Fault Instability Criterion

Calculates the instability criterion $I$ after Vavrycuk (2013, Eq. 3). Instability ranges from 0 (most stable) to 1 (most unstable) The most unstable fault is the optimally oriented fault for shear faulting.

Usage

fault_instability_criterion(fault, R, friction = 0.6)

Arguments

fault: "Fault" object where the rows are the observations, and the columns the coordinates.
R: numeric. Stress ratio after Gephart and Forsyth (1984): $(\sigma_1 - \sigma_2)/(\sigma_1 - \sigma_3)$
friction: numeric. Coefficient of friction (0.6 by default)

Value

numeric. Instability ranges from 0 (most stable) to 1 (most unstable). The most unstable fault is the optimally oriented fault for shear faulting.

Details

$$I = \frac{\tau - \mu(\sigma - \sigma_1)}{\tau_c - \mu(\sigma_c - \sigma_1)}$$

where $\tau_c$ and $\sigma_c$ are the shear traction and effective normal traction along the optimally oriented fault, and $\tau$ and $\sigma$ are the shear traction and effective normal traction along the analysed fault plane.

References

Vavrycuk, V., Bouchaala, F. & Fischer, T., 2013. High-resolution fault image from accurate locations and focal mechanisms of the 2008 swarm earthquakes in West Bohemia, Czech Republic, Tectonophysics, 590, 189–195.

Examples

f <- angelier1990$TYM
tau <- reduced_stress(f)
s <- stress_shape(tau)

fault_instability_criterion(f, s$R)
#>  [1] 0.80583583 0.96786690 0.05589429 0.57145143 0.76778700 0.15189430
#>  [7] 0.13812261 0.81158280 0.45559237 0.66081621 0.58543179 1.13776326
#> [13] 0.87881003 0.41970424 0.63313399 0.96055789 0.97720506 0.88549935
#> [19] 0.28601284 0.92598051 1.39315476 1.04755339 0.30091177 1.38021623
#> [25] 1.04697429 0.70405761 0.64255950 0.59863018 0.46312371 1.08484041
#> [31] 0.90212159 0.82693097 1.00838327 0.87372833 0.34157203 1.09388247
#> [37] 0.22224539 0.19233285