Open AccessInterplay of fault dynamics and fractal dimension in determining Gutenberg & Richter's b ‐value
Author(s) -
LomnitzAdler J.
Publication year - 1992
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1992.tb03482.x
Subject(s) - fractal , fractal dimension , san andreas fault , fault (geology) , geology , magnitude (astronomy) , dimension (graph theory) , basis (linear algebra) , seismic moment , power law , moment (physics) , geometry , mathematics , value (mathematics) , earthquake magnitude , seismology , statistical physics , mathematical analysis , physics , classical mechanics , pure mathematics , statistics , scaling , astronomy
SUMMARY The magnitude‐frequency relation of earthquakes is characterized by a parameter known as the b ‐value which reflects a power‐law decay in the rate of occurrence of earthquakes with seismic moment. This parameter is not universal but varies from region to region, and with the passage of time. We show that the numerical value of b is a sum of a universal quantity associated with the dynamics of any given 2‐D fault plus another term associated with the fractal geometry of a specific fault system. Numerical results are obtained on the basis of a specific fracture model, and are applied to the San Andreas fault system.