Matoza et al St. Helens Infrasound JGR 09

B04305 MATOZA ET AL.: INFRASOUND FROM LPS AT MOUNT ST. HELENS B04305
properties. Consequently, finite difference methods are
usually used in volcano seismology to compute Greens
functions for moment tensor inversions [Chouet et al.,
2003], or travel times for tomographic inversions [Benz et
al., 1996]. In this study, we use a finite difference code,
ASTAROTH [D’Auria and Martini, 2007], to investigate
seismic-acoustic wave conversion and coupling from a
shallow buried source. Following Virieux [1986], seismic
propagation in the elastic solid and acoustic propagation in
the (inviscid) fluid atmosphere are solved simultaneously
using a single velocity-stress computational scheme. The
fluid is defined by a zero S wave velocity (Vs, m = 0), and
appropriate values for the density and sound speed (P wave
velocity, or Vp) of air. This approach does not require
explicit free-surface boundary conditions to define the
coupling at the topography surface between the solid earth
and atmosphere. Seismic-acoustic conversion results from
weak energy transmission controlled by effective material
properties at the solid-fluid interface [van Vossen et al.,
2002].
[33] The governing equations are the equations of elastodynamics
in 3-D Cartesian coordinates:
@ttij ¼ lð@kvkÞdij þ m @ivj þ @jvi
@tvi ¼ r 1 @jtij þ fi
where t ij is the stress tensor, v i is the (Lagrangian) particle
velocity, d ij is the Kronecker delta, m and l are the Lamé
parameters, r is the density, f i is the body forces (source
term), and the Einstein summation convention is assumed.
Equations (1) are equivalent to the acoustics equations in
the fluid when acoustic pressure p = tii/3, m = 0, and l = k
(bulk modulus) = gp0 in an ideal gas (p0 reference pressure,
g = cp/cv ratio of specific heats) [D’Auria and Martini,
2007]. Since the acoustic wave equation is retrieved by
linearizing Euler’s equation [Landau and Lifshitz, 1987],
static wind fields (wind speeds that vary as a function of
position but not time) can be considered simply by adding
advective terms [D’Auria and Martini, 2007]:
@ttij ¼ lð@kvkÞdij þ m @ivj þ @jvi ðwl@ktklÞdij @tvi ¼ r 1 @jtij þ fi wj@jvi ð2Þ
where wi is the wind velocity (wi = 0 in the elastic nodes).
[34] Equations (2) are solved using a staggered grid finite
differences scheme that is second order in space and time.
Arbitrary moment tensor and single-force sources are
implemented as distributions of body forces f i on velocity
nodes [Graves, 1996] with an arbitrary source time function,
and perfectly matched layer (PML) absorbing bound-
ð1Þ
ary conditions are imposed around the edge of the
computational volume [Berenger, 1996; Festa and Nielsen,
2003]. The parallel code is written in C++/MPI, and
proceeds by dividing the computational volume into
equal subvolumes during each time step (master-slave
implementation).
4.1. Model Configuration
[35] The strong velocity contrast considered leads to
some practical limitations. To limit numerical dispersion,
10 grid points per minimum wavelength are required. For an
atmospheric sound speed of 330 m/s, a denser grid sampling
is required than in typical seismic applications. We restricted
our models to frequencies