earthquake dynamic triggering and ground motion scaling j. gomberg, k. felzer, e. brodsky
TRANSCRIPT
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.
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ρ(r) = [Naftershocks(r)
Δr]
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
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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.
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ρ(r) = [N(r)Δr]P(r)
number of aftershocks at distance r
Modeled linear aftershock densities.
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ρ(r) = [N(r)Δr]P(r)
number of aftershocks at distance r
number of potential nucleation sites per unit distance
Modeled linear aftershock densities.
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ρ(r) = [N(r)Δr]P(r)
number of aftershocks at distance 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
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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.
Recall the measured aftershock densities:
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ρ(r) = C10M min10M r−γ
= C10M min D2r−γ
~ constant at all distances!
This model illuminates constraints on triggering deformations...
Measured aftershock densities:
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ρ(r) = C10M min D2r−γ
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ρ(r) = P(r)[N(r)Δr]
Modeled aftershock densities.
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=P(r) [4πA{1+ (D r ) + ( 12π )(D r )2}r(d −1)]
Measured aftershock densities:
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ρ(r) = C10M min D2r−γ
in the near field (r<<D)
ρ(r) P(r) D2 r(d-3)
Modeled aftershock densities.
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ρ(r) = P(r) [4πA{1+ (D r ) + (12π )(D r )2}r(d −1)]
Measured aftershock densities:
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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)
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ρ(r) = P(r) [4πA{1+ (D r ) + (12π )(D r )2}r(d −1)]
Measured:
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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
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:
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P(r) = Dm
[αD + r]n
m = 2, n = 2
or
Uncertainties & Resolution
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[4πA{1+ (D r ) + (12π )(D r )2}r(d −1)] Dm
(αD + r)n = C10M min D2r−γ
Our model implies these equalities
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[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.
Uncertainties & Resolution
Permissible scalings of P(r): or
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Dm (αD + r)n
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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
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Dm
[αDm + rn ]
or
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Dm
[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 Rate(acceleration)
Strain (velocity)
Displacement
Dynamic deformation amplitude
= peak value x rupture duration (proportional to D).
Strain Rate(acceleration)
Strain (velocity)
Displacement
Dynamic deformation amplitude
= average value x duration = cumulative amplitude.
Strain Rate(acceleration)
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.
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.
Our Deformation and Aftershock Density Scaling Observations
We can measure peak ground motion scaling with D and the far field distance decay rate.
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.
Our Deformation and Aftershock Density Scaling Observations
Aftershock densities become uncertain at distances comparable to location errors.
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.
Our Deformation and Aftershock Density Scaling Observations
Scaling the peak velocity or the distance by rupture dimension D removes all size dependence.
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).
Consistent deformations must scale as
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Dm
[αDm + rn ]or
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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
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
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Dm
[αDm + rn ]or
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Dm
[αD + r]n
m,n ~ 2
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
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Dm
[αDm + rn ]or
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Dm
[αD + r]n
m,n ~ 2
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
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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 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.
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Peak Motion = C10−br Dm
Rn
R = h2 + r2 , (r + h), h(D)2 + r2