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We develop the wave-mechanical formalism for phase-correlation computational seismic holography of the shallow subphotosphere under the plane-parallel approximation and apply it to helioseismic Doppler observa- tions from the Michelson Doppler Imager on the SOHO spacecraft of both the quiet Sun and active regions. We compare holographic signatures computed wave-mechanically with similar signatures computed under the widely used eikonal approximation. The major difference between the hydromechanical and eikonal computa- tions can be expressed in terms of acoustic dispersion effects within a few Mm of the solar surface. With an appropriate account for dispersion, the eikonal computations are remarkably accurate over a broad range of practical applications. A major imposition that confronts local diagnostics of the shallow subphotosphere is a phenomenon we call ''ghost signatures,'' artifacts introduced by a local ambiguity in the origin of the waves that give rise to the helioseismic signatures observed in the photosphere. Phase-correlation holographic signatures of the shallow subphotospheres of active regions are predominated by strong, stochastic phase shifts associated with magnetic fields at the solar surface. These introduce effects similar to those of an optical showerglass, signifi- cantly impairing the coherence of waves impinging into the magnetic photosphere from beneath, smearing the holographic signatures of possible subphotospheric anomalies. Subject heading

Principles of Seismic Holography for Diagnostics of the Shallow Subphotosphere