Die Ausgleichung und Genauigkeit Eines Polygonzuges mit Lagengemäss Ungenauen Anschlusspunkten

Summary In adjusting a bilaterally connected polygonal traverse, whether to positionally accurate or inaccurate points of departure, the mean errors are the problem of primary importance. Hitherto, the mean errors of lengths and angles were chosen; the procedure was such that the weights of both quantities were determined from the mean errors chosen, and this fixed the ratio of the mean errors. This ratio did not change as a result of the adjustment, but the absolute values of the mean errors did. Provided the adjustment was carried out on a polygonal traverse with fixed points of departure, this change did not matter. In the case of ellipses of errors in the points of departure, this change is not permissible, because it would include the change of the semi-axes of the ellipses of errors and, therefore, also of the positional rigidity of the points of departure. The contribution of this paper is in the exact method by which it is possible to compute a coefficientc, pertaining to the mean angular error selected (in the case of positionally inaccurate pointsd), which determines the mean errorm=±e √s (orm=±d √s) of the lengthss. The solution is based on the definition of the mean error of a unit weight founded on the work of deformation. In the calculus of observations, the work of deformation has so far been determined as the deformation work of internal forces from the corrections of the individual quantities after the adjustment is concluded. However, it is possible, as was demonstrated in this paper, to express it as the deformation work of external forces, which act during the adjustment in pointO (Fig. 1) on the auxiliary static system in the shape of a console, and which provide it with the necessary deformation. If the external forces are expressed by means of the tensor of the auxiliary system, the equation for the mean error of the unit weight will provide a relation between this error and the coefficientc, ord. If the mean angular error is selected and if its weight is put equal to one, an equation of the fourth degree is obtained in terms ofc (ord), from which it is possible to compute this coefficient. From the external forces, necessary to produce the deformation of the auxiliary system during its adjustment, the corrections of the individual elements of this system may be determined. If we want to determine the ellipse of errors in one of the polygonal points, it is necessary to investigated the shifts of this point, which occur if the point is acted upon by a unit force first in one and then in another direction, perpendicular to the first. Both shifts represent conjugate radii of the deformation ellipse. From this ellipse we proceed to the ellipse of errors. The general solution is supplemented by a numerical example of adjusting a polygonal traverse with positionally inaccurate points and, for sake of comparison, also by the adjustment of this traverse with positionally accurate points.

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Anschrift: Husova 5, Praha 1-Staré Město     

Weiteres zur unmittelbaren Berechnung der durchschnittlichen Geschwindigkeit in der Reflexionsseismik

Zusammenfassung Die Anordnung der Schusspunkte I, II ...,A, B ... und der Geophone 1, 2, ...a, b ... nach Figur 1 ermöglicht — horizontalen Reflektor vorausgesetzt — bei demselben Reflexionspunkt eine gute Bestimmung der durchschnittlichen Geschwindigkeiit und des Reflektors durch Ausgleichung mit den Gleichungen (3)-(6). Die angegebenen Gleichungen können auch bei geneigtem Reflektor verwendet werden, da sogar bei 11° Neigung des Reflektors der dadurch verursachte Fehler inv undN unterhalb 0.5% bleibt. Der Reflexionspunkt wandert in diesem Falle allerdings (vgl. Figur 2) mit dem Betrag r im Sinne der Gleichung (17a) weiter.Kennt man die Neigung der Schnittgeraden in der Reflexionsebene, so kann man mit Hilfe der Gleichungen (12) und (14) die genaueren Werte vonv undN ermitteln.Zur Bestimmung des Neigungswinkels wird man vorteilhaft die Anordnung nach Figur 3 treffen, wo bei einem Schuss in I/A die Geophone in 1, 2 ...,a, b ... angeordnet sind. Aus den Messergebnissen können wir durch Ausgleichung nach den Gleichungen (23) und (24) bestimmen.Im Anhang werden Zahlenbeispiele mit praktischen Folgerungen angegeben.

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Summary The system of shot points I, II, ...A, B ... and geophones 1, 2 ...a, b according to Figure 1 assures — assuming horizontal reflector — by identical reflection point an advantageous determination of the average velocity and of the reflector by adjustment with equations (3)-(6). These equations can also be used if the reflector dips, as the error caused even by a dip of 11° of the reflector inv andN does not exceed 0.5 percent. The reflection point moves, however, simultaneously (see Figure 2) with the quantily r according to equations (17a).If the dip of the intersection line in the reflection plane is known, the more precise values ofv andN can be computed with the aid of equations (12) and (14).To determine the dip , the system of Figure 3 is most convenient, where the geophons 1, 2 ...a, b ... are attached to a shot inI/A.In the appendix some numerical solutions are given and practical consequences drawn.

     

Applicability of palaeomagnetism of pyrrhotite to ore-genetic studies

Pyrrhotite has never before been used in palaeomagnetic investigations, being highly anisotropic magnetically. The aim of this paper is to show that fine-grained pyrrhotite aggregates of hydrothermal origin can be used for palaeomagnetic purposes. This has been proved with polymetallic Turkak veins from Kutná Hora in Central Bohemia as an example. It can be assumed that other localities with occurrence of hydrothermal pyrrhotite aggregates which contain directionless, uniformly scattered pyrrhotite grains and therefore forming a magnetically isotropic medium may be suitable for palaeomagnetic studies.

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Zusammenfassung Pyrrhotin, mit einem hohen Grad magnetischer Anisotropie, ist bisher für die paläomagnetische Datierung unbeachtet geblieben. Diese Arbeit will zeigen, daß feinkörnige Pyrrhotinaggregate hydrothermalen Ursprungs für paläomagnetische Untersuchungen geeignet sind, was am Beispiel polymetallischer Gänge von Turkak in Kutná Hora in Zentralböhmen dargestellt wird. Es ist anzunehmen, daß auch andere Vorkommen hydrothermaler Pyrrhotinaggregate in denen regelmäßig verteilte Körner richtungslos orientiert vorliegen und so ein magnetisch isotropes Medium bilden, sich für paläomagnetische Untersuchungen eignen.

     

Recent movements of the earth's crust

Summary It has been shown that it is necessary to combine several methods to be able to describe and explain recent movements of the Earth's crust.Presented at the XV^th General Assembly of the IUGG, Moscow 1971.     

Petrogenetic relationships of acid and basic rocks in iceland: Sr-isotopes and rare-earth elements in late and postglacial volcanics

Strontium isotope ratios and rare-earth element abundances have been measured in acid, intermediate and basic rocks from three late to postglacial volcanic complexes, and several other postglacial basalts in Iceland. Late and postglacial basalts in Iceland have been generated from a source region which is essentially homogeneous with respect to⁸⁷Sr/⁸⁶Sr. The mean⁸⁷Sr/⁸⁶Sr ratio for the basalts analysed is 0.70328 and the range is from 0.70317 ± 6to0.70334 ± 5 (2σ).Acid rocks from the Kerlinganfjöll and Namafjall volcanic complexes have⁸⁷Sr/⁸⁶Sr ratios which are indistinguishable from analysed basalts from the same complexes. However, intermediate and acid rocks from the Torfajökull complex have significantly higher⁸⁷Sr/⁸⁶Sr ratios and could not have been derived by fractional crystallization from basaltic magmas similar to those found in the same complex. These latter rocks have most probably been produced by remelting of Tertiary gabbroic rocks in Layer 3. Most of the basalts analysed have higher total rare-earth element abundances than typical dredged ocean-ridge tholeiites, and show less light rare-earth depletion. Intermediate and acid compositions show overall higher abundances and light rare-earth enrichments. The measured rare-earth abundances are compared with abundances generated by differential partial melting of various model source regions.It is shown that both the tholeiitic and alkali basalt compositions could be generated from the same source material by different degrees of partial melting. Variable partial melting of gabbroic material may account for the rare-earth element abundances of both the rhyolitic rocks (small degrees of melting) and the intermediate rocks (more extensive melting).     

Peralkaline acid tendencies in Gran Canaria (Canary Islands)

The study of a volcanic series from the island of Gran Canaria (Canary Islands) in which alkaline and peralkaline, saturated and undersaturated rocks coexist, is reported here. Materials with high volatile content (ignimbritic trachytes) were first emitted and the series ended with the eruption of phonolitic lavas. The average peralkalinity index in these rocks is typically about 1.0 and, therefore, peralkaline rocks coexist with non-peralkaline ones. However, a maximum in peralkalinity is found in the ignimbritic rocks of the lower part of the series. In spite of the evident acid peralkaline tendencies of these rocks, it does not seem appropriate to classify them as pantellerites or comendites. Nor are they consistent with the genetic processes proposed for rocks of similar composition and oceanic environment.The crystallization of the feldspars controls the variation trends among the different magmas but the fractionation alone does not sufficiently explain the genesis of successive fluids. Various factors seem to point to the important role which a gas-transfer process causing a geochemical stratification inside the magmatic chamber may have played.The occurrence of peralkaline silicics at Gran Canaria, which is located for away from the active Mid-Atlantic ridge, is not related to transitional basalts. These rocks are a deviation from the main undersaturated alkalic trend which characterizes the volcanism of the Canary Islands, their genesis being related to the realization of favourable local volcanic conditions.