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Min
Chen extends the spectral-element simulations of global
and regional seismic wave propagation to incorporate three-dimentional,
fully anisotropic Earth models. For weakly anisotropic media, we benchmark
the numerical simulations against asymptotic, ray-theoretical predictions
for surface and body waves.
Theory in weakly anisotropic Earth media
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Surfacewave
phase speeds (Smith & Dahlen 1973)
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We
demonstrate that compressional and shear body-wave speeds
can be written as:
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Surfacewave
anisotropy is governed by 13 elastic parameters, and the
azimuthal dependence of the phase speed is represented
by even Fourier series involving degrees two or four;
12/3/07elastic parameters,
bodywave speeds are even Fourier series of incidence angle,
but their azimuthal dependence involves degree one, two,
three and four, which is unlike surface waves.
Table
1.
Comparison of the directional effects of all 21 independent
elastic coefficients on body- and surface-wave speeds.
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Spectral-element Simulation:
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Figure 1. Global experimental setup. The source is pure strike-slip
event located at a depth of 15km at the South Pole (yellow star).
The fast direction of the anisotropy, indicated by yellow dashes.
The background model is transversely isotropic PREM upon which
the constant anisotropy at the 5% level throughout the upper
mantle.Two rings of stations (green cricles) with epicentral
distances of 75 degrees and 120 degrees, respectively, and a
5-degree longitudinal station spacing record the wavefield of
both body waves and surface waves. Left: map view. Right: side
view. |
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Figure
2. Path averaged surface-wave phase-speed anomalies.The black
(50s) and red (150s) lines are ray-theoretical predictions
for Love waves (left column) and Rayleigh waves (right clolumn)
at an epicentral distance of 120 degrees, due to 5% anisotropic
perturbations of particular combinations of anisotropic parameters
Bc,s, Gc,s, Hc,s, and Ec,s. The black (50s) and red (150s)symbols
denote the actual surface-wave phase anomalies mesured from
the SEM simulated seismograms based upon a phase-matched filtering
technique.
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Figure
3. Body-wave traveltime anomalies due to 5% anisotropic perturbations
of particular combinations of anisotropic parameters Bc,s, Gc,s,
Hc,s, and Ec,s are shown for P waves (left column), SV waves
(middle column), and SH waves (right column) at an epicentral
distance of 75 degrees. Lines: ray-theoretical predictions.
Symbols: measurents of SEM synthetics. |
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