Tectonic Critical Phenomena with Dilatancy in Lithosphere Sections

Abstract

Observations in the lithosphere show that driven critical phenomena with dilatancy can lead to spontaneous phenomena with contractancy of the pore system like in lab tests. Their spatial and temporal fractality with variable exponents just below 1 is revealed by borehole loggings and tails of seismic spectra. Evaluations of seismograms, justified by means of a fractional wave equation with stress-dependent incremental stiffness, match nearly equal directions of stress and tectonic stretching rate tensors. Splitting of shear waves confirms that a driven stressing implies dilatancy and that seismogenic chain reactions, enhanced by shock waves and pore pressure increase, imply contractancy and a drop of deviatoric stress. Except rockbursts by excessive pore pressures, this holds true from ca 1 km depth down to the upper mantle in subduction zones. The randomness of such successive critical phenomena is captured by stable L ́evy processes, this is confirmed by data plots from a subduction zone and a pumping test in a graben. The employed field theory could be further developed with observations in the lab and in situ.