[S-SS30] Earthquake Source Processes and Physics of Earthquakes

[SSS30-06] Fractal fault zone geometry and scale-dependent static stress drop

*Kenshiro OTSUKI¹ (1.Department of Geology, Graduate School of Science, Tohoku Univ.)

Keywords:static stress drop, scale dependence, fault zone geometry, hierarchically selfsimilar

I have shown that fault zone geometries, composed of fault segments and jog, are hierarchically selfsimilar (Fig.1a). This inhomogeneous structure breaks down the wellknown relations among fault length, averaged seismic slip and seismic moment. The distribution of seismic slip also is pinned hierarchically by jogs, showing a spectral distribution (Fig.1b). Based on the high quality data of fault traces and slip distributions from 21 surface earthquake strike-slip faults, here I show that average static stress drop ∆σ decreases as L₀.

Key Point 1
If D_avof a fault (L, D_max) is πD_max/4, ∆σ = CπD_max/4L.
For a fault composed of linked n faults with (L/n, D_max) also D_av = πD_max/4, while ∆σ = nCπD_max/4L.
[Symbol fault length:L, maximum slip:D_max and averaged slip:D_av, static stress drop:∆σ, proportional constant:C]

Key Point 2
Slip distributions D_x on fault segments are approximated by two simple cases below.
Cases of homogeneous frictional resistance D_x = 2(1 - ν)/G × (σ_yx^r - σ_yx^c) × (a² - x²)^0.5.
Cases of frictional resistance with a linear gradient D_x = (1 - ν)/G × (2σ_yx^r - σ_yx^c(x/a)) × (a² - x²)^0.5.
[Symbol half length of fault segments:a, Poisson's ratio:ν, remote stress:σ_xy^r, frictional resistance:σ_xy^c]

Key Point 3
When L_s(i,j) < W_s, ∆σ_av(i,j) = (7πG/8)(D_av(i,j)/L_s(i,j).
When Ls(i,j) > W_s, ∆σ_av(i,j) = (2G/π)(D_av (i,j)/W_s.
The static stress drops averaged over the whole fault length L₀ is ∆σ = (∑∆σ_av(i,j)L_s(i,j)/L₀.
[Symbol for j-th segment of hierarchical rank i, segment length:L_s(i,j), averaged slip:D_av(i,j), static stress drop:∆σ_av(i,j), thickness of seismogenic crustal layer:W_s, rigidity:G]

Analytical Results
17 among 21 data are approximated to the equation below (Fig.1c).
∆σ = 79.0 L₀^-0.519 (units km and MPa)