earthquake dynamic triggering and ground motion scaling j. gomberg, k. felzer, e. brodsky

Earthquake Dynamic Triggering and Ground Motion

Scaling

J. Gomberg, K. Felzer, E. Brodsky

We seek to better understand what deformations trigger earthquakes, using

observations of both the triggering deformations and triggered earthquakes.

The most commonly observed triggered earthquakes are “aftershocks”.

Coyote Lake, California earthquake

Aftershocks occur at all distances,

& occasionally are obvious at remote distances.

We measure linear aftershock densities.

ρ(r) = [Naftershocks(r)

number of aftershocks per unit distance, r, at distance r

Measuring densities from earthquake catalogs.

Effectively, at each r we count the number of aftershocks within r

Empirically, measured linear aftershock densities are fit by

ρ(r) = C10M min10M r−γ

number of aftershocks at distance r

M=magnitude ~constant!

Measured Linear Aftershock Densities, from Southern California

Aftershocks within 5 minutes of numerous mainshocks are stacked. From Felzer & Brodsky (2005).

Modeled linear aftershock densities.

ρ(r) = [N(r)Δr]P(r)

number of potential nucleation sites per unit distance

probability of nucleation

distribution of nucleation sites per unit volume

F(r) = A r(d-3)€

N(r) = [ F(r)ds] ΔrS

‘d’ = dimensionality

Number of potential nucleation sites

Sum (integrate) within a volume surrounding the triggering fault, defined by surface S and width r

= [4πA{1+ (Dr ) + (1

2π )(D r )2}r(d −1)] Δr

The integration is simple, resulting in an analytic model. D ~ rupture dimension of the triggering fault.

Recall the measured aftershock densities:

ρ(r) = C10M min10M r−γ

= C10M min D2r−γ

~ constant at all distances!

This model illuminates constraints on triggering deformations...

Measured aftershock densities:

ρ(r) = C10M min D2r−γ

ρ(r) = P(r)[N(r)Δr]

Modeled aftershock densities.

=P(r) [4πA{1+ (D r ) + ( 12π )(D r )2}r(d −1)]

in the near field (r<<D)

ρ(r) P(r) D2 r(d-3)

ρ(r) = P(r) [4πA{1+ (D r ) + (12π )(D r )2}r(d −1)]

in the near field (r<<D)

ρ(r) P(r) D2 r(d-3)

in the far field (r>>D)

ρ(r) P(r) r(d-1)

ρ(r) = P(r) [4πA{1+ (D r ) + (12π )(D r )2}r(d −1)]

Measured:

in the near field

ρ(r) P(r) D2 r(d-3)

Modeled:

in the far field

ρ(r) P(r) r(d-1)

The probability of nucleation MUST scalein the near field as

P(r) constantin the far field as

P(r) D2 r-2

Also, the aftershock density decay rate constrains the nucleation (fault system) dimensionality;

The probability of nucleation MUST scalein the near field as

P(r) constantin the far field as

P(r) D2 r-2

P(r) = Dm

[αDm + rn ]

Consistent Probabilities:

P(r) = Dm

[αD + r]n

m = 2, n = 2

Uncertainties & Resolution

[4πA{1+ (D r ) + (12π )(D r )2}r(d −1)] Dm

(αD + r)n = C10M min D2r−γ

Our model implies these equalities

[4πA{1+ (D r ) + (12π )(D r )2}r(d −1)]Dm

(αDm + rn )= C10M min D2r−γ

If does not vary with r at all, the equalities require m=n=2. However, the observations permit some variability in and thus n~2.

Uncertainties & Resolution

Permissible scalings of P(r): or

Dm (αD + r)n

Dm (αDm + rn )

~1.8<n<~2.2

m may vary by a few percent.

We hypothesize that the probability of

nucleation is proportional to the dynamic

deformation amplitude. This is consistent with a large rupture being comprised of subevents, &laboratory observations and theoretical models of dynamic loading and failure.

We test various measures of dynamic deformation

amplitude. Consistent deformations

must scale as

[αDm + rn ]

[αD + r]n

n ≈ 2 ± 0.2, m ≈ 2 ± 0.03

We test various measures of dynamic deformation

amplitude.

Strain Rate(acceleration)

Strain (velocity)

Displacement

Dynamic deformation amplitude

= peak value.

Strain (velocity)

Displacement

= peak value x rupture duration (proportional to D).

Strain (velocity)

Displacement

= average value x duration = cumulative amplitude.

Strain (velocity)

Displacement

Our Deformation and Aftershock Density Scaling Observations

The Japanese HiNet seemed ideal for measuring both peak ground motions & aftershock densities. We measure them for 22 M3.0 - 6.1 earthquakes.

Small earthquakes are abundant but have hypocentral depths that make surficial ground motion measurements at far field distances.

We can measure peak ground motion scaling with D and the far field distance decay rate.

Southern California also seemed ideal; but even for 2 recent ~M5 earthquakes all ground motion recordings are in the far field. However, they constrain the scaling of peak motions with distance.

Aftershock densities become uncertain at distances comparable to location errors.

Constraining near field deformations requires large and/or very shallow earthquakes & good luck! We examine peak velocities for 16 M4.4 to M7.9 earthquakes with near field recordings.

Scaling the peak velocity or the distance by rupture dimension D removes all size dependence.

These can be fit by the scaling required for triggering deformations;i.e., D2/(D+r)2 or D2/(D2 +r2).

Consistent deformations must scale as

[αDm + rn ]or

[αD + r]n

m,n ~ 2

Results Summary

Data Source

PeakGroundMotion

DScalingm

PeakGroundMotion xRuptureDuration

DScalingm

PeakGroundMotion

rDecayRate

Scalingn

AftershockDensity

r DecayRate

Scaling

Californiaacceleration ~2.1velocity ~1.7displacement ~1.4aftershock ~1.3Japanacceleration ~1.0 ~2.0 ~2.0velocity ~1.5 ~2.5 ~1.7displacement ~2.0 ~3.0 ~1.5aftershock ~0.8Globalvelocity 1.5-2.0 2.5-3.0 1. 5-2.0

Data Source

PeakGroundMotion

DScalingm

PeakGroundMotion

rDecayRate

Scalingn

AftershockDensity

r DecayRate

Scaling

Results Summary Peak Strains Alone are Consistent

[αDm + rn ]or

[αD + r]n

m,n ~ 2

Data Source

PeakGroundMotion

DScalingm

PeakGroundMotion

rDecayRate

Scalingn

AftershockDensity

r DecayRate

Scaling

Results Summary

Peak Strain Rate x Rupture Durations are

Consistent

[αDm + rn ]or

[αD + r]n

m,n ~ 2

Data Source

PeakGroundMotion

DScalingm

PeakGroundMotion

rDecayRate

Scalingn

AftershockDensity

r DecayRate

Scaling

Nucleation Site (Fault Network) Dimensionality:

~1.7 and ~2.2

d = 3− γ

Results Summary

The probability of triggering an earthquake at a particular location and distance r scales with the size of the triggering earthquake.

The probability of triggering an earthquake anywhere at distance r is scale-independent.

More rigorously quantify scaling measurements.

Examine other dynamic deformation measures.

Collect & analyze additional near-field observations.

Relate inferences to physical models of nucleation.

What Next?

Questions?

Thank You!

Published Peak Acceleration & Velocity “Attenuation” Models

Most relations are generally consistent but very difficult to compare with one another or our model.

Peak Motion = C10−br Dm

R = h2 + r2 , (r + h), h(D)2 + r2

earthquake dynamic triggering and ground motion scaling j. gomberg, k. felzer, e. brodsky

distance r slide

width r slide

brodsky slide

unit distance slide

far field r pr r d

near field r pr d

pr constant

near field rd r pr r

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