Thinking about time variable seismic risk

Karen FelzerUSGS, Pasadena

A farmer suffering from low milk production asked for help from a team of academics at the local college..

After two weeks of hard work, the farmer received a report from the physicist leading the team, which started “Consider a

spherical cow...”

Earthquakes are really complex..

So there is a tendency to use lots of spherical cows…

One of the big “spherical cows” is imaging earthquakes as static processes

Static failure occurs when stress over the entire fault reaches failure strength

Is this spherical cow useful?

Yes, if the stress/strength ratio at the hypocenter and over the rest of the fault is similar

No, if the stress/strength ratio at the hypocenter and over the rest of the fault are dissimilar

Dissimilar stress/strength ratios are a problem because earthquakes are really dynamic processes, with rupture at one

point triggering rupture at the next

The stress/strength balance only needs to be satisfied at the hypocenter

After this high crack tip stresses can easily override initial conditions

The first domino

The evidence is very strong that the stress/strength ratio at the hypocenter is very different from the rest of the fault

Borehole measurements find hydrostatic pore pressure, frictional

coefficient ~0.6—1.0. This means that ~100MPa of shear stress should be

required to start rupture.

But a large amount of data indicates that the deviatoric stress on the fault at

rupture is no more than 10 MPa

Data limiting the stress on faults at rupture

Expectation: Decay of heat flow with distance from

the San Andreas fault

Observation: No variation of heat flow across the San

Andreas

Lachenbruch and Sass (1980)

Lack of a San Andreas heat flow anomaly

San Andreas observation later verified (Fulton et al. 2004) and observed around other major faluts (Kano et al, 2006)

Data limiting the stress on faults at rupture

Rotation of focal mechanisms by surrounding earthquakes indicates deviatoric stress <10 MPa

(Hardebeck and Haukkson, 2001; Hasegawa et al., 2011)

Focal mechanism rotation by

surrounding earthquakes over

time from Hardebeck and

Hauksson, (2001)

Data limiting the stress on faults at rupture

Direct borehole measurements of active faults show low stress (Zoback and Healy,

1992; Zoback and Harjes, 1997).

Data limiting the stress on faults at rupture

Earthquake stress drops are usually <10 MPa and there is significant evidence that static stress drops in earthquakes are near complete (Michael et al.1990; Beroza and Zoback, 1993; Hasegawa et al. 2011; Barton and Zoback, 1994)

Static stress drops tend to be <100 bars or <10 MPa, figure

from Abercrombie and Leary (1993).

High fault strength and low fault deviatoric stress mean that:

• After a minimum stress reloading period, most of the fault ruptures because of dynamic high fault tip stresses followed by dynamic weakening.

• The hypocenter must either be at much higher stress or much lower strength than the rest of the fault before rupture. Conditions at the hypocenter and rest of the fault are not similar, so the static approximation cannot be used.

Fault 1 + Hypocenter 1

How it really works

stre

ngth

stre

ngth

stress

stress

Fault 2 + Hypocenter 2

Before triggering, Fault 2 should rupture first

Hypocenter 1

stre

ngth

stre

ngth

stress

stressEarthquake!

But after a neighboring earthquake Fault 1

goes first

Fault 2 + Hypocenter 2

Failure!

Proposed short term hazard map

Thank you very much!

So – is there a place for renewal models?

• It is unlikely that linear stress renewal could operate at the hypocenter and no place else.

• There is data that indicates that forces from preceding earthquakes cause severe localized fault weakening at future hypocenters, allowing earthquakes to start there.

• If this is correct smoothed seismicity maps should be the best forecasters of short term seismicity – and they are ! (Schorlemmer et al., 2010)