Vol51,1,2008_DelNegro 67 ANNALS OF GEOPHYSICS, VOL. 51, N. 1, February 2008 Key words time gravity changes – gravity record – volcanic processes – air pressure admittance 1. Introduction A wide set of dynamic phenomena (i.e. ge- odynamics, seismicity, volcanic activity) can produce temporal gravity changes, with a spec- trum varying from short (1-10 s) to longer (more than 1 year) periods. An impending erup- tion, for instance, is generally associated with the ascent of magma producing changes in the density distribution at depth, and leading to ground deformation and gravity changes ob- served at surface. The amplitude of such gravi- ty variations is often quite small, on the order of 10−9-10-8 g (10-102 nms−2; 1-10 µGal), so their detection requires high quality data and a rigor- ous procedure to split up from the records those weak gravity signals coming from different sources. What exactly would Time-Variable Gravity (TVG) tell us about mass redistribution below a volcano? The detected TVG is the sum Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius Umberto Riccardi (1), Giovanna Berrino (2), Gennaro Corrado (1) and Jacques Hinderer (3) (1) Dipartimento di Scienze della Terra, Università degli Studi di Napoli «Federico II», Napoli, Italy (2) Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Napoli, Italy (3) Ecole et Observatoire des Sciences de la Terre (EOST), Institut de Physique du Globe de Strasbourg, Université Louis Pasteur (UMR 7516 CNRS-ULP), Strasbourg (France) Abstract This research is intended to describe new strategies in the processing and analysis of continuous gravity records collected in active volcanic areas and to assess how permanent gravity stations can improve the geophysical monitoring of a volcano. The experience of 15 years in continuous gravity monitoring on Mt. Vesuvius is dis- cussed. Several geodynamic phenomena can produce temporal gravity changes. An eruption, for instance, is as- sociated with the ascent of magma producing changes in the density distribution at depth, and leading to ground deformation and gravity changes The amplitude of such gravity variations is often quite small, in the order of 10-102 nms-2, so their detection requires high quality data and a rigorous procedure to isolate from the records those weak gravity signals coming from different sources. Ideally we need gravity signals free of all effects which are not of volcanic origin. Therefore solid Earth tide, ocean and atmospheric loading, instrumental drift or any kind of disturbances other than due to the volcano dynamics have to be removed. The state of the art on the modelling of the solid Earth tide is reviewed. The atmospheric dynamics is one of the main sources preclud- ing the detection of small gravity signals. The most advanced methods to reduce the atmospheric effects on grav- ity are presented. As the variations of the calibration factors can prevent the repeatability of high-precision meas- urements, new approaches to model the instrumental response of mechanical gravimeters are proposed too. Moreover, a strategy for an accurate modelling of the instrumental drift and to distinguish it from longterm grav- ity changes is suggested. Mailing address: Dr. Umberto Riccardi, Dipartimento di Scienze della Terra, Università degli Studi di Napoli «Fe- derico II», Largo S. Marcellino 10, 80138 Napoli, Italy; e- mail: umberto.riccardi@unina.it Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 67 68 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer could be useful to characterize the deformation- al behaviour in some geodynamic contexts. Several investigations (e.g., Melchior and Ducarme, 1991; Melchior, 1995; Robinson, 1989, 1991) carried out to date show for in- stance that a correlation exists at «regional» scale between heat flow and the gravity tide. At very local scale Arnoso et al. (2001) suggest that the tidal response can be strongly influ- enced by the structure and mechanical proper- ties of the Crust. Those anomalies are associat- ed, respectively, with areas of thin crust, high heat flow values, and recent basaltic-type vol- canic activity, and with stable structures that have a deeper Moho discontinuity and lower heat flow. Robinson (1989, 1991) relates the correlation found in his studies to features in the upper crust, suggesting a measurable upper crustal tidal response. Arnoso et al. (2001) ob- tained interesting results from the analysis of the gravity tide collected in two continuous sta- tions in Lanzarote island (Canary islands- Spain). After a suitable reduction of the OTL effect by means of global ocean charts comple- mented with regional and local ones, they ob- tained anomalous M2 and O1 delta factors and phases consistent with a body tide effect. These results were interpreted as the response of a porous or cavity-filled, local, upper crust under the influence of tidal strain. Moreover, knowledge of the specific tidal parameters for an area is required to calculate the luni-solar effect, which has to be removed from the gravity record to obtain gravity resid- uals. As we are interested in modelling the trans- fer function between the observed gravity and the underground mass redistribution due to vol- canic activity, ideally we need residual gravity signals free of all effects which are not of vol- canic origin. In fact, natural (mainly body tides), man-made and instrumental sources af- fect the signal to noise ratio and hide the subtle volcanic signals. Therefore solid Earth tide, ocean and atmospheric loading, instrumental drift, hydrological effects or any kind of distur- bances other than due to the volcano dynamics have to be modelled to be reduced in the gravi- ty signal. The atmospheric dynamics is one of the main sources precluding the detection of of the gravitational signals originating from all geophysical sources at work at any given time. Sorting out different geophysical signals in the data is a challenge, but in principle can be facil- itated by recognizing the different temporal and spatial characteristics of different geophysical phenomena (e.g., Chao, 1994). Unlike the repeated relative gravity meas- urements on network, there are limited data on continuous gravity observations at active volca- noes (e.g., Imbò et al., 1965a; Davis, 1981; Vieira et al., 1991; Goodkind and Young, 1991; Berrino et al., 1997; Budetta and Carbone, 1997; Bonvalot et al., 1998; Arnoso et al., 2001, Carbone et al., 2003, 2006). Two different approaches may be adopted to extract from the gravity records some insights related with the volcano dynamics, i.e., the analysis of the tidal gravimetric factor (delta: δ) and the analysis of gravity residuals. According to the recommendations of the Working Group on the Theoretical Tidal Model (SSG of the Earth Tide Commission Sec. V of the IAG), the delta factor (δ) is defined as the Earth’s transfer function between the body tide signal (∆gn(r)) measured at the station by a gravimeter and the amplitude of the vertical component of the gradient of the external tidal potential (Vn) at the station. where r is the radius of the Earth and , ,are volume Love numbers of degree n (complex value), which characterize the spherical elasticity of the Earth. Thus delta factor is the ratio between the observed gravity tide and the luni-solar gravita- tional attraction. As it defines the Earth transfer function of the external tidal potential, the delta factor is frequency-dependent and is related to the elastic property of the Earth. Because of the viscoelastic behaviour of the Earth, its reaction to the external perturbation due to the luni-solar gravitational attraction is characterized by a certain phase shift. So the study of the tidal pa- rameters (delta factor and phase) for the main tidal waves and eventually their time evolution knuhnu n h n n k1 2 1 n n nδ = + - +u u u ( ) n r g r Vn n nδ∆- =u u Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 68 69 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius small amplitude gravity signals. Pressure changes can reach several tens of hecto-Pascal (say 50 hPa) in specific locations, so the ampli- tude of the atmospheric contribution to gravity is as large as 200 nms-2, then it could be higher than volcanic signal. This is why a large part of this paper have been devoted to illustrating the most advanced developments in that field of re- search and the experience of the authors is pre- sented. The goal of this paper is to describe new strategies in the processing and analyses of con- tinuous gravity record collected in active vol- canic areas. The experience of about 15 years at Mt. Vesuvius (Southern Italy) is reported. The time dependent behaviour of the tidal gravimet- ric factors is compared with the results from relative and absolute gravity surveys and seis- mic activity. The results are interpreted in the framework of the present-day dynamics of Mt. Vesuvius. Mt. Vesuvius is a quiescent volcano whose last eruption occurred in March 1944. Current- ly, its activity consists of a low level of seismic- ity, sometimes increasing in numbers of quakes and energy (hereafter called seismic crises), small ground deformation, gravity changes and moderate gas emission. 2. The Mt. Vesuvius permanent gravity station The Mt. Vesuvius recording gravity station (fig. 1) is located at the Osservatorio Vesuviano (fig. 1), where a recording gravity station has been operating since 1987 (Berrino et al., 1993b) and where a first experiment of contin- uous gravity measurements dates back to 1960s (Imbò et al., 1964, 1965a). The permanent sta- tion is assembled on a concrete pillar located in an artificial cave, 20 m deep (ϕ: 40.828N, λ: 14.408E; h: 608 m) (Berrino et al., 1997), where the daily temperature variations are about 0.1°C and the annual ones are within 2°C. The gravity sensor is the LaCoste and Romberg model D, number 126 (LR-D126), equipped with a feedback system (van Ruym- beke, 1991), with a range equivalent to 3⋅104 nm/s2 (implemented at the ROB, Royal Obser- vatory of Belgium in Brussels and upgraded in 1994). The data acquisition is provided by DAS or mDAS systems developed at the ROB (van Ruymbeke et al., 1995) at a sampling rate of 1 data/min (0.01667 Hz). Here we focus on the results of gravity records since 1994 (fig. 2), when the instrument and siting of the station were improved. The station belongs to a rela- tive gravity network, spanning the Vesuvian area, periodically surveyed since 1982. It is close to an absolute gravity station established on the volcano in 1986. The absolute value of g was measured in 1994, 1996, 1998 and 2003 (Berrino, 1995; Berrino, 2000). In order to check the reliability of the grav- ity signals, the instrumentation is periodically calibrated and the background noise level at the station is analyzed. In fact, instrumental sensi- tivity can change, not always linearly, as a con- sequence of mechanical perturbations and the noise level at the gravity station. To character- ize the background noise level, which could af- fect the instrumental response, the 1 min sam- pled residual gravity was analyzed to detect any Fig. 1. Location of the recording gravity station and gravity network on Mt. Vesuvius. Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 69 70 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer Fig. 3. Power spectra of the background noise level computed in each seasons at the Mt. Vesuvius gravity sta- tion, with the indication of the standard New Low Noise Model (NLNM) as reference. Fig. 2a,b. Hourly values of gravity records (a), drift corrected gravity residuals (b). Anomalous record with ab- normal drift and very large residuals are highlighted in circles. possible seasonal dependence or the presence of spectral components which could hide or mask geophysical signals. Several time win- dows lasting about 1 week were selected in each season. The amplitude and spectral con- tent of the noise (Berrino and Riccardi, 2004) show a flat trend in the analyzed spectral band (fig. 3), according to the standard New Low a b Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 70 71 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius Noise Model [NLNM] (Peterson, 1993). The high noise level during the autumn is a conse- quence of the meteorological condition (mainly wind) at Mt. Vesuvius during that season. Changes through time of the calibration fac- tors for different kinds of mechanical gravime- ters have been detected by several authors (e.g., Bonvalot et al., 1998; Budetta and Carbone, 1997; Riccardi et al., 2002). However, a com- plete understanding of the physical processes affecting the instrumental sensitivity is still far from being achieved. As changes in instrumen- tal sensitivity can prevent the repeatability of measurements and affect the phase and ampli- tude of the recorded gravity signals, the accu- rate calibration of gravimeters plays a key role in high precision gravity measurements (Ric- cardi et al., 2002). The calibration of a gravime- ter at an accuracy level of 10−8 to 10−9 g, is dif- ficult to attain because of the many problems in pursuing a known gravity change («standard») at such a level of accuracy. The stability of the calibration factors of LR-D126 has been peri- odically investigated on site. This kind of cali- bration is obtained by inducing changes in the spring length through a known «dial» turning and fitting this, by least-squares, against the in- strumental output. This is the most frequently Table I. Comparison between LR-D126 and superconducting SG-TT70-T015 meters: results (delta factor and phase) of the tidal analysis for the main tidal waves. In the last column the ratio (SG/D) of delta factors obtained by the records from the superconducting and D meters is listed. The tidal waves nomenclature is: O1-Diurnal lu- nar; P1-Diurnal lunar; K1-Diurnal luni-solar; S1-Diurnal solar; M2 Semi-diurnal lunar; S2 semi-diurnal solar. LR-D126 SG-TT70-T015 Wave Delta Phase (°) Delta Phase (°) LR/SG O1 1.147 ± 0.003 -0.2 ± 0.1 1.14 ± 0.01 -0.1 ± 0.6 1.006 ± 0.009 P1S1K1 1.137 ± 0.002 0.0 ± 0.09 1.130 ± 0.009 0.1 ± 0.6 1.006 ± 0.007 M2 1.184 ± 0.001 1.14 ± 0.06 1.176 ± 0.003 0.9 ± 0.2 1.007 ± 0.004 Fig. 4. Calibration factors obtained with on-site and absolute calibration for LR-D126 gravity meter; units of vertical axis (ndiv) are number of scale divisions. Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 71 72 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer adopted calibration procedure for continuous gravity station equipped with relative mechani- cal instruments. Various schemes of dial turn- ing have been tested at Mt. Vesuvius station (Riccardi et al., 2002). Hereafter, such calibra- tions are referred to as «on-site» calibrations. Moreover, two additional calibrations of the feedback were carried out in June 1994 and No- vember 1997 in Sèvres, at the Bureau Interna- tional des Poids et Mesures (BIPM) during the International Comparison of Absolute Gravimeters (Becker et al., 1995, 2000). A cal- ibration of the instrumentation was also ob- tained in 1997 by means of a joint intercompar- ison with the superconducting gravimeter SG- TT70-T015 (table I) and the absolute FG5-206 gravimeter (Riccardi et al., 2002). The inter- comparison between spring and superconduct- ing gravimeters is the most suitable way to de- termine the transfer function of spring gravime- ters in the tidal band. Detailed information on the different calibrations and operational proce- dures carried out at this station are given in Ric- cardi et al. (2002). The time distribution of the calibration factor is shown in fig. 4. In this plot the value from the intercomparison with the FG5-206 absolute gravimeter is shown and the suitable range of repeatability of the calibration factor at 1% level is also drawn. A large scatter- ing of the calibration factor occurs from 1999 to 2001, when some anomalous signals were de- tected. The anomalous signals (highlighted in fig. 2a) were characterized by an abnormal drift and then very large gravity residuals. As a consequence, the tidal analysis on the 1998-2000 data furnished a sharp decrease of the δ factors at the beginning of 1999 (Berrino and Riccardi, 2001). A theoretical value of the instrumental sensitivity was computed and compared with the calibration factors moni- tored «on site» to evaluate whether the calibra- tion factor truly reflects changes in the instru- mental response or is merely due to the adopt- ed «on site» calibration procedures. The theo- retical instrumental sensitivity was determined by a regression analysis between the meter’s output signal and the synthetic gravity tide. Thus, a set of weekly theoretical values of cali- bration factor was obtained and compared with the results from the repeated calibrations (fig. 5). A good agreement between the temporal evolution of the theoretical factors and those obtained through the «on site» calibration was detected (Riccardi et al., 2002). Moreover, the set of the «on site» and theoretical calibration factors has been plotted against the time occur- rence of certain large worldwide earthquakes (ML > 5) that shook the meter strong enough to send it out of range (fig. 5). A time correlation between the larger changes of instrumental sen- sitivity and the occurrence of seismic events can be observed. More detailed discussion con- cerning the instrumental sensitivity changes on the occasion of large earthquakes is given in Fig. 5. On-site and theoretical calibration for LR-D126 against the occurrence of some large earthquakes (ML >5); «shot» on vertical axis is the arbitrary unit for the feedback frequency output. Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 72 73 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius Riccardi et al. (2002) and Berrino and Riccardi (2004). They suggest a mechanical perturbation of the sensor, due to some dominant frequen- cies of the noise at the station on the occasion of large earthquakes. In fact the higher frequen- cy of the seismic free oscillation excited by large earthquakes includes the fundamental mode of oscillation (T0: 15 to 20 s) of the La- Coste and Romberg spring gravimeters (Torge, 1989). These instrumental disturbances due to large earthquakes can last several weeks. 3. Ocean loading and atmospheric reduction The state of the art of the modelling of the ocean loading effect on local gravity data is hereafter reviewed and the most advanced methods in pursuing the reductions of the at- mospheric effects are presented. To focus on the methodological upgrades, we present our attempt to model the barometric «local» effect on gravity data in a stable non-volcanic area by means of a barometric array. However, by the way of the methodological approaches, these results can be fruitfully applied to fix the prob- lem of air pressure effect on local TVG in vol- canic areas. In a very general sense, Ocean Tide Loading (OTL) is the deformation of the Earth due to the weight of the ocean tides. The ocean tides in- duces water mass redistributions causing peri- odic loading of the ocean bottom. The Earth’s deformation (vertical and horizontal displace- ment, TVG, tilt and strain) under this load is called ocean tide loading. The ocean tides as well as the body tides have more than one peri- odicity, so they can be described as the sum of several harmonic components having their own period. Problem areas are mostly islands and shallow seas with large tidal amplitude and fast varying phase lag. These include among the others in Europe: the Mediterranean Sea and the North Sea. To compute the ocean tide loading the ocean tides are integrated with a weighting function G (3.1) Here L is the loading phenomenon (displace- ment, gravity, tilt or strain) at the station locat- ed at distance r. The ocean tide at r’ is given in its complex form Z=Aeiϕ, where ϕ is the phase; ρ is the mean density of sea water and G is Green’s function for the distance |r−rl|. The in- tegral is taken over all global water masses A. ( ) ( )L r Z r G r r dA A ρ= -l l# Table II. Amplitude (L; in nm s-2) and phase (ϕ in degrees) of the main harmonics of the OTL computed for Mt. Vesuvius station by means of different models. SCW80 CSR 3.0 FES 95.2 TPXO 6.2 TPXO 7.0 Wave L ϕ L ϕ L ϕ L ϕ L ϕ M2 11.5 -85.4 9.2 -68.0 10.6 -69.1 9.5 -67.8 9.6 -66.9 S2 4.0 -58.8 3.1 -58.6 4.0 -58.1 4.6 -57.7 3.3 -49.6 N2 2.3 -100.3 1.7 -82.4 2.2 -84.9 2.1 -66.7 2.2 -80.5 K2 1.1 -58.9 0.8 -59.1 1.1 -63.4 0.9 -33.9 1.1 -37.6 K1 1.1 -131.8 2.0 -84.1 2.8 -76.6 1.5 -83.9 1.5 -81.1 O1 1.2 169.0 1.3 -131.7 2.0 -145.3 1.3 -147.4 1.3 -153.0 P1 0.4 -136.8 0.7 -90.0 0.9 -84.4 0.6 -100.3 0.4 -121.8 Q1 0.3 116.2 0.1 167.7 0.3 168.2 0.4 129.9 0.4 131.4 MF 0.4 -16.8 0.5 27.1 0.5 27.1 0.4 33.8 0.3 32.2 MM 0.2 -109.7 0.3 23.2 0.1 22.9 0.3 30.3 0.2 21.0 SSA 0.3 -93.1 0.3 4.5 0.2 3.9 0.3 4.5 0.3 4.5 Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 73 74 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer Green’s function determines how much the Earth deforms due to the point load (a general solution of this problem is given in Farrel, 1972). The next step is to replace the convolu- tion integral by a summation. Most ocean mod- els are given on a 0.5° by 0.5° grid, which jus- tifies direct summation over these ocean grid cells if the station is more than 10 km from the coast. Otherwise some re-gridding is necessary. Some local solutions (models) are obtained by means of a re-gridding the model gradually to- wards the station. Table II lists the amplitude (L) and phase (ϕ) of the main 11 harmonics of the OTL com- puted for Mt. Vesuvius station. These 11 har- monics are the largest in amplitude and repre- sent most of the total tidal signal. These have been computed by means of a free OTL provider developed at the Onsala Space Obser- vatory and maintained by M.S. Bos and H.-G. Scherneck (http://www.oso.chalmers.se/~load- ing/). Solutions coming from classical (SCW80) (Schwiderski, 1980) and most recent models (CSR 3.0; FES95.2, TPXO6.2, TPXO7.0) (Eanes, 1994; Le Provost et al., 1998; Egbert and Erofeeva, 2002) have been obtained. If the stations are close to the coast, like the Mt. Vesuvius one, an automatic interpo- lation is applied using a mask having a coast- line resolution of 0.6 km. Schwiderski’s model (SCW80) is one of the oldest and it has been considered the standard for many years. It is a hydrodynamic model, given on a 1° by 1° grid and uses an interpolation scheme to fit the tide gauges; SCW80 model does not account for the Mediterranean sea tide. FES95.2 is an upgrade of the FES94.1 model, a pure hydrodynamic tide model tuned to fit tide gauges globally, which includes the Mediterranean Sea tide. In FES95.2 the tides in the Arctic were improved and TOPEX/Poseidon satellite altimeter data has been used to adjust the long wavelength be- haviour of FES94.1. It has been calculated on a finite element grid with very fine resolution near the coast. The version used at Mt. Vesu- vius station is given on a 0.5° by 0.5° grid. The CSR3.0 models are nothing other than a long wavelength adjustment of FES94.1 model by using TOPEX/Poseidon data and are given on a 0.5° by 0.5° grid. TPXO.6.2 and 7.0 have been computed using inverse theory using tide gauge and TOPEX/Poseidon data. These models have a resolution of a 0.25° by 0.25° grid. The results lead to a maximum OTL effect at Mt. Vesuvius of about 10 nm/s2 (1 mGal) with a slightly lower amplitude obtained by means of models accounting for Mediterranean Sea tides. The amplitude and phase of such effect has to be accounted for to avoid a tidal modulation (diurnal and semi-diurnal) in the residual grav- ity signals. Besides solid Earth and ocean tides, atmos- pheric pressure variations are one of the major sources of surface gravity perturbations pre- venting a highly accurate detection of small amplitude gravity signals (see e.g., Hinderer and Crossley, 2000, 2004). The continual redis- tribution of air mass in the Earth’s atmosphere causes periodic variations in local gravity at the solar tidal frequencies as well as random varia- tions (Warburton and Goodkind, 1977; Spratt, 1982). Gravity (measured positive down) and local atmospheric pressure correlate with an ad- mittance of about −3.0÷−3.5 nms−2/hPa (e.g., Warburton and Goodkind, 1977; Müller and Zürn, 1983; Merriam, 1992). Knowing that pressure changes can reach 50 hPa in specific locations, the amplitude of atmospheric contri- bution to gravity may be as large as 200 nms−2, which is typically only 10 times less than the solid Earth tides. Moreover, because this effect varies both in time and with frequency (Richter et al., 1995), the contribution is spread over a wide spectral domain and may inhibit the ob- servation of small signals of non-tidal origin. The global atmosphere acts on surface gravity through two competing effects: a direct «New- tonian» attraction by air masses and an elastic contribution due to the Earth’s surface loading. The amplitude and polarity of these two effects vary with distance, so the net contribution of the atmosphere coming from different distances from the gravity station is variable (e.g., Spratt 1982; Merriam, 1992; Mukai et al. 1995; Boy et al. 1998). The coherence scale of pressure fluctuations and some considerations on the hy- drostatic approximation of the atmosphere, led some authors to suggest a division of the globe into «local» (within 50 km), «regional» (50- 1000 km) and «global» zones (> 1000 km) Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 74 75 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius (Atkinson, 1981; Merriam, 1992). In the local zone (< 50 km) pressure can change rapidly in time, but is spatially coherent, so that pressure observations collected at the gravity site are sufficient to obtain an accurate reduction with- in a few tenths of nm/s2 except when a front is passing through the local zone (Rabbel and Zschau, 1985). When a pressure front moves through or larger horizontal gradients affect the local zone, the band from 1 to 10 km from the gravity station becomes a critical area for which more detailed pressure data are needed. Atmospheric effects on gravity are routine- ly reduced using a barometric admittance, which is a simple transfer function adjusted by least square fitting between pressure and gravi- ty, both measured locally. The use of a single scalar admittance has been well established (e.g., Warburton and Goodkind, 1977; Crossley et al. 1995). When atmospheric pressure p (hPa) is recorded jointly with gravity g (nms−2) at a single station, the gravity can be reduced (gr) by using the relation (3.2) where pn is a reference pressure at the station and α is either a nominal value of −3.0 nms-2/hPa or determined by a least squares fit of p to g. The effectiveness and simplicity of this method has led to its widespread use in gravity studies for many purposes. This reduction typi- cally accounts for some 90% of the total atmos- pheric effect. The drawback of this method is that the admittance shows some variation with time (e.g., Richter, 1987; Van Dam and Francis, 1998), usually on seasonal time scales, whereas the atmosphere is certainly variable on short time scales and local weather systems can move rapidly over a station in a few hours (Müller and Zürn, 1983; Rabbel and Zschau, 1985). So there is no guarantee that the correlation im- plied by eq. (3.2) is satisfied over all length and time scales. Furthermore Crossley et al. (2002) found that the admittance is sensitive to the time averaging windows applied on data, name- ly a higher admittance is found for shorter win- dowing. Moreover, the simple reduction using only the local pressure measurements cannot take into account either the global scale or re- ( )g g p pr nα= - - gional (1000 km around the gravimeter) atmos- pheric effects. Several approaches using the local pressure more effectively have been attempted, particu- larly with a frequency dependent admittance (e.g., Warburton and Goodkind, 1977; Crossley et al. 1995; Neumeyer, 1995; Neumeyer et al., 1998; Kroner and Jentzsch, 1998; Van Dam and Francis, 1998). The method represents a trans- formation of the eq. (3.2) from the time domain to the frequency (ω) domain and allowing the admittance (α) to be frequency dependent (3.3) Minimising ⎮Gr(w)⎮2 over the whole frequen- cy range leads to (3.4) which is equivalent to the complex admittance defined by Warburton and Goodkind (1977). Crossley et al. (1995) demonstrated that the complex admittance, as expressed in eq. (3.4), is a powerful and versatile tool to model both local atmospheric effect and contribution due to the solar harmonics Sn and allows to select the frequency ranges of the air pressure reduction. 3.1. Atmospheric reduction by means of a barometric array Riccardi et al. (2007) investigated the effi- ciency of a barometric array (fig. 6) to improve the reduction of the «local» atmospheric effects on gravity data in normal weather conditions and also under extreme weather conditions. This research has been developed by using Su- perconducting Gravity (SG) data collected in Strasbourg and barometric records in five sites around the SG station at distances ranging be- tween 10 and 60 km (fig. 6). Six months of gravity and air pressure records (fig. 7) have been analyzed both in the time and frequency domains. Some further analyses have been ad- dressed on three time intervals (highlighted in fig. 7) characterized by large and fast air pres- sure changes. ( ) ( ) ( ) ( ) P G P 2α ω ω ω ω = / / ( ) ( ) ( ) ( )G G Pr ω ω α ω ω= - Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 75 76 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer Riccardi et al. (2007) used the multi-linear regression (MLR) method of Van Camp and Vauterin (2005) to express an objective signal sobj (gravity residuals) as a linear combination of a set of m component signals sc (air pressure record of each station) (3.5)drift residuals a sobj lm cm n m = + +/ Fig. 6. Location map of the superconducting gravimeter (filled circle) and the stations of the barometric array. Fig. 7a-c. The Strasbourg hourly data sets: a) gravity record; b) gravity residuals; c) air pressure. The time spans highlighted in gray are characterized by large and fast pressure changes and are the target of further analy- ses. b c a Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 76 77 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius In this study we set n=1 (a linear regression). The drift term, which is used to model the long- term instrumental behaviour in the gravity record consists of a polynomial of degree k (t is the time) (3.6) The parameters a1 ... an, b1 ... bn, were estimat- ed by least squares adjustment. b t$+fb b t b t b t$ $ $+ + + +=( )drift a p k0 1 2 2 3 3 Fig. 8a-f. Residual gravity obtained for a time span 11 days long during December 2000 (ref. fig. 7a-c). Com- parison of different kinds of reduction: a) by means of: a single admittance coefficient; b) a fit to pressure data from Strasbourg only; c) a fit to pressure data from the whole array; d) a frequency dependent admittance; e) air loading computed with the hybrid model; f) fourier spectrum of the reduced residual gravity. a b c d e f Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 77 78 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer The MLR approach allows us to jointly ac- count for the atmospheric effect as it can be probed trough the barometric array. A similar methodology has also been applied by Dittfeld (1995) and Kroner and Jentzsch (1998). The results obtained on the whole data set (6 months) demonstrated that negligible im- provement in the «local» atmospheric reduction derives from the use of an array, as also shown by Dittfeld (1995). Moreover the short length of our study did not permit us to investigate sea- sonal variations in the pressure reduction to gravity. We further compared the efficiency of the atmospheric reduction by means of the baro- metric array with the one performed through global loading computation (Boy et al., 2002; Petrov and Boy, 2004). We use ECMWF (Euro- pean Centre for Medium-range Weather Fore- casts) surface pressure fields from the 4Dvar model as they have the highest temporal (3 h) and spatial (0.5°) resolution. A more detailed description of the global loading computation is given in Riccardi et al. (2007) and Petrov and Boy (2004). The results showed that gravity residuals reduced by means of the atmospheric loading using the 4Dvar surface pressure are slightly worse than those obtained by applying a single admittance coefficient. This is likely due to the low resolution of the loading model, which is unable to reconstruct high frequency local barometric changes. These considerations could be extended when the mean atmospheric conditions are not far from the hydrostatic equilibrium. So we de- cided to analyze data during shorter time inter- vals, mainly characterized by abnormal weath- er conditions like when an atmospheric front is passing. Here the results for 11 days during De- cember 2000 are shown (figs. 7 and 8). In order to improve the time and spatial res- olution of the computed global atmospheric loading, we tested a hybrid method which con- sists in the following steps: – a global loading reduction using the 3 h and 0.5°×0.5° grided surface pressure fields everywhere except in the local zone. The glob- al contribution has been recomputed from the 4Dvar model and oversampled to 60 s with spline interpolating functions; – a local loading reduction obtained by di- viding the local zone into a smaller grid using interpolated data and the 60 s pressure samples from the closest stations of the barometric ar- ray, except the central zone; – a central zone reduction using the J9 sta- tion pressure. All three contributions have been added leading to a hybrid time series of the atmos- pheric loading. The effect of the hybrid model in the load computation is clear, the increase in the model resolution has led to improve the ef- ficiency of the global loading reduction giving results similar to those obtained through the barometric array (fig. 8c,e). To evaluate the po- tentiality of each aforesaid method of reduction Riccardi et al. (2007) considered the standard deviation (σ) of the reduced gravity residuals as an estimator of the efficiency of the applied air pressure reduction. The standard deviations of gravity residuals reduced by means of the baro- metric array have been better than to those re- duced by using an air pressure record collected in a single station. The use of the barometer ar- ray lowers the standard deviation of the gravity residuals by about 30%. The improvement is essentially due to a removal of an almost quad- ratic background trend by using the array (see fig. 8a-c). The trend could be related to some coherent features of the barometric field at local scale sensed by the array. Moreover an im- provement in the atmospheric reduction has been achieved with a frequency dependent ad- mittance (fig. 8d); as demonstrated by several authors (Crossley et al., 1995), the reduction is significantly better mainly at high frequency (>2 cpd), because large-scale pressure fluctua- tions are less correlated with gravity than are local pressure fluctuations. In only one of the 3 periods of rapid changes we investigated did the array improve on standard methods, and even in that case the improvement was noticeable only in the low frequencies, but actually worse at high frequencies. The spectra of the unreduced and reduced gravity residuals according to all the reduction methods are also drawn (fig. 8f). They clearly show that a single admittance co- efficient is enough to reduce the energy in all the spectral bands. Data from the barometer network improve the reduction at low frequen- Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 78 79 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius cies (<2.5 cpd) while at higher frequencies the results are worse. In fact, comparing the gravi- ty residuals reduced by a single admittance co- efficient with those reduced through data from the barometric array (fig. 8a,c), an increase in high-frequency (>3 cpd) noise is quite evident. These features could be due to the summation of correlated high-frequency noise in the pres- sure data series. Hence the use of pressure data acquired by an array to improve the gravity re- duction requires special care, because they could introduce an artificial high-frequency noise. The application of the hybrid method im- proves the air pressure reduction in almost the entire spectral band except for the 2.0 cpd band (fig. 8e). This would be the result of two model defaults i.e. an inefficient tidal fitting in the residual gravity computation and an inadequate modelling of the air loading due to the thermal S2 component (see Ponte and Ray, 2002). Finally we note that during normal atmos- pheric conditions, when the atmosphere is in ap- parent hydrostatic equilibrium, the use of our lo- cal array of barometers gave no improvement over the use of the pressure at the station itself. Accounting for the geometry of the available barometric array and the typical amplitude (10−2 hPa) of the pressure signal in the «local» zone, we could expect some improvement with a more dense array of higher quality sensors using the methods described in this paper. A more general consideration arises from this experience: the highest level of develop- ment in air pressure reduction of local gravity data make sense only for gravity signals col- lected by superconducting gravimeters. Other- wise a single barometer can be enough to ac- count for the main part of the pressure effect originating in the local zone. However it is noteworthy that a significant progress in model- ling atmospheric effects, as demonstrated by several authors, can be pursued by using a fre- quency dependent admittance, which allows us to model the weather contribution at different frequency ranges. The reduction is significantly improved mainly at high frequency (>2 cpd) and consequently the reduced gravity residuals are much smoother than the others obtained by applying different kind of reductions. 4. Analysis of gravity record at Mt. Vesuvius and results This section reports the most remarkable re- sults coming from the experience of about 15 years of gravity recording at Mt. Vesuvius (Southern Italy). The time dependent behaviour Fig. 9. Calibration functions (dotted and continuous lines) interpolating the factors obtained with the on-site calibrations (points with error bars) and polynomial fitting (dashed line). The thickest line is the calibration func- tion adopted to convert gravity records in nm/s2. Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 79 80 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer of the tidal gravimetric factors is compared with the results from relative and absolute grav- ity surveys and seismic activity. The results are interpreted in the framework of the present-day dynamics of Mt. Vesuvius. To reduce the instrumental effect on tidal parameters (δ factors and phases) computed at Mt. Vesvius gravity station, a calibration func- tion has been computed to convert the recorded signal into nm/s2 (fig. 9); this function derives from the available data-set of the calibration factors periodically checked at the gravity sta- tion. In detail, two calibration functions have been computed respectively by including or ex- cluding the highest outlier of the calibration factors data-set obtained in 1999. The harmonic tidal analyses were repeated on the gravity record calibrated by means of the two functions to rule out any dependence of δ factors and phases from instrumental effects, namely the temporal changes of the calibration factors. Thus, taking into account these results, the first calibration function (dotted line in fig. 9) was rejected and we adopted the second function (bold continuous line in fig. 9) to cali- brate the gravity record (fig. 2) spanning 1999- 2001 interval. All of the gravity records were analysed to obtain tidal parameters and gravity residuals (fig. 2). The latter have been computed by sub- tracting the luni-solar effect (body tide), ac- cording to Tamura’s gravity potential catalogue (Tamura, 1987) from the gravity record, as well as a first order correction for the atmospheric effect and instrumental drift. The mean coeffi- cient, −3.5 nms−2/hPa, has been adopted to re- duce the atmospheric effect in gravity record (Berrino et al., 1997, 2000). The Wahr-Dehant- Zschau (WDZ) Earth model (Wahr, 1981; De- hant, 1987; Zschau and Wang, 1987) has been adopted to compute tidal parameters, while for the computation of gravity residuals a synthetic tide was calculated using tidal parameters com- puted from the local gravity records since 1994. As regards the reduction of the drift, accurate modelling is necessary to remove the instru- mental drift and to distinguish it from longterm gravity changes due to volcanic sources. This is mainly required in quiescent volcanic areas, where «slow» and small temporal gravity changes are expected. Otherwise in the case of large short-lasting (few hours or days) gravity variations, as observed in open-conduit volca- noes (Carbone et al., 2006), the instrumental drift can be easily modelled. Here, drift has been constrained by taking into account the temporal gravity changes ob- tained by both relative and absolute measure- ments periodically performed at Mt. Vesuvius. The latter show a negligible contribution on the trend observable in fig. 2b; thus, the long term component of the gravity record can be consid- ered instrumental drift. The drift corrected gravity residuals are shown in fig. 2b. The data set has been analysed by means of an algorithm for tidal analysis: «ETERNA 3.3» (Wenzel, 1996). The results for the main tidal waves are summarized in table III. The analyses have been performed on the gravity record re- arranged in some temporal subsets to check the time stability of the solutions and investigate the temporal changes of δ factors with a better resolution. The results of these tidal analyses have also been compared with the previous ones from 1987-1991 and the 1960 (table III, fig. 10c). Table III. Comparison among tidal gravimetric factors determined during the 1960s, 1987-91 and 1994-2000 (for tidal waves nomenclature refer to table I). Wave 1959-1961 1961-1965 1987-1991 1994-1998 1999-2000 Imbò et al. (1965a) Imbò et al. (1965a) Berrino et al. (1993b) O1 1.156 1.038 1.08±0.02 1.126±0.002 1.143±0.004 K1 P1S1K1:0.928 1.083 1.05±0.01 1.117±0.001 1.123v0.003 M2 1.154 1.068 1.11±0.01 1.1488±0.0007 1.155±0.001 S2 1.147 1.107 1.03±0.02 1.144±0.004 1.155±0.003 Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 80 81 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius Although a calibration function has been adopted, aimed at eliminating or at least reduc- ing the instrumental effects, the results of the tidal analyses (table III) show an increase in the δ factor in the period 1999-2000. Anyway the as- sumption of a calibration function and all the ef- forts aimed at achieve a rigorous calibration of the LCR D126 do not rule out bona fide some in- strumental effects on the observed delta tempo- ral changes at Mt. Vesuvius gravity station. It is noteworthy that these variations are well correlated with some changes in the activ- ity of Mt. Vesuvius. In fact a seismic crisis be- gan in October 1999 (Iannaccone et al., 2001) and a significant inversion of the trend of the gravity changes occurred in 1994 as deduced by both relative and absolute measurements. In order to better understand the relation- ship, if any, between the results of tidal analy- ses and volcano dynamics, δ factor and gravity changes have been reconstructed by the avail- able data for the last forty years and interpreted in the context of the activity of Mt. Vesuvius (fig. 10a-c). Fig. 10a-d. Time behaviour of Vesuvius dynamics from 1959 to 2001: a-b) seismic activity; c) tidal gravity fac- tor for M2 tidal wave; d) gravity changes (µGal) at the Osservatorio Vesuviano station plus gravity and elevation changes at Torre del Greco. a b c d Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 81 82 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer Figure 10d shows the observed TVG at the Osservatorio Vesuviano station. The reliability of this gravity change may be strongly con- strained by taking into account data from others stations of the Mt. Vesuvius relative gravity net- work. As an example, fig. 10d shows the gravi- ty changes at Torre del Greco, about 5 km SW of the Mt. Vesuvius crater, and the vertical ground movement continuously obtained by tide gauge data. Tide gauge data were collected very close to the Torre del Greco gravity sta- tion. An inversion of the trend, detected in 1993-1994, is also evident in the ground move- ment. A high degree of similarity in the changes observed at both stations is clear. The results of these tidal analyses have also been compared with the previous ones from 1987-1991 and the 1960s (table III, fig. 10c). An increasing trend from 1961 to the present in the amplitude of the tidal waves is clearly de- tectable. Taking into account the logistic and in- strumental differences between the 1959-1965 (Askania meter Gs9, Gs11) and 1987-2001 recording stations, a rough comparison among the different data can be made. From 1961- 1965 to 1987-1991, changes in the tidal param- eters cannot be considered significant, while an increase can be noted from 1991 to 1994 and, as previously discussed, in 1999-2000. The latter shows tidal parameters similar to the values de- termined in the 1959-61 time interval. It is noteworthy that the main changes in tidal parameters again seem well correlated with the temporal behaviour of the activity of Mt. Vesuvius (Berrino et al., 2006). At least three crises (1989-1991, 1996, 1999-2000) (figs. 10a-b) are reported (Berrino et al., 1993a; Vilardo et al., 1996; Iannaccone et al., 2001). Moreover, an increase in seismicity was also well documented in 1963-1964 (Imbò et al., 1965b). Concerning gravity changes, here we focus on the results of the episodic gravity measurements since 1982 collected on Mt. Vesuvius relative gravity network (Berrino, 2000; Berrino and Riccardi, 2000). The ob- served temporal gravity change at the Osserva- torio Vesuviano station (fig. 10d) shows an in- crease (more then 20 µGal/year) in the 1959- 1983 time interval (Berrino and Riccardi, 2000; 2001), as inferred by reviewing data collected during 1959-1960 (Tribalto and Maino, 1962) and 1965 (Bonasia, unpublished data) gravity surveys. This trend fits the gravity data collect- ed during the 1980s, when a continuous gravity increase affected the whole area (Berrino, 2000). Focusing on the most recent data (fig. 10), it is interesting to note that the increase of the d factor from 1991 to 1994 (fig. 10c) occurred during or soon after the 1989-91 seismic crisis. A gravity decrease of about 60 µGal (fig. 10d) (Berrino et al., 1993a) was also detected be- tween 1989 and 1991 at the Osservatorio Vesu- viano gravity station by both relative and ab- solute gravity measurements. The tidal response of the investigated area could indicate a variation in the deformational behaviour probably due to the change in the mean mechanical properties of Mt. Vesuvius, as already suggested by Berrino et al. (1997). Up to now any additional information on volcanic sources may be inferred by the gravity residuals. Although their time distribution clearly shows an increase in amplitude and scattering during 1998-2001, coinciding with the increasing seismicity, there are not enough clear gravity signals to detect or hypothesize the presence of volcanic input. 5. Conclusions The above described results show how the continuous gravity record on active volcanoes could be a useful investigative tool to detect volcanic inputs, but much care must be taken to remove from the recorded signals the effects due to the instrumental response and non-vol- canic sources. As changes in instrument sensi- tivity can reduce the repeatability of measure- ments and affect the phase and amplitude of recorded gravity signals, the accurate calibra- tion of gravimeters in high-precision gravime- try is topical. The stability of the calibration factors has to be deeply investigated through different calibration methods (e.g., inter-com- parison with AG and SG). Concerning the modelling of the non-vol- canic contribution to TVG, currently the tide generating potential is at a suitable level of ac- Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 82 83 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius curacy (1 nm/s2), so highly accurate catalogues of tide potential are available. Even the OTL modelling is highly accurate. The TOPEX/Po- seidon satellite altimeter data deeply improved the studies on the OTL effects. Nevertheless some local solutions are needed for instance for volcanic islands. Moreover the state of the art demonstrates that the gravity record could be able to charac- terize the deformational behaviour of the vol- cano through the time evolution of the δ factor. However, as mentioned by several authors (e.g., Arnoso et al., 2001; Robinson, 1991; Melchior, 1995), this points out the existing necessity of theoretical studies and observations of the high- est quality to answer the different questions re- garding the significance of the tidal gravity anomaly and how it relates to mechanical prop- erties of the upper crust. On the other hand, the capability of gravity residuals at least in the vol- canic area characterized by a low level dynam- ics, requires a significant improvement in mod- elling mainly instrumental drift. However, the joint application of relative, absolute and con- tinuous gravimetry is strongly recommended, to better remove the longterm instrumental drift. Thus the recognition of real gravity changes from apparent ones, due to instrumen- tal behaviour, becomes more reliable. Current- ly, no additional information on volcanic sources may be inferred from the gravity resid- uals at Mt. Vesuvius permanent station. An im- provement in the study of the mass redistribu- tion due to volcanic processes by means of gravity residuals could derive from the use of at least a reference station outside the volcano, which would make it possible to model and ex- clude long-term and non-volcanic «regional» effects (Berrino et al., 1997). In quiescent volcanic areas, undertaken by «slow» and small temporal gravity changes, it is hard to recover signals (residual gravity) re- lated to volcanic activity by means of mechani- cal gravimeters. This is mainly due to the strong and non-linear instrumental drift affecting the signals acquired by such sensors. The availabil- ity of SGs in active volcanic areas is hoped for because of their very small instrumental drift, high and stable sensitivity. SGs would allow to detect very slow and small TVGs often related with re-filling process of magma chamber. The reduction of the air pressure effects on local gravity through the most advanced meth- ods, such as global loading computation or ar- ray application, is redundant for TVG collected by means of mechanical gravimeters. Acknowledgements The authors are very grateful to J.-P. Boy from EOST for the computation of the global loading air pressure effect on local gravity. The authors are deeply indebted to the anonymous referee who greatly improved the paper with his/her comments and suggestions. For the final form of this manuscript the comments of D. Carbone have also been considered. The au- thors thank C. Del Negro from INGV for his editorial work. REFERENCES ARNOSO, J., J. FERNANDEZ and R. VIEIRA (2001): Interpreta- tion of tidal gravity anomalies in Lanzarote, Canary Is- lands, J. Geodyn., 31, 341-354. ATKINSON, B. W. (1981): Meso-Scale Atmospheric Circula- tions (Academic Press, London), pp. 495. BECKER, M., L. BALESTRI , L. BARTELL, G. BERRINO, S. BON- VALOT, G. CSAPÒ, M. DIAMENT, V. D’ERRICO , C. GAGNON, C. GERSTENECKER, P. ,JOUSSET, A. KOPAEV, J. LIARD, I. MARSON, B. MEURES, I. NOWAK, S. NAKAI, F. REHREN, B. RICHTER, M. SCHNÜLL, A. SOMERHAUSEN, W. SPITA, G. SZATMARI, M. VAN RUYMBEKE,H-G. WENZEL, H. WILMES, M. ZUCCHI and W. ZÜRN (1995): Microgravimetric meas- urements at the 1994 international comparison of ab- solute gravimeters, Metrologia, 32, 145-152. BECKER, M., G. BERRINO, A.G. CAMACHO, R. FALK, O. FRANCIS, J.E. FRIEDERICH, C. GAGNON, C. GERSTE- NECKER, G. LÄUFER, J. LIARD, B. MEURES, F.-J. NAVAR- RO, I. NOWAK, F. REHREN, U. RICCARDI, B. RICHTER, M. SCHNÜLL, D. STIZZA, M. VAN RUYMBEKE, P. VAUTERIN and H. WILMES (2000): Results of relative gravimeter measurements at the ICAG97 intercomparison, Bureau Gravim. Int. Bull. Inf., 85, 61-72. BERRINO, G. (1995): Absolute gravimetry and gradiometry on active volcanoes of Southern Italy, Boll. Geofis. Teor. Appl., 37 (146), 131-144. BERRINO, G. (2000): Combined gravimetry in the observa- tion of volcanic processes in Southern Italy, J. Geody- namics, 30, 371-388. BERRINO, G. and U. RICCARDI (2000): Non-statyonary compo- nents of the gravity field at Mt. Vesuvius (Southern Italy): correlations with different aspects of its present-day dy- namics, Comptes Rendus of 88th Journées Luxembour- geoises de Géodynamique (JLG), Munsbach 32-37. Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 83 84 U. Riccardi, G. Berrino, G. Corrado and J. Hinderer BERRINO, G. and U. RICCARDI (2001): Gravity tide at Mt. Vesuvius (Southern Italy): correlations with different geophysical data and volcanological implications, J. Geod. Soc. Japan, 47 (1), 121-127. BERRINO, G. and U. RICCARDI (2004): Far-field gravity and tilt signals by large earthquakes: real or instrumental effects?, Pure Appl. Geophys., 161, 1379-1397. dyn., 30, 371-388. BERRINO, G., U. COPPA, G. DE NATALE and F. PINGUE (1993a): Recent geophysical investigation at Somma- Vesuvius volcanic complex, J. Volcanol. Geotherm. Res., 53, 11-26. BERRINO, G., G. CORRADO, R. MAGLIULO and U. RICCARDI (1997): Continuous record of the gravity changes at Mt. Vesuvius, Ann. Geofis., 40 (5), 1019-1028. BERRINO, G., G. CORRADO, R. MAGLIULO and U. RICCARDI (2000): Continuous gravity record at Mount Vesuvius: a tool to monitor its dynamics, Phys. Chem. Earth A, 25 (9-11), 713-717. BERRINO, G., G. CORRADO, U. RICCARDI (2006): On the ca- pability of recording gravity stations to detect signals coming from volcanic activity: The case of Vesuvius, J. Volcanol. Geotherm. Res., 150, 270-282. BERRINO, G., B. DUCARME and R. MAGLIULO (1993b): Gravity tide and volcanic activity in Southern Italy, in Proceedings of the XII National Meeting Gruppo Nazionale Geofisica della Terra Solida, 997-1001. BONVALOT, S., M. DIAMENT and G. GABALDA (1998): Con- tinuous gravity recording with Scintrex CG-3M me- ters: a promising tool for monitoring active zones, Geo- phys. J. Int., 135, 470-494. BOY, J.-P., P. GEGOUT and J. HINDERER (2002): Reduction of surface gravity data from global atmospheric pressure loading, Geophys. J. Int., 149, 534-545. BOY, J.-P., J. HINDERER and P. GEGOUT (1998): Global at- mospheric pressure loading and gravity, Phys. Earth Planet. Int., 109, 161-177. BUDETTA, G. and D. CARBONE (1997): Potential application of the Scintrex CG-3M gravimeter for monitoring vol- canic activity: results of field trials on Mt. Etna, Sicily, J. Volcanol. Geotherm. Res., 76, 199-214. CARBONE, D., G. BUDETTA, F. GRECO and H. RYMER (2003): Combined discrete and continuous gravity observations at Mt. Etna, J. Volcanol. Geotherm. Res., 123, 123-135. CARBONE, D., L. ZUCCARELLO, G. SACCOROTTI and F. GRE- CO (2006): Analysis of simultaneous gravity and tremor anomalies observed during the 2002-2003 Etna eruption, Earth Planet. Sci. Lett., 245, 616-629. CHAO, B.F. (1994): The geoid and Earth rotation, in Geo- physical Interpretations of Geoid, edited by P. VANICEK and N. CHRISTOU ( CRC Press, Boca Raton), 285-298. CROSSLEY, D. and J. HINDERER (1995): Global Geodynam- ics Project – GGP, Cahiers du Centre Europeen de Géodynamique et de Séismologie, 11, 244-271. CROSSLEY, D.J., O.G. JENSEN and J. HINDERER (1995): Ef- fective barometric admittance and gravity residuals, Phys. Earth Planet. Int., 90, 221-241. CROSSLEY, D.J., J. HINDERER and S. ROSAT (2002): Using at- mosphere-gravity correlation to derive a time-depend- ent admittance, Bull. Inf. Marées Terrestres, 136, 10809-10820. DAVIS, P.M. (1981): Gravity and Earth tides measured on an active volcano, Mt Etna, Sicily, J. Volcanol. Geotherm. Res., 11, 213-223. DEHANT, V. (1987): Tidal parameters for an inelastic Earth, Phys. Earth Planet. Int., 49, 97-116. DITTFELD, H.-J. (1995): Non-tidal features in the SG-record at Potsdam, Cahiers du Centre Européen de Géody- namique et de Séismologie, 11, 79-88. EANES, R.J. (1994): Diurnal and semidiurnal tides from TOPEX/POSEIDON altimetry, Eos, 75, 108. EGBERT, G.D. and L. EROFEEVA (2002): Efficient inverse modeling of barotropic ocean tides, J. Atmos. Oceanic Technol., 19, 183-204. FARRELL, W. E. (1972): Deformation of the Earth by Surface Loads, Rev. Geophys. Space Phys., 10 (3), 761-797. GOODKIND, J.M. and C. YOUNG (1991): Gravity and hydrol- ogy at Kilauea volcano, the Geysers and Miami, Cahiers du Centre Européen de Géodynamique et de Séismologie, 3, 163-167. HINDERER, J. and D. CROSSLEY (2000): Time variations and inferences on the Earth’s structure and dynamics, Surv. Geophys., 21, 1-45. HINDERER, J. and D. CROSSLEY (2004): Scientific achieve- ments from the first phase (1997-2003) of the Global Geodynamics Project using a worldwide network of superconducting gravimeters, J. Geodyn., 38, 237-262. IANNACCONE, G., G. ALESSIO, G. BORRIELLO, P. CUSANO, S. PETROSINO, P. RICCIOLINO, G. TALARICO and V. TOREL- LO (2001): Characteristics of the seismicity of Vesuvius and Campi Flegrei during the year 2000, Ann. Geofis., 44 (5-6), 1075-1091. IMBÒ, G., V. BONASIA and A. LO BASCIO (1964): Marea gravimetrica all’Osservatorio Vesuviano, Ann. Osser- vatorio Vesuviano, 5 (S6), 161-184. IMBÒ, G., V. BONASIA and A. LO BASCIO (1965a): Variazioni della marea della crosta all’Osservatorio Vesuviano. Ann. Osservatorio Vesuviano, 7 (S6), 181-198. IMBÒ, G., L. CASERTANO and V. BONASIA (1965b): Consid- erazioni sismo-gravimetriche sulle manifestazioni vesuviane del Maggio 1964, in Proceedings of the XIV Convegno nazionale Associazione Geofisica Italiana, 291-300. KRONER, C. and G. JENTZSCH (1998): Comparison of air pressure reducing methods and discussion of other in- fluences on gravity, in Proceedings of the 13th Earth Tide Symposium, Brussels, 423-430,. LE PROVOST, C., F. LYARD, J.M. MOLINES, M.L. GENCO and F. RABILLOUD (1998): A hydrodynamic ocean tide model improved by assimilating a satellite altimeter- derived data set, J. Geophys. Res., 103 (C3), 5513- 5529. MELCHIOR, P. (1995): A continuing discussion about the correlation of tidal gravity anomalies and heat flow densities, Phys. Earth Planet. Int., 88, 223-256. MELCHIOR, P. and B. DUCARME (1991): Tidal gravity anom- alies and tectonics, in Proceedings of the 11th Inter. Symp. Earth Tides, Helsinki, edited by J. KAKKURI, 445-454. MERRIAM, J. B. (1992): Atmospheric pressure and gravity, Geophys. J. Int., 109, 488-500. MUKAI, A., T. HIGASHI, S. TAKEMOTO, I. NAKAGAWA and I. NAITO (1995): Accurate estimation of atmospheric ef- fects on gravity observations made with a supercon- ducting gravity meter at Kyoto, Phys. Earth Planet. Int., 91, 149-159. Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 84 85 Strategies in the processing and analysis of continuous gravity record in active volcanic areas: the case of Mt. Vesuvius MÜLLER, T. and W. ZÜRN (1983): Observation of the gravi- ty changes during the passage of cold fronts, J. Geo- phys., 53, 155-162. NEUMEYER, J. (1995): Frequency dependent atmospheric pressure corrections on gravity variations by means of cross spectral analysis, Bull. Inf. Marées Terrestres, 122, 9212-9220. NEUMEYER, J., F. BARTHELMES and D. WOLF (1998): Atmos- pheric pressure correction for gravity data using differ- ent methods, in Proceedings of the 13th Earth Tide Symposium, Brussels, 431-438,. PETERSON, J. (1993): Observations and modelling of seis- mic background noise, Open File Report 93-322 (U.S. Department of Interior Geological Survey, Albu- querque, New Mexico). PETROV, L. and J.-P. BOY (2004): Study of the atmospheric pressure loading signal in VLBI observations, J. Geo- phys. Res., 109, B03405, 10.1029/2003JB002500. PONTE, R.M. and R.D. RAY (2002): Atmospheric pressure corrections in geodesy and oceanography: a strategy for handling air tides, Geophys. Res. Lett., 29, 2153, doi: 10.1029/2002GL016340. RABBEL, W. and J. ZSCHAU (1985): Static deformations and gravity changes at the Earth’s surface due to atmos- pheric loading, J. Geophys., 56, 81-99. RICCARDI, U., G. BERRINO and G. CORRADO (2002): Changes in the instrumental sensitivity for same feed- back equipping LaCoste and Romberg gravity meters, Metrologia, 39, 509-515. RICCARDI, U., J. HINDERER and J.-P. BOY (2007): On the ef- ficiency of barometric arrays to improve the correc- tions of atmospheric effects on gravity data, Phys. Earth Planet. Int., 161, 224-242. RICHTER, B. (1987): Das supraleitende Gravimeter, Ph.D. Thesis (Deutsche Geodät. Komm., C 329, Frankfurt am Main), pp. 124. RICHTER, B., H.G. WENZEL, W. ZÜRN and F. KLOPPING (1995): From Chandler wobble to free oscillations: com- parison of cryogenic and other instruments in a wide pe- riod range, Phys. Earth Planet. Int., 91, 131-148. ROBINSON, E.S. (1989): Tidal gravity, heat flow, and the up- per crust, Phys. Earth Planet. Int., 56, 181-185. ROBINSON, E.S. (1991): Correlation of tidal gravity and heat flow in eastern North America, Phys. Earth Planet. Int., 67, 231-236. SCHWIDERSKI, E.W. (1980): On charting global ocean tides. Rev. Geophys. Space. Physics., 18 (1), 243-268. SPRATT, R.S. (1982): Modelling the effect of atmospheric pressure variations on gravity, Geophys. J.R. Astron. Soc., 71, 173-186. TAMURA, Y. (1987): A harmonic development of the tide- generating potential, Bull. Inf. Marées Terrestres, 99, 6813-6855. TORGE, W. (1989): Gravimetry (de Gruyter, Berlin, New York), pp. 465. TRIBALTO, G. and A. MAINO (1962): Rilevamento gravimet- rico della zona circumvesuviana, Ann. Osservatorio Vesuviano, 6 (S4), 134-172. VAN CAMP, M. and P. VAUTERIN (2005): Tsoft: graphical and interactive software for the analysis of time series and Earth tides, Comput. Geosci., 31 (5), 631-640. VAN DAM, T. and O. FRANCIS (1998): Two years of continu- ous gravity measurements of tidal and non-tidal varia- tions of gravity in Boulder, Colorado, Geophys. Res. Lett., 25, 393-396. VAN RUYMBEKE, M. (1991): New Feedback Electronics for La- Coste & Romberg Gravimeters, Cahiers du Centre Eu- ropéen de Géodynamique et de Séismologie, 4, 333-337. VAN RUYMBEKE, M., R. VIEIRA, N. D'OREYE, A. SOMER- HAUSEN and N. GRAMMATIKA (1995): Technological Approach from Walferdange to Lanzarote: the EDAS Concept, in Proceeding 12th Int. Symp. on Earth tides, (Science press, Beijing, China), 53-62. VIEIRA, R., M. VAN RUYMBEKE, J. FERNANDEZ, J. ARNOSO and C. DE TORO (1991): The Lanzarote underground laboratory, Cahiers du Centre Européen de Géody- namique et de Séismologie, 4, 71-86. VILARDO, G., G. DE NATALE, G. MILANO and U. COPPA (1996): The seismicity of Mt. Vesuvius, Tectono- physics, 261, 127-138. WAHR, J.M. (1981): Body tides on an elliptical, rotating, elastic and oceanless Earth, Geophys. J. R. Astr. Soc., 64, 677-703. WARBURTON, R.J. and J.M. GOODKIND (1977): The influ- ence of barometric-pressure variations on gravity, Geo- phys. J. R. Astr. Soc., 48, 281-292. WENZEL, H.G. (1996): The nanoGal software: Earth tide data processing package ETERNA 3.30, Bull. Inf. Marées Terrestres, Bruxelles, 9425-9438. ZSCHAU, J. and R. WANG (1987): Imperfect elasticity in the Earth’s mantle. Implication for Earth tides and long period deformation, in Proceedings of the 9th In- ternational Symposium on Earth Tides, New York, 605-629. Vol51,1,2008_DelNegro 16-02-2009 21:27 Pagina 85