Clasmatic seismodynamics—Oxymoron or pleonasm?: Fid-Bau Portal

Clasmatic seismodynamics—Oxymoron or pleonasm?

Gudehus, Gerd / Touplikiotis, Asterios

Abstract Clasmatic means fractional in a physical and a mathematical sense, seismic means shaking. Truncated Lévy-processes and related fractional differential equations are introduced by means of statistics and balances. Isoclasmatic balance equations are proposed for sand samples, they imply energy-based hypoplastic and hypoelastic relations for the subcritical range and can be extended for rock. Balances of conserved and not conserved quantities with isoclasmatic distributions in spacetime are represented by coupled partial fractional differential equations, these can be transformed into classical balance equations for the subcritical range. Micro-seismic power-law spectra of sand are obtained with a fractional Schrödinger equation, its extension for polar effects and rock is indicated. Critical phenomena beyond the verge of energetic convexity are related with a degeneration of the fractional wave propagation. Due to them the lithosphere is polyclasmatic. Focussing on qualitative aspects, we show that clasmatic seismodynamics is no oxymoron, but rather a pleonasm and a promising new paradigm.

Highlights ► Evolutions of sand and fissured rock with seismic excitations can be perceived as successions of truncated Levy distributions which can be captured with fractional calculus. ► Seismic energy is released alongside with heat by sudden bursts of jammed rock fractions, propagated by elastic waves and attenuated by triggering further bursts. ► A fractional balance equation with input and loss terms represents a fractal evolution. ► Evolutions in subcritical sections of the lithosphere can be captured by coupled partial fractional differential equations.