Computational Seismic Holography of Acoustic Waves in the Solar Interior

Abstract

1.1 Helioseismology The advent of solar seismology is widely recognized as the independent discoveries by Leighton, Noyes & Simon (1963) and Evans, Michard & Servajean (1962) of Doppler oscillations in the Sun’s surface, mostly with periods ranging from about 2 to 8 minutes. This was recognized as the surface signature of waves traveling beneath the Sun’s surface. These waves, now understood to be generated by convection a few hundred km beneath the Sun’s surface (Stein et al. , 2004), penetrate deep beneath the surface, filling the solar interior. The idea of using observations of these waves as a diagnostic of the Sun’s interior structure was introduced by Ulrich (1970), and developed at length by Deubner (1975) and Rhodes, Ulrich & Simon (1977). Continued development followed many different avenues, some of these similar in some ways to geoseismic diagnostics of the Earth’s interior. Indeed, helioseismic holography and “migration theory”, the latter developed by Claerbout (1970) for applications in geoseismology, share basic concepts in wave optics in very similar contexts. However, solar seismology has overwhelming advantages, both in the quality, extent and uniformity of the observations and in the optical quality of the solar interior as an acoustic medium. Solar seismology gave us maps of the solar interior rotation rate (Rhodes, Deubner & Ulrich , 1979), affirming that the Sun is a differentially rotating fluid, its convection zone continuously being warped as the equatorial region rotates significantly faster than the inner polar region and the outer equatorial convection zone rotates faster than the deep convection zone. Helioseismology is also the significant observational basis of our present understanding of the thermal structure of the solar interior in standard models such as Christensen-Dalsgaard, Proffitt & Thompson (1993). Solar seismology has been largely developed along two significantly separate lines. What is now generally recognized as “global helioseismology” views the Sun as a system of harmonic oscillators and relies heavily on the frequencies of its thousands of normal modes to build a model of the general thermal structure of the Sun and how different layers of it rotate. These diagnostics give us significant discrimination in depth and some in latitude, but none in longitude. What is recognized as “local helioseismology” uses perspectives that tend to be more familiar to optics to focus on relatively compact regions. The local discrimination our 4