The Polar Regions are not covered by satellite gravity gradiometry data if the orbital inclination of the satellite is not equal to 90°. This paper investigates the feasibility of determining gravity anomaly (at sea level) by inversion of satellite gravity gradiometry data in these regions. Inversion of each element of tensor of gravitation as well as their joint inversion are investigated. Numerical studies show that gravity anomaly can be recovered with an error of 3 mGal in the north polar gap and 5 mGal in south polar gaps in the presence of 1 mE white noise in the satellite data. These errors can be reduced to 1 mGal and 3 mGal, respectively, by removing the regularization bias from the recovered gravity anomalies.
Numerical studies indicate that information can be gained about the layering even in the transition zone of the source, down to a considerable depth with a properly planned frequency sounding measuring system. As it has been demonstrated, the high resistivity basement can be revealed even with a source-receiver separation 2-times larger than its depth.Model studies demonstrate that the transformation of the measured field into the so-called effective resistivity — with the use of a set of homogeneous earth responses calculated for several different resistivity values — offers a useful tool in the controlled electric bipole source measurement. Effective resistivity frequency sounding curves in the transition zone also give information about layering, and make additional transformations useful in preliminary interpretation.Effective resistivity sounding curves of arbitrary configuration can be determined from any individual field amplitude and phase, or from quantities derived from them. Therefore they can be applied for single — either electric or magnetic — field component frequency sounding as well.
There are different criteria for designing a geodetic network in an optimal way. An optimum network can be regarded as a network having high precision, reliability and low cost. Accordingly, corresponding to these criteria different single-objective models can be defined. Each one can be subjected to two other criteria as constraints. Sometimes the constraints can be contradictory so that some of the constraints are violated. In this contribution, these models are mathematically reviewed. It is numerically shown how to prepare these mathematical models for optimization process through a simulated network. We found that the reliability model yields small position changes between those obtained using precision respectively. Elimination of some observations may happen using precision and cost model while the reliability model tries to save number of observations. In our numerical studies, no contradictions can be seen in reliability model and this model seems to be more suitable for designing of the geodetic and deformation networks.
An efficient and rapid heuristic local search method is dealt with, which can be applied for a wide class of nonlinear functions. The algorithm does not use gradients of the objective, and can be implemented in a very simple way. As it is demonstrated, its computational requirements are also low. The method is working using a coordinate-wise search step in each iteration cycle. Our implementation is described, shown, and analyzed through some test functions of the literature. The illustrative numerical study is attached, as well as a comparison with the well-known gradient method. The simplicity and easy-to-program nature of the method makes it to be able to be used in education.
Authors:Adriana Ioan, Aurel Stratan, and Dan Dubina
Eccentrically braced frames are widely used as lateral-force resisting system for multi-storey buildings located in seismic areas. Capacity design principles used in modern seismic design codes are deemed to constrain plastic deformations to dissipative elements only, which in eccentrically braced frames are represented by links. The aim of using these frames is to reduce the repair costs and downtime of a structure hit by an earthquake. This objective is to be attained through removable dissipative members (bolted links) and re-centering capability of the structure. Numerical studies are performed in order to investigate the practical feasibility of the replacement procedure; analyzing dual frames obtained by combining steel eccentrically braced frames with removable bolted links with moment resisting frames. Practical solutions regarding order in which bolted links need to be replaced are proposed, as well as the mounting of some temporary tie braces, for safety measures during the link removal procedure.
There are numerous methods to modify Stokes’ formula with the usually common feature of reducing the truncation error committed by the lack of gravity data in the far-zone, resulting in an integral formula over the near-zone combined with an Earth Gravity Model that mainly contributes with the long-wavelength information. Here we study the reverse problem, namely to estimate the geoid height with data missing in a cap around the computation point but available in the far-zone outside the cap. Secondly, we study also the problem with gravity data available only in a spherical ring around the computation point. In both cases the modified Stokes formulas are derived using Molodensky and least squares types of solutions. The numerical studies show that the Molodensky type of modification is useless, while the latter method efficiently depresses the various errors contributing to the geoid error. The least squares methods can be used for estimating geoid heights in regions with gravity data gaps, such as in Polar Regions, over great lakes and in some developing countries with lacking gravity data.
In precise geoid modelling the combination of terrestrial gravity data and an Earth Gravitational Model (EGM) is standard. The proper combination of these data sets is of great importance, and spectral combination is one alternative utilized here. In this method data from satellite gravity gradiometry (SGG), terrestrial gravity and an EGM are combined in a least squares sense by minimizing the expected global mean square error. The spectral filtering process also allows the SGG data to be downward continued to the Earth’s surface without solving a system of equations, which is likely to be ill-conditioned. Each practical formula is presented as a combination of one or two integral formulas and the harmonic series of the EGM.Numerical studies show that the kernels of the integral part of the geoid and gravity anomaly estimators approach zero at a spherical distance of about 5°. Also shown (by the expected root mean square errors) is the necessity to combine EGM08 with local data, such as terrestrial gravimetric data, and/or SGG data to attain the 1-cm accuracy in local geoid determination.
The gravimetric model of the Moho discontinuity is usually derived based on isostatic adjustment theories considering floating crust on the viscous mantle. In computation of such a model some a priori information about the density contrast between the crust and mantle and the mean Moho depth are required. Due to our poor knowledge about them they are assumed unrealistically constant. In this paper, our idea is to improve a computed gravimetric Moho model, by the Vening Meinesz-Moritz theory, using the seismic model in Fennoscandia and estimate the error of each model through a combined adjustment with variance component estimation process. Corrective surfaces of bi-linear, bi-quadratic, bi-cubic and multi-quadric radial based function are used to model the discrepancies between the models and estimating the errors of the models. Numerical studies show that in the case of using the bi-linear surface negative variance components were come out, the bi-quadratic can model the difference better and delivers errors of 2.7 km and 1.5 km for the gravimetric and seismic models, respectively. These errors are 2.1 km and 1.6 km in the case of using the bi-cubic surface and 1 km and 1.5 km when the multi-quadric radial base function is used. The combined gravimetric models will be computed based on the estimated errors and each corrective surface.