9:15 AM - 9:30 AM
[SSS09-02] SH-wave propagation through the random distribution of aligned line cracks
Keywords:seismic waves, cracks, scattering, wave theory, radiative transfer theory
Recent seismological observations have revealed that random heterogeneities spread over the solid Earth for a wide range of scales. There are two possible candidates for the source of seismic wave scattering: one is a random fluctuation of velocity; the other is a random distribution of cracks or faults. This paper studies the propagation of SH waves through the random distribution of aligned line cracks as the simplest mathematical model.
The differential scattering cross-section of a single line crack is well described by using Mathieu functions. Note that the differential scattering cross-section is anisotropic and depends on both incident and scattering angles. The random distribution of cracks assures the mutual incoherence of scattered waves, which allows us to use the radiative transfer theory. The directional scattering power per unit area is given by the scattering coefficient, which is a product of the number density of cracks and the differential scattering cross-section. Stochastically interpreting the scattering coefficient, we synthesize the space-time distribution of the wave intensity for a unit isotropic radiation from a point source by the Monte Carlo simulation. This paper precisely studies the case that the wavenumber is larger than the reciprocal of the crack length. Syntheses show that direct wavelets around the direction normal to the aligned line cracks rapidly decrease with increasing distance because of strong scattering, but those around the direction parallel to the aligned line cracks decrease according to the geometrical decay only. At large lapse times, multiple scattering produces a swelling around the source location, which is prolonged to the crack line direction. Those characteristics well reflect the anisotropy of the line crack scattering.
Our next target is to solve more realistic cases, for example, the propagation of elastic-waves through the random distribution of penny shaped cracks in a 3-D elastic medium.
The differential scattering cross-section of a single line crack is well described by using Mathieu functions. Note that the differential scattering cross-section is anisotropic and depends on both incident and scattering angles. The random distribution of cracks assures the mutual incoherence of scattered waves, which allows us to use the radiative transfer theory. The directional scattering power per unit area is given by the scattering coefficient, which is a product of the number density of cracks and the differential scattering cross-section. Stochastically interpreting the scattering coefficient, we synthesize the space-time distribution of the wave intensity for a unit isotropic radiation from a point source by the Monte Carlo simulation. This paper precisely studies the case that the wavenumber is larger than the reciprocal of the crack length. Syntheses show that direct wavelets around the direction normal to the aligned line cracks rapidly decrease with increasing distance because of strong scattering, but those around the direction parallel to the aligned line cracks decrease according to the geometrical decay only. At large lapse times, multiple scattering produces a swelling around the source location, which is prolonged to the crack line direction. Those characteristics well reflect the anisotropy of the line crack scattering.
Our next target is to solve more realistic cases, for example, the propagation of elastic-waves through the random distribution of penny shaped cracks in a 3-D elastic medium.