Analysis of aftershocks in a lithospheric model with seismogenic zone governed by damage rheology

Abstract

S U M M A R YWe 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.

Anomalous early aftershock decay rate of the 2004 Mw6.0 Parkfield, California, earthquake

“…Yet this period marks the transition from mainshock to aftershocks, and holds valuable information about the underlying mechanisms that control the aftershock occurrence [e.g., Nur and Booker, 1972;Das and Scholz, 1981;Dieterich, 1994;Ben-Zion and Lyakhovsky, 2006].…”

Structural Properties and Deformation Patterns of Evolving Strike-slip Faults: Numerical Simulations Incorporating Damage Rheology

“…The compliance, or inverse of viscosity (C v Áda/dt), relates the deviatoric stress to the rate of irreversible strain accumulation. BEN-ZION and LYAKHOVSKY (2006) connected the rate of irreversible strain accumulation with partitioning between seismic and aseismic deformation in the seismogenic zone, and showed that the fraction of elastic strain released seismically, referred to as the seismic coupling coefficient v, can be estimated as:…”

“…LYAKHOVSKY et al (2001) and BEN-ZION and LYAKHOVSKY (2006) suggested that damage zone structure is primarily controlled by (1) the ratio between loading rate and healing rate, (2) the overall degree of ''brittleness'' of crustal deformation which may be parameterized by the seismic coupling coefficient v, and (3) the susceptibility to propagation of rupture associated with dynamic weakening and related dynamic time scale s r . Below we review the main material parameters and outline their effect on fault zone evolution.…”

Shear Band Formation in Numerical Simulations Applying a Continuum Damage Rheology Model

“…This damage rheology is applicable to volumes with a sufficiently large number of cracks that allow quantitative description through properties of the crack distribution rather than those of the individual cracks MYASNIKOV, 1984, 1985). Detailed reviews and recent developments of the model can be found in LYAKHOVSKY (2006) and, examples of model applications showing the dominant role damage processes play in the evolution of fault systems and their internal structure can be found in FINZI et al (2009. Here we only summarize the main ingredients of the model that are relevant for our work.…”

“…The damage-related viscosity enables representation of the permanent inelastic deformation before brittle failure associated with micro-crack growth and frictional sliding between grains (HAMIEL et al, 2004a, b). Various studies have shown it is required to adequately describe processes such as subcritical crack growth and aseismic deformation in the seismogenic crust BEN-ZION and LYAKHOVSKY, 2006). Combining Eqs.…”