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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. 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 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. number of aftershocks at distance r

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Modeled linear aftershock densities. number of aftershocks at distance r number of potential nucleation sites per unit distance

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Modeled linear aftershock densities. 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) ‘d’ = dimensionality Number of potential nucleation sites

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

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cylinder sphere rectangle Surface S is comprised of simple shapes,

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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: ~ constant at all distances! This model illuminates constraints on triggering deformations...

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Measured aftershock densities: Modeled aftershock densities.

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Measured aftershock densities: in the near field (r<

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Measured aftershock densities: in the near field (r<

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Measured: in the near field (r) P(r) D 2 r (d-3) Modeled: in the far field (r) P(r) r (d-1) The probability of nucleation MUST scale in the near field as P(r) constant in the far field as P(r) D 2 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 scale in the near field as P(r) constant in the far field as P(r) D 2 r -2

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Consistent Probabilities: or

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Uncertainties & Resolution Aftershock densities decay as r - In the most precise cases, is constant within about +0.1 km -1 at far field distances and +0.3 km -1 in the near field.

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Uncertainties & Resolution Our model implies these equalities 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 How much can the scaling of P(r) differ from or ? If P(r) is consistent, ratios of the terms on each side of the equalities should be ~constant, or have slopes that differ by less than the uncertainties in .

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Uncertainties & Resolution How much can the scaling of P(r) differ from or ? If P(r) is consistent, ratios of the terms on each side of the equalities should be ~constant, or have slopes that differ by less than the uncertainties in .

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Uncertainties & Resolution Deviations from a constant slope can be derived from the derivatives of these curves. How much can the scaling of P(r) differ from or ?

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Uncertainties & Resolution Deviations from a constant slope can be derived from the derivatives of these curves. decay rate change (km -1 ) How much can the scaling of P(r) differ from or ?

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Uncertainties & Resolution In the far field, the observed decay rate (or slope) is constant within about +0.1 km -1. decay rate change (km -1 ) How much can the scaling of P(r) differ from or ?

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Uncertainties & Resolution In the near field, the observed decay rate (or slope) is constant within about +0.3 km -1. decay rate change (km -1 ) How much can the scaling of P(r) differ from or ?

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Uncertainties & Resolution Permissible scalings of P(r): or with ~1.8

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Uncertainties & Resolution Permissible scalings of P(r): or ~1.8

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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 or

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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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Published Peak Acceleration & Velocity “Attenuation” Models D scaling ranges from m~0.6 to m~2 with a mean of ~1 for peak accelerations, and m is greater by ~0.5 for peak velocities. This suggests nucleation depends only on peak strain rates (accelerations) times the rupture duration, or perhaps peak strains (velocities) alone.

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Published Peak Acceleration & Velocity “Attenuation” Models r scalings are difficult to compare; often b~0 but not always, r represents different distances, the definition of R varies.

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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 M 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., D 2 /( D+r) 2 or D 2 /( D 2 +r 2 ).

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Consistent deformations must scale as or Results Summary

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Peak Strains Alone are Consistent or

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Results Summary Peak Strain Rate x Rupture Durations are Consistent or

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Nucleation Site (Fault Network) Dimensionality: ~1.7 and ~2.2 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 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.

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