ALBERT

Description: By introducing two types of zenith troposphere delay (ZTD) products in precise point positioning (PPP), we developed the ZTD-corrected PPP and the ZTD-constrained PPP, both of them reduced the PPP convergence time. Both enhanced PPP methods are examined by global empirical ZTD models and regional ZTD corrections. For global ZTD models, we verified that ZTD-corrected PPP will deviate the positioning results, while ZTD-constrained PPP could produce unbiased estimations. Therefore, the latter is utilized to study the performance of global ZTD models (ITG, GPT2w, GZTD and UNB3m). After numerous experiments, we found that the performance of ZTD models was positively related to the real ZTD accuracy, and we proposed a universal tropospheric stochastic model 2SQR(9rms) which denotes double the square of nine times ZTD rms, to constrain ZTD in PPP. The proposed model subsequently was validated by real-time static and kinematic ZTD-constrained PPP on the premise that the ZTD rms on every station was known. Compared with traditional PPP, in static PPP, the number of improved stations is increased by 15.5 per cent (ITG), 14.4 per cent (GPT2w), 11.1 per cent (GZTD) and 8.3 per cent (UNB3m). For kinematic PPP, PPP constrained by ITG model still had the best performance, the number of improved stations is increased by 14.4 per cent, after 30 min of initialization time, 13.4 cm east, 13.4 cm north and 11.7 cm up positioning accuracy was obtained, compared with 15.3 cm east, 15.3 cm north and 14.3 cm up accuracy by traditional PPP. In addition, experiments using regional ZTD corrections to enhance real-time PPP showed that both ZTD-corrected PPP and ZTD-constrained PPP can notably reduce the convergence time on the vertical component (within 15 cm).

Description: We study fluctuations in the degree-2 zonal spherical harmonic coefficient of the Earth's gravity potential, C 20 , over the period 2003–2015. This coefficient is related to the Earth's oblateness and studying its temporal variations, C 20 , can be used to monitor large-scale mass movements between high and low latitude regions. We examine C 20 inferred from six different sources, including satellite laser ranging (SLR), GRACE and global geophysical fluids models. We further include estimates that we derive from measured variations in the length-of-day (LOD), from the inversion of global crustal displacements as measured by GPS, as well as from the combination of GRACE and the output of an ocean model as described by Sun et al. We apply a sequence of trend and seasonal moving average filters to the different time-series in order to decompose them into an interannual, a seasonal and an intraseasonal component. We then perform a comparison analysis for each component, and we further estimate the noise level contained in the different series using an extended version of the three-cornered-hat method. For the seasonal component, we generally obtain a very good agreement between the different sources, and except for the LOD-derived series, we find that over 90 per cent of the variance in the seasonal components can be explained by the sum of an annual and semiannual oscillation of constant amplitudes and phases, indicating that the seasonal pattern is stable over the considered time period. High consistency between the different estimates is also observed for the intraseasonal component, except for the solution from GRACE, which is known to be affected by a strong tide-like alias with a period of about 161 d. Estimated interannual components from the different sources are generally in agreement with each other, although estimates from GRACE and LOD present some discrepancies. Slight deviations are further observed for the estimate from the geophysical models, likely to be related to the omission of polar ice and groundwater changes in the model combination we use. On the other hand, these processes do not seem to play an important role at seasonal and shorter timescales, as the sum of modelled atmospheric, oceanic and hydrological effects effectively explains the observed C 20 variations at those scales. We generally obtain very good results for the solution from SLR, and we confirm that this well-established technique accurately tracks changes in C 20 . Good agreement is further observed for the estimate from the GPS inversion, showing that this indirect method is successful in capturing fluctuations in C 20 on scales ranging from intra- to interannual. Obtaining accurate estimates from LOD, however, remains a challenging task and more reliable models of atmospheric wind fields are needed in order to obtain high-quality C 20 , in particular at the seasonal scale. The combination of GRACE data and the output of an ocean model appears to be a promising approach, particularly since corresponding C 20 is not affected by tide-like aliases, and generally gives better results than the solution from GRACE, which still seems to be of rather poor quality.

Description: We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.

Description: We have developed a method to estimate the geometry, location and densities of anomalies coming from 2-D gravity data based on compact gravity inversion technique. Compact gravity inversion is simple, fast and user friendly but severely depends on the number of model parameters, that is, by increasing the model parameters, the anomalies tend to concentrate near the surface. To overcome this ambiguity new weighting functions based on density contrast, depth, and compactness models have been introduced. Variable compactness factors have been defined here to get either a sharp or a smooth model based on the depth of the source or existence of prior information. Depth weighting derived from one station of gravity data whereas the effect of gravity data is 2-D and 3-D. To compensate this limitation an innovating weighting function namely kernel function has been introduced which multiplies with weight and compactness matrixes to yield a general model weighting function. The method is tested using three different sets of synthetic examples: a body at various depths (20, 40, 80 and 140 m), two bodies at the same depth but various distances to estimate lateral resolution and three bodies with negative and positive density contrast in different depths. The method is also applied to three real gravity data of Woodlawn massive sulphide body, sulphides mineralization of British Colombia and iron ore body of Missouri. The method produces solutions consistent with the known geologic attributes of the gravity sources, illustrating its potential practicality.

Description: In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau et al. have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ~20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or Q –1 . In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of Q –1 and its frequency dependence in studies that have treated Q –1 determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent Q –1 ) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau et al. into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.

Description: Traditional processing of Global Navigation Satellite System (GNSS) data using dedicated scientific software has provided the highest levels of positional accuracy, and has been used extensively in geophysical deformation studies. To achieve these accuracies a significant level of understanding and training is required, limiting their availability to the general scientific community. Various online GNSS processing services, now freely available, address some of these difficulties and allow users to easily process their own GNSS data and potentially obtain high quality results. Previous research into these services has focused on Continually Operating Reference Station (CORS) GNSS data. Less research exists on the results achievable with these services using large campaign GNSS data sets, which are inherently noisier than CORS data. Even less research exists on the quality of velocity fields derived from campaign GNSS data processed through online precise point positioning services. Particularly, whether they are suitable for geodynamic and deformation studies where precise and reliable velocities are needed. In this research, we process a very large campaign GPS data set (spanning 10 yr) with the online Jet Propulsion Laboratory Automated Precise Positioning Service. This data set is taken from a GNSS network specifically designed and surveyed to measure deformation through the central North Island of New Zealand. This includes regional CORS stations. We then use these coordinates to derive a horizontal and vertical velocity field. This is the first time that a large campaign GPS data set has been processed solely using an online service and the solutions used to determine a horizontal and vertical velocity field. We compared this velocity field to that of another well utilized GNSS scientific software package. The results show a good agreement between the CORS positions and campaign station velocities obtained from the two approaches. We discuss the implications of these results for how future GNSS campaign field surveys might be conducted and how their data might be processed.

Description: In this paper we present the potential of a new compact superconducting gravimeter (GWR iGrav) designed for groundwater monitoring. At first, 3 yr of continuous gravity data are evaluated and the performance of the instrument is investigated. With repeated absolute gravity measurements using a Micro-g Lacoste FG5, the calibration factor (–894.8 nm s –2 V –1 ) and the long-term drift of this instrument (45 nm s –2 yr –1 ) are estimated for the first time with a high precision and found to be respectively constant and linear for this particular iGrav. The low noise level performance is found similar to those of previous superconducting gravimeters and leads to gravity residuals coherent with local hydrology. The iGrav is located in a fully instrumented hydrogeophysical observatory on the Durzon karstic basin (Larzac plateau, south of France). Rain gauges and a flux tower (evapo-transpiration measurements) are used to evaluate the groundwater mass balance at the local scale. Water mass balance demonstrates that the karst is only capacitive: all the rainwater is temporarily stored in the matrix and fast transfers to the spring through fractures are insignificant in this area. Moreover, the upper part of the karst around the observatory appears to be representative of slow transfer of the whole catchment. Indeed, slow transfer estimated on the site fully supports the low-flow discharge at the only spring which represents all groundwater outflows from the catchment. In the last part of the paper, reservoir models are used to characterize the water transfer and storage processes. Particular highlights are done on the advantages of continuous gravity data (compared to repeated campaigns) and on the importance of local accurate meteorological data to limit misinterpretation of the gravity observations. The results are complementary with previous studies at the basin scale and show a clear potential for continuous gravity time-series assimilation in hydrological simulations, even on heterogeneous karstic systems.

Description: A thorough understanding of time-dependent noise in Global Navigation Satellite System (GNSS) position time-series is necessary for computing uncertainties in any signals found in the data. However, estimation of time-correlated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the time-series. In this paper, we investigate how linear trends affect the estimation of noise in daily GNSS position time-series. We use synthetic time-series to study the relationship between linear trends and estimates of time-correlated noise for the six most commonly cited noise models. We find that the effects of added linear trends, or conversely de-trending, vary depending on the noise model. The commonly adopted model of random walk (RW), flicker noise (FN) and white noise (WN) is the most severely affected by de-trending, with estimates of low-amplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Non-integer power-law noise estimates are also less affected by de-trending, but are very sensitive to the addition of trend when the spectral index is less than one. We derive an analytical relationship between linear trends and the estimated RW variance for the special case of pure RW noise. Overall, we find that to ascertain the correct noise model for GNSS position time-series and to estimate the correct noise parameters, it is important to have independent constraints on the actual trends in the data.

Description: Geophysical parameters of the deep Earth's interior can be evaluated through the resonance effects associated with the core and inner-core wobbles on the forced nutations of the Earth's figure axis, as observed by very long baseline interferometry (VLBI), or on the diurnal tidal waves, retrieved from the time-varying surface gravity recorded by superconducting gravimeters (SGs). In this paper, we inverse for the rotational mode parameters from both techniques to retrieve geophysical parameters of the deep Earth. We analyse surface gravity data from 15 SG stations and VLBI delays accumulated over the last 35 yr. We show existing correlations between several basic Earth parameters and then decide to inverse for the rotational modes parameters. We employ a Bayesian inversion based on the Metropolis–Hastings algorithm with a Markov-chain Monte Carlo method. We obtain estimates of the free core nutation resonant period and quality factor that are consistent for both techniques. We also attempt an inversion for the free inner-core nutation (FICN) resonant period from gravity data. The most probable solution gives a period close to the annual prograde term (or S 1 tide). However the 95 per cent confidence interval extends the possible values between roughly 28 and 725 d for gravity, and from 362 to 414 d from nutation data, depending on the prior bounds. The precisions of the estimated long-period nutation and respective small diurnal tidal constituents are hence not accurate enough for a correct determination of the FICN complex frequency.

Description: Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyperparameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30–35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basin, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.