Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006geoji.165..197b&link_type=abstract
Geophysical Journal International, Volume 165, Issue 10, pp. 197-210.
Astronomy and Astrophysics
Astronomy
29
Aftershocks, Cracked Media, Damage Rheology, Earthquake Dynamics, Fault Mechanics, Lithospheric Model
Scientific paper
We perform analytical and numerical studies of aftershock sequences following abrupt steps of strain in a rheologically layered model of the lithosphere. The model consists of a weak sedimentary layer, over a seismogenic zone governed by a viscoelastic damage rheology, underlain by a viscoelastic upper mantle. The damage rheology accounts for fundamental irreversible aspects of brittle rock deformation and is constrained by laboratory data of fracture and friction experiments. A 1-D version of the viscoelastic damage rheology leads to an exponential analytical solution for aftershock rates. The corresponding solution for a 3-D volume is expected to be sum of exponentials. The exponential solution depends primarily on a material parameter R given by the ratio of timescale for damage increase to timescale for accumulation of gradual inelastic deformation, and to a lesser extent on the initial damage and a threshold strain state for material degradation. The parameter R is also inversely proportional to the degree of seismic coupling across the fault. Simplifying the governing equations leads to a solution following the modified Omori power-law decay with an analytical exponent p= 1. In addition, the results associated with the general exponential expression can be fitted for various values of R with the modified Omori law. The same holds for the decay rates of aftershocks simulated numerically using the 3-D layered lithospheric model. The results indicate that low R values (e.g. R<= 1) corresponding to cold brittle material produce long Omori-type aftershock sequences with high event productivity, while high R values (e.g. R>= 5) corresponding to hot viscous material produce short diffuse response with low event productivity. The frequency-size statistics of aftershocks simulated in 3-D cases with low R values follow the Gutenberg-Richter power law relation, while events simulated for high R values are concentrated in a narrow magnitude range. Increasing thickness of the weak sedimentary cover produces results that are similar to those associated with higher R values. Increasing the assumed geothermal gradient reduces the depth extent of the simulated earthquakes. The magnitude of the largest simulated aftershocks is compatible with the Båth law for a range of values of a dynamic damage-weakening parameter. The results provide a physical basis for interpreting the main observed features of aftershock sequences in terms of basic structural and material properties.
Ben-Zion Yehuda
Lyakhovsky Vladimir
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