Analyze statistical characteristics of surface rupture data

load compiled data

data source: Anderson et al. (2017), Biasi (2013), Wesnousky (2008) and FDHI

Two analytical solution of surface rupture displacement

Shaw (2013)

A generic version of Shaw's model is

which contains two stress drops: Delta sigma_0 is the stress drop at smaller rupture length while Delta sigma_infinite is the stress drop at larger length

Chinnery (1963)

If fault is scale independent, i.e. stress drop and fault width are independent on the rupture length (thus magnitude)

(0.01, 100.0)

Let's see analytical prediction from a scale-dependent model (M1 stress drop is scale dependent; M2 width is scale dependent)

Text(3.1622776601683795, 13.089106850636249, 'Wesnousky (2008)')

Let's overlay the real data to see

Text(0, 0.5, 'Width (km)')

Above figures show that the model (Chinnery, 1963) with scale-independent stress drop and rupture width cannot fit the compiled data. Now we try Shaw (2013)'s model

(0.01, 100.0)
Text(0, 0.5, 'Width (km)')

Questions needed to be addressed:

  • what happened to the data in the lower left corner?
  • Do we make a concensus that the average displacement continues growing with rupture length (Scholz, 1982) instead of eventually saturation (Shaw xxx)? Those are involving two different physical mechanisms.
  • Wether is the constant stress drop assumption valid?
  • Do we prefer models with scale-dependent stress drop or width?

Anderson et al. (1996,2017) claimed that including the fault-slip rate can improve scaling of magnitude versus rupture length and implied that the slip-rate (fault maturity) may affect the scaling. We collect the slip-rate data from the updated paper (Anderson et al, 2017) and some other materials and make a new dataset (including AD, M, L and SR) of 51 strike-slip earthquakes.

Text(0, 0.5, 'Slip rate (mm/yr)')

Anderson et al (2017) concluded that two groups of earthquake (larger and smaller than 4.8 mm/yr) show different scalings

Slip rate may reflect the fault maturity, there are some studies showing the fault maturity will affect

  • cumulative displacement
  • slip rate
  • fault initiation age
  • stress drop
  • earthquake occurence time
  • asperity size
  • seismicity localization width

Let's see our data again

We develop another matric to reflect the fault maturity (AD/SR) to mimic the average occurence time

Text(0, 0.5, 'SR (mm/yr)')
Text(0, 0.5, 'Stress Drop (MPa)')

It is shown from the above figures that the lower left corner corresponds to a mature fault zone and the upper outlier corresponds to a immuture fault zone. It is consistent with Manighetti et al. (2007).

We also overlay Manighetti (2007)'s models on our dataset

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