Volume 1, Issue 4 -

Extension and slip rate partitioning in NW Iran constrained by GPS measurements Convergence of 22±2 mm yr -1 between the northward motion of the Arabian Plate relative to Eurasia at N8° ±5° E is accommodated by a combination of thrust and strike-slip faults in different parts of Iran. Dislocation modeling is used to examine the GPS data for this part of the Alpine-Himalayan mountain belt with more concentration in NW Iran. First, the vectors due to known Arabia-Eurasia rotation are reproduced by introducing structures that approximate the large-scale tectonics of the Middle East. Observed features of the smaller scale fault system are then progressively included in the model. Slip rate amplitudes and directions adjusted to fit available GPS data. Geological evidences show strike-slip and reverse-slip faulting in NW Iran, but GPS data show normal faults in this region too. By slip partitioning we propose four locations for normal faults based on extensions observed by GPS data. Slip rate values were estimated between 2 ~ 5 mm/yr for proposed normal faults. Our modeling results prove that the NW Iran is not only affected by Arabia-Eurasia collision but also contributes in the subduction motion of the South Caspian and Kura basins basement beneath the Apsheron-Balkhan sill and the Great Caucasus respectively.

Precise computation of the direct and indirect topographic effects of Helmert's 2 nd method of condensation using SRTM30 digital elevation model The direct topographic effect (DTE) and indirect topographic effect (ITE) of Helmert's 2 nd method of condensation are computed using the digital elevation model (DEM) SRTM30 in 30 arc-seconds globally. The computations assume a constant density of the topographic masses. Closed formulas are used in the inner zone of half degree, and Nagy's formulas are used in the innermost column to treat the singularity of integrals. To speed up the computations, 1-dimensional fast Fourier transform (1D FFT) is applied in outer zone computations. The computation accuracy is limited to 0.1 mGal and 0.1cm for the direct and indirect effect, respectively. The mean value and standard deviation of the DTE are -0.8 and ±7.6 mGal over land areas. The extreme value -274.3 mGal is located at latitude -13.579° and longitude 289.496°, at the height of 1426 meter in the Andes Mountains. The ITE is negative everywhere and has its minimum of -235.9 cm at the peak of Himalayas (8685 meter). The standard deviation and mean value over land areas are ±15.6 cm and -6.4 cm, respectively. Because the Stokes kernel does not contain the zero and first degree spherical harmonics, the mean value of the ITE can't be compensated through the remove-restore procedure under the Stokes-Helmert scheme, and careful treatment of the mean value in the ITE is required.

Single Frequency Ionosphere-free Precise Point Positioning: A Cross-correlation Problem? This research investigates the feasibility of applying the code and the ionosphere-free code and phase delay observables for single frequency Precise Point Positioning (PPP) processing. Two observation models were studied: the single frequency ionosphere-free code and phase delay, termed the quasi-phase observable, and the code and quasi-phase combination. When implementing the code and quasi-phase combination, the cross-correlation between the observables must be considered. However, the development of an appropriate weight matrix, which can adequately describe the noise characteristics of the single frequency code and quasi-phase observations, is not a trivial task. The noise in the code measurements is highly dependent on the effects of the ionosphere; while the quasi-phase measurements are basically free from the effects of the ionospheric error. Therefore, it is of interest to investigate whether the correlation between the two measurements can be neglected when the code measurements were re-introduced to constrain the initial parameters estimation and thereby improving the phase ambiguities initialization process. It is revealed that the assumed uncorrelated code and quasi-phase combination provided comparable if not better positioning precision than the quasi-phase measurement alone. The level of improvement in the estimated positions is between 1 - 18 cm RMS.

Combined approach for the unification of levelling networks in New Zealand The unification of levelling networks in New Zealand is done using a combined approach. It utilises the joint levelling network adjustment and the geopotential-value approach. The levelling and normal gravity data are used for a joint adjustment of the levelling networks at the South and North Islands of New Zealand while fixing the heights of tide gauges in Dunedin and Wellington. The results reveal a good quality of levelling data; the STD of residuals is 2 mm for the whole country. The comparison of the newly determined and original normal-orthometric heights confirms the presence of large local vertical datum offsets and systematic levelling errors. Since the geopotential-value approach is based on the Molodensky's theory, the newly adjusted normal-orthometric heights are converted to the normal heights. This conversion is based on applying the cumulative normal to normal-orthometric height correction computed from levelling and gravity anomaly data. In the absence of the observed gravity data the gravity anomalies along levelling lines are generated fromEGM2008. The GPS-levelling data and EGM2008 are used to estimate the average offsets of the jointly adjusted levelling networks at the North and South Islands with respect to World Height System defined by the adopted geoidal geopotential value of W 0 = 62636856 ± 0.5 m 2 s -2 ; the estimated offsets are 10.6 cm and 27.5 cm.

Comparison and testing of GOCE global gravity models in Central Europe Three different global gravity model solutions have been released by the European GOCE Gravity Consortium: a direct solution, a time-wise solution and a space-wise solution. To date, two releases of each solution have been issued. Each of these solutions has specific positives and weaknesses. This paper shows and analyzes the differences between each solution in Central Europe by means of comparison with respect to the EGM2008 and GOCO02S global gravity models. In order to make an independent comparison, the global GOCE models are tested by the SKTRF (Slovak Terrestrial Reference Frame) network in Slovakia.

Polyaxial Figures of the Moon This study investigates various models to represent the gross geometric shape of the Moon. Asymmetric polyaxial geometric models-namely three-, four- and six-axial lunar figure - are compared and contrasted with the axially symmetric three-axis ellipsoidal model derived from Chang'e 1 and SELENE laser altimetry data. All solutions confirm a hydrostatically stable lunar shape shifted with respect to the lunar center of mass by topography. Model solutions with increasing complexity offer additional information about the regional properties of the lunar topography. Solution statistics suggest that axially symmetric lunar figures and their center of figure parameters can be replaced by an equivalent asymmetric lunar shape centered at the center of mass of the Moon. Thus, using only three shape parameters, one can derive an "egg" shape that better accommodates the true geometry of the Moon.

Local Least Squares Spectral Filtering and Combination by Harmonic Functions on the Sphere Least squares spectral combination is a well-known technique in physical geodesy. The established technique either suffers from the assumption of no correlations of errors between degrees or from a global optimisation of the variance or mean square error of the estimator. Today Earth gravitational models are available together with their full covariance matrices to rather high degrees, extra information that should be properly taken care of. Here we derive the local least squares spectral filter for a stochastic function on the sphere based on the spectral representation of the observable and its error covariance matrix. Second, the spectral combination of two erroneous harmonic series is derived based on their full covariance matrices. In both cases the transition from spectral representation of an estimator to an integral representation is demonstrated. Practical examples are given. Taking advantage of the full covariance matrices in the spectral combination implies a huge computational burden in determining the least squares filters and combinations for high-degree spherical harmonic series. A reasonable compromise between accuracy of estimator and workload could be to consider only one weight parameter/degree, yielding the optimum filtering and combination of Laplace series.

Quality Estimates in Geoid Computation by EGM08 The high-degree Earth Gravitational Model EGM08 allows for geoid determination with a resolution of the order of 5'. Using this model for estimating the quasigeoid height, we estimate the global root mean square (rms) commission error to 5 and 11 cm, based on the assumptions that terrestrial gravity contributes to the model with an rms standard error of 5 mGal and correlation length 0:01° and 0:1°, respectively. The omission error is estimated to—0:7Δg [mm], where Δg is the regional mean gravity anomaly in units of mGal. In case of geoid determination by EGM08, the topographic bias must also be considered. This is because the Earth's gravitational potential, in contrast to its spherical harmonic representation by EGM08, is not a harmonic function at the geoid inside the topography. If a correction is applied for the bias, the main uncertainty that remains is that from the uncertainty in the topographic density, which will still contribute to the overall geoid error.

On Precision Kinematic Accelerations for Airborne Gravimetry Advances in accelerometer technology promise many orders of magnitude improvement in sensitivity; which, consequently, also suggest progress in Earth Science applications, such as through new airborne gravimetric systems. However, a new capability for one sensor then usually demands commensurate requirements from auxiliary sensors in order to realize its full potential. Specifically, airborne gravimetry would benefit from improved inertial accelerometry only if the kinematic acceleration derived from vehicle tracking or positioning is equally precise. The latter is investigated in this study to determine the limits in precision due to errors in modeling the numerical derivative and due to errors in the positions, themselves. Simulations with actual aircraft trajectories show that the kinematic acceleration using current positioning capability (that is, GPS or similar satellite navigation systems) can be determined to an accuracy at the sub-milligal level only with sufficient smoothing over intervals of 60 s or longer. The effects of position error still dominate over the model error, and both are many orders of magnitude greater than the predicted precision of state-of-the-art accelerometry. This suggests that airborne gravity field determination likely will profit more if the advances in inertial sensor technology are directed toward gravity gradiometry.

Spherical Spline Application to Radio Occultation Data In recent years, the importance of the Radio Occultation Method (ROM), an observation procedure of atmospheric quantities such as temperature, density, pressure, and water vapor, increased in value. Based on the global distribution and the high accuracy of the measurements between the Earth's surface up to 35km altitude, ROM offers new perspectives for climate monitoring. In order to compare the measurements, the data have to be visualized. This paper gives the basic definitions and theorems of spline approximation on the sphere. Via its adjustable smoothing parameters, ROM can be suitably adapted to approximate the given data. Further on, it demonstrates, splines as approximation structures realizing a minimal bending energy of their graphs provide a good approximation of the data at hand. Our results demonstrate that spherical spline approximation is an appropriate method to visualize the change over time of a given layer and to illustrate the vertical composition of the Earth's atmosphere. Moreover, ROM enables us to compare the layers of the atmosphere at different points in time as well as the approximation of parameters between the measurements on arbitrary points on the Earth.