surrounding region in terms of parallelepipeds and compute their for-
ward responses using an analytic solution52. e parallelepipeds making up the central and interior part of the
modeling domain are discretized with side-lengths of 100 m. Model cells that intersect the topography or the
bathymetry of the Mediterranean Sea are rened to account for the topography at a spatial resolution of 5 m. e
horizontal extent of the modeling domain over which topography is accounted for is 30 km × 30 km. e model
cell dimensions grow towards the sides and with depth. A total of 564,988 model cells are used in the inversion.
ere is an innite number of density models that can explain a given gravimetric data set53. To obtain a
unique solution, it is necessary to add penalties on how model parameters vary in magnitude and space (this is
termed model regularization). Here, we rely on traditional isotropic roughness constraints in each spatial direc-
tion to ensure that the inferred density varies smoothly. Repeated inversions are performed (by trial-and-error)
to nd the regularization weight, λ, that provides a model with a forward response that explains the observed data
to a user-dened error level. is procedure enables us to avoid obtaining a model that ts the data poorly (yield-
ing a too smooth model) or a model that overts the data (yielding a too rough model with inversion artifacts).
Most inversion algorithms are based on a least-squares formalism54. Aer a rst least-squares inversion step, we
employ an additional iteration using iteratively reweighted least-squares55. By mimicking l1-norms (i.e., assuming
underlying symmetric exponential distributions of the data mist and model roughness), we decrease the sensi-
tivity to data outliers and image sharper density contrasts. Compared with previous work at Stromboli volcano31,
we also employ sensitivity scaling56 to enhance the imaging of structure at depth. is is achieved by scaling the
regularization weight of every model cell to its accumulated sensitivity to all gravity data (i.e., the sum of absolute
values). is ensures that model cells with a high data sensitivity will have strong roughness constraints. e
sensitivity scaling leads to slightly lower density variations close to the surface (where the sensitivity is very high)
and enhanced imaging of structures at larger depths. Nevertheless, the results are overall similar to those obtained
without sensitivity scaling.
Another methodological addition is that we also incorporate a model regularization term that weakly penal-
izes deviations (so-called damping constraints) from a homogeneous pre-dened density model. By performing
several inversions with dierent reference densities, we can assess to what extent the data (and not the model
regularization) determines the inferred density values. is is achieved by using the concept of depth of investi-
gation (DOI)33 that is widely used in geoelectrical studies to quantify model resolution in non-linear inversions.
is approach is used herein to highlight the regions of the inversion model that are the most reliable. e DOI
is obtained by performing two separate inversions with damping constraints around two dierent homogeneous
reference models. e DOI for a given model cell is given by the dierence between the two inversion results
divided by the dierence between the two reference models. A DOI of 0 suggests that the inferred density value
is very well resolved (the inversion result is insensitive to the reference model), while a value of 1 suggests that
the inferred density value is completely unresolved (the reference model wholly determines the inferred value).
We consider relative gravity data from which the inuence of instrumental dri, earth tide, latitude, the accel-
eration of the sea mass for a known bathymetric model and the free-air eects have been removed53. e latitude
and free-air corrections (associated with the normal gravity at the observation points) are made with respect to
the reference station. is is done because our forward code provides relative responses of the density model with
respect to the local reference, and not with respect to the normal reference ellipsoid. ese local free-air anom-
alies with the sea eect removed that are used for inversion are only aected by the mass distribution below the
discretized topographic surface31. We invert these residual anomalies on the topographic surface and account for

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the density distribution within our model domain that is bounded on the top by the irregular topography. is
is the reason that we do not (and should not) make any topographic corrections to our data prior to inversion.
e local Bouguer anomalies presented in Fig.2 are not used for inversion, only for visualization. e inversion
algorithm nds the most appropriate density value of each model cell together with parameters that describe a
linear trend in the gravity data. is linear trend estimate is used to partly remove the inuence of deep structures
that we cannot resolve with our station distribution. e bathymetry is described by a bathymetric model with a
resolution of 20 m57, while the land surface is described by an upscaled (5 m) version of a high-resolution (1 m)
DEM obtained from LIDAR data (Digital Terrain Model by INGV-Osservatorio Vesuviano). is high-resolution
DEM does not cover the whole area of interest and the topography of some of the external areas of the model
domain is represented using the 20 m resolution DEM57.
Data acquisition and processing. The new gravimetric data were acquired during the time period of
October 5–20, 2014. e survey was designed to obtain a rather uniform distribution within a radius of 10 km
from the Vesuvius crater with a renement in the summit area and other areas of particular interest (see Fig.2b).
e relative gravimeter (CG-5, Scintrex) used returned the average response aer measuring 30 s at 5 Hz. At each
station, this sequence was repeated ve times and the median value was retrieved for further analysis. e dri of
the gravimeter was estimated by performing measurements at our local base station before and aer the survey of
each day. In addition, a network of additional reference stations was used to tie the measurements with the data from
the previous days. e average dri correction each day was on the order or 0.03 mGal. e measurement locations
and heights were obtained using DGPS (Topcon GR-5) and the local continuous GPS monitoring network58. It was
sometimes dicult to obtain accurate positions for stations in the lower-lying areas located within pine forests. To
improve the positioning capacity, we used the DGPS to search for station locations in the vicinity of the intended
measurement point that had the best satellite conguration. e agreement between the DEM altitude and the one
obtained by the DGPS was nevertheless not always good. To avoid inversion artifacts, we had to discard 25 stations
with poor positioning accuracy. ese points are mainly found in the forested landscape and it is likely that both the
DGPS and the DEM positioning are less accurate in such regions. is leaves us with 297 new data points that were
used in the subsequent inversion aer the processing described above (free-air anomalies with sea eect removed).
The processed data set was merged with historic data21 that had previously been referenced to an absolute
gravity station in Naples59. By occupying repeated points of the gravimetric monitoring network60, it was
possible to link our relative measurements to the absolute gravity and, thus, to the historic data. The meas-
urement locations of these old data are not very precisely determined as the data were acquired before the
advent of DGPS. We assume uncorrelated data errors and that the combined errors of our new data have a
mean deviation of 0.1 mGal. We assigned a mean deviation of 1 mGal for the historic data even if the actual
errors might be slightly lower. For example, previous works suggest that the offshore data have a standard
deviation below 0.7 mGal32 and the historic land-based data have been fitted to a standard deviation of
0.36 mGal21. Our reasoning for choosing the relatively high error level in the historic data was to force
the inversion to resolve large-scale regional features and trends by including the larger survey area of the
historic data (Fig.2a), while ensuring that the new data (Fig.2b) carry most of the weight in resolving the
structure below the SVVC. For the new data, we have complete control and knowledge of the acquisition,
positioning and processing.
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Acknowledgements
We are grateful to the Herbette Foundation for covering the field expenses. We are indebted to INGV -
Osservatorio Vesuviano for the logistic support and for providing continuous GPS data and Digital Elevation
Models, to Parco Nazionale del Vesuvio and Corpo Forestale dello Stato for granting access to restricted roads
and areas of the National Park and to Guide Alpine e Vulcanologiche del Vesuvio for their courtesy and support
during the eld campaign and to Guido Ventura for insightful discussions.
Author Contributions
N.L., T.R., A.S. and L.B. conceived the experimental layout and conducted the measurements, N.L., A.S. and L.B.
processed the data, N.L. inverted the data, N.L., T.R., L.B., A.S. and G.B. interpreted the results and wrote the
article, G.B. provided the historic gravity data.
Additional Information
Competing Interests: e authors declare that they have no competing interests.
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