Tutorial to Calculate Stress Changes by Earthquakes


ΔCFF = Δτ + μ(Δσn + ΔP)

or ΔCFF = Δτ + μ’ Δσn

We can calculate static stress changes using software Coulomb [Link]

Assumption: computed in a homogeneous elastic half-space (Okada, 1992) [Link]

Some parameter need:

μ’ = 0.4  [possible value 0.0 -0.8] [Link] Strong fault: large μ (> 0.5). For example Sandstone, μ=06~0.8.

-Poisson ratio = 0.25

-Young’s modulus = 80 GPa

-Shear modulus = 32 GPa

Lower young modulus: Reduce magnitude of stress changes

Higher young modulus: Increase magnitude of stress changes

-Friction and Skempton coefficient not in substantial way providing variation.

-Shear and normal stresses produced by source can be resolved onto specific “receiver” fault or dyke.

-The receiver are defined by strike, dip and rake but Rake does not influence the normal stress changes!


Normal stress changes Δσn, positive if fault is unclamped

Shear stress changes Δτ, positive in the direction of fault slip.

We can calculated using published source fault models that I have compiled in here [Link].

Or you can use empirical fault geometry from Wells and Coppersmith (1994). [Link]

A new perspective on new paper: What Is Better Than Coulomb Failure Stress? A Ranking of Scalar Static Stress Triggering Mechanisms from 10^5 Mainshock-Aftershock Pairs (Meade et al., 2017) [Link]



σd = G. PGV / vs

where σd = radial peak dynamic stress; PGV = peak ground velocities; vs = shear wave velocity; G = shear modulus.

Shear modulus G can be derived from: G = ρ.vs^2 where ρ = rock density.

General value: G=35 GPa, vs=3.5 km/s

Rule of thumbs: 1 cm/s corresponds to ~ 0.1 MPa or 100 kPa.

PGV are observed from seismogram!

Note: raw data from data center must be corrected with instrument response using pole and zero file.

Simply using transfer command in SAC. [see this tutorial].

Using command transfer to vel using BMKG waveform usually resulted in m/s (see the RESP file!)

How to get predicted PGV to calculate predicted dynamic stress?

(a) Using empirical relationship from magnitude

for near field (distance <= 500 km) using Campbell and Bozorgnia (2007)

log10 PGV = c1 + c2M – c3 log10 SQRT (r^2+c4^2)

where PGV in cm/s, M = magnitude, r = hypocentral distance (km), ci = fit parameters.

For unconstrained case, used c1=-2.29; c2=0.85; c3=1.29; c4=0.04.

For teleseismic field (distance > 500 km) using Lay and Wallace (1995) using Ms (surface wave magnitude) formula

log10 A20 = Ms – 1.66 log10 Δ – 2

A20= displacement in micrometers, Δ=distance in degrees

PGV ≈ 2πA20 / T

(Here we assume long-period surface wave with T = 20 seconds)

Both is available in van der Elst and Brodsky (2010) [Link]

Note: if using catalog with different magnitude type, convert to Ms using some empirical relationships. For example: Das et al. (2011) [Link] or Scordilis (2006) [Link]

(b) Using predicted PGV in shake map

Simply extract PGV data from shake map produced by some agencies such as USGS, or BMKG (in Indonesia).


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