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Bulletin of the Seismological Society of America; December 1978; v. 68; no. 6; p. 1613-1622
© 1978 Seismological Society of America
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Gravitational energy and faulting

J. C. SAVAGE and J. B. WALSH

U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025
DEPARTMENT OF EARTH AND PLANETARY SCIENCE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS 02139

Abstract

A simple discussion of the energy changes involved in faulting within a self-gravitating body shows that the energy released in faulting is simply {propto} (p'ij + pij/2) uidSj, where p'ij is the ambient stress before faulting, pij and ui are the stress change and displacement associated with faulting and the integral is over the fault surface. This result was obtained earlier by Dahlen. A new expression for the work done against gravity (– {propto} {rho}giuidv where {rho} is density, and gi is the acceleration of gravity, and the integral is over the entire volume of the body) is given in the form of an integral over the fault surface. For dip-slip faulting in the earth, the gravitational energy change may be several orders of magnitude greater than the energy released; that large change in gravitational energy is compensated for by a similar change in stored elastic initial energy. In such cases the energy released is the relatively small difference between large changes in the potential energy of the elastic and gravitational fields, as recognized by Dahlen.




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Dynamic Earthquake Ruptures in the Presence of Lithostatic Normal Stresses: Implications for Friction Models and Heat Production
Bulletin of the Seismological Society of America, December 1, 2001; 91(6): 1765 - 1796.



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