The Antarctic continent is unique in a variety of respect, one being that it appears to lie at a geological nodal point formed by the junction of major tectonic elements extending southward from Atlantic, Indian and Pacific Oceans, South America and New Zealand. The distribution of volcanic activity in Antarctica, especially the later part of Cenozoic time, has considerable bearing on any interpretations of orogenic patterns or history. The greatest development of Cenozoic volcanoes and the most widespread extent of volcanic rocks is in west Antarctica, occuping nearly all of the great sweep of Marie Byrd Land across 50° of longitude, a distance of about 1, 600 km. This volcanic province forms a band extending roughly 450 km inland from the coast. Another large volcanic province, through less extensive than that in Marie Byrd Land, lies along the coast of Victoria Land facing the Ross Sea. In the almost continuous out-crop along the coast for a distance of 250 km. At least ten domes or shield-volcanoes overlap to form the Hallett volcanic province. On the continent proper, no volcanic rocks are known to occur between the Melbourne volcanic province and the Dry Valley-Mt. Discovery area of the McMurdo volcanic province, more than 380km farther south. At the latter locality, small cinder cones are scattered along the sides of Taylor Valley. In this province, offshore, Black and White Islands, Ross Island, and some little islands are of volcanic origin. Late Tertiary and Quaternary volcanic rocks, mainly olivine basalt, are more common near the northern end of the Antarctic Peninsula where several islands off both the eastern and western coast are of volcanic origin. Best known, of course, is Deception Island on which violent eruptions occurred in 1967 and 1969. The Ross Island of McMurdo volcanic province in Southern Victoria Land is similarly situated generally east of the continental margin. Subsidiary centres and lines of cones on Ross Island have a radial symmetry around Mt. Erebus (3, 794 m) as an active volcano, and their distribution may thus be related to radial fractures at approximately120° to each other. Mt. Erebus and other volcanoes of Ross Island consist of basanitoid, alkali olivine basalt, trachyte and phonolite. The volcanic rocks vary considerably in composition throughout the Marie Byrd Land and Victoria Land, forming a large alkalic province, in which alkali basalt, trachyte and phonolite are representative rocks. Ultramafic inclusions are frequently found throughout this region. The South Shetland Island, lying off the Antarctic Peninsula, contain several composite strato-volcanoes including Deception Island which recently erupted along the ring fractures of caldera. These volcanic islands are composed of olivine basalt and andesite, all of which are rich in soda, but their mineralogy is similar to that of high-alkali tholeiite with high-alumina content and its derivatives. It is true that the most of the volcanic rocks erupted along the orogenic belt are of calc-alkali rock series. The rocks of the South Sandwich Islands are considered to have derived by fractional crystallization of a primary low-alkali tholeiitic magma. It is also suggested that the rocks of the South Shetland Islands and some volcanoes of the southern Andes have derived by fractional crystallization of a primary high-alkali tholeiitic magma with high-alumina content. The 87Sr/86Sr ratios in the island-arc low-alkali tholeiite series from the South Sandwich Islands cluster about a value of 0.7040. The uniformity of the 87Sr/86Sr values is consistent with the fractional crystallization relationship. The 87Sr/86Sr ratios of the volcanic rocks from Deception Island have a mean value of 0.7036. This value is very similar to the ratios of basaltic rocks from Island Arcs.
An investigation is made of some other geomorphic parameters as well as the bifurcation ratio of the most probable channel networks based on the set-theory. The following equations are derived for the set S (nl, nl+1, …, nη, …, nλ) of all topologically distinct networks having nl, nl+1, …, nη, …nλ, streams of order l, (l-1), η, … λ respectively and the set Smax (nl, nl+1, …, nη…, nλ) having the largest number of topologically distinct networks among S (nl, nl+1, …, nη2, …, nλ) for the given value of nl and various values of nl+1, …, nη, …, nλ, where l is the lowest order.When nl is infinite, Smax (nl, nl+1, …, nη, …, nλ) =S (nl, 1/4 nl, … (1/4) η-l nl…, (1/4) λ- nl) Smax (nl, nl+1, …, nη, …, nλ-1) ⊃Smax (nl, nl+1, …, nη, …, nλ) Then the mean me of number of streams of order k entering into a stream of order mfrom sides in Smax (nl, nl+1, …, nη, nη, …, nλ) is given as follows. mεm=2m-k-1 It is, therefore, proved that the bifurcation ratio of the most probable networks of infinite magnitude quite agrees with the mean bifurcation ratio of all infinite topologically distinct networks and me, shows the same value in both. When ni is finite, nl+1, …, nη, …, nλ take the closed values to (1/4) nl, … (1/4) λ-lnl…, (1/4) λ-lnl respectively. The same conclusion is deduced for the other geomorphic parameters, for example, the basin area ratio, the stream length ratio, etc, which are derived from mεk.
Many hypothesis have been suggested in Japan, related to the plate-tectonic theory ; (1) “the high pressure metamorphic belts of the Sangun and the Sambagawa were produced within the subduction zones of oceanic plates”, (2) “the so-called ophiolites in the Sangun and the Mikabu zone are of the ancient oceanic crusts”, (3) “the Shimanto terrain was ancient trench area”, (4) “Hokkaido, which has its backbone range with a high pressure metamorphic belt on the continental side and a high temperature metamorphic belt on the oceanic side at present, has been rotated in a 180-degree”, and others. These hypothesis are not well fitted to the geology of Japan. In Honshu, there are no great fault which suggests the ancient boundary between the oceanic and continental plates, and no strata which have the characters of an ancient oceanic crust itself or of those made in the subduction zone of an oceanic plate. However, geological developments of Japan, in the Sambosan, the Shimanto and later stages, can well be explained by the movemnents of ancient oceanic plates, their positions and the changes of the positions, although many earth movements were produced by up-and-down movements probably related to granite intrusions.