Sources of ground movement at Vesuvius before the AD 79 eruption: Evidence from contemporary accounts and archaeological studies

Journal of Volcanology and Geothermal Research 177 (2008) 959–970

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Sources of ground movement at Vesuvius before the AD 79 eruption: Evidence from contemporary accounts and archaeological studies Aldo Marturano ⁎ Istituto Nazionale di Geofisica e Vulcanologia, sezione Osservatorio Vesuviano, Via Diocleziano 328, 80124 Naples, Italy

a r t i c l e

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Article history: Received 11 April 2008 Accepted 11 July 2008 Available online 3 August 2008 Keywords: Vesuvius ground deformation seismicity stress changes

a b s t r a c t Historical sources have recorded earthquake shocks, their effects and difficulties that local inhabitants experienced before the AD 79 Pompeii eruption. Archaeological studies pointed out the effects of such seismicity, and have also evidenced that several water crises were occurring at Pompeii in that period. Indeed numerous sources show that, at the time of eruption, and probably some time before, the civic aqueduct, having ceased to be supplied by the regional one, was out of order and that a new one was being built. Since Roman aqueducts were usually built with a recommended minimum mean slope of 20 cm/km and Pompeii's aqueduct sloped from the nearby Apennines toward the town, this slope could have been easily cancelled by uplift that occurred in the area even if this was only moderate. For the crustal deformations a volcanic origin is proposed and a point source model is used to explain the observations. Simple analysis of the available data suggests that the ground deformations were caused by a b 2 km3 volumetric change at a depth of ∼ 8 km that happened over the course of several decades. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The Somma–Vesuvius volcano formed mostly during the last 25 ka (Andronico et al., 1995) and has been characterized either by periods of semipersistent activity or by long periods of quiescence, interrupted by Plinian or subplinian eruptions. The volcano produced at least four Plinian eruptions before AD 79 (at 18, 16, 8 and 4 ka B.P.) and many smaller-scale subplinian eruptions (Rolandi et al., 1998; Andronico and Cioni, 2002; Santacroce and Sbrana, 2003). By means of reports and geological investigations it has been ascertained that from the early centuries of the first millennium, two subplinian eruptions at least (AD 472 and 1631), and several significant explosive events in the III (AD 203) and VI (AD 512) centuries as well as in AD 685 and AD 1036 occurred (Figliuolo and Marturano, 1997, 1998; Santacroce and Sbrana, 2003). From 1631 to 1944 the volcano produced eighteen eruptive periods of small and medium-sized eruptions from both summit and side vents (Arrighi et al., 2001; Santacroce and Sbrana, 2003). After the 1944 eruption Mt. Vesuvius has been quiescent. The AD 79 eruption has been widely studied in the last forty years and several interpretations of its dynamics have been proposed (e.g. Lirer et al., 1973; Sigurdsson et al., 1985; Carey and Sigurdsson, 1987; Cioni et al., 1990, 1992, 1996; Yokoyama and Marturano, 1997; Mastrolorenzo et al., 2001; Luongo et al., 2003; Gurioli et al., 2005; Rolandi et al., 2007). The eruption was characterized by phreatomag-

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matic explosions and by two styles of activity: a first Plinian phase, during which widespread fallout deposits were emplaced, followed by a second phase characterized by numerous pyroclastic flows. About 4 km3 of material was discharged and the surrounding towns of Pompeii, Herculaneum, Oplonti and Stabie were destroyed (Sigurdsson et al., 1985). Several earthquakes preceded the eruption. The strongest of them that occurred in AD 62, and that affected the city of Pompeii severely, is considered strictly related to the AD 79 event (Marturano and Rinaldis, 1995; Luongo et al., 1995; Cubellis and Marturano, 2002; Cubellis et al., 2007). In the last years of the Roman Empire and Medieval times the available sources recorded no significant seismic activity in the Vesuvian area in spite of the occurrence of some large eruptions (Figliuolo and Marturano, 1997, 1998). There is evidence for seismic activity since the eruption of the 1631 up to recent times, but it was generally of low to moderate energy and related to eruptive activity (Marturano and Scaramella, 1995, 1997; Cubellis and Marturano, 2002; Principe et al., 2004; Bertagnini et al., 2006). Since 1944, seismicity at Vesuvius has been marked by events with a frequency of a few hundred per year with some episodes of higher seismicity and higher magnitudes concentrated in the summit caldera at a depth of less than 6 km below sea level (Vilardo et al., 1996; Bianco et al., 1999; Capuano et al., 1999; Zollo et al., 2002; Cubellis and Marturano, 2002; Del Pezzo et al., 2004; De Natale et al., 2004, 2006). In spite of the rich volcanologic and seismic records, ground deformations have been rarely associated to Vesuvian eruptions. Sigurdsson et al. (1985) evidenced ground subsidence at Herculaneum,

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A. Marturano / Journal of Volcanology and Geothermal Research 177 (2008) 959–970

probably due to deflation as a consequence of the AD 79 eruption, and Palmieri et al. (1862) associated ground deformations to the lateral eruption of 1861 that opened vents at low altitude. The collection of systematic ground deformation data for Mt. Vesuvius started in the second half of 1970 with the installation of a planimetric network along its flanks (Bonasia and Pingue, 1981; Berrino et al., 1993; Tammaro et al., 2007). Since that time, the volcano has shown no significant dynamics. Indeed, high precision levellings, tiltmeters, tide-gauges along the coast, GPS measurements and InSAR images (Lanari et al., 2002; Pingue et al., 2004, 2005; Tammaro et al., 2006) indicate two well-defined zones of subsidence: in the upper part of the volcano and in a narrow strip on the plain around it. Knowledge of past precursor patterns, specific in each volcanic system, is crucial for high-risk volcanoes (e.g. McNutt et al., 2000; Sparks, 2003). For Vesuvius, the absence of significant recent and past ground movements linked to internal dynamical processes makes unusual thing to relate the evolution of the surface displacement to the variation in pressure in a shallow reservoir. Furthermore, numerical modelling found maximum vertical displacements to be only a few centimetres (Russo et al., 1997); therefore, evidences from past ground deformations associated to magmatic sources cannot be left out. Archaeological proofs suggest that a long period of intense ground deformation preceded the AD 79 eruption.

This paper aims mainly to ascertain whether the ground deformations recorded by archaeological studies can be reasonably modelled by volcanic sources and aims to comprehend whether the processes involved are consistent with the seismicity recorded by historical sources. 2. Geostructural setting The Somma–Vesuvius complex (Fig. 1) lies at the southern end of the Campanian plain, which is bordered by Mesozoic platform carbonates forming the basement dissected by a Plio-Pleistocene NE–SW and NW–SE trending regional fault system related to the opening of the Tyrrhenian basin (Patacca and Scandone, 1989). The whole southern Apennines area is characterized by NE–SW oriented extension (Montone et al., 2004). The buried geometry of the carbonate basement under Somma– Vesuvius is delineated by a sharp increase in P- and S-wave velocities around 2 km b.s.l. (Zollo et al., 1998) according to data from deep drilling on the volcano's southern slope (Principe et al., 1987). Calibrated Bouguer anomalies modelled the basement around the volcano confirming the slight west dipping (Bruno et al., 1998). Volcanic and sedimentary sequences cover the carbonate basement that overlies the crystalline basement at a depth of 12 km (Berrino et al., 1998).

Fig. 1. Main tectonic structures of Mt. Vesuvius and the Campanian Plain. Continuous lines: topographic lineaments and faults (by: Milia and Torrente, 1999; Acocella and Funiciello, 2006; Cubellis et al., 2007). Dashed lines and points: faults and fractures of the shallow basement from geophysical surveys (by: Maino et al., 1964; Bruno et al., 1998; Ventura and Vilardo, 1999; Cubellis et al., 2001). Bold lines (aqueducts): Serino–Misenum (dashed); Avella–Torricella (dashed); Torricella–Pompeii (continuous). Inserts: A, geologic sketch map of Southern Italy; B, schematic section crossing Somma–Vesuvius (see text for bibliography): a) volcanic deposits and lavas; b) interbedded lavas, volcanoclastic, marine, and fluvial sedimentary rocks of Pleistocene age; c) Mesozoic carbonate basement; d) low velocity layer.

A. Marturano / Journal of Volcanology and Geothermal Research 177 (2008) 959–970

Recently, the studies of seismic tomography evidenced a marked discontinuity at a depth of 8–10 km, producing strong converted P–Sv waves which should represent a thin magma body (Zollo et al., 1998; Auger et al., 2001; De Natale et al., 2001; Gasparini et al., 2001). Consequently, it was excluded that shallow magmatic reservoirs of significant size (more than 1 km diameter) occur in the 0–6 km depth range (Lomax et al 2001). Finally Marianelli et al. (2005), in a study on explosive activity of Vesuvius over the last three centuries, proposed a volatile-rich magma storage zone located in the crust at a depth of ≥8 km. 3. Seismicity before the AD 79 eruption The apparent quiescence of the volcano in Roman times led to underestimation of the risk, so much so that two famous protagonists of the impending scenario, Seneca and Pliny the Elder, did not hold it in any consideration. However, seismicity was felt (Guidoboni, 1989; Scandone and Giacomelli, 2008). Recently Marturano (2006) was able to offer an articulate description of the seismicity considering not only historical sources but also archaeological and social evidence (Fig. 2). A synthesis of key points is reported. The earliest seismic event in the Vesuvian area has been dated to AD 37 when Tiberius died and earthquakes damaged the pharos on Capri (Suetonius, Tiberius 74.2). An earthquake on 5 February AD 62 caused significant damage at Pompeii, Herculaneum, Nuceria and Neapolis (Tacitus, Ann. XV.22.2; Seneca, NQ VI.1.2). This shock has to be considered the most energetic of the many events that occurred in the area before February 5 (Seneca, NQ VI.1.2) and after this date, some of which causing further damage. The event represented on two marble reliefs found in the House of Caecilius Jucundus (Adam, 1989) was probably that of AD 62. The reliefs show damaged buildings, objects in unstable equilibrium, frightened mules and the Castellum aquae, about which I shall speak later, that appears to have suffered no damage owing to the earthquake (cfr. figure in Adam, 1989 or Cubellis and Marturano, 2006). In AD 64 an earthquake occurred during a representation of Nero at the theatre in Neapolis (Suetonius, Nero 20.3; Tacitus, Ann. XV.34.1). It is noteworthy that the shock was recorded because of the presence of the Emperor, the real subject of the written record, as what occurred with the earthquakes on Tiberius' death.

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During the AD 79 eruption, as well as in the following years, seismic activity was considerable (Diodorus, Bibl. Hist. 66.22.3; Pliny the Younger, Ep. VI.16, VI.20; Statius, Silvae 4.78). By contrast, little is known about the seismicity before the eruption. Only a laconic sentence by Pliny the Younger (Ep. VI.20.2) states that the population in Campania was used to live with seismic events and hence they were not too frightened by seismicity shortly preceding the eruption. Indeed, current excavations in several houses at Pompeii and at many other sites around Vesuvius indicate that the eruption was preceded by a number of earthquakes in addition to those of AD 62 and 64 which were historically reported (AA. VV., 1995). The finding of furniture tidily set aside in one room, of statues, some of which were broken, and valuable manufactures stored in safe places, bricks of collapsed walls accurately lined up, and the presence of construction materials in rooms with incomplete decorations, reveal general conditions of life due to events which could not be associated to the remote AD 62 earthquake, just as they cannot be ascribed to the phase immediately prior to the eruption in AD 79. Only rare, albeit significant, evidence allows us to date restorations, e.g. the imprint of a coin on a decoration (Allison, 1995), or an epigraph (e.g. Guidoboni, 1989) actually referring to an earthquake. However, it is evident that the picture of the seismicity in the period preceding the eruption of AD 79, as can be inferred from all the available sources, has been only partly drawn. Only the contribution from historical sources has to be considered completely analyzed, but it is not exhaustive. In Fig. 2 the seismicity recorded before the AD 79 is synthesized. Historical contributions allow us to date the events that occurred in AD 37, 62, 64 and 79, but it is very difficult to define the earthquakes from 37 to 62. They are expressly but vaguely mentioned, as well as the seismicity immediately following the AD 62 event. From 64 to 79 Pliny the Younger (Ep. VI.20.2) summarily describes historical records of earthquakes. Seismicity is present but indefinable. However, the events responsible for damage to the structures of buildings, as pointed out by archaeological studies, probably date back to that period (AD 62–79). The years 72 and 78 are indicative of seismic periods in addition to 62 and 79. In particular, the event dated one year before and subsequent events up to the eruption would account for the generalized presence of works in progress in the area. In conclusion, magnitudes (M ≤ 4.5) were generally obtained for seismic event that preceded the eruption (Fig. 2). Only the AD 62

Fig. 2. Earthquakes before the AD 79 eruption. hist.: earthquakes by historical sources occurred in AD 37, 62, 64 and 79 (full colour) and undatable ones but expressly mentioned; arch.: earthquakes by archaeological sources (modified by Marturano, 2006).

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shows a clearly higher magnitude (M N 5), that appears to be a singularity in the pre-eruptive seismic history, and separates two distinct seismic energy levels activated before and after that date (Marturano and Rinaldis, 1995, 1998; Cubellis and Marturano, 2002; Cubellis et al., 2007). 4. Ground deformation before the AD 79 eruption The roman aqueduct (aqueductus) conveyed the water from the source to its destination by a channel (specus) having a slight declivity. The great circuit, which most of aqueducts of Rome made, was taken chiefly to prevent the too rapid descent of the water. Valleys were crossed by solid substructions or arches of masonry, hills by tunnels. At convenient points on the course of the aqueduct there was generally a reservoir (piscina) in which the water might deposit any sediment. The Serino aqueduct filled to the end the so-called Piscina Mirabilis at Misenum, one of largest cisterns in the Roman world. Generally the water in the city was received in a reservoir (castellum) from which flowed into other castella whence it was distributed for public and private use. The Castellum Aquae of Pompeii was placed at the highest point of the city and distributed water through three primary channels by a system of sluice-gates. Numerous finds in Pompeii show that at the time of the eruption, and probably a long time before, the civic aqueduct was out of use and a new one was being built (Maiuri, 1931). This was the strange situation: deep trenches ran along most of the streets for laying the new pipes (Marturano et al., 2006) (Fig. 3). As the old surface pipes were being removed, and the provisional pipe network was split into useless stumps, fountains, piscinae and thermae (pools and baths) were no longer supplied. Indeed, it has been ascertained that the Castellum Aquae, the distribution centre for water in Pompeii, was not supplied by the regional aqueduct and the outlet for the water was not connected with the civic pipe network (Ohlig, 2002; Marturano et al., 2006). Water flowed to Pompeii by a regional aqueduct from the nearby Apennines crossing the Campanian Plain (Sgobbo, 1938; Ohlig, 2002; Marturano et al., 2006). An ancient aqueduct was probably working

from the Roman conquest of the city (80 BC) connecting sources near Avella to Pompeii (Ohlig, 2002). The structure, on reaching the plain, probably ran along the watershed between the Sarno and Clanio basin, and then on the eastward side of the volcano (Figs. 1 and 3). In Augustan times the Serino aqueduct was built (Sgobbo, 1938) (Fig. 1), then part of the old line (Avella–Pompeii) was connected at Torricella with the new line (Serino–Misenum) (Ohlig, 2002; Marturano et al., 2006). Therefore the water now flowed to Pompeii by a branch of the Serino–Misenum aqueduct. In fact, two different chemical calcareous deposits in the water main of the branch to Pompeii, placed one upon another, indicate two different water supply sources: the former, higher has a chemical composition similar to the Avella water; the latter, lower, has a chemical composition similar to the Piscina Mirabilis deposit, at Misenum, the point of arrival of the Serino aqueduct (Ohlig, 2002; Marturano et al., 2006). The Serino aqueduct is known through historical sources (e.g. Abate, 1840) and from the remains of sections of bridges, arches, some major tunnels and cisterns (e.g. Potenza, 1996). Today, as regards the line to Pompeii, the parts near the Castellum Aquae and the branching at Torricella are recognizable (Fig. 3). The difference in level between these two points is about 8 m, enough to allow a hydraulic connection. This information, however, does not help to obtain the real difference in level before AD 79 because of the great uncertainty arising from some sources of ground deformation active from that time, like magmatic and tectonic activity, gravitational spreading or water table change (Luongo et al., 1991; Pingue et al., 1998; Milia and Torrente, 1999; Lanari et al., 2002; Lambeck et al., 2004a,b; Borgia et al., 2005; Acocella and Funiciello, 2006). Therefore, in this work, a constant mean slope is fixed for the whole course of the aqueduct from Torricella to Pompeii, about 14 km long. Following Vitruvius (De Architectura, VIII.6) and Pliny the Elder (Nat. Hist., XXXI.31), the slope of the aqueducts, in order to give the water a proper fall, had to not be less than a silicus (0.62 cm) in every 100 pedes (1 pes = 26.9 cm), or 21 cm/km (0.02%). A 0.02% mean slope it is considered as a rule for the aqueduct of Pompeii that sloped toward Vesuvius and the town. This could easily

Fig. 3. The aqueduct of Pompeii from Torricella to Pompeii. Trench in Pompeii with lapilli in the bottom, the old pipes had been already removed (a); trench with new pipes in place (deeper) and old ones being removed (shallower) (b); branching at Torricella, the Serino aqueducts is on the left (c); Castellum Aquae at Pompeii (d). Photos a and b kindly from S.C. Nappo.

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have been cancelled by even moderate uplift in the area and the town could have encountered difficulties long before the eruption. By the archaeological data, taking into account varying water connections and related works, the life of the Pompeian aqueduct can be divided into three periods, each connected to ground deformation: 1) ancient aqueduct (sources of Avella) connecting Torricella to Pompeii. Some ground deformations have begun at that time (episode 1), making the early part of the structure unusable; 2) connection to Torricella with the Serino aqueduct, with new calcareous deposition beginning inside the water channel. During this period a new episode (episode 2) evidently compromised the water supply again, disabling the part of the structure closer to the town. Indeed, to solve the problem it was necessary to build a new civic aqueduct at a lower level; 3) pre-eruptive. The works at Pompeii were carrying out since some time before the eruption, but the water level changed continuously, rendering all efforts vain. The duration of periods is unknown, but in the model the variation of the crustal deformation is planned to happen according to the above reported periods. 5. Model and results Uplift and subsidence of the Earth's surface observed in many volcanic areas have been attributed to migration of magma or other geological fluids at depth (e.g. Mogi, 1958; Dvorak and Dzurisin, 1997). Inferred ground deformations often exhibit a nearly axi-symmetric pattern and are commonly interpreted in terms of a point pressure source at depth (‘Mogi model’). The Mogi model physically represents a uniformly pressurized spherical cavity in an elastic half space (e.g. McTigue, 1987). This model has a simple analytical solution for surface displacements, and in many cases reproduces successfully the pattern of vertical displacement during either uplift or subsidence (Dvorak and Dzurisin, 1997). Recent advances in quality and quantity of geodetic measurements motivate more detailed studies of the morphology and dynamics of the inferred deformation sources (e.g. Davis, 1986; Okada, 1992; Fialko et al., 2001). For ground deformations evidenced by archaeological sources reported above, I propose a volcanic origin and a dislocation model based on the formulas of Okada (1992) to simulate them. In order to achieve the main aim of this study — to ascertain whether the ground deformations recorded can be reasonably modelled by volcanic sources — magma chambers are simulated by isotropic point sources corresponding to the episodes above reported. The plausibility of the model representing magma intrusion is reinforced since an eruption actually took place in AD 79. Generally the parameters estimated by the model for magma chamber inflation are determined globally across all data sets. However, the processes causing inflation could be better characterized if some parameters were to remain relatively constant from one event to another or be constrained by other geophysical and volcanological results. Such a strategy was pursued by Yang et al. (1992), who found that apparent migration of the centre of the ground surface uplift at Kilauea Volcano (Hawai i) could be explained by the coincidence of magma reservoir inflation with the growth of nearby dikes. Here the

Table 1 Elastic deformation model. F0: isotropic point source; FT: tensile point source; c: depth; uzmax: maximum uplift; ΔV: volumetric change; M0G: geodetic moment Model

F0 FT

c

uzmax

ΔV

Dip 3

(km)

(m)

(km )

8 8

3.1 3.9

0.8 0.5

M0G

(deg)

(dyn cm)

0

7E + 26 2E + 26

Fig. 4. Layout of aqueduct from Torricella (0 km) to Pompeii (14 km). a) Z0 = original level (m) relative to Pompeii according to mean recommended slope of 20 cm/km (Pliny the Elder, XXXI.31; Vitruvius, VIII.6); Z1 = level changes according to episode 1 (source model F0 in Table 1); Z1c = level restored; b) S0, S1 and S1c, slopes (‰) corresponding to levels Z0, Z1 and Z1c respectively.

sources are centred along the crater axis and the top of the magma chamber is fixed at h = 8 km b.s.l. in accordance with the top of the sill indicated by Auger et al. (2001) and the chamber modelled by de Lorenzo et al. (2006). The parameters of the source (according to episode 1) are calibrated to obtain a critical slope in the ancient working branch of the aqueduct from Torricella to Pompeii (the structure will be about the same after the new connection to the Serino aqueduct, though at a different altitude, as considered below). The data were fitted by an isotropic point source, the solution F0 is in Table 1, and the equation (Delaney and McTigue, 1994)
ΔV= πuzmax c2 =ð1−nÞ

ð1Þ

was used to calculate the volume change (ΔV) of the isotropic point source, where uzmax is the maximum uplift, c the fixed depth and n = 0.25 the Poisson ratio (Table 1). In Fig. 4 the level of the aqueduct (relative to Pompeii) is reported for the 14 km stretch from Torricella to Pompeii (Fig. 4a), as well as its slope (Fig. 4b), prior to the beginning of ground deformation until when the slope becomes negative. Due to ground deformation the section closest to Torricella was out of order. To overcome this situation a new section was built to link up with the Serino aqueduct, evidently running at a higher altitude.

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A. Marturano / Journal of Volcanology and Geothermal Research 177 (2008) 959–970

The new section is reported as a dashed line in Fig. 4. A new calcareous deposit is going to form inside the channel on the previous one. According to episode 2, a new pressure increase within the shallow reservoir newly compromised the water supply at Pompeii. The new source volume change equals the F0 one and represents an enlargement of the magma chamber with a total volume change ΔV = 1.6 km3. New works began (episode 3) and implicated entirely the city of Pompeii (Marturano et al., 2006); in fact the civic aqueduct was still in the course of construction when the eruption occurred. Unfortunately the source of inflation related to this last period cannot be modelled; however, the computed total volume change related to the two preceding periods (ΔV = 1.6 km3), lies within the range of volumes of ejecta, 1.5–3.6 km3 DRE, estimated by Cioni et al. (1999, 2003a,b) and Sigurdsson et al. (1985) respectively. The sea-level change related to ground deformation was certainly noted at the harbour of Pompeii and in the cities situated along the coast. Herculaneum was a city on the sea ∼8 km eastward from Vesuvius (Fig. 1) buried under the pyroclastic flows of the eruption of AD 79. Sigurdsson et al. (1985) evidenced ground subsidence referred to sea level of ∼4 m at Herculaneum, probably, they supposed, due to deflation of the magma reservoir, as a consequence of the AD 79 eruption, or to regional tectonic tilting. The Campanian plain, where the Somma–Vesuvius complex lies (Fig. 1), subsided at variable strain rates (∼0.2–0.5 mm/y) consistently with volcano-tectonic collapse following emplacement of the Campanian Ignimbrite around 39 ka ago (De Vivo et al., 2001; Ferranti et al., 2006). Therefore, it is possible to valuate the tectonic subsidence at Herculaneum since the AD 79 eruption as 1 m at the most. In the same period the Mediterranean sea level rose by ∼ 1.3 m (Lambeck et al., 2004a,b); the remaining ∼2 m of subsidence can be assigned to deflation. By utilizing the point source model it is possible to evaluate ∼ 2 m of uplift at Herculaneum related at the total volume change (ΔV = 1.6 km3), a value very close to the deflation estimated above. It is noteworthy that independent data from opposite sides of the volcano coherently demonstrate a surface displacement associated with the AD 79 eruption. In order to estimate the volume of the magma chamber some considerations may be carried out. Circular magma chambers, when subjected to internal pressure, give rise to both subvertical and shallow dipping sheets; sills are ex-

pected to rise at their margins where the highest tensile stress concentrations occur (e.g. Gudmundsson, 1988). The maximum tensile stress (sx) at the surface occurs above the centre of the chamber

sx =4Pe r 2 = c2 −r 2

ð2Þ

and the maximum tensile stress (st) at the boundary of the chamber can be estimated by

st =−Pe r 2 +c2 = c2 −r 2

ð3Þ

where r is the radius of the chamber, c the depth and Pe is the overpressure, or the difference between the total magma pressure in the chamber (P) and the lithostatic stress (p) at the time of rupture (Jeffrey, 1921; Gudmundsson, 2006). The maximum tensile stress sx at the surface can be computed from Okada's (1992) formulas assuming the value of Lamé's first constant to be µ = 3 × 104 MPa (e.g. Scandone et al., 2008). If ΔV = 0.8 km3, c = 8 km, sx ≈ 5 MPa, from Eq. (2) it is possible to estimate Pe ≈ 8 MPa and then from (3), st ≈ 10 MPa for r = 2.5–3 km and corresponding chamber volumes V = 65–110 km3 (F0 in Fig. 5). Both Pe and st are near the tensile strength of rock, normally of the order of 10 MPa. Similar overpressures were considered recently by Chen and Jin (2006) to explore a viscoelastic energy dissipation theory for subcritical dike growth from a magma chamber. They showed that Pe ≈ 6.5 MPa corresponds to a subcritical growth velocity (v) around v ≈ 10− 5 m/s, which means that the dikes can reach the state of unstable propagation and erupt out of the magma chamber. If ΔV = 1.6 km3 the value of Pe calculated above is doubled. A more realistic thin magma body 8–10 km deep under Vesuvius was recently suggested by many studies (Zollo et al., 1998; Auger et al., 2001; De Natale et al., 2001; de Lorenzo et al., 2006). Deformation due to sill-like magma intrusion can be considered by using a horizontal dislocation model in which the surface uplift volume exactly equals the volume of the inflation (Delaney and McTigue, 1994). As a check, the data were fitted by a horizontal infinitesimal sheet (Okada, 1992): the solution FT is in Table 1. The sheet area shown as an example in Fig. 5 is 5 × 5 km large. As expected (e.g. Delaney and McTigue, 1994), at the same source depth, the predicted volume change (ΔV) of the isotropic point source is greater than the other value, which produces a narrower uplift.

Fig. 5. Schematic image of magma sources. Spherical magma source F0, volume V ≈ 100 km3; sill-like magma reservoir FT (L = W = 5 km; dip = 0°). The magma reservoir FT is inferred connected with a vertical sheet d, the parameters are as in Fig. 7 (L = 4 km; W = 1 km; U = 10 m; dip = 90°; strike = N100E). Insert: (bold line arc), sector from N15°E to N150°E covered by aqueduct; (point and line), NW–SE (N142°E), NE–SW (N54°E) and (N80–90°E) structural trending (Bianco et al., 1998); (double arrow): stress direction N76°E (Montone et al., 2004); (filled sector): dike strike range N80°E–N115°E (this article).

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6. Comparison with seismicity Earthquake swarms are often observed in association with large crustal deformations. The random relation between the two processes was evidenced in the 1970–1980s when three calderas, Campi Flegrei, Rabaul and Long Valley, quasi-contemporaneously experienced dramatic uplift and intense earthquake swarms (Corrado et al., 1976; Savage and Clark, 1982; Barberi et al., 1984; Hill, 1984; McKee et al., 1984; Savage and Cockerham, 1984). Relations between magmatic processes and seismicity have been frequently reported since then (e.g. Yokoyama, 1988; Langbein et al., 1993; Ukawa and Tsukahara, 1996; Okada et al., 2000; Toda et al., 2002; Fujita et al., 2002). As the mechanisms of inducing earthquakes, pore pressure increases and stress change in the crust as a result of intrusions have been proposed. The pore-pressure model expects seismicity to be activated around the chamber or continue to be active around the dike over the whole depth range in the seismogenetic crust during the period when the dike propagates due to excess pressure (e.g. Healy et al., 1968; Ohtake, 1974; Delaney, 1982). Earthquakes are also expected to occur over the whole depth range of the dike emplacement if the dike is composed of a lot of small cracks, and the earthquakes are caused by faults connecting one crack tip to another (Hill, 1977). Toda et al. (2002) suggested that the seismicity occurs in lobes of increased stress independently of dike connections. Here I hypothesize that inflation at 8 km triggers earthquakes in the brittle overlying crust. Previously, the ground deformation occurring before the eruption of AD 79 has been modelled using two isotropic point sources linked to the life of the aqueduct of Pompeii. From the beginning of the unrest, in succession, a water crisis occurred, part of the aqueduct was reconstructed, new calcareous deposits covered the inner walls of the aqueduct, a new water crisis followed, and, at the end, new works started, lasted some time but did not finish. It is difficult to estimate how long the unrest lasted: reasonably several decades. As reported in Section 3 and shown in Fig. 2, since the AD 60s, the earthquakes intensified in number and energy. For the duration of the unrest two distinct seismic energy levels can be distinguished: before and after the AD 62 event, evidently activated by change in associated stress fields. To test this hypothesis I calculated the change in Coulomb failure stress induced by the sources by fitting the deformation field recorded by the aqueduct (Table 1). Modelling of Coulomb stress change due to fault slip in tectonic areas has become a widely used tool since the early 1990s (e.g. Stein et al., 1992). In volcanic areas, few examples can be reported one

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decade later (Cayol et al., 1998; Rubin and Gillard, 1998; Feigl et al., 2000; Troise, 2001). To simulate strain and stress changes generated during the unrest episodes the formulas of Okada (1992) are used. Coulomb stress change (Δσf) is computed for the source F0 on the optimally oriented fault mechanism by Δσ f =Δτ+μ′ðΔμ n Þ

ð4Þ

where Δτ is the change in shear stress, Δμn is the change in normal stress and μ′ = 0.4 is the effective coefficient of friction. Possible changes in pore fluid pressure are not considered. There is evidence that small static stress changes around 0.01 MPa can promote volcano seismicity, and that microearthquakes are modulated or triggered by tidal stress of just 0.003 MPa (e.g. Vidale et al., 1998; Stein, 1999). Fig. 6 shows the Coulomb stress change computed on vertical faults in the vertical section passing through the centre of the modelled volcanic point source (indicated by a black circle). Stress changes are computed in a homogeneous half space. Seismicity is favoured in zones indicated by positive values. Yokoyama (1988) discussed the relationships between seismic energy release and deformation for the activities at Usu volcano and the Phlegraean Fields by using the relation η=∑Es =σΔV

ð5Þ

where Es is the seismic energy, σ the overburden stress and ΔV the volume change. At Usu volcano η was a few percent, at the Phlegraean Fields it was two orders smaller too, given the anomalously low crust rigidity (Yokoyama, 1988). In a rectangular fault model, the seismic moment M0S is related to magnitude Ms and average dislocation U by the relations (Aki, 1967; Lay and Wallace, 1995): log M0S =16:1+1:5Ms

ð6Þ

M0S =cUA

ð7Þ

where µ is the shear modulus and A the fault area. Recently, for a spherical dilatational source Langbein et al. (1993) and Feigl et al. (2000) used the relation M0G =3cΔV

ð8Þ

to evaluate the elastic energy accumulated in the rock as elastic deformation, where ΔV is the volume change and µ the shear modulus.

Fig. 6. Coulomb stress change due to a point source F0 simulating a spherical magma chamber (indicated by the black circle) on faults parallel to the y direction. The dashed line at 2 km depth denotes the top of the carbonates.

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They noted that geodetic moment (M0G) exceeded the cumulative seismic moment (M0S) from a factor k = 2–4 up to more than one order of magnitude. According to the above results, for ΔV = 0.8 km3 and µ = 30 GPa, one obtains M0G ≈ 7 × 1026 dyn cm. Furthermore, for a factor k = 3, M0G = 7 × 1026 corresponds to M0S = 2 × 1026 dyn cm, the equivalent of a single earthquake of magnitude Ms ≈ 6.9 following the relation (6). Not a single event of this magnitude has been recorded in the Vesuvian area; the largest is that of 62 AD of magnitude M = 5.1 ± 0.3 (Cubellis and Marturano, 2002). Probably the deformation was not instantaneously released and, moreover, it is speculated that the injected magma induced viscous or plastic flow. In the first case, if it is supposed that the magma source is inflating at a fairly constant rate of 0.04 km3/yr, for k = 3 a seismic moment release of M0S ≈ 1 × 1025 dyn cm/yr is expected that can have been dissipated by an event of Ms ≈ 6.0 earthquake/yr or by many smaller events. In this hypothesis a source type F0 was roughly able to accumulate in the rock as elastic deformation the energy seismically released in the last 20 years. As regards the second case, there is scant knowledge on the state of the magma chamber and how the magma chamber connects with the deeper melt zone. However, tomography, seismological and thermal models suggest a brittle–ductile transition under Vesuvius (Zollo et al., 1998; Auger et al., 2001; De Natale et al., 2001; de Lorenzo et al., 2006). In addition, seismicity in this region is well known to occur at shallower (h b 6 km) depths (Del Pezzo et al., 2004; Nunziata et al., 2006; De Natale et al., 2006). Accordingly, it may be imagined that for some time the source of deformation produces crustal deformation without seismic activity or releasing smaller events following magma source inflation at a lower rate, or both. 7. Discussion and conclusions The ground deformation occurring before the eruption of AD 79 was modelled by using isotropic point sources of magmatic origin linked to three periods characterizing the life of the aqueduct of Pompeii as pointed out by archaeological evidence. The source parameters were assigned when a negative slope was calculated along the section of the aqueduct supposed having a 0.20‰ mean slope. This is an oversimplification that does not consider changes in the original gradient or hydraulic parameters (e.g. roughness) and the considerable variation in the declivity of Roman aqueducts, from 0.2% to near 0%, as verified today. Beside, the sources are centred along the crater axis, and possible lateral migrations or deflating sources were not analyzed. Overpressure and volume of the magma chamber were estimated in the range Pe = 8–16 MPa and V = 65–110 km3 respectively. Recently Scandone and Giacomelli (2001) hypothesized depressurization of the magma chamber of about 35 MPa at the end of the magmatic phase of the AD 79 eruption and estimated a magma chamber volume of 100 km3. Jellinek and De Paolo (2003) observed that in the range of overpressure Pe = 10–40 MPa, magma chamber volume (V), wall rock viscosity (µ) and temperature (T) are important controls of possible eruptions. In the elastic regime, for µ = 1019– 1020 Pa s− 1 and T ≈ 350 °C dike formation is expected to cause eruption if V b 100 km3. The chamber volumes above estimated are near this upper bound (V ≈ 100 km3); therefore, magma storage by radial creep in the wall rocks before the propagation of dikes to the surface in the elastic regime cannot be quite excluded. Moreover, the temperature for a ductile transition (250–350 °C) was located at Vesuvius around 6 km by the maximum depth of the earthquake foci (e.g. Lomax et al., 2001) and de Lorenzo et al. (2006) were able to reproduce it by a thermal model. The pressure generated by movement of magma related to the eruption of AD 79 was released by ground inflation, earthquakes and finally by a phreatomagmatic explosion (Sigurdsson et al., 1985; Marturano et al., 2006). The whole process probably lasted several decades divided into two events modelled by an inflation point that

provides a good approximation to the expansion of a finite magma chamber like a horizontal sill 8 km deep in accordance with seismological and volcanological indications (Auger et al., 2001; Marianelli et al., 2005; Nunziata et al., 2006; De Natale et al., 2006). For every deformation event the expansion of the chamber was estimated as ∼ 0.8 km3, corresponding to a geodetic moment of 7 × 1026 dyn cm. In the first deformation event low stressing rates imparted by magma expansion as well as ductile behaviour of the deeper crust controlled the level of the seismicity and M ≤ 4 earthquakes occurred. Shallow earthquakes of this magnitude are felt up to distance of 30–40 km but produce very little damage in the epicentral area (Cubellis and Marturano, 2002). These shocks were possibly recorded by sources only in combining with major events, like Tiberius' death. That is why they are underestimated in number. On the contrary, in the second deformation event the elastic regime prevailed. The stress transferred by intrusion caused large earthquakes in the shallower seismogenetic zone formed by colder, brittle rock. The larger earthquakes of the early 1960s were the early ones activated in this phase for a term of ∼20 years. To take into account different mechanisms like mixing and volatile exolution, second boiling, stress corrosion (Sparks et al., 1977; Anderson and Grew, 1977; Blake, 1984) as well as episodic injections of new magma and flow rates varying strongly in time (Dvorak and Dzurisin, 1997), it was supposed that the magma source is inflating at a fairly constant rate of 0.04 km3/yr. This is an order of magnitude higher than the canonical magma supply rate 0.002–0.004 km3/yr generally considered (e.g. Joron et al., 1987; Cioni et al., 2003a,b; de Lorenzo et al., 2006), or close to one, persisting only for a limited amount of time, estimated in the period 1631–1944 (Scandone et al., 2008). Therefore, 0.04 km3/yr and 20 years represent the maximum and minimum values for rate and duration respectively. The duration of the process, which lasted several decades, is also confirmed by recent studies on sanidine crystals proposing distinct magma chamber recharge events occurring in the century before the eruption (Morgan et al., 2006). It is worth noting that recent petrologic, or melt inclusion and development of silicic caldera studies (e.g. Cioni, 2000; Lima et al., 2007; Scandone and Acocella, 2007), suggest that the magma chamber feeding the 79 AD eruption was shallower than that inferred by tomographic ones (e.g. Auger et al 2001) possibly with a much smaller volume reservoir. Unfortunately, shallower sources causing larger deformation on a smaller area, are poorly constrained by my data because the aqueduct is distant by almost 2–3 times their depth. The pre-eruptive period (P3) well represents this stage in which connection between the storage system and surface takes place and seismic swarms are triggered in the upper part of the volcanic edifice. The volume of magma overall involved was less than 2 km3, modelled as magma chamber inflation producing an axi-symmetric deformation field. However, the archaeological data indicate that the situation was changing: initially the problems for the aqueduct affected the section near Torricella, modelled by an axis-symmetrical source; on the contrary in the last period the problems seem to affect the section nearer Pompeii (period 3: works in the city started but not terminated). The deformation field is probably no longer radially symmetric. A simple mode to represent the new field is by a source like a sheet (Okada, 1992) in which the fault parameters are: length (L), width (W), strike, dip angle and dislocation (U) perpendicular to fault planes. Quantitative modelling in volcano geodesy requires a quite complete data set of vertical and horizontal deformation measurements to uniquely constrain the source of volcano unrest (e.g. Dvorak and Dzurisin, 1997). Without robust bounds on the source, any analysis of dike intrusion, stress transfer and induced seismicity is not going to be very strong (e.g. Gudmundsson, 2006). Taking into account these limitations, a solution is proposed that determines a possible range for the strike of a vertical dike only, the bottom being fixed

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confined by the chamber (the other parameters have little influence on the result). Our “archaeological sensors” are located between 7 and 10 km from the crater axis, in a sector from N15°E to N150°E (insert in Fig. 5). By changing the strike in the range N0-180°E, it is noted that a dike with strike only from N80°E to N115°E encourages critical conditions near Pompeii. It is deduced that near W–E trending represents the probable main direction for pressurized fractures that connected the storage system to the surface for the eruption of AD 79 (period P3). Although the quality of the available information is naturally limited, it is shown that the overlap of the solution with the orientation and characteristics of local and regional tectonic structures, all concur with an interpretation that would be completely lost

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otherwise. In fact, it is likely that dikes tend to intrude perpendicular to the minimum principal stress axis and expand parallel to the maximum principal stress axis (Nakamura et al., 1977). Structural and seismic studies of the Somma–Vesuvius volcanic complex, the trend of eruptive fissures and tomomorphometric analysis are consistent with two main NW–SE and NE–SW trending faults in according with those at a regional scale (insert in Fig. 5) (Hyppolite et al., 1994; Bianco et al., 1998; Bruno and Rapolla, 1999; Marinoni, 2001; Ventura and Vilardo 2006). Di Maio et al. (1998) suggested a W– E fracture system along which the volcanic activity of Vesuvius has developed and migrated in recent times. The regional stress geometry in southern Italy and the Tyrrhenian coast indicates a nearly horizontal extension NE–SW orientated, confirmed by a minimum horizontal stress direction of N76 (±25)°E (insert in Fig. 5) determined

Fig. 7. Coulomb stress change due to the opening of the vertical dike modelled as a rectangular sheet (L = 4 km; W = 1 km; U = 10 m) on faults parallel to the dike strike. The dike is indicated by a bold line. (a) Vertical section crossing the centre of the dike (x = 0). The dashed line at 2 km depth denotes the top of the carbonates. (b) Plane view at 3 km depth.

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by borehole breakout data on the volcano (Montone et al., 2004). Though it did not consider tectonic load, the results here proposed are in line with a N–S extension and a W–E orientated structural discontinuity. Naturally, the stress implied by the sheet is different from that in Fig. 6. For comparison, Fig. 7 shows the Coulomb stress change due to the opening of a vertical dike (d in Fig. 5) with 10 m of dislocation normal to the sheet surface (L = 4 km; W = 1 km) 8 km in depth, computed on vertical faults oriented parallel to the dike strike. The positive lobes take up the whole seismogenetic thickness, whose top is indicated by a shaded line in Fig. 7a. Fig. 7b shows the plane view at 3 km depth. The most evident signs preceding volcanic eruptions are increases in seismicity and ground deformation (e.g. Scarpa and Tilling, 1996; Sigurdsson, 2000), which have a good chance of being detected for past eruptions too. Seismicity had been felt for many years before the AD 79 eruption (Fig. 2). It appears that seismic events at Vesuvius had always been of moderate energy, except for the earthquake of AD 62 (Cubellis and Marturano, 2002; Cubellis et al., 2007). Although this earthquake could only produce a negligible percentage of deformation on the aqueduct, it may represent an important time-marker in the evolution of the process. Mt. Vesuvius is a very dangerous volcano: due to intense urbanization on its slopes the risk today is very high. Since the AD 1944 eruption Vesuvius has been quiescent, as it has shown no signs of unrest. Previously, appreciable ground deformations were rarely associated to Vesuvian eruptions. On the contrary, a long pre-eruptive period of intense ground deformations seems to have preceded the eruption of AD 79, and raises the hope that large eruptions may be predictable despite the ambiguity of Vesuvian seismic precursors known. I also hope that additional historical and geoarchaeological studies can furnish new constraints for understanding past phenomena and their dynamics as well as possible. Acknowledgments I am grateful to Lionel Wilson, Lucia Gurioli and Roberto Scandone for their thorough reviews of the manuscript, and Herman Engelen for his editorial advice and cooperation. References AA. VV., 1995. Archäologie und Seismologie, La Regione Vesuviana dal 62 al 79 D.C. Problemi Archeologici e Sismologici, Colloquium Boscoreale · 26–27 November 1993. Deut. Arch. Inst. Rom, Sopr. Arch. Pompei, Oss. Ves. Biering & Brinkmann, Munchen. 219 pp. Abate, F., 1840. Intorno alle acque pubbliche di Napoli. Annali civili del Regno delle Due Sicilie Fasc. XXXXIII. Acocella, V., Funiciello, R., 2006. Transverse systems along the extensional Tyrrhenian margin of central Italy and their influence on volcanism. Tectonics 25, TC2003. doi:10.1029/2005TC001845. Adam, J.P., 1989. Il terremoto rappresentato: i bassorilievi di Pompei. In: Guidoboni, E. (Ed.), I terremoti prima del Mille in Italia e nell'area mediterranea. ING-SGA, Bologna, pp. 168–171. Aki, K., 1967. Scaling law of seismic spectrum. Bull. Seismol. Soc. Am. 72, 1217–1231. Allison, P., 1995. On-going seismic activity and effects on the living conditions in Pompeii in the last decades. In: AA. VV. (Ed.), Archäologie und Seismologie, La Regione Vesuviana dal 62 al 79 D.C. Problemi Archeologici e Sismologici, Colloquium · Boscoreale · 26–27 November 1993. Deut. Arch. Inst. Rom, SoprArch. Pompei, Oss. Ves. Biering & Brinkmann, Munchen, pp. 183–189. Anderson, O.L., Grew, P.C., 1977. Stress corrosion theory of crack propagation with applications to geophysics. Rev. Geophys. 15, 77. Andronico, D., Cioni, R., 2002. Contrasting styles of Mount Vesuvius activity in the period between the Avellino and Pompeii Plinian eruptions, and some implications for the assessment of future hazards. Bull. Volcanol. 64, 372–391. Andronico, D., Calderoni, G., Cioni, R., Sbrana, A., Sulpizio, R., Santacroce, R., 1995. Geological map of Somma–Vesuvius volcano. Per. Min. 64, 77–78. Arrighi, S., Principe, C., Rosi, M., 2001. Violent Strombolian and sub-Plinian eruptions at Vesuvius during post-1631 activity. Bull. Volcanol. 63, 126–150. Auger, E., Gasparini, P., Virieux, J., Zollo, A., 2001. Seismic evidence of an extended magmatic sill under Mt. Vesuvius. Science 294, 1510–1512. Barberi, F., Corrado, G., Innocenti, F., Luongo, G., 1984. Phlegraean Fields 1982–1984: brief chronicle of a volcano emergency in a densely populated area. Bull. Volcanol. 47 (2), 175–186.

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