Derivation of the Gutenberg-Richter empirical formula from the solution of the generalized logistic equation

Abstract

We have written a new equation to study the statistics of earthquake distributions. We call this equation "the generalized logistic equation". The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case for the approximation of large magnitude earthquakes. To illustrate how the solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N -25N, 5W -35W), Canary Islands, Magellan Mountains (20N -9S, 148E -170E), and the Sea of Japan. This approximation showed an excellent correlation between the theoretical curves and observed data for earthquakes of magnitudes 1 < m < 9.

Simple nonlinear models suggest variable star universality

“…The exponent b is of order one but is smaller interior to tectonic plates, larger between plates, and even larger for oceanic ridges. Indeed, b ≈ 1.5 for the volcanic Canary Islands [21], so KIC 5520878 stellar flux frequency components scale like Canary Islands earthquake amplitudes. While this quantitative agreement between earthquakes and variable stars is merely an advantageous coincidence, the corresponding intuitions may transfer.…”

Modeling statistics and kinetics of the natural aggregation structures and processes with the solution of generalized logistic equation

“…is the cumulative distribution function of the random size of an element of a structure. Equation ( 4) is presented first in (Maslov, Anokhin, 2012). If 0≤α<1, then equation ( 4) can be written in the form of a classical logistic equation:…”