Jerky Motion in Slowly Driven Magnetic and Earthquake Fault Systems, Physics of

Article Outline Glossary Definition of the Subject Introduction Models Theoretical Results Summary Future Directions Acknowledgments Bibliography Glossary Mean field theory A theoretical approximation with an interaction field that has constant strength and infinite range. In mean field approximation every domain interacts equally strongly with every other domain, regardless of their relative distance. Critical point A (phase transition) point in the parameter space of a physical system where the length scale characteristic of its structure, called the correlation length , becomes infinite and the system displays power law scaling behavior on all available scales. The associated critical power law exponents are universal, i. e. they are independent of the microscopic details of the system. Universality Power law scaling exponents and scaling functions near a critical point are the same for a class of systems, referred to as universality class, independent of the microscopic details. Universal aspects typically depend only on a few basic physical attributes, such as symmetries, range of interactions, dimensions, and dynamics. Tuning parameters Parameters such as disorder, temperature , pressure, driving force etc. that span phase diagrams. Critical values of the tuning parameters describe critical points of the phase diagrams. Renormalization group (RG) A set of mathematical tools and concepts used to describe the change of physics with the observation scale. Renormalization Group techniques can be used to identify critical points of a system as fixed points under a coarse grain-ing transformation, and to calculate the associated critical power law exponents and the relevant tuning parameters. They can also be used to determine what changes to the system will leave the scaling exponents unchanged, and thus to establish the extent of the associated universality class of the critical point. Earthquake quantities The most common form of earthquake data consists of seismic catalogs that list the time, location, and size of earthquakes in a given space-time domain. The size of earthquakes is usually specified by magnitudes associated with spectral amplitudes of seismograms at a given frequency and site-instrument conditions. The seismic potency and moment provide better physical characterizations for the overall size of earthquakes. Additional important quantities are the geometry of faulting (e. g., strike slip), stress drop at the source region, and radiated seismic energy. Seismic potency A physical measure for the size of earthquakes given by the integral of slip over the rupture area during a seismic event. Seismic moment A physical measure of earthquakes given by …