REGULAR LONG-PERIOD VARIATIONS IN THE VELOCITY OF THE EARTH'S ROTATION AND RELATED DEFORMATIONS OF THE EARTH'S CRUST A majority of hypotheses on the origin of deformations in the outer portion of the Earth's shell, known as the exosphere or the Earth's crust, attribute deformations exclusively to the intrinsic physicochemical changes of the matter composing the Earth. As a rule, all the assumed alterations of the matter (heating and cooling, phase transitions, recrystallization, differentiation, etc.) ultimately lead to changes in density which are responsible for the inevitable deformation of the upper, near-surface portion of the Earth's shell. V.V. Belousov's hypothesis, widely accepted in the USSR, asserts that the fundamental cause of folding is the local heating of matter at a certain depth in the outer part of the shell. Heating causes swelling of the crust and results in its stretching, while subsequent cooling leads to the subsidence and contraction of the crust, and thus to folding.
However, physicochemical changes of matter taking place in spatially limited areas of the Earth's shell are incapable of producing any con siderable compression deformations of the crust. This conclusion is borne out by approximate determination of the magnitude of compressive and tensile stresses generated, for instance, in the roof of a magmatic chamber (i. e., in the case of the most reliably known alternations in the aggregate state of the shell). For an approximate determination of the rise in subcrustal pressure caused by the fusion of the shell substance sufficient for irreversible crust deformations, let us assume the fusion of a shell layer located in the interval between 100 km and some very large depth. In this case the 100-km thick exoshell may be compared, without large error, to a thin-walled spherical shell filled with a viscous liquid and subjected to internal pressure. In order to produce irreversible tensile deformations (viz. ruptures and shifts) in this exoshell the tensile stresses must reach the magnitude of its tensile strength.
The tensile strength (and the elastic limit) of the near-surface portion of the shell about 40km thick has been universally estimated by many geophysicists as having a mean value of about which is approximately equivalent to 1.02 The strength of the shell in its
deeper horizons is estimated at and even Gutenberg (1949) estimated the strength of the Earth's shell to be at a depth of 40-50km, and approximately at a depth of 100km. According to Jeffreys (quoted by Gutenberg) the strength of the matter constituting the Earth's shell reaches approximately at a depth of 600 km. According to Harrell, the strength of the shell near the Earth's surface is about and at a depth of 20km. The strength decreases in a downward direction, rapidly at first, down to approximately 2 at a depth of 50km, and then slowly, reaching about at a depth of 100 km and about at a depth of several hundred kilometers. The strength of most rocks on the Earth's surface is also approximately Let us determine the minimum increase of internal pressure on the lower surface of the exosphere necessary to generate irreversible tensile deformations, assuming that the strength of the exosphere (a shell 100km thick) is 1 The radial and tangential tensile or compressive stresses in a thin-walled spherical shell are proportional to the product of the pressure on the lower surface of the shell and the radius (i. e., the distance from the center to the median surface of the thin-walled shell under consideration) and inversely proportional to twice its thickness.
Let us determine the difference between the internal pressure and the weight of the thin-walled shell, assuming its mean radius to be 632 and the critical tensile stress in its latitudinal and meridional sections The result is approximately Consequently, a 31 excess of the subcrustal pressure over the weight of the crust (i.e., the exosphere) 100 km thick is critical, and its further increase would generate irreversible tensile deformations in the exoshell. Such a rise in the subcrustal pressure would increase the radius by approximately 3.1 km.