Internal structure of Ustica volcanic complex (Italy) based on a 3D inversion of magnetic data

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1 DOI /s RESEARCH ARTICLE Internal structure of Ustica volcanic complex (Italy) based on a 3D inversion of magnetic data Rosalba Napoli & Gilda Currenti & Ciro Del Negro Received: 29 March 2006 / Accepted: 3 January 2007 # Springer-Verlag 2007 Abstract A ground magnetic study of Ustica Island was performed to provide new insights into subsurface tectonic and volcanic structures. The total-intensity anomaly field, obtained after a data-reduction procedure, shows the presence of a W E-striking magnetic anomaly in the middle of the island and another two intense anomalies, which seem to continue offshore, in the southwestern and the northeastern sides, respectively. The detected anomalies were analyzed by a quadratic programming (QP) algorithm to obtain a 3D subsurface magnetization distribution. The volcano magnetization model reveals the presence of intensely magnetized volumes, interpreted as the feeding systems of the main eruptive centers of the island, which roughly follow the trend of the main regional structural lineaments. These findings highlight how regional tectonics has strongly affected the structural and magmatic evolution of the Ustica volcanic complex producing preferential ways for magma ascent. Keywords Magnetic survey. Volcanic complex. Inverse magnetic modeling. Ustica Island Introduction The volcanic island of Ustica has been the site of several geological and geophysical investigations for many years, mainly because of the peculiarity of its tectonic setting and Editorial responsibility: M. Ripepe R. Napoli (*) : G. Currenti : C. Del Negro Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania, Italy napoli@ct.ingv.it the geochemical characteristics of the volcanism. Indeed, the island lies on the transitional zone between the extensional domain of the Tyrrhenian Sea to the north and the collisional belt of the Apennine thrust system to the south (Bousquet and Lanzafame 1992). In this part of the Tyrrhenian Sea, the island of Ustica is the only site that shows subaerial evidences of tectonics related to the opening of the Tyrrhenian basin (de Vita et al. 1995). Moreover, regarding volcanic activity, the island is characterized by intraplate magmatism (Etiope et al. 1999), generally associated with extensional tectonics (Schiano et al. 2004), which is rather peculiar in an area where predominantly orogenic magmatism (Aeolian arc) is found (Peccerillo 2003). Because of these characteristics, the island of Ustica plays a key role in the southern Tyrrhenian basin, and the knowledge of its tectonic features could provide a useful contribution to better clarify the geodynamics of the entire region. To date, the relationships between local and regional structures have not been entirely elucidated because most of the contacts are buried by accumulations of lava flows and pyroclastic deposits over a partially outcropping basement of submarine lavas. To fill this gap, a ground magnetic survey was carried out in 2002 of the entire island that was aimed at providing new insights into both the local and regional role of the main structural features of the island. In order to recover 3-D subsurface magnetization distribution responsible for the detected magnetic anomalies, we inverted the magnetic data using quadratic programming (QP) algorithm with bound constraints on remanent magnetization values. The magnetic inversion was formulated as an optimization problem that minimizes a global objective function accounting for a measure of data misfit and a measure of magnetic properties of the subsurface medium. The analysis of magnetic anomalies has highlighted some tectonic and volcanic

2 features that define some important aspects of the structural framework of the island. Geological setting Located approximately 60 km N NW off the coast of Sicily, the volcanic island of Ustica rises 240 m a.s.l., but represents the emergent part of a submarine volcanic complex over 2,000 m high. The island, elongated in a NE SW direction 4 km long and 2.5 km wide (Romano and Sturiale 1971; de Vita et al. 1998), is made up of lava flows and pyroclastic products lying over a submarine basal formation formed by pillow lavas and pillow breccias (Cinque et al. 1988; Etiope et al. 1999). The subaerial activity, which took place from to Ma (Barberi and Innocenti 1980; de Vita et al. 1995), was concentrated along fractures producing small eruptive centers with preferential E W and NE SW alignments (Beneduce and Schiattarella 1991). The two main volcanic edifices, Mt. Costa del Fallo and Mt. Guardia dei Turchi, are the main morphologic features of the island and bound a large collapsed caldera to the north. Notwithstanding that the volcanic activity of Ustica is partially coeval (Barberi and Innocenti 1980; Gillot 1987; Cinque et al. 1988; de Vita et al. 1995) with the nearby (20 km eastwards) calc-alkaline volcanism of the Aeolian Islands, the volcanoes of Ustica show Na-alkaline affinity (Etiope et al. 1999; Schiano et al. 2004). These products are typical of intraplate magmatism (anorogenic), which is unusual in an area characterized by orogenic volcanism (Peccerillo 2003) and range in composition from alkali basalt to trachyte, showing petrographical and chemical similarities with comparable rocks from Mount Etna (Schiano et al. 2004), about 300 km to the southeast. The structural framework of Ustica was dominated by cycles of extensional and compressive tectonics that activated the main and well recognizable fault systems in the southern part of the island. These tectonic cycles are also testified by the magmatic history of the island which is characterized by a succession of hawaiitic products (primary magma) related to the extensional events, and mugearites (evolved magma) indicating a slow process of uprising, consequently linked to the shortening period (Bousquet and Lanzafame 1992). Most of the structures affecting the island show N S and NE SW alignments parallel to the main structural lineaments of the Tyrrhenian sea-floor. They mainly consist of fault systems characterized by the superposition of extensional to compressive regimes (Bousquet and Lanzafame 1992), and dikes that are particularly well exposed on the western side of the island showing N S and E W orientation. Survey and data processing During the spring of 2002, we performed a ground magnetic survey of Ustica Island covering an area of about 9km 2 (Fig. 1). Digital magnetic data were gathered in a time span of 6 days by a GSM19 Overhauser effect magnetometer with 0.01-nT resolution. Simultaneously, GPS data were also collected by a Garmin s etrex Venture receiver with optional Differential Beacon Receiver Input. When differential correction data are received from GPS satellites (numbers 32 or below) it is possible to obtain an accurate position (3-m nominal). Fig. 1 Simplified geologic map of Ustica Island modified after Alletti et al. (2005); black dots represent the position of the rock specimens collected for J NRM and χ measurements. The inset shows the location of magnetic reference station working during the survey (black square); black dashed lines represent measurement tracks

3 Carrying out a ground magnetic survey in a volcanic area presents some difficulties. Major problems arose because in a volcano such as Ustica, built up by a stack of basic lavas, magnetizations are frequently high (Hildenbrand et al. 1993; Del Negro and Napoli 2002) and the spatial gradients on the ground may exceed 1,000 nt/m. In this context, the shallower the magnetic structures, the more the measurements are affected by high-frequency noise. This problem has been solved by extensive oversampling the investigated area with 18,000 measurements performed along lines describing an irregular grid with sides close to 500 m. In other words, the real resolution of the survey is the average grid size, even if we adopted a very close sampling step (3 m) along lines. The data-reduction procedure included removal of the diurnal variation of the magnetic field utilizing data continuously recorded at one reference station temporary installed on the island in an area of low magnetic gradient (Del Negro et al. 2002). It is worth noting that the magnetic surveys were carried out during quiet days, (geomagnetic K index values less than 2). This enables to sufficiently remove time variations from our data and consequently to maintain a suitable accuracy in the time reduction. The observed magnetic field was not reduced with respect to the reference field, IGRF, because of the limited extension of the island. For a relatively small survey area, the removal of IGRF is not appropriate because of its low resolution and definition (Kearey and Brooks 1991). The total-intensity anomaly map is shown in Fig. 2. The anomalies are very complex in shape, dimension, and intensity. In particular, the middle area of the island is characterized by a wide magnetic anomaly striking in a W E direction on the summit and on the northern flank of the Mt. Guardia dei Turchi, where an endogenous dome crops out. Another two intense anomalies of irregular shape are observed in the southwestern and northeastern parts of the island, respectively. Both are truncated close to the cliffs and seem to continue offshore. When magnetic data are observed on an irregular surface, such as in areas of rugged topography, some spurious anomalies may be generated in the signal. To suppress the noise from small magnetic bodies near the surface, it is recommended, in general, that the data be continued upward to a horizontal plane located as close as possible to the observation surface before inversion (Li and Oldenburg 1996). Numerous methods have been used for upward continuation, but most of them require data on a regular grid (Ciminale and Loddo 1989; Pilkington and Urquhart 1990; Xia et al. 1993). This is seldom the case, so gridding must be used. However, gridding can introduce errors that affect the continued data in an unpredictable way (Cordell 1992). The interpolation is commonly performed using 2D methods. Generally speaking, potential fields are functions f (x, y, z) of three spatial coordinates. The 2D interpolation algorithms can handle only functions g (x, y) and ignore the vertical coordinate z. Synthetic examples show how gridding-related errors may affect the continuation when an irregular distribution of data points and a variable topography are considered. Therefore, the effect of a magnetic body was calculated over an irregular surface. The magnetic source is a km homogeneous prism, and its top is 0.8 km below ground level. Its magnetization contrast is 4 Am 1. Fig. 2 Total-field magnetic anomaly map

4 Successively, the magnetic body effect was computed on a horizontal plane (to a height of 2.8 km) above the field plain in two different ways: i) it was firstly interpolated on thegroundsurfaceandthencontinuedonthehorizontal plane, and ii) it was firstly continued on the horizontal plane and then interpolated. The interpolation is performed using the Kriging method, while the continuation is based on the method proposed by Ducruix et al. (1974) and revised by Fedi et al. (1999) dealing directly with scattered data. Two profiles along a smooth (a) and a rough (b) topographic relief are shown, where the magnetic anomaly is sampled (Fig. 3). The results of continuation are compared with the exact values (synthetic data) calculated directly on the same horizontal plane. From this comparison it was possible to note that the error produced by the interpolation of data on an irregular surface always becomes less negligible with increasing roughness of the topography (Fig. 3a, b). On the grounds of these results, it is recommended to firstly upward continue and successively interpolate the magnetic survey data of Ustica Island. To keep all the information related to shallow and deep sources (Garcia et al. 1999), we upward continued the data to a level altitude of 250 m, namely 10 m from the highest elevation of the island (Mt. Guardia dei Turchi). This was done to identify the effect of anomalies with shorter wavelengths correlating with surface sources, such as an endogenous dome outcropping on the summit of Mt Guardia dei Turchi. A regional field was then defined as a 3D linear trend that fitted the upward continued data by the least-squares criterion, and was subsequently subtracted from them. Figure 4 shows the map of local residual anomalies obtained. It reveals an intense maximum located in the middle area of the island in correspondence of Mt Guardia dei Turchi, and other anomalies which continue offshore. Inverse magnetic modelling The magnetic field B at any observation point r generated by a magnetization distribution J(r ) in a volume V is given by: Z B ¼ m 0 r Jr ð 0 1 Þr V jr r 0 dr 0 ð1þ j The total magnetic field T, as measured by total magnetometers, represents the projection of the magnetic field B generated by the anomalous source onto the ambient magnetic field, such as: T ¼ B v ð2þ where v is the unitary vector along the direction of the ambient geomagnetic field. To solve the integral Eq. (1) numerically, we modeled the domain V, which contains the magnetic source, by using a set of m=n x N y N z rectangular prisms whose magnetization J j is uniform inside each prism (Blakely 1995). Applying this numerical approach, the total anomaly field at i-th observation point is computed by: T i ¼ Xm j¼1 J j a ij ð3þ where elements a ij quantify the contribution to the total magnetic anomaly at i-th point due to the magnetization of the j-th prism. Therefore, the inverse problem can be formulated as the solution of a system of n linear equations as: Ax¼T ð4þ where x is the m vector of unknown magnetization values of the prisms, T is the n vector of observed magnetic data, and A is a matrix with elements a ij. The analytical Fig. 3 Continuations of the magnetic body effect at 2.8 km. Magnetic data along the smooth (a) and rough (b) profiles. Dotted lines represent the continued and after interpolated data; continuous lines represent the interpolated and after continued data; dashed lines represent the exact values computed directly on the horizontal plane. Below each figure, the topography along the profile is plotted as well as the horizontal plane

5 Fig. 4 Map of the local residual anomalies produced by subtracting the 3D regional trend on the upward continued field expression of the a ij term for a prismatic body was devised by Bhattacharyya (1964) and Rao and Babu (1991). Based on discretization, the number of prisms is usually larger than the number of observation points, thus the linear inverse problem in Eq. (2) proves to be unavoidably underdetermined. In such a case, the linear system leads to a solution with m-n degree of freedom. A further difficulty in solving the system in Eq. (4) is due to the inherent non-uniqueness of the potential field: there is an infinite number of inverse models that can explain the same observed magnetic anomaly within error limits. These observations highlight that the magnetic inverse problem is ill-posed and requires some regularization techniques. In such a case, it is necessary to impose further assumptions by incorporating a priori knowledge about the solution. The idea of reducing the class of possible solutions to some set on which the solution is stable lies in the fundamental concept of introducing a regularizing operator. The inverse problem can be re-formulated as an optimization problem aimed at finding the unknown magnetization values x that minimize a functional φ defined as: φ ¼ φ d þ 1φ r ¼ 1 h i ðt T obs Þ T ðt T obs Þ þ 1φ 2 r ð5þ where 1 is a regularization parameter, namely a trade-off between minimizing a measure of the data misfit φ d and a smoothing functional φ r. Since 1 controls the sensitivity of the regularized solution, it should be chosen so that a good balance is assigned to smoothing functional, thereby warranting that the observations are well reproduced by the model. Because of the lack of depth resolution in the modeling procedure (Fedi and Rapolla 1999), when the inversion is performed to minimize the functional in (Eq. 5), the magnetization solution x is concentrated close to the observation points. Therefore, the smoothing functional is defined in a way to give prisms at different depths equal probability to enter in the solution. Li and Oldenburg (1996) introduced a depth-weighting function that leads to the following functional: φ ¼ 1 2 ½ðAx T obsþ T ðax T obs Þ þ1ðx x 0 Þ T W T Wðx x 0 ÞŠ ð6þ where W is a diagonal weighting matrix whose elements are the weights associated with all the elements in the m vector of unknown prisms magnetizations. The weighting matrix takes into account that a magnetized prism acts like a dipole source whose magnetic field decays as the inverse distance is cubed. Therefore, the weights are computed using the values of the field due to a prismatic source, computed by means of the Blakely (1995) solution. The weighting values are then normalized so that the maximum value is unity. The minimization of this functional could provide an unfeasible solution if no bounds are imposed on the magnetization values. To ensure that the solution is geologically reasonable, it is advisable to prescribe realistic bounds on the magnetization values on the basis of rock samples or available information on local geology. The constraints on the magnetization values allow guaranteeing that no abnormal solution is retrieved in the model. The

6 minimization of the quadratic functional in Eq. (5) subjected to bound constraints can be solved by using a quadratic programming (QP) algorithm based on an active set strategy (Gill et al. 1991): min φ ¼ min 1 2 xt Qx d T x ; L x U ð7þ where Q ¼ A T A þ lw T W and d ¼ A T T þ lw T Wx 0, and L and U are the vectors of lower and upper bounds of magnetization values. The quadratic formulation of the problem is solved iteratively by generating a sequence of feasible solutions that converge toward the optimal solution. The iteration is stopped when no relative improvements in the functional are achieved. 3D magnetic model In order to allow the maximum flexibility for the model to represent geologically realistic structures, the island was represented as a crustal block, 4 3 km 2 in area and about 1.2 km in thickness, and was discretized into a set of rectangular prisms having a constant magnetization. Horizontal and vertical dimensions of rectangular prisms were taken as variables (Fig. 5) to account for the higher resolution required in diverse areas. In particular, in order to better approximate the topographic relief, we considered a set of prisms above the sea level, each km 3 in size. Below sea level, prisms have km 2 horizontal area and a thickness of 0.2 km, and, to take the side effect of source bodies surrounding the observational area into account, we introduced a regular array of prisms which are km in horizontal extent and 0.4 km in vertical extent. Finally, the bottom depth of the model was assumed to be 1.2 km b.s.l. This depth has no particular geologic and geophysical meaning but is closely related to the extension of the survey. Indeed, it is well known that depth resolution depends on the real source-observation Table 1 Parameters used for data inversion Parameters Observed level km a.s.l. Grid width m; m Inclination of the Earth s N magnetic field Declination of the Earth s W magnetic field Window dimension 4 3 km Depth to the bottom 1km of the synthetic model Constraint 0< J NRM <10 Am 1 distance (Fedi and Rapolla 1999) and, in particular, it decreases as the cube of this distance. The anomaly field was inverted assuming that the average direction of the total magnetization is close to Earth s present-day field direction (inclination of 54 N, declination of 1.5 W). The remanent magnetization is generally much greater than induced magnetization and rocks of Ustica were emplaced about 0.73 Ma (de Vita et al. 1995) after the last field reversal (0.78 Ma; Champion et al. 1988). Since the magnetic properties of volcanic rocks cropping out in the Ustica island had not been measured in the past, more than 20 specimens (Fig. 1) were collected over the whole island during the survey to characterize their magnetic properties (Angelino et al. 2004). Different volcanic units, including lava flows, dikes, submarine basaltic lavas, tuff, hyaloclastites and pillow lava, were sampled and 2 3 specimens were gathered for each. Remanent magnetization (J NRM ) and susceptibility (χ) of rock specimens were measured in laboratory tests. These measurements show J NRM and χ values ranging from 1 to 5 Am 1 and from to S.I., respectively. The Fig. 5 Schematic configuration of the synthetic model used for the inversion process Fig. 6 The L-curves of the data misfit versus the model norm as a function of the regularization parameter. The point of maximum curvature lies on a corresponding value of 1= λ=200

7 Fig. 7 Computed magnetic anomaly map related to the value of 1=200 highest values are associated to dikes, while the lower ones are related to volcaniclastic deposits. On the basis of these magnetization values, the inversion of the data set was performed constraining the range of J NRM for the assumed sources from 0 to 10 Am 1. Actually, the J NRM observed at Ustica range from 1 to 5 Am 1, but considering that intensity of magnetization can vary widely within volcanic units, both laterally and vertically because of changes in composition, grain size, and concentration of magnetic minerals (Rosenbaum 1993), magnetization values outside this range should be taken into account. Parameters used for the data inversion are summarized in Table 1. The iterations were continued until the minimization of the functional φ showed no further improvements. Additional studies may lead to choose the most geologically reasonable model. However, in our case, no drills and interpretations from other geophysical data are available, therefore the solution was chosen on the basis of the regularization parameter 1. Among the several techniques developed to properly estimate 1 in an ill-posed inverse problem we used the L-curve criterion (Farquharson and Oldenburg 2004). Following this method, a family of solutions is achieved by varying 1 from 0 to and the data misfit φ d of the regularized solutions is plotted versus the corresponding Fig. 8 Residual, total-field magnetic anomaly map produced by subtracting the computed field from the observed field

8

9 R Fig. 9 The 3D magnetization model of the Ustica volcanic complex. Horizontal sections of the model: above sea level (a) and from 100 1,100 m in depth (b) smoothing functional φ r (Fig. 6). In the horizontal part of the L-curve (data misfit constant), the smoothing functional ϕ r increases rapidly without much of a decrease in the data misfit φ d. For lower value of 1, the overall functional φ is less influenced by φ r. Since the smoothing functional φ r balances the contributions of deeper prisms by means of a depth-weighting function, the models obtained in correspondence of the horizontal part of the L-curve tend to overestimate the magnetization values of shallower prisms. In the vertical part of the L-curve (smoothing functional constant), the data misfit φ d increases without reducing the smoothing functional φ r. For higher values of 1, the overall functional ϕ is more influenced by φ r. Therefore, the models obtained in correspondence of the vertical part of the L-curve tend to strongly enhance the contribution of deeper prisms. The 1 value in correspondence of the point of maximum curvature represents a compromise between minimizing the data misfit φ d and the smoothing functional φ r (Farquharson and Oldenburg 2004). A value of 1=200 was achieved and the related computed magnetic anomalies field is shown in Fig. 7. It agrees well with the observed field. The residual field, the difference between the observed field and the calculated field, shows a standard deviation of 5.3 nt (Fig. 8). Only in the northeast and southwest area of the island two small anomalies remain having an amplitude greater than 10 nt and this is probably due to the volume discretization. The volcano magnetization model resulting from the constrained inversion of data set is shown in Fig. 9. Calculated magnetizations range between 0 and 6 Am 1, which are in good agreement with the measured values. The accuracy on the obtained magnetization values for the unknown prisms was estimated from the square-root of the diagonal elements of the inverse Q matrix in Eq. (7) (Gill et al. 1981). The accuracy is related to the prisms' depth, location, and, in particular, it reaches a maximum value of about 0.9 Am 1 for deeper prisms, whereas it is below 0.5 Am 1 for shallower ones. Discussion A 3D magnetic model allows one to reveal the tectonic and volcanic features defining some fundamental aspects of the structural framework of the Ustica volcanic complex. The western side of the island is characterized by a N S alignment of magnetization highs with an intensity of 3 Am 1 (Fig. 9a). The magnetization values decrease with depth up to disappearing at about 0.5 km b.s.l. (Fig. 9b). The distribution of magnetization seems to correspond to the N S basaltic dikes cropping out in the north of this area, but its extension, about 2 km, reveals more subsurface dikes and/or shallow and local volcanic structures than exposed ones. Another area of magnetization highs is located on the eastern side of the island between the volcanic edifice of Mt. Guardia dei Turchi and the cone of Capo Falconiera, which are the oldest (500 ka in age) and the most recent (150 ka) subaerial eruptive centers (Romano and Sturiale 1971; Cinque et al. 1988), respectively. At very shallow depth, this volume shows a N S orientation with a magnetization intensity of 4 Am 1, but with increasing depth the magnetization intensity diminishes and the relative source which, reasonably, may be related to the volcanic edifice of Capo Falconiera seems to continue offshore. In the middle of the island, in correspondence with Mt. Guardia dei Turchi, the model reveals an area of magnetization intensity of about 2.5 Am 1.At the surface (Fig. 9a), it is roughly elliptical in shape, with a W E orientation and corresponds mainly to the endogenous dome cropping out on the summit of Mt. Guardia dei Turchi. Both the intensity and areal extent increase with depth reaching the maximum values of 4 Am 1 and 2.5 km, respectively, at about 500 m b.s.l. Below this depth it extends in a NE SW direction and the rocks' magnetization gradually decreases (Fig. 9b). This intense magnetization may be related to the presence of a magnetic body interpreted as the feeding conduits of basaltic eruptions and magma intrusions that supplied the construction of this volcanic centre. It is worth stressing that the NE SW trend is one of the main regional fault systems characterizing Ustica Island (Bousquet and Lanzafame 1992); therefore, this assumed preferential way for magma ascents seems to be controlled by the regional stress field. From 100 to 1,100 m b.s.l., on the westernmost side of the island, an area with magnetization intensity of about 3.5 Am 1, is detected, which continues offshore, Also in this case, the rocks' magnetization reaches a maximum intensity at about 500 m b.s.l. and gradually decreases with depth. The old ( ka) (Romano and Sturiale 1971; Cinqueetal. 1988) submarine/subaerial eruptive centers of Case Zacame and Contrada Spalmatore and their products, mostly consisting of hyaloclastites and pillow lavas, are interpreted as the source volumes of this magnetization intensity. Finally, it appears clear that the magnetized volumes ascribed to the N S basalt dikes outcropping on the western side of the island are related to the plumbing system of the Mt. Guardia dei Turchi. In contrast, the magnetized highs found in the westernmost and eastern areas are well isolated, but not completely described since they continue offshore. It is worth noting that at the model bottom, at about 1.1 km b.s.l., magnetizations greater than 1 Am 1 are still present in the middle and on the western side of the Ustica volcanic complex. Considering that the island represents

10 the emergent part of a volcanic complex over 2,000 m high and extending about 100 km 2 in area (Alletti et al. 2005), it is reasonable to assume that magnetized rocks also extend below the investigated depth. The magnetic features described show three main trends, NE SW, N S, and E W, which are in good agreement with the surface geology, and are coincident with the main structural lineaments of the Tyrrhenian seafloor (Bousquet and Lanzafame 1992). This evidence supports the strong influence of the regional tectonic both on the volcanic activity and structural development of the island. Moreover, considering that the NE SW trend prevails only in the deeper part of the model and is replaced at the shallow and intermediate depths by the N S and E W orientations, it is possible to assume that a change of the tectonic style and/or its orientation took place in the past. This observation is consistent with alternation of cycles of extensional and compressive tectonic events that dominated the structural framework of the complex and which are related to the interference between the compressive domain of the Apennine chain and the extensional one of the Tyrrhenian basin. Conclusions Three-dimensional inversion of magnetic field data was performed to produce a magnetization model that provides useful information to reconstruct the subsurface structure of the Ustica volcanic complex. Though the linear inverse problem is underdetermined, the quadratic programming algorithm allows reducing the class of possible solutions by imposing constraints on the magnetization value in a geologically reasonable range. The algorithm proved to converge toward the optimal solution in a finite number of iterations. The 3D model reveals the presence of three main magnetic trends, N S, E W, and NE SW, which are coincident with the main regional structural lineaments. This evidence supports the key role played by the regional tectonics in the structural and magmatic evolution of the Ustica volcanic complex. In particular, the N S and E W trends, which are of more recent origin, prevail in the shallow part of the model, while the NE SW is relevant below 0.4 km b.s.l. At this depth, the model reveals a magnetized body in the central area, which may be interpreted as the preferential area for magma storage and ascent and which supplied the feeding systems of the main subaerial volcanic centers of the island, Mt. Guardia dei Turchi and Mt. Costa del Fallo. Two other magnetized volumes were identified and ascribed to the small submarine/subaerial eruptive centers of the western island and to the younger cone of Capo Falconiera, respectively. These volumes are not completely defined since they continue offshore, therefore marine or aeromagnetic surveys of the surrounding areas of the island could help to better clarify further features of our model. 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