 Tako, prema plikacije, da vse z vsej teg vzivnih gavitov, gaviti se veliko vzivno od slodnjiženju z vsej gavitajske, ki vzivno vsej gavitacije je naživno, prizivno, kaj je način vzivno, da je vzivno, pomečnje, vzivno, pridej. Ljube, kar od odmahaj, skopir od zelo, ispešenik na svojo, pletite, kak je. 9.8 m per sekund. The earth gravity acceleration is supposed to be constant, but there are small changes over both space and time. We normally use in geophysics the micro-gal as the measurements unit, which is 10 rise to minus 9g. Zelo izgledaj biti in izgledaj biti v tem veliko hrdi, in izgledaj biti in stvari. In da je pripočenja masova izgledaj biti ne vsak pristopirč, in da je izgledaj biti in stvari je bilo zelo izgledaj biti. In da je učiljena masov izgledaj biti in izgledaj biti. Druga je, da v trgahem pristini skupi so jazne v večsid, lahko je 10 Picture 2 – 7z, no že크 in se začujemo mene jazne, in tudi je etne o večsid, na čistih instrumentu imajo. Gremirjev tebno meže odvarjenja vnenju vratin, in tudi barem dve stavit Stravanie, tudi skupi in izgledanje, Sredinječki instrument snes prezip nespečne zčužite tyi povednih spremnih povednih, evolvečna in tačno v terzove in tračne obenje tudi. PLAAzOKO in z vz Mondičnih instrumentami je nezavala, in nekaj ima včeska, ki je naredilje iz kvalita pravdi. Proti za prosesnimi gravidami iz čistim pos exemploem, vsečenje. V geofiziku da smo počutili vsečenje način, da imače vsečenje masov v zelo, nekaj da smo počutili taj začin, tako da smo počutili, kako vsečenje masov vsečenje način. Taj začin je vsečenje kaj smo pričasnili o stati gravimetry. Vzpečenje to je posledno za vse počičje, in pravno postavimo, da bi lahko se zinojimo, in da se dovoljimo in pričasnimo. Če lahko se vzpečenje za raziljene in raziljene vzpečenje za raziljene učenje. Vzpečenje raziljene je vstupenje in taj delče efekte, efekte, kaj do zelo začetanje izbih, zelo začetanje in zelo začetanje, ki boli nekaj spas, nekaj nekaj vših kajte odkrati v posješenju, nekaj pojavnih pojavnih, zelo začetanje in efekte, kaj do zelo začetanje izbranje izbranju, na zelo začetanje. So her tides are due to the attraction basically of moon and sun. And you can see here, here we have the model of the tidal effect at Etna and Kilauea during about 20 days in 2013. You can see that there is an effect up to about 250 microgals and it's naturally different depending on the position of the observation point. As for effect of a space, so we must correct, if we have an observation point here, since it's at a different elevation with respect to the reference, we must correct for this different elevation. And this is due normally using a standard gradient, which is this one, free air gradient. Also we have to correct for the fact that between the observation point and the reference there is not a void, but there is some mass. So the first order correction is done through the bouge correction, which assumes the presence of an infinite slab with an elevation, which is equal to the difference in elevation between the observation point and the reference. And so the standard value of this correction is this one. And also we have to correct for the fact that we have masses in excess and in defect with respect to the bouge plate. And so this is called terrain corrections. Once all these corrections have been performed, we can develop our bouge map, which is a map now only reflecting the distribution of density below the surface. So this is the bouge map for etna, which has been developed using data published by Schiavon and Lodo in 2007. And here you can see that you have two main components, a regional component with this trend here, which is mainly due to very deep structures. And also there are some residual anomalies, like this one here or this one here, which are due to shallower structures. We are usually interested more in the residual anomalies, so the regional field is usually filtered out through different techniques. And for example, if we invert for etna these bouge anomalies here, we get these maps. So these are maps of the density distribution with respect to a medium value, reference value, which has been chosen by the people who did this inversion. And so we have density in excess, so in effect with respect to this reference value. So here we have density maps for two elevations, two and four kilometers below the sea level. And here we can see that there are many density anomalies in this map. One of these is this one, this density high, which is in the southern part of the Valedalbove here. And we can see it also here. It's interesting because the same anomaly is also found in the seismic tomography. You can see it here and here, same elevation, so with the same, more or less the same features. So this gravity high corresponds to high velocity body, which is actually a plutonic body at an elevation between two and, more or less, eight kilometers below the sea level. Another application of static gravimetry is this one coming from Piton de la Fornes. Here these rotors made a detailed profile across the lava flow that was produced by the 2007 eruption. And this study was done because before reconstructing the roads, the local authorities wanted to know where there was the possibility to have some tunnels in the lava. Because this could be a danger for the people involved in the work because it could be a problem to work with very heavy machines over the parts of this lava flow where there could be some voj. So the authors made this study, and through gravity they could identify zones where it was likely the presence of a tunnel. So switching to changes in time, this is a scheme by Torge, which can be found in this book by Torge, published in 1984. And here you can see that among the different processes that can use time changes, non-tidal time changes, volcanic processes are among the ones that can use stronger changes over time in gravity. You can see that we can have some hundreds of microgal changes. And this book was published in 1984, and here they said that the period of these changes could go between one day and a few years. But actually later studies demonstrated that we can have also changes over time scale shorter than these and down to a few minutes, actually. So gravity anomalies depend on the characteristic of the source, and we can have a great range of possibility as a wavelength of the gravity changes, periods, and amplitude. The amplitude and wavelength depends on the mass involved in the depth of the source, while the period depends on the evolution speed of the process involved in the change. And so, since this period can range between minutes and actually years, we perform both continuous measurements and time-lapse measurements. Time-lapse measurements are that the volcanoes are usually performed through spring-grime meters, so relative instruments. And so each campaign is referred to reference points. This is the gravity network of Mount Etna, and you can see that here we have reference points, so all the measurements are referred to this point, where we assume that the changes induced by the activity of the volcano are very small. And then the, since the campaign are repeated every few months or even years, these kind of measurements are normally used to detect changes over long-time scales. So usually changes over long-time scales are related to processes that also induce pressure changes, so usually this kind of gravity changes are interpreted together with deformation. And one of the most used forward models in analytic formulation is the Mogi model to interpret jointly gravity and deformation. And this model predicts that the ratio between variation of gravity and variation of elevation is linear. There are other models that are used to invert jointly gravity and deformation changes. For example, the analytic expressions proposed by Okada and Okubo can account for the effect of tensile fault, while the model proposed by Okubo can be used to predict the effect of intrusion in a fractured zone, because this model accounts for intrusion inside the pattern of small cracks which are uniformly distributed inside this narrow fractured zone. So these models do not predict a simple linear relation between deformation and gravity. So usually when we assume that the gravity changes and the deformation are due to processes involving the dynamic of Mogi source, we can use this framework, this scheme to assess the likelihood and also the type of volcanic activity. So if the ratio between gravity changes and elevation changes cluster along this line, the boge corrected fear gradient, we are in a situation where there is a pure mechanism of magma intrusion. This has been seen several times. For example, in this case, in the case of the Isobolkano in Japan during this arrest, during this elapsion phase between 1998 and 2000, we had very strong gravity and elevation changes and the ratio between gravity and elevation cluster actually around this boge corrected fear gradient. So we have in this case the intrusion of magma with the density very close to what is expected, 2.4 grams per cubic centimeter. In other cases we have that the points are clustered somewhere between the two lines, the boge corrected fear gradient and the fear gradient, so somewhere here. And this can occur because of two reasons. One is that we can have that the arrest processes driven not by only magma but by magma plus gases. So we have in this case that the density of the material is lower than expected. We don't have points clustering along this line but rather points clustering in this space here. Otherwise we could have a situation like this one where the arrest process is driven by hydrothermal fluids. This is a case referring to the arrest phase between 1980 and 1984 at Camp Le Fegré and this arrest phase was found to be to be due to a material with a density between 0.1 and around 1 gram per cubic centimeter so a density much lower than magma. And so this result, these results point to the regression of fluids in the hydrothermal system rather than intrusion of magma. In other cases we have that the volume of magma which is deduced from the study of deformation can account only for a small portion of the volume of magma which is needed to explain the gravity changes. Like in these cases in this case here these are measurements from Kilauea, measured between 2011 and 2012. And here you can see that the volume of magma deduced from deformation can account for less than 10% of the mass addition that we need to explain the gravity changes. So even though we have the pattern of deformation and gravity are well correlated over space we have this discrepancy. So we must assume some kind of mechanism able to induce bulk mass changes without volume changes and for example substitution of less dense magma with higher density or feeling of open spaces around the magma chamber. So this concept of excess mass also works in cases of deflation. Here we have a situation where the deflation the volume during the phase of deflation in Iceland deduced from deformation is much less that the mass decrease that we need to explain the gravity changes. And so the explanation given by these authors was that a part of the volume needed to explain the gravity change was actually due to this volume change was actually compensated by the formation of gas bubbles inside the magma chamber. We also have cases where the gravity changes are the only change that we have so we have strong gravity changes without deformation which is comparable with these gravity changes. Like in this case here this case refer to the the changes which were observed between 1990-1991 at Etna and so these changes observed before the 1991-93 eruption and so we have very strong gravity changes associated with very small deformation and deformation with a pattern which is not in keeping with the pattern which would be associated to this gravity change. And so in this case the author concluded that gravity changes were due to intrusion of magma along pre-existing open voids in particular along fracture here so from the central conduit going towards southeast. There are also cases where we can have that the gravity changes are not directly related to the dynamics of magma at Etna between 1994-2001 we observed strong changes which were associated to a source in the south-distance sector the volcano, a quite shallow source about 2 km below the sea level so we have both positive and negative gravity changes and the negative phase are associated with a stronger release of energy and this seismic energy was released from a volume which is in the same position as the volume, as the gravity source actually. So here we compared the gravity change at one station around here in time with the strain release which was reduced for a linear trend and also was multiplied by a negative coefficient here. A strong coupling between gravity and strain release this is actually anti-correlation because we multiplied the strain release by a negative factor. So we have the situation where gravity changes acute in a volume which is separated from the volume where the pressure source deduced from the formation was placed which is in the northwestern sector of the volcano and is actually deeper than the gravity source. So interpretation that was given was that these gravity changes were due to changes in the rate of micro fracturing along pregsysting fractured zone in this position here and also in this paper we proposed that when a structure link formed between the pressure source and this pressure zone the magma used this pressure zone to reach the surface and there was the breakout of the 2001 eruption. So this is a quite complicated framework where we have deeper pressure source beneath the northwestern flank of the volcano giving the deformation most of the deformation observed during the period while the gravity and seismicity were mainly driven by changes in the rate of fracturing along this fracture zone here in another position and this mechanism worked until the breakout of the 2001 eruption and so we think that this eruption actually changed this kind of framework somehow because we didn't observe this pattern of changes anymore after this eruption. So switching to continuous gravity changes so continuous gravity measurements these measurements are usually done through spring guide meters and because of some limitation of these instruments they don't give high quality data over periods longer than say some days this is because these instruments are affected by many parameters mainly by temperature and also they are affected by instrumental drift here we can see quite long records from Etna and Kilauea and we can see in both cases we have quite linear drift over the record and also the both records are modulated by the seasonal component of temperature so if we use a good setup with suitable protection against temperature we can limit this effect and in many cases we observe that the strong correlation this is analysis in frequency domain and we can see that the high correlation is only found over the lowest part of the spectrum so we have a period range which is free from temperature effects and the period range which is affected by these temperature changes and so this period range is up to some days so that's why most of the past studies about continuous gravity changes are focused on processes occurring over short time scales so the process is able to induce changes of these time scales are processes related to the dynamics of involving magma and gas in the upper part of the system of the volcano and we can have different processes here we can see only some of them for example if we have a big slag raising along the conduit we will have actually a body with a very low density being progressively closer to the observation point where we will have gravity degrees also if we have accumulation of the form liar in a position relatively close to the observation point also in this case we will have gravity degrees we will observe gravity degrees and also fast magma movements in the conduit or along a rift zone depending on the position of the observation point with respect of the magma moving will give a change with a positive or negative also the mixing of magma with different densities can give gravity changes this is a study where the authors simulated the mixing of magma in a shallow magma chamber and you can see that in different cases at different distances between magma chamber we will have gravity changes over periods as short as a few minutes let's say a few tens of minutes so the first case of study comes from Kilauea where in 2011 there was an eruption along the east rift zone 10 km from the summit active vent this is a case very similar to what Claude Jobar was talking about yesterday because there was a sudden decrease in the level of the lava lake here in the summit crater and soon after this sharp decrease there was the eruption so the idea is that the magma from the central conduit that's why we observed this sudden decrease in the level of the lava lake so we have many data about this this process so we have data coming from a gravity meter that was installed very close to the lava lake only 150 meters and also we have the images from a thermal camera here in the edge of the crater and looking at the surface of the lava lake so these are two images coming from this thermal camera and so this movie is a movie where we synchronized the images from the thermal camera with the gravity change so we have a difference in time because this is Hawaii local time in GMT time from gravity and so we can see that as soon as we have a decrease in the level of the lake we will have a decrease also in gravity at the same time which is quite impressive and so afterwards the gravity reaches a new level which is more or less 150 migragalts lower than the previous level I mean they are real but if you consider that the gravity meter is at the same time measures gravity acceleration and inertial acceleration so it behaves as a seismometer basically so since there was some seismic activity also we have for example this one is an earthquake we don't need to correct for that because the only information we need at this time is just the development of the decrease so you can see also that the noise here which is higher than the noise here is because of the eruption so I guess it's because of the transferring of this magma transferring from the central conduit to the rift zone so that's why we have this increase in the background noise so what we did it was to try to invert the the gravity data to find the density of the material inside the upper part of the vent and to do that we used the numerical model of the vent taking into account its real shape so using this model and the images from the thermal camera we could calculate the gravity effect due to a change in the level of lava inside the vent so basically we have gravity here lava level deduced from the images of the thermal camera and here is GPS so we corrected the gravity for this also for this deformation which accompanied the decrease in the lava level and so to get a good fit between observed and calculate gravity we had to use a very low density a density which is actually lower than water and that means that this upper part of the system is actually very rich in gas bubbles more than half of the material inside its gas this analysis was extended of a much longer period about 4 years so here you can see lava level ground tilt and GPS and also gravity you can see that lava level and tilt and also GPS are very similar to each other very correlated while gravity doesn't seem to be correlated because of other effects like temperature and the effect of gravity is very correct for the seasonal part we still don't see any coupling between gravity and lava level but actually if we go to shorter periods for example these two ones here we can see that actually there is quite close coupling also between gravity and lava level in the two cases so we used wavelet coherence analysis to try to calculate the correlation between ground tilt and lava level and here you can see that there is a very strong correlation of wavelet scales that correspond to periods between about one day and a few months and this arrows here point towards the right means that this is two phase correlation so there is no time delay between lava level and tilt also we performed correlation analysis of 15 days window running along the signals and the results shows that the ratio between lava level and tilt it's quite constant in time and the average is 0.17 which means about 5 to 7 meters per lava level for micro radiant the same analysis was performed between gravity and lava level and here we can see again that the correlation is not as good as before because of the perturbations of the gravity signal but still we have some correlation in some times and also in this case the correlated part of the diagram we have in phase correlation we also performed an analysis of the same time window in this case for each step of the window we calculated the density needed to explain the gravity changes considering that all the gravity changes was due to the change in the lava level so what we get is that the density seems to increase during this period from a value of about 1 to a value of about 1.5 gram per cubic centimeter and so this could be an actual change in density otherwise could be due to the fact that the size of the event was increasing because here actually we are measuring not a real density but rather increasing the mass involved in the process so it could be a real density but also it could be the fact that the event was during this period was actually getting larger well apparent density means that we did this calculation we actually tried to calculate the best density that can fit our data but we are using always the same model for the event so if for example there is a difference in the geometry of the event this means that this is not real density it's a change in the mass involved in the same change of level so it means that we are not measuring a change of a time of density we are measuring a change of a time of the mass involved in the same change of level so that's the sense of this apparent density so if it's interesting to see that if we combine the two equations the question for the lava level change and the question for radial tilt assuming moggy source we see that our ratio the ratio we found before depends on the density of the material inside the conduit it's also related to the dimension of the magma chamber and also the position of the magma chamber itself and so if we use the value we found for the ratio and for density we find that the other parameters are as expected from previous publications and so this means that at least over the time and space scales that we consider that the system behaves elastically had the data from Kilauea here we can see that we have data from these two stations one very close to the active vent the other one about two kilometers from the vent so this is the signal acquired in May 2010 and we can see that the wavelet transform of the signal shows two main components this one with a period of about 30 seconds and the other one is this one with a period of about 150 seconds so this is basically seismic noise while this component here that we can see in this chart here which is actually a zoom of this part from the two signals which has been filtered around 6.7 millihertz and we can see that there are these oscillations very well correlated between the two instruments the amplitude it's larger in the instrument which is closer to the vent to the active vent and so considering this ratio between the amplitude of the oscillation at the observation sites we have that the source can be again the shallow magma source beneath the north-western, north-eastern part of the Alemaumau crater and so we propose that this oscillation were due to density inversion related to convection inside the shallow magma chamber so assuming that the convection was driven by thermalist abilities with some calculation relating the time scale of convection to the position inside of the reservoir and these calculations suggest the temperature contrast which is in keeping with the density gradient that we need between upper and lower part to explain the gravity changes that we observed so the last case of study comes from Etna where in the summer of 2011 we stole a gravity meter very close to the summit praders at the distance of about one kilometer from the summit praders and during this the period of the installation there were a sequence of nine lava fountains from this crater here the news of this crater so there are many past studies that propose that these lava fountains are triggered by the collapse of the form layer that accumulates somewhere in a shallow position probably at the roof of a small magma chamber which is at shallow depth beneath the summit praders and so we observed before each fountain we observed the gravity decrease at the station very close to the summit praders and so we propose that this gravity decrease could be due to the accumulation of the form layer in this position here in the top of this magma chamber and actually this gravity decrease occurs during the phase of the strombolian activity preceding in development of the lava fountain here we don't have data during the lava fountain because the volcanic tremor is too high and so gravity data are impossible to use because they are too noisy in this part here so in overview of what we have seen so the term gravity changes are usually interpreted together in the ground deformation and by coupling gravity in the formation we can have more information about the processes which are driven the arrest of the eruption in particular we can have information about the density of the intruding material which is important because we can distinguish between magma versus intertermal processes or also we can see processes that induce mass changes without deformation like in the case when magma moves through open fissures in the upper part of the plumbing system or we can detect complex processes involving beside the direct effect of magma also second order effects like changes in the rate of fracturing of the medium using continuous measurements as short term changes that are related to the shallow dynamics involving magma and gas in the shallow part of the plumbing system of open conduit systems and from gravity we can have information about gas segregation for example possibly leading to explosive events like we have seen lava fountains or density inversion related to convection or rapid transfer of magma from the conduit to the lateral zones and that's all, thanks