On averaged time-distance autocorrelation diagrams

Details On averaged time-distance autocorrelation diagrams On averaged time-distance autocorrelation diagrams

Feb 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003esasp.517..389s&link_type=abstract

In: Proceedings of SOHO 12 / GONG+ 2002. Local and global helioseismology: the present and future, 27 October - 1 November 2002,

Physics

2

Data Analysis, Helioseismology

Scientific paper

To calculate time-distance autocorrelation for local-helioseismic analyses, the correlation function is often put in a form which permits application of the convolution theorem so that CPU-intensive direct integration is alleviated. It is normally justified by a statistical argument with a certain assumption on properties of power distribution of the wavefield; the results are then interpreted as ensemble averages of the autocorrelation. However, the same results can also be obtained by taking spatial averages without any assumption on the power distribution, thereby providing a different interpretation to the results obtained through convolution theorem. It is straightforward to demonstrate the above in the case of wavefield in infinite two-dimensional space. Here we present a direct demonstration of the same equivalence of the averages in the case of spherical geometry, which has turned out to be less straightforward.

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