Energy and moment of the Earth’s rotation elastic field

Abstract

The problem of an elastic stress field in a rotating medium is formulated and solved analytically within the limits of the classical theory of elasticity with a symmetrical stress tensor. This is a rotation elastic field of action at a distance. There are two specific types of elastic waves with a moment in rotating media: solitons and excitons, or rotation waves. The soliton solutions to the wave equation represent waves of global earthquake migration (slow tectonic waves) which are no faster than ∼1 cm/s, i.e., approach the migration velocity of large and great earthquakes (M > 7.5). The exciton solutions correspond to waves of local migration of foreshocks and aftershocks in earthquake sources (fast tectonic waves) and have their maximum velocity comparable to faulting rate and/or to S-wave velocities.

Migration of seismic and volcanic activity as display of wave geodynamic process

“…The velocity yielded from the above equation is typical of block rotating media, including geomedium, in the same way as elastic longitudinal and transverse waves is typical for 'normal' solids [Vikulin, 2008]. The extreme value of local migration velocity of earthquakes foci fore-aftershocks in the rotational model is the speed of elastic seismic waves 1 -10 km/s [Vikulin, 2010].…”

“…Under the concept of block geomedium, the analysis of seismicity of the Earth's most active Pacific zone highlighted ways to solving the problem of earthquake migration waves and establishing a relationship between earthquake migration, tectonic and seismic waves [Vikulin, 2008[Vikulin, , 2010. Independent studies conducted by different researchers yielded over 50 migration velocities of the Pacific earthquakes with different magnitudes on the plane with the coordinates of 'energy (earthquake magnitude M) -velocity (the logarithm of velocity LgV)'; from this database, two types of migration are clearly distinguishable as they are represented by two compact fields of points.…”

“…Thus, the analysis of earthquakes migration processes within the Pacific margin allowed us to distinguish between two types of rotational velocities controlling interactions between the earthquake foci in conditions of the planet's rotation around its axis [Vikulin, 2008[Vikulin, , 2010. The first type (with the limiting value of velocity, c 0 ) is responsible for long-range mechanism of interaction between blocks within the entire Pacific margin, and the second type (with the limiting value of seismic velocities) is responsible for the short range of foreshocks and aftershocks within foci of individual earthquakes .…”

Nonlinear waves and solitons in models of fault block geological media

“…According to the solution, the soliton is always slower than seismic waves. Vikulin (2008) suggested a rotation model based on the SG equation explaining some features of the seismic process, in which strain waves in a chain of seismogenic blocks are generated by the Earth's rotation.…”

“…Faulting, rotation, and slippage of crust blocks that induce strain waves have been modeled in recent two decades using the sine-Gordon (SG) equation, applied also to interpret the related tectonic effects (Bykov, 2001a(Bykov, , 2006(Bykov, , 2008Garagash, 1996;Gershenzon et al, 2009Gershenzon et al, , 2011Majewski, 2006a,b;Mikhailov and Nikolaevskiy, 2000;Nikolaevskiy, 1995Nikolaevskiy, , 1996Vikulin, 2008). The classical SG equation has several qualitatively different analytical solutions in the form of kinks, breathers, solitons, and slow and fast cnoidal waves, each referring to a certain evolution pattern of blocks and faults (Bykov, 2000a).…”