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Differential wave equation and seismic events Sean Ford & Holly Brown Berkeley Seismological Laboratory
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Outline Holly and Sean 101 Quick intro: Wave equation Monitoring nuclear tests Predicting ground motion for a future event on the Hayward Fault Hayward Fault tour
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Introduction Seismic sources Earthquake Explosion Slip on a plane Pressure pulse on a sphere
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Start with Newton Add ‘constitutive equation’ to relate stress to strain to displacement Seismic wave equation
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Can decompose to P and S wave solutions of the form Wave equation can be solved by plane- wave Seismic wave equation
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The wave equation is solved on a computer by using a discrete representation of the differential equation Finite differences
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Possible project: Sumatra earthquake Time (sec)
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Possible project Time (sec)
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Possible project T Time (sec)
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Seismic sources Earthquake - slip on a plane Explosion - pressure pulse on a sphere Compressional (P-wave) radiation pattern Shear (S-wave) radiation pattern No volume change Compressional (P-wave) radiation constant No Shear (S-wave) radiation Volume change
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From Walter et al. (2008)
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North Korea Nuclear Test From Walter et al. (2008)
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Seismic moment tensors M represents all possible force couple components due to a seismic source in a cartesian coordinate system Necessary to have two force couples (double couple, DC), so that angular momentum is conserved in the source sphere, which leads to M ij = M ji and the moment tensor is symmetric
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Seismic moment tensors Double-couple (DC) y z x Compensated linear vector dipole (CLVD) Isotropic y z x y z x Model Source M Couples Focal Ring Fault Explosion Strike-slip Mechanism
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Moment tensor inversion in matrix form d = Gm m = vector of 6 independent moment tensor elements m = (G T G) -1 G T d
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Western US
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Source-type plot We calculate source-type plot parameters (Hudson et al., 1989)
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Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion Implosion
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Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion Implosion DC-CLVD+CLVD
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Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion Implosion DC-CLVD+CLVD HOYA Little Skull
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Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion Implosion DC-CLVD+CLVD HOYA Little Skull HOYA Little Skull
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Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion Implosion DC-CLVD+CLVD HOYA Little Skull HOYA Little Skull
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Western US
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9 Oct 06 North Korea test
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Crandall Canyon, Utah Site of 6 Aug 08 Mine Collapse Crandall Canyon, Utah Site of 6 Aug 08 Mine Collapse
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Can be implosion
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Or shallow normal event
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Use method for nuclear test explosions to find source at Crandall Canyon
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Crandall Canyon event plotted near where a closing crack or collapse source should plot Dominantly implosional Crandall Canyon
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Crandall Canyon event plotted near where a closing crack or collapse source should plot Dominantly implosional But also some shear portion
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Hayward Fault
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Hayward fault GoogleEarth tour 1868 Hayward event M6.8 Scenario events from USGS http://earthquake.usgs.gov/regional/nca/simulations/hayward/ San Pablo epicenter Fremont epicenter View from Concord
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