A Caltech Library Service

Beginning of Earthquakes Modeled with the Griffith's Fracture Criterion

Sato, Tamao and Kanamori, Hiroo (1999) Beginning of Earthquakes Modeled with the Griffith's Fracture Criterion. Bulletin of the Seismological Society of America, 89 (1). pp. 80-93. ISSN 0037-1106.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


We present a source model for the beginning of earthquakes based on the Griffith's fracture criterion. The initial state is a critical state of pre-existing circular fault, which is on the verge of instability. After the onset of instability, the fault grows with a progressively increasing rupture speed, satisfying the condition of fracture energy balance at the crack tip. We investigate the difference in rupture growth patterns in two classes of models that are considered to represent end-member cases. In the first model (Spontaneous model), we assume that the surface energy varies smoothly as a function of position in the crust. In this model, faults with small initial dimensions grow in regions with small surface energy, and those with large initial dimensions, in large surface energy. The rupture velocity increases progressively until it reaches its limiting value. The synthetic velocity seismogram at far field shows a weak initial phase during the transitional stage to limiting velocity. The time taken to reach the limiting velocity is proportional to the initial length of pre-existing fault. Therefore, the duration of the weak initial phase scales with the initial length of fault. In the second model (Trigger model), we envisage that there are many pre-existing faults in the crust with various lengths. These faults are stable because they encounter some obstacle at their ends (e.g., fault segmentation, strong asperity, etc.). This situation is modeled with a local increase of surface energy near the ends of fault. An earthquake is triggered when the obstacle is suddenly removed (i.e., sudden weakening) or the stress is suddenly increased locally to overcome the obstacle. Once an earthquake is triggered, the fault growth is governed by the ambient surface energy. In this model, the rupture speed attains its limiting velocity almost instantly. The synthetic velocity seismogram at far field shows an abrupt, linear increase in amplitude without the weak initial phase that appears in the Spontaneous model. Both models can be unified using a trigger factor defined as a fractional perturbation of the surface energy at the ends of fault relative to the ambient surface energy. The Spontaneous model is characterized by a small trigger factor, and the Trigger model, by a large trigger factor. Thus, the seismic initiation phase with and without the slow initial phase can both occur depending on the trigger factor. The variability in the observed seismic initiation phase may represent a variation surface energy (strength) distribution surrounding the pre-existing cracks. A theoretical consideration of rupture arrest by barriers using the Griffith's fracture criterion does not support the scaling relation between the nucleation moment and the eventual size of earthquake.

Item Type:Article
Related URLs:
URLURL TypeDescription
Kanamori, Hiroo0000-0001-8219-9428
Additional Information:© 1999, by the Seismological Society of America. Manuscript received 20 April 1998. We thank Y. Iio, B. Shibazaki, E. Fukuyama, J. Moil, T. Mikumo, S. K. Singh, R. Madariaga, and W. L. Ellsworth for valuable discussion. We are grateful to Yehuda Ben-Zion for a constructive review. This research was done while one of the authors (T.S.) visited the Division of Geological and Planetary Sciences at the California Institute of Technology as a research fellow supported by the Japanese Ministry of Education. The DGPS Contribution Number is 8538. This research was partially supported by the Southern California Earthquake Center. SCEC is funded by NSF Cooperative Agreement EAR-8920136 and USGS Cooperative Agreements 14-08-0001-A0899 and 1434-HQ-97AG01718. The SCEC Contribution Number is 434.
Group:UNSPECIFIED, Division of Geological and Planetary Sciences
Funding AgencyGrant Number
Southern California Earthquake Center (SCEC)UNSPECIFIED
NSF Cooperative AgreementEAR-8920136
USGS Cooperative Agreement14-08-0001-A0899
USGS Cooperative Agreement1434-HQ-97AG01718
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Southern California Earthquake Center (SCEC)434UNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20140805-145553677
Persistent URL:
Official Citation:Tamao Sato and Hiroo Kanamori Beginning of earthquakes modeled with the Griffith's fracture criterion Bulletin of the Seismological Society of America, February 1999, v. 89, p. 80-93
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48011
Deposited By: Ruth Sustaita
Deposited On:05 Aug 2014 22:07
Last Modified:09 Mar 2020 13:18

Repository Staff Only: item control page