ALBERT

Description: Previous formalisms for determining the static perturbation of spherically symmetric self-gravitating elastic Earth models due to displacement dislocations deal with each infinitesimal element of the fault system in its epicentral reference frame. In this work, we overcome this restriction and present novel and compact formulas for obtaining the perturbation due to the whole fault system in an arbitrary and common reference frame. Furthermore, we show that, even in an arbitrary reference frame, it is still possible to discriminate the contributions associated with the polar, bipolar and quadrupolar patterns of the seismic source response, as well as their relation with the along strike, along dip and tensile components of the displacement dislocation. These results allow a better understanding of the relation between the static perturbation and the whole fault system, and find direct applications in geodetic problems, like the modelling of long-wavelength geoid or gravity data from GRACE and GOCE space missions and of the perturbation of the deviatoric inertia tensor of the Earth.

Description: Sensitive instruments like strainmeters and tiltmeters are necessary for measuring slowly varying low amplitude Earth deformations. Nonetheless, laser and fibre interferometers are particularly suitable for interrogating such instruments due to their extreme precision and accuracy. In this paper, a practical design of a simple pendulum borehole tiltmeter based on laser fibre interferometric displacement sensors is presented. A prototype instrument has been constructed using welded borosilicate with a pendulum length of 0.85 m resulting in a main resonance frequency of 0.6 Hz. By implementing three coplanar extrinsic fibre Fabry-Perot interferometric probes and appropriate signal filtering, our instrument provides tilt measurements that are insensitive to parasitic deformations caused by temperature and pressure variations. This prototype has been installed in an underground facility (Rustrel, France) where results show accurate measurements of Earth strains derived from Earth and ocean tides, local hydrologic effects, as well as local and remote earthquakes. The large dynamic range and the high sensitivity of this tiltmeter render it an invaluable tool for numerous geophysical applications such as transient fault motion, volcanic strain and reservoir monitoring.

Description: The geocentre motion is the motion of the centre of mass of the entire Earth, considered an isolated system, in a terrestrial system of reference. We first derive a formula relating the harmonic degree-1 Lagrangian variation of the gravity at a station to both the harmonic degree-1 vertical displacement of the station and the displacement of the whole Earth's centre of mass. The relationship is independent of the nature of the Earth deformation and is valid for any source of deformation. We impose no constraint on the system of reference, except that its origin must initially coincide with the centre of mass of the spherically symmetric Earth model. Next, we consider the geocentre motion caused by surface loading. In a system of reference whose origin is the centre of mass of the solid Earth, we obtain a specific relationship between the gravity variation at the surface, the geocentre displacement and the load Love number $h^{\prime }_1$ , which demands the Earth's structure and rheological behaviour be known. For various networks of real or fictitious stations, we invert synthetic signals of surface gravity variations caused by atmospheric loading to retrieve the degree-1 variation of gravity. We then select six well-distributed stations of the Global Geodynamics Project, which is a world network of superconducting gravimeters, to invert actual gravity data for the degree-1 variations and determine the geocentre displacement between the end of 2004 and the beginning of 2012, assuming it to be due to surface loading. We find annual and semi-annual displacements with amplitude 0.5–2.3 mm.

Description: We review the theory of the Earth's elastic and gravitational response to a surface disk load. The solutions for displacement of the surface and the geoid are developed using expansions of Legendre polynomials, their derivatives and the load Love numbers. We provide a matlab  function called diskload that computes the solutions for both uncompensated and compensated disk loads. In order to numerically implement the Legendre expansions, it is necessary to choose a harmonic degree, n max , at which to truncate the series used to construct the solutions. We present a rule of thumb (ROT) for choosing an appropriate value of n max , describe the consequences of truncating the expansions prematurely and provide a means to judiciously violate the ROT when that becomes a practical necessity.

Description: Two types of signals are clearly visible in continuous GPS (cGPS) time-series in Iceland, in particular in the vertical component. The first one is a yearly seasonal cycle, usually sinusoid-like with a minimum in the spring and a maximum in the fall. The second one is a trend of uplift, with higher values the closer the cGPS stations are to the centre of Iceland and ice caps. Here, we study the seasonal cycle signal by deriving its average at 71 GPS sites in Iceland. We estimate the annual and semi-annual components of the cycle in their horizontal and vertical components using a least-squares adjustment. The peak-to-peak amplitude of the cycle of the vertical component at the studied sites ranges from 4 mm near the coastline up to 27 mm at the centre of the Vatnajökull, the largest ice cap in Iceland. The minimum of the seasonal cycle occurs earlier in low lying areas than in the central part of Iceland, consistent with snow load having a large influence on seasonal deformation. Modelling shows that the seasonal cycle is well explained by accounting for elastically induced surface displacements due to snow, atmosphere, reservoir lake and ocean variations. Model displacement fields are derived considering surface loads on a multilayered isotropic spherical Earth. Through forward and inverse modelling, we were able to reproduce a priori information on the average seasonal cycle of known loads (atmosphere, snow in non-glaciated areas and lake reservoir) and get an estimation of other loads (glacier mass balance and ocean). The seasonal glacier mass balance cycle in glaciated areas and snow load in non-glaciated areas are the main contributions to the seasonal deformation. For these loads, induced seasonal vertical displacements range from a few millimetres far from the loads in Iceland, to more than 20 mm at their centres. Lake reservoir load also has to be taken into account on local scale as it can generate up to 20 mm of vertical deformation. Atmosphere load and ocean load are observable and generate vertical displacements in the order of a few millimetres. Inversion results also shows that the Iceland crust is less rigid than the world average. Interannual deviation from the GPS seasonal cycle can occur and are caused by unusual weather conditions over extended period of time.

Description: Data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission can be used to estimate the mass change rate for separate drainage systems (DSs) of the Greenland Ice Sheet (GrIS). One approach to do so is by inversion of the level-2 spherical harmonic data to surface mass changes in predefined regions, or mascons. However, the inversion can be numerically unstable for some individual DSs. This occurs mainly for DSs with a small mass change signal that are located in the interior region of Greenland. In this study, we present a modified mascon inversion approach with an improved implementation of the constraint equations to obtain better estimates for individual DSs. We use separate constraints for mass change variability in the coastal zone, where run-off takes place, and for the ice sheet interior above 2000 m, where mass changes are smaller. A multi-objective optimization approach is used to find optimal prior variances for these two areas based on a simulation model. Correlations between adjacent DSs are suppressed when our optimized prior variances are used, while the mass balance estimates for the combination of the DSs that make up the GrIS above 2000 m are not affected significantly. The resulting mass balance estimates for some DSs in the interior are significantly improved compared to an inversion with a single constraint, as determined by a comparison with mass balance estimates from surface mass balance modelling and discharge measurements. The rate of mass change of the GrIS for the period of January 2003 to December 2012 is found to be –266.1 ± 17.2 Gt yr –1 in the coastal zone and areas below 2000 m, and +8.2 ± 8.6 Gt yr –1 in the interior region.

Description: The static and transient deformations produced by earthquakes cause density perturbations which, in turn, generate immediate, long-range perturbations of the Earth's gravity field. Here, an analytical solution is derived for gravity perturbations produced by a point double-couple source in homogeneous, infinite, non-self-gravitating elastic media. The solution features transient gravity perturbations that occur at any distance from the source between the rupture onset time and the arrival time of seismic P waves, which are of potential interest for real-time earthquake source studies and early warning. An analytical solution for such prompt gravity perturbations is presented in compact form. We show that it approximates adequately the prompt gravity perturbations generated by strike-slip and dip-slip finite fault ruptures in a half-space obtained by numerical simulations based on the spectral element method. Based on the analytical solution, we estimate that the observability of prompt gravity perturbations within 10 s after rupture onset by current instruments is severely challenged by the background microseism noise but may be achieved by high-precision gravity strainmeters currently under development. Our analytical results facilitate parametric studies of the expected prompt gravity signals that could be recorded by gravity strainmeters.

Description: Seismic waves produced by fault ruptures give rise to gravity perturbations. So far, these perturbations have either been modelled as permanent coseismic gravity change in a half-space or spherical Earth model, or as full time-domain model in infinite space. In this paper, we present the explicit solution of gravity perturbations in time domain produced by a double-couple buried in a homogeneous half-space. This result is especially suited to study gravity perturbations up to a few hundreds of kilometres from the epicentre. It facilitates detailed parametric studies of gravity perturbations from fault rupture, and predicts gravity perturbations of real earthquakes with greatly improved accuracy. The results may serve to develop first designs of gravity-assisted earthquake early-warning systems, made possible by a new generation of ultrasensitive gravity gradiometers, which is currently under development.

Description: Continuous gravimetric observations have been made with three successive generations of superconducting gravimeter over 20 yr at Syowa Station ( $39.6\deg$ E, $69.0\deg$ S), East Antarctica. The third-generation instrument, OSG#058, was installed in January 2010 and was calibrated by an absolute gravimeter during January and February, 2010. The estimated scale factor was –73.823 ± 0.053 μGal V –1 (1 μGal = 10 –8 m s –2 ). The first 5 yr of OSG#058 data from 2010 January 7 to 2015 January 10 were decomposed into tidal waves (M3 to Ssa) and other non-tidal components by applying the Bayesian tidal analysis program BAYTAP. Long-term non-tidal gravity residuals, which were obtained by subtracting annual and 18.6 year tidal waves and the predicted gravity response to the Earth's variable rotation, showed significant correlation with the accumulated snow depth measured at Syowa Station. The greatest correlation occurred when the gravity variations lagged the accumulated snow depth by 21 d. To estimate the gravitational effect of the accumulated snow mass, we inferred a conversion factor of 3.13 ± 0.08 μGal m –1 from this relation. The accumulated snow depth at Syowa Station was found to represent an extensive terrestrial water storage (the snow accumulation) around Syowa Station, which was estimated from the Gravity Recovery and Climate Experiment satellite gravity data. The snow accumulation around Syowa Station was detectable by the superconducting gravimeter.

Description: The new release AIUB-RL02 of monthly gravity models from GRACE GPS and K-Band range-rate data is based on reprocessed satellite orbits referring to the reference frame IGb08. The release is consistent with the IERS2010 conventions. Improvements with respect to its predecessor AIUB-RL01 include the use of reprocessed (RL02) GRACE observations, new atmosphere and ocean dealiasing products (RL05), an upgraded ocean tide model (EOT11A), and the interpolation of shallow ocean tides (admittances). The stochastic parametrization of AIUB-RL02 was adapted to include daily accelerometer scale factors, which drastically reduces spurious signal at the 161 d period in C 20 and at other low degree and order gravity field coefficients. Moreover, the correlation between the noise in the monthly gravity models and solar activity is considerably reduced in the new release. The signal and the noise content of the new AIUB-RL02 monthly gravity fields are studied and calibrated errors are derived from their non-secular and non-seasonal variability. The short-period time-variable signal over the oceans, mostly representing noise, is reduced by 50 per cent with respect to AIUB-RL01. Compared to the official GFZ-RL05a and CSR-RL05 monthly models, the AIUB-RL02 stands out by its low noise at high degrees, a fact emerging from the estimation of seasonal variations for selected river basins and of mass trends in polar regions. Two versions of the monthly AIUB-RL02 gravity models, with spherical harmonics resolution of degree and order 60 and 90, respectively, are available for the time period from March 2003 to March 2014 at the International Center for Global Earth Models or from ftp://ftp.unibe.ch/aiub/GRAVITY/GRACE (last accessed 22 March 2016).