A (re-) New (ed) Spin on Renewal Models

Karen FelzerUSGS Pasadena

The time-predictable renewal model

Two key predictions:1) There is a minimum wait time before a fault patch is

eligible for re-rupture.

2) Faults >> their average rupture time are highest risk.

The seismologist’s

dream

Key Prediction #1: There is a minimum wait time before re-rupture of the same fault patch

Supported by observation

Observation 1: Friction is very low during seismic slip

Lab experiments imply near total stress drop during rupture => a need to rebuild stress

Observation 2: Few aftershocks where the mainshock slipped

Rubin (2002): Stacking aftershocks of micro-earthquakes reveals a gap over the mainshock

Trouble with Key Prediction #1: Hard to apply in the real world!

• Large earthquakes are complex. Large fault patches that did not slip may persist after rupture and host new earthquake nucleations.

• Unknown subfaults of various orientations may host additional earthquakes.

Key Prediction #2: Faults >> their average rupture time are at highest risk

Not supported by observation

Nishenko (1991) global seismic gap forecast was unsuccessful

The Parkfield Prediction 95% chance of a M 6

earthquake by January 1993 (Bakun and Lindh, 1985)

Geodetic study by Murray and Segall (2002) confirmed that the Parkfield segment should reload every 6.7-20.7 years

But - we all know what

happened!

Why Key Prediction #2 Fails

• Borehole measurements and theoretical considerations indicate that faults should be strong, requiring 100-160 MPa of shear stress for failure (Scholz, 2000).

• But observations indicate that shear stress is only ~10 MPa at failure (Di Toro et al., 2004; Hardebeck and Hauksson, 2001; Hardebeck and Michael, 2004.)

• An explanation is that earthquake interaction involves one earthquake severely weakening the nucleation patch of another. This would allow ordinary fault strength to be high, strength at time of rupture to be low, and make predictions with the renewal model very difficult.

Fault 1

Why Key Prediction #2 Fails: Instead of faults gradually building stress towards a set fault strength, fault strength drops randomly and catastrophically via

earthquake interaction

stre

ngth

stre

ngth

stress

stress

Fault 2

Before triggering, Fault 2 should rupture first

Fault 1

stre

ngth

stre

ngth

stress

stress

Fault 2Eart

hq

uake!

But after an earthquake occurs near

Fault 1, it goes first

Implication: The vast majority of earthquakes are aftershocks…

(although in some cases it may not be obvious due to a

small/distant/old mainshock)

Recommendations

• A given fault patch that has failed should not be forecast to re-rupture immediately, but nearby and overlapping ruptures should be expected.

• After the initial recovery period forecasts should not be based on the idea that faults become more hazardous with time. This model may fail because fault strength is strongly decreased by earthquake interaction.

• Faults should be assigned rupture probabilities according to current activity rates (empirical model), which are upgraded when a potential triggering earthquake occurs nearby.

My hypothesis: Elastic rebound forecasts fail because the shaking from one earthquake can cause catastrophic loss in strength in locations on neighboring faults

This causes the stress=strength relationship to be satisfied on triggered faults much more rapidly, and results in earthquakes occurring in clusters rather than at regular repeating intervals

House with loss of strength due to earthquake

shaking

Proposed new time-dependent model

Start with a time-independent assumption and modify as activity rises/falls near the fault

Width of line based on probable 0.5-

10Mpa stress drop

Why Key Prediction #2 Fails: Earthquake interaction (aftershock triggering) involves severe fault weakening

stre

ngth

stress

Fault before earthquake interaction

100-160 MPa Scholz (2000)

stre

ngth

stress

Fault at nucleation patch after interaction

1-10MPa (observed stress drop)

If most earthquakes are aftershocks, this model reconciles total stress drop and borehole stress measurements

Hardebeck and Hauksson (2001), deviatoric stress on the order of 10

MPa

Proposal

• A minimum wait time may be imposed between identical earthquakes, but complementary ruptures on the same fault should be allowed.

• Sources which are beyond their minimum wait time should be assigned a constant probability of occurrence , until or unless they occur in the aftershock zone of a neighboring earthquake. Can guide by stress drop – is there stress drop predictability??

• Address why no slip predictability – mostly because of magnitude variability

Example: Parkfield earthquakes may have left room for significant complementary earthquakes

“The three most recent Parkfield earthquakes… did not produce uniform strain release along strike over multiple

seismic cycles…” Murray and Langbein (2006)

Global CMT catalog M≥6;

Δ focal mechanism <7°, ΔM<0.2

In practice, earthquakes close together in space tend to be close in time

Additional evidence that faults are weak at failure

Hardebeck and Michael (2004) make a convincing argument that stress orientations near faults, stress rotations by

mainshocks, and fault striations (at Kobe) indicate that all faults may be weak (at least at the time of failure!)