Coulomb Stress Changes and Coulomb Stress Changes and the Triggering of Earthquakesthe Triggering of Earthquakes

King et al., 1994

OutlineOutline

Mohr CircleMohr CircleCoulomb Failure CriterionCoulomb Failure CriterionProcedures to Calculate Coulomb Stress Procedures to Calculate Coulomb Stress

Change Change ResultsResults

Mohr CircleMohr Circle

Mohr Circle is a graphical Mohr Circle is a graphical representation of calculating representation of calculating shear and normal tractions shear and normal tractions on any plane in terms of the on any plane in terms of the principal stress principal stress components.components.

3

1 1

3

3

1

0

0

~

Coordinate TransformationCoordinate Transformation To write matrices or vectors in a rotated coordinate frame, we need a coordinate transformation

Or more mathematically, we can write a vector in two Or more mathematically, we can write a vector in two coordinate frames and calculate the transformation matrix.coordinate frames and calculate the transformation matrix.

Coordinate Transformation of the Stress Tensor

Normal and Shear TractionNormal and Shear Traction

1 1

3

Considering = 90 –, or 2=180-2We get the eq (2) and (3) of the paper.

Coulomb Failure CriterionCoulomb Failure Criterion

δf/ δ=0 => =1/2. arctan(-`)

2

Tan(=

Coulomb Stress on a Randomly Coulomb Stress on a Randomly Oriented Fault PlaneOriented Fault Plane

yyxy

xyxx

~ Given we can calculate shear and normal

traction on any plane by transforming this vector with transformation matrix as before so `=A..AT

Coulomb Stress Change Calculation procedureCoulomb Stress Change Calculation procedure

1. Impose the initial displacement field and calculate deformation

2. Calculate stress tensor at all points of interest.

3. Rotate them to the pre determined “fault” orientations.

4. Calculate shear and normal tractions

5. Calculate coulomb stress change to see whether it would increase or decrease seismicity.

Adding Regional Stress and Optimally Adding Regional Stress and Optimally Oriented FaultsOriented Faults

Assumption: There are many faults with various orientations on every Assumption: There are many faults with various orientations on every part of the region. So faults exist at every point with angle part of the region. So faults exist at every point with angle from the from the principal stress direction of the orientation of tan(2.principal stress direction of the orientation of tan(2.)=-)=-..

The orientation of the “fault” is determined from the summation of The orientation of the “fault” is determined from the summation of earthquake induced stress and the regional stress. earthquake induced stress and the regional stress.

After determining the optimally oriented faults, the Coulomb stress changes are calculated using the stress changes due to earthquake only.

The significance of Regional StressThe significance of Regional Stress

King et al., 1994

2003 Big Bear EQ

Results from Homestead Valley & Joshua Tree Results from Homestead Valley & Joshua Tree EarthquakesEarthquakes

Depth Profile and Fault Length ExtentDepth Profile and Fault Length Extent

Landers and pre-Landers LoadingLanders and pre-Landers Loading

The Coulomb failure stress change due to 5 largest earthquakes around landers, might have advanced the occurance of the Landers earthquake by couple of centuries.

Effects of Landers on SAF and SJFEffects of Landers on SAF and SJF

ConclusionsConclusions Coulomb failure criterion estimate the aftershocks of Coulomb failure criterion estimate the aftershocks of

Homestead Valley, Big Bear and Landers earthquakes.Homestead Valley, Big Bear and Landers earthquakes. 0.5 bar of Coulomb stress change is sufficient to trigger 0.5 bar of Coulomb stress change is sufficient to trigger

earthquakes.earthquakes. The forces on the adjacent fault will be higher than the The forces on the adjacent fault will be higher than the

ones estimated from Coulomb stress change ones estimated from Coulomb stress change calculations due to later inelastic stress relaxation in the calculations due to later inelastic stress relaxation in the lower crustlower crust

Regions of enhanced Coulomb stress are candidates for Regions of enhanced Coulomb stress are candidates for future events.future events.

Problems with King et al., 1994 Coulomb Problems with King et al., 1994 Coulomb Stress Triggering StudyStress Triggering Study

Does not address the time dependence of the triggering.Does not address the time dependence of the triggering. (Tidal forces cannot trigger similar number of earthquakes).(Tidal forces cannot trigger similar number of earthquakes). Omori’s Law can not be obtained.Omori’s Law can not be obtained.

Optimally oriented faults might be a big assumption.Optimally oriented faults might be a big assumption. The background seismicity is ignored.The background seismicity is ignored. More robust statistical tests should have been done to More robust statistical tests should have been done to

understand the level of confidence.understand the level of confidence.

Addressing optimally oriented faults IssueAddressing optimally oriented faults Issue

Do aftershocks actually occur in the planes that are estimated by Do aftershocks actually occur in the planes that are estimated by Coulomb stress changes?Coulomb stress changes?

This issue is addressed by Hardebeck et al., 1998.This issue is addressed by Hardebeck et al., 1998. They do a statistical test, to check if the orientations of aftershocks They do a statistical test, to check if the orientations of aftershocks

are consistent with the ones estimated from Coulomb stress are consistent with the ones estimated from Coulomb stress changes.changes. Method: take events with aftershocks that have well determined source Method: take events with aftershocks that have well determined source

mechanisms (Landers 1992 and Northridge 1989).mechanisms (Landers 1992 and Northridge 1989). Calculate a synthetic random mechanism catalog.Calculate a synthetic random mechanism catalog. Compare whether the real catalog has a statistically more closer to Compare whether the real catalog has a statistically more closer to

“optimally oriented plane”.“optimally oriented plane”. This article assumes 0 tectonic stress.This article assumes 0 tectonic stress.

Result of the testResult of the test

For Landers, there is a statistically significant difference between the random mechanisms and the real mechanism orientations.

For Northridge the null hypothesis cannot be rejected.

LandersLanders

(a) Aftershocks with at least one plane consistent with static stress change triggering direction

(b) Both planes inconsistent with static change triggering direction

NorthridgeNorthridge

For events very close to the fault (<5km) or far from fault (>75 km), there is no statistical improvement of optimal orientations compared to random catalog.

Aftershocks are more consistent with regional stress field. Depending on how much of the regional stress field is released, the aftershock orientations become more or less consistent with maximum Coulomb stress change direction.

I think both of the issues are addressed in the King et al, 1994 paper.

Static vs. Dynamic Triggering (Kilb et al., 2002)Static vs. Dynamic Triggering (Kilb et al., 2002)

Static vs. Dynamic TriggeringStatic vs. Dynamic Triggering

Kilb et al., 2002

Near the fault, dynamic stresses are much higher than the static stress changes.

Kilb et al., 2002, studies dynamic CFS change to understand whether dynamic stress change can explain earthquake triggering better.

Removing Seismicity Rate ChangeRemoving Seismicity Rate Change

Seismicity Rate Change and peak of CFS(t)>4 MPa

Seismicity Rate Change and CFS>0.1MPa contours