The relationship between the time-distance and modal-decomposition approaches to solar active region seismology is clarified through the consideration of the oscillations of a plane-parallel, isentropic polytrope. It is demonstrated by direct construction that a wave packet formed through the superposition of neighboring p-modes interferes constructively along a ray bundle that basically follows the appropriate WKBJ ray path obtained by using the eikonal approximation. Because the ~ 10(7) solar p-modes populate k-omega ridges with only rather modest radial orders, these ray bundles are rather diffuse and sample portions of the solar envelope that are some ~ 10--30 Mm distant from the nominal WKBJ ray path. This lack of localization along the ray path for solar p-modes is consistent with the fact that the eikonal approximation becomes valid only in the limiting case of large radial orders (n >> 1). Thus the p-mode wave packets that are isolated by employing the time-distance methods developed by Duvall et al (1993, Nature, 362, 430) must be described either as a sum of individual p-modes (a wave packet), or as a superposition of ray paths (a ray bundle), depending upon which representation proves to be optimal for the given circumstances.
American Astronomical Society Meeting Abstracts #188
- Pub Date:
- May 1996