Post on 25-Feb-2016
description
transcript
Differential wave equation and seismic events
Sean Ford & Holly BrownBerkeley Seismological
Laboratory
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
Introduction• Seismic sources
• Earthquake
• Explosion
Slip on a plane
Pressure pulse on a sphere
• Start with Newton
• Add ‘constitutive equation’ to relate stress to strain to displacement
Seismic wave equation
€
F = ma
F = ρ ∂2u∂t 2
• Can decompose to P and S wave solutions of the form
• Wave equation can be solved by plane-wave
Seismic wave equation
€
∇2u− 1α 2
∂2u∂t 2
= 0 or in 1− D α 2 ∂2u∂x 2 = ∂
2u∂t 2
€
u(x,t) = Acos[ω(t − x c)]
• The wave equation is solved on a computer by using a discrete representation of the differential equation
Finite differences
€
∂2u∂x 2 = ui+1 − 2ui + ui−1
dx 2
Possible project: Sumatra earthquake
Time (sec)
Possible project
Time (sec)
Possible project
T
Time (sec)
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
From
Wal
ter e
t al.
(200
8)
North Korea Nuclear Test
From Walter et al. (2008)
Seismic moment tensors
M represents all possible force couple components due to a seismic source in a cartesian coordinate systemNecessary to have two force couples (double couple, DC), so that angular momentum is conserved in the source sphere, which leads to Mij = Mji and the moment tensor is symmetric
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
Moment tensor inversion
in matrix formd = Gm
m = vector of 6 independent moment tensor elementsm = (GTG)-1GTd
Western US
Western US
Western US
Western US
Source-type plotWe calculate source-type plot parameters (Hudson et al., 1989)
Source-type plotWe calculate source-type plot parameters (Hudson et al., 1989)
Explosion
Implosion
Source-type plotWe calculate source-type plot parameters (Hudson et al., 1989)
Explosion
Implosion
DC -CLVD+CLVD
Source-type plotWe calculate source-type plot parameters (Hudson et al., 1989)
Explosion
Implosion
DC -CLVD+CLVD
HOYA
Little Skull
Source-type plotWe calculate source-type plot parameters (Hudson et al., 1989)
Explosion
Implosion
DC -CLVD+CLVD
HOYA
Little Skull
HOYA
Little Skull
Source-type plotWe calculate source-type plot parameters (Hudson et al., 1989)
Explosion
Implosion
DC -CLVD+CLVD
HOYA
Little Skull
HOYA
Little Skull
Western US
9 Oct 06 North Korea test
Crandall Canyon, Utah
Site of 6 Aug 08 Mine Collapse
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Can be implosion
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Or shallow normal event
Use method for nuclear test explosions to find source at Crandall Canyon
Crandall Canyon event plotted near where a closing crack or collapse source should plot
Dominantly implosional
Crandall Canyon
Crandall Canyon event plotted near where a closing crack or collapse source should plot
Dominantly implosional
But also some shear portion
Hayward Fault
Hayward fault
• GoogleEarth tour• 1868 Hayward event M6.8• Scenario events from USGShttp://earthquake.usgs.gov/regional/nca/simulations/hayward/
• San Pablo epicenter• Fremont epicenter• View from Concord