Abstract for paper accepted by Solar Physics, 1999.
Calculation of the sun's acoustic impulse response by
multi-dimensional spectral factorization
by
James E. Rickett and Jon F. Claerbout
Geophysics Department, Stanford University, CA 94305
ABSTRACT
Calculation of time-distance curves in helioseismology can
be formulated as a blind-deconvolution (or system identification) problem.
A classical solution in one-dimensional space
is Kolmogorov's Fourier domain spectral-factorization method.
The helical coordinate system maps two-dimensions to one.
Likewise a three-dimensional volume is representable as a
concatenation of many one-dimensional signals.
Thus concatenating a cube of helioseismic data into
a very long 1-D signal and applying Kolmogorov's factorization,
we find we can construct the three-dimensional causal
impulse response of the sun
by deconcatenating the Kolmogorov result.
Time-distance curves calculated in this way have the same spatial and
temporal bandwidth as the original data, rather than the decreased
bandwidth obtained obtained by cross-correlating traces.
Additionally, the spectral factorization impulse response is minimum
phase, as opposed to the zero phase time-distance curves produced by
cross-correlation.
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