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
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)
Page: 2
The 2D modeling algorithm
Page: 3
2-D Equations of Motion
Euler-Newton’s Equations:
Constitutive Equations:
Memory Variables:
Page: 4
Scholte wave dispersion equation
Relevant roots: Scholte wave
Leaky Rayleigh wave
Page: 5
Inhomogeneous waves
Plane waveElliptical polarization
Page: 6
Reflection and transmission
Page: 7
From a stiff ocean floor...
Page: 8
to a soft ocean floor
Page: 9
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
Page: 10
Test with the analytical solution
Page: 11
AVA analysis
Elastic case
Anelastic case
Page: 12
Rayleigh Window:Water/stainless steel
Page: 13
Water/oceanic crust
Page: 14
Water/plexiglass (soft bottom)
No leaky Rayleigh wave
Page: 15
Water/glass (stiff bottom)
Page: 16
Test with analytical solution
Water/plexiglass interface
Page: 17
Test with analytical solution
Water/glass interface
Page: 18
Dispersive Scholte waves
Page: 19
Dispersive Scholte waves
Elastic case Anelastic case
North Sea. 70 m water depth. Airgun source.
Page: 20
Ocean overlying the crust
Phase velocity
Page: 21
Ocean overlying the crust
Group velocity
Dissipation factor
Page: 22
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)
Page: 23
Ocean overlying the crust
Phase/group velocities
Page: 24
Ocean overlying the crust
High-frequency case
Elastic and anelastic solutions
Page: 25
Ocean overlying the crust
Low-frequency case
AnelasticElastic
Page: 26
Sediment layer overlying the crust
Low-frequency case
Elastic Anelastic
Page: 27
January 7 (2000) Earthquake
Page: 28
Real seismograms
Page: 29
Geological model
From CRUST 5.1
Page: 30
Synthetic seismograms
Page: 31
The 3D modeling algorithm
Page: 32
The Kelvin-Voigt stress-strain relation
s = stress componentse = strain componentsu = displacements = Lamé constants’ ’ = damping Lamé constants
Page: 33
Input damping parameters
0 = reference frequencyQP0 = reference P-wave quality factorQS0 = reference S-wave quality factor
Page: 34
The equations of motion
Page: 35
The equations of motion
v = particle velocity = densityf = body forces
Page: 36
Tests with analytical solutions
Rayleigh waves -- Cagniard-de Hoop solution
Pekeris (1955) solution -- unbounded media
Page: 37
Simulation of Rayleigh waves. Model.
Page: 38
Simulation of Rayleigh waves. Seismograms.
Lossless case
Page: 39
Simulation of Rayleigh waves. Seismograms.
Lossy case
Page: 40
Simulation of Love waves. Model.
Page: 41
Simulation of Love waves. Seismograms.
Lossless case Lossy case
Page: 42
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