Free-air Effect Research Articles

Postseismic gravity changes after the 2011 Tohoku earthquake observed by superconducting gravimeters at Mizusawa, Japan

Postseismic gravity changes after the 2011 Tohoku earthquake (Mw9.0) were investigated using the data from superconducting gravimeters (SGs) at Mizusawa, Japan. The data in the period from 2014 to 2021 were used in the analysis. The SG data were first corrected for instrumental drift using the results of absolute gravity measurements. Then, correction for the hydrological effect was applied based on physical modeling of soil moisture. Finally, the effect of vertical displacement of the station (free-air effect) was corrected using GNSS data. After these corrections, residual gravity indicated a long-term increase, with its rate gradually decreasing with time. This fact suggests that viscoelastic relaxation after the earthquake played an important role in producing the long-term gravity changes. Fitting a decaying exponential function of time to the residual series yielded 89.4 ± 4.4 µGal (1 µGal = 10–8 ms–2) as the total gravity change and 635 ± 17 days as the characteristic time scale. In addition to the ground-based observations, the data from satellite gravity missions GRACE/GRACE-FO were analyzed to retrieve gravity changes at Mizusawa. Similar analysis of the satellite-based data yielded 15.2 ± 1.6 µGal as the total gravity change and 3444 ± 599 days as the characteristic time scale. The difference in the estimates of the total gravity change, of a factor of about 6, from the ground-based and the satellite-based observations may be attributed to the limited spatial resolution in the latter method. The difference in the estimates of the time scale, of a factor of about 1/5, may originate from the difference in the depth where the two kinds of gravimetry are mainly sensitive. Referring to recent theoretical studies on postseismic deformations after the 2011 Tohoku earthquake, our results can be interpreted consistently by assuming the existence of a layer of viscoelastic materials with viscosity 2times {10}^{18} text{Pa s} underneath the Tohoku area of Japan.Graphical

Novel treatment of the deformation–induced topographic effect for interpretation of spatiotemporal gravity changes: Laguna del Maule (Chile)

In volcano gravimetry, when analyzing residual spatiotemporal (time-lapse) gravity changes, the accurate deformation-induced topographic effect (DITE) should be used to account for the gravitational effect of surface deformation. Numerical realization of DITE requires the deformation field available in grid form. We compute the accurate DITE correction for gravity changes observed at the Laguna del Maule volcanic field in Chile over three nearly annual periods spanning 2013–2016 and compare it numerically with the previously used free-air effect (FAE) correction. We assess the impact of replacing the FAE by DITE on the model source parameters of analytic inversion solutions and apply a new inversion approach based on model exploration and growing source bodies. The new inversion results based on the DITE correction shift the position of the mass intrusion upwards by a few hundred meters and lower the total mass of the migrated fluids to roughly a half, compared to the inversion results based on the local-FAE correction. Our new Growth inversion results indicate that vertical dip-slip faults beneath the lake, as well as the Troncoso fault play active roles in hosting migrating liquid. We also show that for the study period, the DITE at Laguna del Maule can be accurately evaluated by the planar Bouguer approximation, which only requires the availability of elevation changes at gravity network benchmarks. We hypothesize that this finding may be generalized to all volcanic areas with flatter or less rugged terrain and may modify interpretations based on the commonly used FAE corrections.

Analysis of surface gravity and ground deformation responses of geological CO2 reservoirs to variations in CO2 mass and density and reservoir depth and size

The strength and direction of gravity and ground deformation anomaly vectors over normal and tight reservoirs after injection of CO2 depend on the reservoir and CO2 properties. Some of these properties, such as porosity, permeability, and size, define the reservoir type and therefore determine the existence or sign of the anomalies, indirectly. However, some other properties of reservoirs, such as reservoir depth, horizontal extension of CO2 plume, and CO2 mass amount and density, affect the strength of the measurements directly. Gravimetric and geodetic modelling of synthetic CO2 reservoirs can quantify each of the direct effects that represent the expected signals over different geological settings. We present gravity signal as the gravity increase due to CO2 mass attraction, and its combination with the gravity decrease caused by ground uplift. Our results indicate that the reservoir depth and horizontal extension, along with the injected mass, have significant influences on both ground deformation and gravity signals. The results also demonstrate that the horizontal extension of the CO2 distribution decreases the dependency on the depth. In addition, the observed gravity signal over CO2 reservoirs is dominated by the free-air effect from large ground deformation. Finally, the gravity effect over both normal and tight reservoirs and the ground surface deformation over tight reservoirs are highly dependent on the density change of the injected CO2 inside the reservoir as a result of depth dependant changes of pressure and temperature.

Deformation-Induced Topographic Effects in Interpretation of Spatiotemporal Gravity Changes: Review of Approaches and New Insights

We investigate the origin and implications of deformation-induced gravitational effects in interpretation of spatiotemporal gravity changes. We review the traditional approaches to handling the attraction of subsurface and surface deformations. These effects are relevant when inferring magmatic processes in volcano geodetic studies. We focus on the surface constituent, the deformation-induced topographic effect (DITE), which consists of a gradient effect called the free-air effect (FAE) and an attraction effect referred here as the topographic deformation effect. We present defining, alternate, as well as approximate expressions for evaluating the DITE. The alternate expressions shed light on the physical nature of DITE. By simulating numerically synthetic displacement fields of diverse shapes and areal extents imposed over terrain of various relief shapes in a referential volcanic area of prominent and rugged topographic relief, we assess the suitability and accuracy of the various approximations of DITE. Synthetic case studies are carried out using a high-resolution high-accuracy DEM and the Toposk software for evaluation of topographic attraction terms. We discuss the particularities and complications in numerical evaluation of each of the DITE expressions. We close with a conclusion that the best numerical prescription for accurate evaluation of DITE is Eq. (18) derived herein. Its numerical realization requires the knowledge of the deformation field in areal form. If the vertical displacements are known only at benchmarks, two approximations of DITE are at hand that can be numerically evaluated: the normal-FAE approximation (nFAE-DITE) and the planar Bouguer approximation (BCFAG-DITE). Based on synthetic simulations, we specify under what circumstances which approximation performs better.

Long-term dynamics across a volcanic rift: 21 years of microgravity and GPS observations on the southern flank of Mt. Etna volcano

In this paper, an integrated analysis of microgravity and ground deformation measurements at Mt. Etna is performed over a 21-years time span (1994–2014), a period encompassing several flank and summit eruptions. Data were collected along a common gravity and ground deformation network located on the volcano's southern flank to monitor the dynamics of the main volcanic and tectonic processes. Gravity variations have first been corrected for the free-air effect using the vertical deformation and the experimental vertical gravity gradients measured at each station. The free-air corrected gravity changes were then reduced for seasonal fluctuations, mainly imputable to water-table fluctuations, and for high frequency variations (noise).This long-term dataset constitutes a unique opportunity to examine the behavior of Mt. Etna in a period in which the volcano exhibited different styles of activity characterized by recharging, flank eruptions and fountaining episodes at summit craters. The joint analysis highlights common periods in which gravity and deformation underwent contemporaneous changes occurring mainly in the central and eastern stations of the profile. Specifically, it was possible to distinguish three different sectors, showing significant deformation and gravity patterns: a western sector, lying west of the South Rift, a central one between the South Rift and the 1989 fracture zone, and an eastern one lying east of the 1989 fracture system. The data shows that the deflation dynamics accompanying the eruptive phases mainly affect the western portion of the profile, gradually disappearing toward East, where the more constant sliding dynamics dominates. This pattern defines a transition zone corresponding to the sector comprised between the South Rift and the 1989 fracture. Furthermore, it was also possible to detect at least three main magma charging phases in 1996, 2000 and 2011 which preceded and accompanied the onset of intense flank eruptions and lava fountaining activity at the summit craters.

Deformation induced topographic effects in inversion of temporal gravity changes: First look at Free Air and Bouguer terms

Abstract We review here the gravitational effects on the temporal (time-lapse) gravity changes induced by the surface deformation (vertical displacements). We focus on two terms, one induced by the displacement of the benchmark (gravity station) in the ambient gravity field, and the other imposed by the attraction of the masses within the topographic deformation rind. The first term, coined often the Free Air Effect (FAE), is the product of the vertical gradient of gravity (VGG) and the vertical displacement of the benchmark. We examine the use of the vertical gradient of normal gravity, typically called the theoretical or normal Free Air Gradient (normal FAG), as a replacement for the true VGG in the FAE, as well as the contribution of the topography to the VGG. We compute a topographic correction to the normal FAG, to offer a better approximation of the VGG, and evaluate its size and shape (spatial behavior) for a volcanic study area selected as the Central Volcanic Complex (CVC) on Tenerife, where this correction reaches 77% of the normal FAG and varies rapidly with terrain. The second term, imposed by the attraction of the vertically displaced topo-masses, referred to here as the Topographic Deformation Effect (TDE) must be computed by numerical evaluation of the Newton volumetric integral. As the effect wanes off quickly with distance, a high resolution DEM is required for its evaluation. In practice this effect is often approximated by the planar or spherical Bouguer deformation effect (BDE). By a synthetic simulation at the CVC of Tenerife we show the difference between the rigorously evaluated TDE and its approximation by the planar BDE. The complete effect, coined here the Deformation Induced Topographic Effect (DITE) is the sum of FAE and TDE. Next we compare by means of synthetic simulations the DITE with two approximations of DITE typically used in practice: one amounting only to the first term in which the VGG is approximated by normal FAG, the other adopting a Bouguer corrected normal FAG (BCFAG).

Expected temporal absolute gravity change across the Taiwanese Orogen, a modeling approach

The island of Taiwan is located on the convergent boundary between the Philippine Sea plate and the Chinese continental margin. It offers very active mountain building and collapsing processes well illustrated by the rugged topography, rapid uplift and denudation, young tectonic landforms, active faulting and numerous earthquakes. In this paper, using simple models, we have estimated vertical movements and associated absolute gravity variations which can be expected along a profile crossing the southern part of the island and probably suffering the highest rates of rising. The two different tectonic styles proposed for the island, thin-skinned and thick-skinned, were taken into account. Horizontal and vertical movements were modeled by an elastic deformation code. Gravity variations due to these deformations are then modeled at a second step. They are dominated by plate and free-air effects, i.e. elevation of the topography, with several Gal yr −1 . By comparison, gravity changes generated by mass transfers are weak: maximum 0.1Gal yr−1 with the thin-skinned tectonic and 0.3Gal yr−1 with the thick-skinned tectonic. Though elastic rheology has limitations, this modeling offers interesting results on what gravity signal can be expected from the AGTO project (Absolute Gravity in the Taiwanese Orogen), which proposes to study the dynamic of these mountain ranges using absolute gravimetry (AG) and also including relative gravimetry (RG) and GPS measurements.

A search for the ratio between gravity variation and vertical displacement due to a surface load

We study the ratio between the gravity variation and vertical displacement at the surface of a self-gravitating spherical elastic earth model when a load is applied at the surface. By expanding both the gravity variation and vertical displacement in series of spherical harmonics, we investigate the spectral behaviour of the ratio of the harmonic components of the gravity variation and vertical displacement. Special attention is paid to the asymptotic limit, that is, for large degrees, and to the mean value for a given degree range, without considering the spectral properties of the load itself. First, we split the gravity variation into two parts: the first term stems from the direct attraction of the load, the second one is due to the elastic deformation of the model. The origin of the second term is twofold: the surface is displaced in the Earth's gravity field and the position of the Earth's mass particles is changed. The ratio between the gravity variation associated to the displacement of the surface and this displacement is the well-known free-air gradient of −0.30 μGal mm−1. We show, by considering different earth models, that the ratio between the harmonic components of the elastic gravity variation (i.e. mass redistribution and free-air effect) and the corresponding components of the vertical displacement tends to the Bouguer corrected gradient of −0.20 μGal mm−1 when both the harmonic degree n of the components is very large and the top layer of the earth model is incompressible. Second, we compute, for each n, the ratio of the components of the gravity variation and those of the vertical displacement omitting the local Newtonian attraction term. Whereas it weakly depends on n for n≲ 6, it is nearly constant for n≳ 6. By defining an average value for those ratios, we obtain a fairly good approximation of the ratio between the total gravity variation and vertical displacement, only valid outside the loaded area, which is −0.26 μGal mm−1. Finally, to check out our spectral result, we consider the loading effect of spherical caps of various angular apertures. We find a mean value of −0.21 μGal mm−1 outside the loaded area which is by 20 per cent in agreement with our spectral result.

The mechanics of unrest at Long Valley caldera, California. 2. Constraining the nature of the source using geodetic and micro-gravity data

We model the source of inflation of Long Valley caldera by combining geodetic and micro-gravity data. Uplift from GPS and leveling, two-color EDM measurements, and residual gravity change determinations are used to estimate the intrusion geometry, assuming a vertical prolate ellipsoidal source. The U.S. Geological Survey occupied the Long Valley gravity network six times from 1980 to 1985. We reoccupied this network twice, in the summer of 1998 (33 stations), and the summer of 1999 (37 stations). Before gravity data can be used to estimate the density of the intrusion, they must be corrected for the effect of vertical deformation (the free-air effect) and changes in the water table. We use geostatistical techniques to interpolate uplift and water table changes at the gravity stations. The inflation source (a vertical prolate ellipsoid) is located 5.9 km beneath the resurgent dome with an aspect ratio equal to 0.475, a volume change from 1982 to 1999 of 0.136 km 3 and a density of around 1700 kg/m 3. A bootstrap method was employed to estimate 95% confidence bounds for the parameters of the inflation model. We obtained a range of 0.105–0.187 km 3 for the volume change, and 1180–2330 kg/m 3 for the density. Our results do not support hydrothermal fluid intrusion as the primary cause of unrest, and confirm the intrusion of silicic magma beneath Long Valley caldera. Failure to account for the ellipsoidal nature of the source biases the estimated source depth by 2.9 km (a 33% increase), the volume change by 0.019 km 3 (a 14% increase) and the density by about 1200 kg/m 3 (a 40% increase).

Residual gravity changes and eruption magnitudes

Research during the last four decades has demonstrated that systematic temporal gravity changes are associated with eruptive activity. These gravity changes are caused by the free-air effect of elevation changes induced by magma bodies and by mass redistributions. Where gravity change data are accompanied by concurrent elevation control, observed gravity changes can be corrected for the free-air effect giving residual gravity changes. Residual gravity changes reflect only mass redistributions. At most volcanoes residual gravity changes can be accounted for by the addition of mass during pre-eruption time, and by the removal or addition of mass during post-eruption time. At explosive volcanoes, however, the data show mass must be removed from near surface magma systems during preeruptive time. The only reasonable mechanism acounting for these negative pre-eruption mass redistributions is displacing dense country rock or magma with gas bubbles in vesiculated magma. Application of Gauss' theorem to areal residual gravity changes and an assumed density for the displaced material, give an estimate of the volume of exsolved gas contained within the magma body. The kinetic energy released in explosive magmatic eruptions, to a first approximation, is caused by the explosive expansion of exsolved and dissolved gases contained within magma. If the density and temperature of magma, and if the amount, pressure, and composition of volatiles contained in magma bodies are known (or assumed), then the kinetic energy released by explosive gas decompression can be computed (or estimated ) using simple thermodynamic relationships. Kinetic energy estimates for explosive magmatic eruptions computed from muzzle velocities, and computed for isothermal and adiabatic gas decompression using assumed volatile contents, pressures, and temperatures give similar results. Minimum pre-eruption exsolved volatile contents estimated from negative pre-eruption mass deficits and assumed magma densities, temperatures, and pressures were used to compute predicted kinetic energies for five eruption-gravity change sequences at Pacaya, Mihara, Usu, and Mt. St. Helens volcanoes. Although the data are too few to be conclusive, they do indicate the possibility of forecasting eruption magnitudes at some volcanoes using precursory gravity changes.

Ground deformation and gravity changes accompanying the 1982 Pozzuoli uplift

During the summer of 1982 a continuous uplift began at Phlegraean Fields, an active volcanic area in southern Italy (Fig. 1), that persisted up to September 1984. The uplift, which reached a maximum value of about 160 cm in the central part of the Phlegraean caldera, was characterized by variable velocity and occurred within an area that extended about 7 km outward from the town of Pozzuoli (Fig. 1); the surface deformation performs a bell-shape pattern. The uplift was accompanied by horizontal displacements and gravity changes that closely correlate with the described elevation changes. The horizontal displacements displayed an anomalous pattern within a narrow belt about 1 km from the center of the uplift and approximately coincident with the area of maximum seismic activity. The change in gravity is attributed primarily to a free-air effect to which a small Bouguer effect must be added. Several models have been invoked in order to explain the observed phenomenon. The one which gives the best fit to the observed data is an increasing pressure source of radial simmetry, at a constant depth of about 3 km beneath the town of Pozzuoli, and having a diameter of several hundred meters. Migration of magma at depth is believed to be responsible for the observed activity in the Phlegraean Fields caldera.