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ALLCAL

Steven N. Ward

University of California Santa Cruz

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Heart of any EQ simulator are displacements and stresses from dislocation elements. ALLCAL uses triangle elements in whole space. Static values are simple dot and cross products of known vectors. Co-ordinate free.

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ALLCAL approximates the effects of the Earth’s free surface using simple image source.

Same formulas with y--> -y

Sorry, no fancy earth structure or rheology.

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Each of ~15000 Fault Elements are given Fixed Static and Dynamic Strengths Ss, Sd.

When current stress exceeds current strength, the element slips.

(1) Velocity Weakening Slope α =[Ss-Sd]/Vc

(2) Maximum Patch size prior to healing LH .

Basically vc --> vc(1+U/LH) . U is slip in the event.

Decreasing the velocity weakening slope during rupture PROMOTES HEALING. WITH HEALING BROKEN FAULT BITS CAN RESTRESS. Without healing, ruptures are too periodic.

ALLCAL uses a Velocity Weakening Friction Law.

Apart from Ss, Sd there are only TWO Universal Parameters in this. All elements share the same…

Representation of Fault Friction

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Approximation to Elastodynamics

ALLCAL uses the static stresses from dislocations , but stresses do vary with time in earthquakes because slip u(r0,t) on the dislocations varies in time

τ(r,t) = Ts(r,r0) u(r0,ˆ t ),dˆ t 0

t

∫r0∫

Slip variations happen because there is feed back between stress and slip during quakes through the Friction Law.

ALLCAL produces fully dynamic ruptures, it just ignores the waves ---

In a half space there are few waves anyway!

Exact whole space seismogram.So called, “dynamic field”, is the stuff prior to the dot.

€

Ts(r,r0)

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Moreover, ALLCAL uses a Modified Quasi-Static Approach. It limits the quasi-static stress changes from a dislocation slip at r0 at t0 to those points r, where the signal could have reached by time t.

insteadof this,

τ(r,t) = Ts(r,r0) u(r0,ˆ t ),dˆ t 0

t

∫r0

∫

this

τ(r,t) = Ts(r,r0) u(r0,ˆ t ),dˆ t 0

t−Δ / vp

∫r0

∫

Δ = r−r0

This gives a ‘propagation delay time’ in distant response.

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What happens after nucleation depends of stress state of the fault. In this case, the fault is unstressed outside of the patch and the rupture dies out.

1) Overstressed Patch > Lc

2) Fault Strength Falls slowly first, then Faster3) Fault Slips to re-balance stress and strength. – The “dynamic part”.4) Excess Stress is driven elsewhere. Slip stops and fault heals.

How quakes start. Typical EQ Nucleation Event

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In the simulator, initial stress and fault segment strength vary too. Generally, stronger segments make fewer but larger quakes.

Fault Strength Fixed by comparison with paleoseismic data - tuning

More Complex Fault Strength, More Complex Initial Stress

Relation between local slip and local stress change is messy. Note re-stressing and re-rupture in this example.

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Currently, ALLCAL is driven by backslip. In the long term, the sum of slip in all earthquakes at a point equals the specified slip rate at that point times the simulation

duration.

Soon, ALLCAL will be driven by stresses derived from a continuous, 3D interseismic deformation field that satisfies the

static force balance equations and whose surface velocities are consistent with geodetic data.

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This velocity field reasonably reproduces GEODETIC interseismic motions AND it drives the fault system at rates reasonably close to their GEOLOGICAL values.

By employing this driving deformation field to stress the faults -- together with the SIMULATOR to release those stresses in a plausible sequences of earthquakes -- we are well on our way to a realization of a Master Model. vision

of a “Master Model” .

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WHAT HAPPENS WHEN THE ALLCAL IS TURNED ON?

Given variable initial stresses and fault strengths, a complex yet organized pattern of dynamic ruptures develops. Just the M7.7+ ones shown below.

4000 Years of M7.7+ San Andreas Fault Ruptures. Black number is year. Yellow box, time in seconds within rupture.

3D view here: White Boxes: Slip, Slip Velocity, Stress versus depth

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CONCLUSIONS:

(1) We already have the capacity to make realistic

and useful simulations on a large scale that reproduce

much of what seismologists and geologists can tell us.

(2) Simulators give us window into the origin of

certain earthquake statistics that UCERF can obtain by

no better means.

Clustering/Mode Switching

Triggering

Acc. Moment Release

Extreme Behaviors