on the physics and simulation of waves at fluid-solid interfaces: application to ndt, seismic...
DESCRIPTION
Page: 3 2-D Equations of Motion Euler-Newton’s Equations: Constitutive Equations: Memory Variables:TRANSCRIPT
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On the Physics and Simulation of Waves at Fluid-Solid Interfaces:
Application to NDT, Seismic Exploration and Earthquake Seismology
by
José M. Carcione (OGS, Italy)
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The 2D modeling algorithm
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2-D Equations of Motion
Euler-Newton’s Equations:
Constitutive Equations:
Memory Variables:
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Scholte wave dispersion equation
Relevant roots: Scholte wave
Leaky Rayleigh wave
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Inhomogeneous waves
Plane waveElliptical polarization
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Reflection and transmission
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From a stiff ocean floor...
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to a soft ocean floor
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Numerical algorithm
Two grids (domain decomposition): ocean and oceanic crust
Fourier method in the horizontal direction
Chebyshev method in the vertical direction
Spatial derivatives
Time integration
4th-order Runge-Kutta
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Test with the analytical solution
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AVA analysis
Elastic case
Anelastic case
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Rayleigh Window:Water/stainless steel
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Water/oceanic crust
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Water/plexiglass (soft bottom)
No leaky Rayleigh wave
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Water/glass (stiff bottom)
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Test with analytical solution
Water/plexiglass interface
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Test with analytical solution
Water/glass interface
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Dispersive Scholte waves
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Dispersive Scholte waves
Elastic case Anelastic case
North Sea. 70 m water depth. Airgun source.
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Ocean overlying the crust
Phase velocity
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Ocean overlying the crust
Group velocity
Dissipation factor
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Ocean overlying the crust
Attenuation coefficientBen_Menahem and Singh (1981)
Experimental data (Fig. 10.3)
0 20 40 60 80
0,1
1,0
10,0
x 104
(km-1
)5
10
H=15 km
ΓP
ΓS
Γ
T (sec)
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Ocean overlying the crust
Phase/group velocities
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Ocean overlying the crust
High-frequency case
Elastic and anelastic solutions
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Ocean overlying the crust
Low-frequency case
AnelasticElastic
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Sediment layer overlying the crust
Low-frequency case
Elastic Anelastic
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January 7 (2000) Earthquake
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Real seismograms
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Geological model
From CRUST 5.1
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Synthetic seismograms
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The 3D modeling algorithm
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The Kelvin-Voigt stress-strain relation
s = stress componentse = strain componentsu = displacements = Lamé constants’ ’ = damping Lamé constants
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Input damping parameters
0 = reference frequencyQP0 = reference P-wave quality factorQS0 = reference S-wave quality factor
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The equations of motion
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The equations of motion
v = particle velocity = densityf = body forces
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Tests with analytical solutions
Rayleigh waves -- Cagniard-de Hoop solution
Pekeris (1955) solution -- unbounded media
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Simulation of Rayleigh waves. Model.
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Simulation of Rayleigh waves. Seismograms.
Lossless case
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Simulation of Rayleigh waves. Seismograms.
Lossy case
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Simulation of Love waves. Model.
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Simulation of Love waves. Seismograms.
Lossless case Lossy case
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Conclusions
Effects of anelastic attenuation
Pseudospectral numerical method
Inhomogeneous viscoelastic waves
Differences at critical and post-critical angles
Rayleigh-window effect
Verified for reflection/transmission and interface waves
Effective tool for seismic exploration studies, NDT and earthquake seismology