Download - Earthquake Dynamic Triggering and Ground Motion Scaling J. Gomberg, K. Felzer, E. Brodsky
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Earthquake Dynamic Triggering and Ground Motion
Scaling
J. Gomberg, K. Felzer, E. Brodsky
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We seek to better understand what deformations trigger earthquakes, using
observations of both the triggering deformations and triggered earthquakes.
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The most commonly observed triggered earthquakes are “aftershocks”.
Coyote Lake, California earthquake
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Aftershocks occur at all distances,
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& occasionally are obvious at remote distances.
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We measure linear aftershock densities.
€
ρ(r) = [Naftershocks(r)
Δr]
number of aftershocks per unit distance, r, at distance r
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Measuring densities from earthquake catalogs.
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Effectively, at each r we count the number of aftershocks within r
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Empirically, measured linear aftershock densities are fit by
€
ρ(r) = C10M min10M r−γ
number of aftershocks at distance r
M=magnitude ~constant!
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Measured Linear Aftershock Densities, from Southern California
Aftershocks within 5 minutes of numerous mainshocks are stacked. From Felzer & Brodsky (2005).
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Modeled linear aftershock densities.
€
ρ(r) = [N(r)Δr]P(r)
number of aftershocks at distance r
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Modeled linear aftershock densities.
€
ρ(r) = [N(r)Δr]P(r)
number of aftershocks at distance r
number of potential nucleation sites per unit distance
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Modeled linear aftershock densities.
€
ρ(r) = [N(r)Δr]P(r)
number of aftershocks at distance r
number of potential nucleation sites per unit distance
probability of nucleation
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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
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€
N(r) = [ F(r)ds] ΔrS
∫
Sum (integrate) within a volume surrounding the triggering fault, defined by surface S and width r
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€
N(r) = [ F(r)ds] ΔrS
∫
= [4πA{1+ (Dr ) + (1
2π )(D r )2}r(d −1)] Δr
D
The integration is simple, resulting in an analytic model. D ~ rupture dimension of the triggering fault.
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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...
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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)]
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Measured aftershock densities:
€
ρ(r) = C10M min D2r−γ
in the near field (r<<D)
ρ(r) P(r) D2 r(d-3)
Modeled aftershock densities.
€
ρ(r) = P(r) [4πA{1+ (D r ) + (12π )(D r )2}r(d −1)]
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Measured aftershock densities:
€
ρ(r) = C10M min D2r−γ
in the near field (r<<D)
ρ(r) P(r) D2 r(d-3)
Modeled aftershock densities.
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)]
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Measured:
€
ρ(r) = C10M min D2r−γ
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
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Also, the aftershock density decay rate constrains the nucleation (fault system) dimensionality;
d=3-
The probability of nucleation MUST scalein the near field as
P(r) constantin the far field as
P(r) D2 r-2
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€
P(r) = Dm
[αDm + rn ]
Consistent Probabilities:
€
P(r) = Dm
[αD + r]n
m = 2, n = 2
or
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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
or
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.
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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.
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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.
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We test various measures of dynamic deformation
amplitude. Consistent deformations
must scale as
€
Dm
[αDm + rn ]
or
€
Dm
[αD + r]n
n ≈ 2 ± 0.2, m ≈ 2 ± 0.03
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We test various measures of dynamic deformation
amplitude.
Strain Rate(acceleration)
Strain (velocity)
Displacement
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Dynamic deformation amplitude
= peak value.
Strain Rate(acceleration)
Strain (velocity)
Displacement
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Dynamic deformation amplitude
= peak value x rupture duration (proportional to D).
Strain Rate(acceleration)
Strain (velocity)
Displacement
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Dynamic deformation amplitude
= average value x duration = cumulative amplitude.
Strain Rate(acceleration)
Strain (velocity)
Displacement
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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.
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Our Deformation and Aftershock Density Scaling Observations
Small earthquakes are abundant but have hypocentral depths that make surficial ground motion measurements at far field distances.
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Our Deformation and Aftershock Density Scaling Observations
We can measure peak ground motion scaling with D and the far field distance decay rate.
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Our Deformation and Aftershock Density Scaling Observations
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.
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Our Deformation and Aftershock Density Scaling Observations
Aftershock densities become uncertain at distances comparable to location errors.
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Our Deformation and Aftershock Density Scaling Observations
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.
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Our Deformation and Aftershock Density Scaling Observations
Scaling the peak velocity or the distance by rupture dimension D removes all size dependence.
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Our Deformation and Aftershock Density Scaling Observations
These can be fit by the scaling required for triggering deformations;i.e., D2/(D+r)2 or D2/(D2 +r2).
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Consistent deformations must scale as
€
Dm
[αDm + rn ]or
€
Dm
[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
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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
Results Summary Peak Strains Alone are Consistent
€
Dm
[αDm + rn ]or
€
Dm
[αD + r]n
m,n ~ 2
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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
Results Summary
Peak Strain Rate x Rupture Durations are
Consistent
€
Dm
[αDm + rn ]or
€
Dm
[αD + r]n
m,n ~ 2
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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
Nucleation Site (Fault Network) Dimensionality:
~1.7 and ~2.2
€
d = 3− γ
Results Summary
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The probability of triggering an earthquake at a particular location and distance r scales with the size of the triggering earthquake.
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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.
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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?
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Questions?
Thank You!
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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
Rn
R = h2 + r2 , (r + h), h(D)2 + r2