Helioseismic holography

We describe the basic principles of ''helioseismic holography,'' an analytic technique intended for local helioseismology of subsurface structure. The purpose of this technique is to provide depth discrimination of subsurface structure that manifests a surface signature in acoustic waves. It is based on the computational application of spatially resolved helioseismic observations to the surface of an acoustic model of the solar interior that contains no local structure. The observed surface oscillations are applied to the model in time reverse, and the model is then computationally sampled at various depths in its interior. This technique takes advantage of the coherence retained by waves in a smooth acoustic medium following an interaction with subsurface structure, allowing us to extrapolate the acoustic field with high accuracy to the depth where the structure lies. Depth discrimination is then accomplished by focus-defocus diagnostics. We describe computational approaches to the technique from two different perspectives, the ''spectral'' and the ''spatial.'' For rigorous models of the solar interior, the computational demands of the spectral and spatial approaches are approximately the same. For diagnostics of relatively shallow structure, the plane-parallel approximation of the model is useful. In this case the spectral approach reduces computational holography essentially to Fourier transforms, which can be performed rapidly with very modest hardware. We illustrate the technique in this case, using artificial data characterizing waves in an idealized plane-parallel medium with acoustic absorbers located at various depths. At present, we prefer to maintain a secure distinction between holography and modeling. While we do not discuss modeling in this paper, we think that it is important to develop an approach to modeling that takes advantage of holographic reconstruction. The prospect of viewing local subsurface magnetic regions and flows opens an entirely new dimension to helioseismology and to solar and stellar physics in general. It may make it possible to anticipate solar activity far in advance of its emergence to the surface. Local acoustic diagnostics could revolutionize our understanding of the solar dynamo and the 22 yr activity cycle.