4:15 PM - 4:30 PM
[SSS15-04] Criticality of cascade-up and its dependence on velocity on various fault geometry
Keywords:scale independent rupture initiation, criticality of cascade up
Could rupture propagation be interpreted as continuing cascading-up process under fluctuation due to heterogeneity? Seismological observations (Ellsworth and Beroza, 1995; Uchide and Ide, 2007; Meier et al. 2016) suggest that there is no specific scale in initiation process, and rupture is influenced by fault heterogeneity during its growing phase. Criticality of cascading-up or halt is going be discussed in this study in the same way which many conventional studies have done for quasi-static rupture growth (e.g., Andrews, 1976; Day, 1982; Rubin and Ampuero; 2005).
We examined the situation that self-similar crack with constant rupture velocity(Vr) in a small patch encounters surrounding barrier region of unique larger fracture energy. There is a minimum patch size (Rcdyn.: the critical dynamic crack size of the fault) that crack cascades up in surrounding region, depending the fracture energy of barrier. If the patch is larger than Rcdyn., its rupture speed once decelerates but afterwards it spontaneously accelerates once the crack size exceeds the static critical crack size (Rcsta.).
Rcdyn. is obtained in this study by numerical simulation using BIE method of Mode II, III (Tada and Madariaga, 2000) and three-dimensional elliptical crack (Fukuyama and Madariaga, 1998). We gave following slip-weakening distance to a planer fault with homogeneous stress (Tp: yield strength, Te: uniform stress, μ: rigidity). H[x] is Heaviside function. Dc is discontinuous at Rdyn..
Dc(r) = Dc’r ·H[Rdyn.-r] + DcBG·H[r-Rdyn.]
The result, the proportion of Rcdyn./Rcsta. is obtained as a function of rupture velocity for each fault geometry, where both Rcsta. and Vr are functions of μTpDc’/Te2.
or, proportion of discontinuity of fracture energy at Rcdyn. is also written in a similar form.
i.e., Rcdyn.=ƒ(Vr) Rcsta. and DcBG=g(Vr)·Dc’Rcdyn.
Both f(Vr) and g(Vr) is qualitatively similar in Mode II, III, and three-dimensional crack, which is depicted in attached figure.
These results may suggest that rupture with fast rupture velocity (~0.7Vs) is far more capable of cascading-up in barrier made by fault heterogeneity than that of slow rupture velocity (~0.1Vs)
We examined the situation that self-similar crack with constant rupture velocity(Vr) in a small patch encounters surrounding barrier region of unique larger fracture energy. There is a minimum patch size (Rcdyn.: the critical dynamic crack size of the fault) that crack cascades up in surrounding region, depending the fracture energy of barrier. If the patch is larger than Rcdyn., its rupture speed once decelerates but afterwards it spontaneously accelerates once the crack size exceeds the static critical crack size (Rcsta.).
Rcdyn. is obtained in this study by numerical simulation using BIE method of Mode II, III (Tada and Madariaga, 2000) and three-dimensional elliptical crack (Fukuyama and Madariaga, 1998). We gave following slip-weakening distance to a planer fault with homogeneous stress (Tp: yield strength, Te: uniform stress, μ: rigidity). H[x] is Heaviside function. Dc is discontinuous at Rdyn..
Dc(r) = Dc’r ·H[Rdyn.-r] + DcBG·H[r-Rdyn.]
The result, the proportion of Rcdyn./Rcsta. is obtained as a function of rupture velocity for each fault geometry, where both Rcsta. and Vr are functions of μTpDc’/Te2.
or, proportion of discontinuity of fracture energy at Rcdyn. is also written in a similar form.
i.e., Rcdyn.=ƒ(Vr) Rcsta. and DcBG=g(Vr)·Dc’Rcdyn.
Both f(Vr) and g(Vr) is qualitatively similar in Mode II, III, and three-dimensional crack, which is depicted in attached figure.
These results may suggest that rupture with fast rupture velocity (~0.7Vs) is far more capable of cascading-up in barrier made by fault heterogeneity than that of slow rupture velocity (~0.1Vs)