Title: Deviations from the Gutenberg–Richter law on account of a random distribution of block sizes

This paper studies properties of a continuum with structure. The characteristic size of the structure governs the fact that difference relations are nonautomatically transformed into differential ones. It is impossible to consider an infinitesimal volume of a body, to which the major conservation laws could be applied, because the minimum representative volume of the body must contain at least a few elementary microstructures. The corresponding equations of motion are equations of infinite order, solutions of which include, along with usual sound waves, unusual waves with abnormally low velocities without a lower limit. It is shown that in such media weak perturbations can increase or decrease outside the limits. The number of complex roots of the corresponding dispersion equation, which can be interpreted as the number of unstable solutions, depends on the specific surface of cracks and is an almost linear dependence on a logarithmic scale, as in the seismological Gutenberg–Richter law. If the distance between one pore (crack) to another one is a random value with some distribution, we must write another dispersion equation and examine different scenarios depending on the statistical characteristics of the random distribution. In this case, there are sufficient deviations from the Gutenberg–Richter law and thismore » theoretical result corresponds to some field and laboratory observations.« less

Trofimuk Institute of Oil and Gas Geology and Geophysics SB RAS, Novosibirsk, 630090 (Russian Federation)

(Russian Federation)

Publication Date:

OSTI Identifier:

22492590

Resource Type:

Journal Article

Resource Relation:

Journal Name: AIP Conference Proceedings; Journal Volume: 1683; Journal Issue: 1; Conference: International conference on advanced materials with hierarchical structure for new technologies and reliable structures 2015, Tomsk (Russian Federation), 21-25 Sep 2015; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONSERVATION LAWS; CRACKS; DISTANCE; DISTRIBUTION; DISTURBANCES; EQUATIONS OF MOTION; MATHEMATICAL SOLUTIONS; MICROSTRUCTURE; PERTURBATION THEORY; RANDOMNESS; SOUND WAVES; SURFACES; VELOCITY