Semi-stochastic modification of second-order radial derivative of Abel–Poisson’s formula for validating satellite gravity gradiometry data

The geoid can be used to validate the satellite gravity gradiometry data. Validation of such data is important prior to their downward continuation because of amplification of the data errors through this process. In this paper, the second-order radial derivative of Abel–Poisson’s formula is modified stochastically to reduce the effect of the far-zone geoid and generate the second-order radial derivative of geopotential at 250 km level. The numerical studies over Fennoscandia show that this method yields the gradients with an error of 10 mE and when the long wavelength of geoid is removed from the estimator and restored after the computations (remove–compute–restore) the error will be in 1 mE level. We name this method semi-stochastic modification. The best case scenario is found when the degree of modification of the integral formula is 200 and the long wavelength geoid to degree 100 is removed and restored. In this case the geoid should have a resolution of 15′ × 15′ and the integration should be performed over a cap size of 3°.     

Inversion of satellite gradiometry data using statistically modified integral formulas for local gravity field recovery

The satellite gravity gradiometric data can be used directly to recover the gravity anomaly at sea level using inversion of integral formulas. This approach suffers by the spatial truncation errors of the integrals, but these errors can be reduced by modifying the formulas. It allows us to consider smaller coverage of the satellite data over the region of recovery. In this study, we consider the second-order radial derivative (SORD) of disturbing potential (T_rr) and determine the gravity anomaly with a resolution of 1° × 1° at sea level by inverting the statistically modified version of SORD of extended Stokes’ formula. Also we investigate the effect of the spatial truncation error on the quality of inversion considering noise of T_rr. The numerical investigations show satisfactory results when the area of T_rr coverage is the same with that of the gravity anomaly and the integral formula is modified by the biased least-squares modification. The error of recovery will be about 6 mGal after removing the regularization bias in the presence of 1 mE noise in T_rr measured on the orbit.     

The use of Gaussian equations of motions of a satellite for local gravity anomaly recovery

The orbital elements of a low Earth orbiting satellite and their velocities can be used for local determination of gravity anomaly. The important issue is to find direct relations among the anomalies and these parameters. Here, a primary theoretical study is presented for this purpose. The Gaussian equations of motion of a satellite are used to develop integral formulas for recovering the gravity anomalies. The behaviour of kernels of the integrals are investigated for a two-month simulated orbit similar to that of the Gravity field and steady-state ocean circulation explorer (GOCE) mission over Fennoscandia. Numerical investigations show that the integral formulas have neither isotropic nor well-behaved kernels. In such a case, gravity anomaly recovery is not successful due to large spatial truncation error of the integral formulas. Reformulation of the problem by combining the orbital elements and their velocities leads to an integral with a well-behaved kernel which is suitable for our purpose. Also based on these combinations some general relations among the orbital elements and their velocities are obtained which can be used for validation of orbital parameters and their velocities.     

The effect of spatial truncation error on variance of gravity anomalies derived from inversion of satellite orbital and gradiometric data

The spatial truncation error (STE) is a significant systematic error in the integral inversion of satellite gradiometric and orbital data to gravity anomalies at sea level. In order to reduce the effect of STE, a larger area than the desired one is considered in the inversion process, but the anomalies located in its central part are selected as the final results. The STE influences the variance of the results as well because the residual vector, which is contaminated with STE, is used for its estimation. The situation is even more complicated in variance component estimation because of its iterative nature. In this paper, we present a strategy to reduce the effect of STE on the a posteriori   variance factor and the variance components for inversion of satellite orbital and gradiometric data to gravity anomalies at sea level. The idea is to define two windowing matrices for reducing this error from the estimated residuals and anomalies. Our simulation studies over Fennoscandia show that the differences between the 0.5°×0.5°$0.5°\times 0.5°$ gravity anomalies obtained from orbital data and an existing gravity model have standard deviation (STD) and root mean squared error (RMSE) of 10.9 and 12.1 mGal, respectively, and those obtained from gradiometric data have 7.9 and 10.1 in the same units. In the case that they are combined using windowed variance components the STD and RMSE become 6.1 and 8.4 mGal. Also, the mean value of the estimated RMSE after using the windowed variances is in agreement with the RMSE of the differences between the estimated anomalies and those obtained from the gravity model.     

Mercury’s Weather-Beaten Surface: Understanding Mercury in the Context of Lunar and Asteroidal Space Weathering Studies

Mercury’s regolith, derived from the crustal bedrock, has been altered by a set of space weathering processes. Before we can interpret crustal composition, it is necessary to understand the nature of these surface alterations. The processes that space weather the surface are the same as those that form Mercury’s exosphere (micrometeoroid flux and solar wind interactions) and are moderated by the local space environment and the presence of a global magnetic field. To comprehend how space weathering acts on Mercury’s regolith, an understanding is needed of how contributing processes act as an interactive system. As no direct information (e.g., from returned samples) is available about how the system of space weathering affects Mercury’s regolith, we use as a basis for comparison the current understanding of these same processes on lunar and asteroidal regoliths as well as laboratory simulations. These comparisons suggest that Mercury’s regolith is overturned more frequently (though the characteristic surface time for a grain is unknown even relative to the lunar case), more than an order of magnitude more melt and vapor per unit time and unit area is produced by impact processes than on the Moon (creating a higher glass content via grain coatings and agglutinates), the degree of surface irradiation is comparable to or greater than that on the Moon, and photon irradiation is up to an order of magnitude greater (creating amorphous grain rims, chemically reducing the upper layers of grains to produce nanometer-scale particles of metallic iron, and depleting surface grains in volatile elements and alkali metals). The processes that chemically reduce the surface and produce nanometer-scale particles on Mercury are suggested to be more effective than similar processes on the Moon. Estimated abundances of nanometer-scale particles can account for Mercury’s dark surface relative to that of the Moon without requiring macroscopic grains of opaque minerals. The presence of nanometer-scale particles may also account for Mercury’s relatively featureless visible–near-infrared reflectance spectra. Characteristics of material returned from asteroid 25143 Itokawa demonstrate that this nanometer-scale material need not be pure iron, raising the possibility that the nanometer-scale material on Mercury may have a composition different from iron metal [such as (Fe,Mg)S]. The expected depletion of volatiles and particularly alkali metals from solar-wind interaction processes are inconsistent with the detection of sodium, potassium, and sulfur within the regolith. One plausible explanation invokes a larger fine fraction (grain size <45 μm) and more radiation-damaged grains than in the lunar surface material to create a regolith that is a more efficient reservoir for these volatiles. By this view the volatile elements detected are present not only within the grain structures, but also as adsorbates within the regolith and deposits on the surfaces of the regolith grains. The comparisons with findings from the Moon and asteroids provide a basis for predicting how compositional modifications induced by space weathering have affected Mercury’s surface composition.     

Spatial modeling of flood probability using geo-environmental variables and machine learning models,case study: Tajan watershed,Iran

The main objective of this study was to produce flood susceptibility maps for Tajan watershed, Sari, Iran using three machine learning (ML) models including Self-Organization Map (SOM), Radial Basis Function Neural Network (RBFNN), and Multi-layers Perceptron (MLP). To reach such a goal, different physical-geographical factors (criteria) were integrated and mapped. 212 flood inventory map was randomly divided into training and testing datasets, where 148 flood locations (70%) were used for training and the remaining 64 locations (30%) were employed for testing. Model validation was performed using several statistical indices and the area under the curve (AUC). The results of the correlation matrix showed, three factors slope (0.277), distance from river (0.263), and altitude (0.223) were the most important factors affecting flood. The accuracy evaluation of the flood susceptibility maps through the AUC method and K-index shows that in the validation phase RBFNN (AUC = 0.90) outperform the MLP (AUC = 0.839) and SOM (AUC = 0.882) models. The highest percentage flood susceptibility of the area in MLP, SOM and RBFNN models is related to moderate (28.7%), very low (40%) and low (37%), respectively. Also, the validation results of the models using the Relative Flood Density (RFD) approach showed that very high class had the highest RFD value.     

Multi precursors analysis associated with the powerful Ecuador (MW = 7.8) earthquake of 16 April 2016 using Swarm satellites data in conjunction with other multi-platform satellite and ground data

After DEMETER satellite mission (2004–2010), the launch of the Swarm satellites (Alpha (A), Bravo (B) and Charlie (C)) has created a new opportunity in the study of earthquake ionospheric precursors. Nowadays, there is no doubt that multi precursors analysis is a necessary phase to better understand the LAIC (Lithosphere Atmosphere Ionosphere Coupling) mechanism before large earthquakes. In this study, using absolute scalar magnetometer, vector field magnetometer and electric field instrument on board Swarm satellites, GPS (Global Positioning System) measurements, MODIS-Aqua satellite and ECMWF (European Centre for Medium-Range Weather Forecasts) data, the variations of the electron density and temperature, magnetic field, TEC (Total Electron Content), LST (Land Surface Temperature), AOD (Aerosol Optical Depth) and SKT (SKin Temperature) have been surveyed to find the potential seismic anomalies around the strong Ecuador (M_w = 7.8) earthquake of 16 April 2016. The four solar and geomagnetic indices: F10.7, D_st, K_p and a_p were investigated to distinguish whether the preliminary detected anomalies might be associated with the solar-geomagnetic activities instead of the seismo-ionospheric anomalies. The Swarm satellites (A, B and C) data analysis indicate the anomalies in time series of electron density variations on 7, 11 and 12 days before the event; the unusual variations in time series of electron temperature on 8 days preceding the earthquake; the analysis of the magnetic field scalar and vectors data show the considerable anomalies 52, 48, 23, 16, 11, 9 and 7 days before the main shock. A striking anomaly is detected in TEC variations on 1 day before earthquake at 9:00 UTC. The analysis of MODIS-Aqua night-time images shows that LST increase unusually on 11 days prior to main shock. In addition, the AOD variations obtained from MODIS measurements reach the maximum value on 10 days before the earthquake. The SKT around epicentral region presents anomalous higher value about 40 days before the earthquake. It should be noted that the different lead times of the observed anomalies could be acknowledged based on a reasonable LAIC earthquake mechanism. Our results emphasize that the Swarm satellites measurements play an undeniable role in progress the studies of the ionospheric precursors.     

Solitary and periodic waves in magneto–rotating plasmas: Effect of the Kappa–Cairns distributed electrons

The nonlinear propagation of ion–acoustic (IA) waves in a magneto–rotating plasma is studied by considering the Kappa-Cairns electron distribution. Employing the perturbation scheme, Korteweg–de Vries equation is derived. It is seen that both positive and negative potential solitons can be supported in the present plasma model. The numerical results reveal that the Kappa-Cairns distributed electrons modify features of the electrostatic waves significantly. The effects of non–thermal parameters, plasma rotation frequency, ion temperature, and the wave propagation angle on electrostatic solitary wave structures are also discussed here. It is found that the plasma parameters considerably influence the propagation of IA waves in rotating plasmas. Furthermore, using the bifurcation theory of planar dynamical systems to the K-dV equation, we have presented the existence of solitary and periodic traveling waves. Our study may be helpful to understand the behavior of ion–acoustic wave in the rotating plasma.     

Recovery of Moho’s undulations based on the Vening Meinesz–Moritz theory from satellite gravity gradiometry data: A simulation study

In the gravimetric approach to determine the Moho depth an isostatic hypothesis can be used. The Vening Meinesz–Moritz isostatic hypothesis is the recent theory for such a purpose. Here, this theory is further developed so that the satellite gravity gradiometry (SGG) data are used for recovering the Moho depth through a nonlinear integral inversion procedure. The kernels of its forward and inverse problems show that the inversion should be done in a larger area by 5° than the desired one to reduce the effect of the spatial truncation error of the integral formula. Our numerical study shows that the effect of this error on the recovered Moho depths can reach 6 km in Persia and it is very significant. The iterative Tikhonov regularization in a combination with either generalized cross validation or quasi-optimal criterion of estimating the regularization parameter seems to be suitable and the solution is semi-convergent up to the third iteration. Also the Moho depth recovered from the simulated SGG data will be more or less the same as that obtained from the terrestrial gravimetric data with a root mean square error of 2 km and they are statistically consistent.     

The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data

The satellite gravity gradiometry (SGG) data can be used for local modelling of the Earth’s gravity field. In this study, the SGG data in the local north-oriented and orbital frames are inverted to the gravity anomaly at sea level using the second-order partial derivatives of the extended Stokes formula. The emphasis is on the spatial truncation error and the kernel behaviour of the integral formulas in the aforementioned frames. The paper will show that only the diagonal elements of gravitational tensor at satellite level are suitable for recovering the gravity anomaly at sea level. Numerical studies show that the gravity anomaly can be recovered in Fennoscandia with an accuracy of about 6 mGal directly from on-orbit SGG data.