PROPAGATION OF SEISMIC WAVES THROUGH A SPATIO-TEMPORALLY FLUCTUATING MEDIUM: HOMOGENIZATION
- Department of Geosciences, Princeton University, Princeton, NJ 08544 (United States)
- Max-Planck-Institut fuer Sonnensystemforschung, D-37191 Katlenburg-Lindau (Germany)
- Department of Applied and Physical Mathematics, Columbia University, New York, NY 10027 (United States)
Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally stationary medium is almost universally invoked. However, the Sun is in a constant state of evolution, on a broad range of spatio-temporal scales. At the zero-wavelength limit, i.e., when the wavelength is much shorter than the scale over which the medium varies, the WKBJ (ray) approximation may be applied. Here, we address the other asymptotic end of the spectrum, the infinite-wavelength limit, using the technique of homogenization. We apply homogenization to scenarios where waves are propagating through rapidly varying media (spatially and temporally), and derive effective models for the media. One consequence is that a scalar sound speed becomes a tensorial wave speed in the effective model and anisotropies can be induced depending on the nature of the perturbation. The second term in this asymptotic two-scale expansion, the so-called corrector, contains contributions due to higher-order scattering, leading to the decoherence of the wave field. This decoherence may be causally linked to the observed wave attenuation in the Sun. Although the examples we consider here consist of periodic arrays of perturbations to the background, homogenization may be extended to ergodic and stationary random media. This method may have broad implications for the manner in which we interpret seismic measurements in the Sun and for modeling the effects of granulation on the scattering of waves and distortion of normal-mode eigenfunctions.
- OSTI ID:
- 22131015
- Journal Information:
- Astrophysical Journal, Vol. 773, Issue 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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