Modern Statistical Methods for Helioseismic Spectrum Estimation

Principal Investigator / Institution:  Philip B. Stark/UC Berkeley

Significant breakthroughs in the statistical analysis of temporal and 
spatial spectra over the last half century have yet to be applied  
to helio-seismological data.  In particular, spatial and temporal 
mutli-taper spectrum estimation, and one-dimensional and spherical 
wavelet shrinkage, all developed in the last 15 years, seem
very likely to result in substantial improvements in estimates of 
the spatiotemporal spectrum of solar acoustic oscillations from 
SOHO-SOI/MDI data.  Numerical experiments with GONG data 
confirm this in part.  The proposed work is to produce and make 
public a set of portable software tools implementing the latest 
statistical techniques for spectrum estimation; spherical 
wavelet shrinkage "de-noising" of MDI velocity images, followed 
by multitaper estimates of the spatial spectrum of each  
velocity image, followed by multitaper estimates of the temporal 
spectrum of each spherical harmonic coefficient, followed 
by one-dimensional wavelet shrinkage de-noising of the temporal 
spectra.  The details of this pipeline will be adapted 
specifically to estimate the spatio-temporal spectrum of solar 
free oscillations from SOHO-SOI/MDI data, including the choice of
various free parameters, using simulated and  real data.

The software will be developed in the following order: 

(1)	Multitaper estimation of the temporal spectrum of solar 
	oscillations with a given spatial frequency. 

(2)	Wavelet shrinkage post-processing of those temporal spectra.

(3)	Multitaper estimation of the spatial spectrum of the sequence 
	of images remapped to heliographic coordinates. 

(4)	Spherical wavelet denoising of remapped solar images.

The proposed research will produce software tools to analyze 
SOHO/SOI/MDI observations that are expected to perform 
substantially better than the methods currently used, yielding 
improved estimates of normal mode frequencies, amplitudes, 
linewidths, and their corresponding uncertainties.