Theory of fast tectonic waves

Abstract

A two-dimensional model is proposed for the propagation of tectonic stress waves that are the trigger of earthquakes in seismoactive regions, and are due to bending-compression of the lithospheric slab on the asthenospheric surface flow thereby neglecting inertia forces. The lithosphere is modelled by a thin elastic slab, and the asthenosphere by the flow of a highly viscous incompressible fluid. Their interaction occurs because of the presence of a vertical shift and the action of viscous tangential forces on the lithosphere-asthenosphere interface. To obtain a system of linear equations, longitudinal and transverse potentials are introduced. The periodic low-intensity waves turn out to be standing waves, although also diffusely expanding if there is just no solid-body displacement of the lithosphère on the asthenosphere. If motion of the lithosphère over the earth's crust exists, then solitary waves are possible that take their energy from the stationary asthenospheric flow. The tectonic waves under consideration /1,2/ with characteristic periods of 2,3,6,11 years and propagation velocities of 10–100 km/yr are extremely slow compared with seismic waves, but are sufficiently rapid in the tine scale of ordinary tectonic processes, comprising millions of years. The reality of the existence of such waves can be judged, for instance, from the recently detected /3/ change of the tectonic stresses (with an 11 year cycle and an amplitude of the order of 0.1 GPa) in the subductable lithospheric slabs. The characteristic shear modulus G of the lithosphere and the viscosity μ of the asthenosphere are estimated by the numbers 5.10 10 Pa and 10 20 Pa.sec, and 10 10 Pa and 10 16 Pa.sec, respectively; consequently, the relaxation time μ G, of processes in the lithosphere has the requisite order of from 1–30 years only for the “lithosphere + asthenosphere” complex. This suggests the construction of an adequate model of the process by analogy with surface waves on a moving film of fluid /4/, but by replacing the capillary layer by an elastic plate. The adequacy of such an approach was confirmed by a simple preliminary analysis /2/ of a one-dimensional process. Meanwhile, the actual processes occur along two-dimensicnal lithospheric slabs, which requires the construction of a two-dimensional theory as well as a more careful consideration of the forces acting on. the lithospheric slab.