Effect of common point selection on coordinate transformation parameter determination

The use of satellite positioning techniques commonly requires a transformation from a Conventional Terrestrial coordinate system to a Geodetic coordinate system, or vice versa. For such a transformation, the main problem is the determination of transformation parameters between these coordinate systems. The transformation parameters are estimated by a least-squares process using “common” points, i.e., those points whose coordinates are known in both systems. Therefore, the precision of so estimated transformation parameters is closely related to certain characteristics of the common points. In this contribution, we have formulated some theoretical relations between the transformation parameters and the number and the distribution of common points, and corroborated the theoretical results numerically, using a simulated geodetic network.     

Explicit formula for the geoid-quasigeoid separation

The explicit formula for the geoid-to-quasigeoid correction is derived in this paper. On comparing the geoidal height and height anomaly, this correction is found to be a function of the mean value of gravity disturbance along the plumbline within the topography. To evaluate the mean gravity disturbance, the gravity field of the Earth is decomposed into components generated by masses within the geoid, topography and atmosphere. Newton’s integration is then used for the computation of topography-and atmosphere-generated components of the mean gravity, while the combined solution for the downward continuation of gravity anomalies and Stokes’ boundary-value problem is utilized in computing the component of mean gravity disturbance generated by mass irregularities within the geoid. On application of this explicit formulism a theoretical accuracy of a few millimetres can be achieved in evaluation of the geoid-to-quasigeoid correction. However, the real accuracy could be lower due to deficiencies within the numerical methods and to errors within the input data (digital terrain and density models and gravity observations).     

Seeding agent dispersion within convective cloud as simulated by a 3-D numerical model

Summary The three-dimensional mesoscale cloud-resolving model ARPS (Advanced Regional Prediction System) was used to investigate the dispersal of an inert seeding agent within a cumulonimbus (Cb) cloud developing from two different initial states. In this paper, we stress the influence vortices in the cloud have on seeding agent dispersion. If a strong directional ambient wind shear is present in the lowest layer, a vortex pair formed at the flanks of the simulated cloud. Following the velocity field, a considerable amount of the injected seeding agent would be thrown out to the rear of the cloud, where both updrafts associated with vortices and downdrafts occurred. After a short time the agent was present only in the cloud periphery. If the Cb cloud developed under conditions where directional ambient wind shear did not exist, seeding agent dispersion would be quite different. In this case, almost all the seeding agent was transported into the main updraft, while the residence time of the agent within the cloud was longer due to the weaker cloud dynamics. Therefore, we must pay attention to whether or not the cloud contains vortices when we make the decision where to seed. This is necessary in order to minimize the loss of seeding material.     

Variable resolution on quasi-uniform grids: linear advection experiments

Summary A couple of different techniques for implementing the variable resolution within numerical models of the atmosphere that use quasi-uniform grids are estimated and compared based on their merit in the simple linear advection experiments. These techniques are: grid stretching, Schmidt transforming and grid overlapping. The quasi-uniform grids are: a conformal cubic and an octagonal grid. The techniques for the variable resolution are evaluated from the perspective of their effects on numerical solution and the practicality of their application. Our analysis suggests that the grid stretching is for now the most optimal choice. However, a special form of grid overlapping is presented that has potential to become a viable alternative in the future.     

Amazonite from the alkali granite of the Avdar Massif,Mongolia

Summary The green feldspar in alkali granite from the Avdar deposit of decoration stone (150 km W of Ulan-Bator) has been identified by means of physical and chemical methods as amazonite. Its structural state corresponds to that of microcline with a high degree of triclinicity and displaying the following anomalous dimensions of the unit cell (nm):a=0.8568,b=1.2967,c=0.7217 nm, =90.732, =115.851, =87.702°;V=0.72115 nm³.The amazonite contains in increased amount of Pb (1950 ppm) as well as of Rb (1.15 mass %). The genesis of this amazonite is associated with younger metasomatic processes in the alkali granite.

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Amazonit aus dem Alkali-Granit des Avdar-Massivs, Mongolei

Zusammenfassung Der grüne Feldspat im Alkaligranit aus der Dekorationsstein-Lagerstätte im Avdar Massiv (150 km W von Ulan-Bator) wurde auf Grund physikalischer und chemischer Methoden als Amazonit bestimmt. Sein Strukturzustand entspricht demjenigen eines Mikroklins, der eine hohe Triklinität und anomale Elementarzelle aufweist (in nm):a=0.8568,b=1.2967,c=0.7217 nm, =90.732, =115.851, =87.702°;V=0.72115 nm³.Der Amazonit hat einen erhöhten Gehalt an Pb (1950 ppm) und an Rb (1.15 Gew.-%). Die Genesis dieses Amazonits ist mit jüngeren metasomatischen Prozessen im Alkaligranit verknüpft.

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A comment on determining the induced magnetic field in bodies of arbitrary shape

Summary The authors prove that the solution of Laplace's equation under Neumann's boundary conditions can be transformed to an advantage into determining the field which is generated by charges, induced by the external field at surfaces of discontinuity.     

Changes of anisotropy of the magnetic susceptibility of rocks induced by a magnetic field

Summary The changes of the anisotropy of magnetic susceptibility of igneous rocks, induced by a magnetic field, are studied. It is proved that changes in the degree of anisotropy of susceptibility and of the orientation of the susceptibility ellispoid of specimens occur due to the configuration of the domain structure under the effect of the magnetic field. The influence of this effect on the total anisotropy of rocks depends on the degree of anisotropy due to the shape factor and on the stability of the domain structure. A model concept is presented, explaining the qualitatively different pattern of the changes of the anisotropy of susceptibility under the effect of the magnetic field in various directions of the specimens.     

An algorithm for the minimum-length least-squares solution of a set of observation equations

Summary A new computer-oriented algorithm GSO is presented for solving overdetermined systems of linear observation equations according to the principle of the least-squares method. The matrix of the system of observation equations may be of deficient rank. In this case the algorithm leads to the vector of unknowns with a minimum Euclidean norm. Alternatively, it is possible to minimize the norm of a subvector formed by a selected group of unknowns. The weight coefficient matrix, corresponding to the vector (subvector) of unknows, has the least possible trace. The algorithm GSO is based on the Gram-Schmidt Orthogonalization of suitably defined augmented matrices. The establishing and solving of normal equations is not necessary. Apart from the unknowns and residuals, GSO also determines the factorized weight coefficient matrices of the adjusted values.Presented at the I.A.G. International Symposium on Optimization of Design and Computation of Control Networks, Sopron, Hungary 1977.     

Elastic constants computed for a medium composed of this anisotropic layers

Summary The problem of the elastic properties of a medium composed of thin anisotropic layers is treated. The study is based on the conditions of stress and strain and on Hooke's Law under the assumption of close contact between the layers. The algorithm described is suitable for a computer.Dedicated to RNDr. Jan Pícha, CSc., on his 60th Birthday     

Electrical conductivity of rocks in the heating and cooling cycle

Summary The values of the electrical conductivity, recorded during the heating and cooling cycle, of eclogites and basalts are compared. The observed difference in the values is explained by reversible and irreversible changes which take place in the samples.