Time-distance functions compared

Figure  shows a comparison between the impulse response derived from Kolmogorov spectral factorization, and the impulse response derived by crosscorrelation.

The raw MDI data has a narrow temporal bandwidth with most of its energy having a period of about five minutes: squaring the amplitude spectrum reduces this bandwidth even more resulting in the monochromatic appearance of the left panel in Figure . Moreover, it is not just the temporal bandwidth that is decreased by crosscorrelating traces; but the spatial bandwidth is reduced as well. The steep dips associated with the l- and low p-modes are clearly visible near the origin in the right panel of Figure  are very heavily attenuated in the crosscorrelation impulse response (left panel).

This difference in spatial bandwidth can be also be seen in the amplitude spectra of Figure . The amplitude of l- and low p-modes are much lower in the autocorrelation result than in the Kolmogorov result.

Whereas, the temporal bandwidth may be broadened relatively simply by conventional deconvolution, recovering the full spatial bandwidth that is present in the original data would be more difficult.

 

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Figure 5 Time-distance impulse responses computed by (a) three-dimensional autocorrelation, and (b) three-dimensional Kolmogorov spectral factorization. Traces have been binned as a function of radius from the origin, averaging the impulse response over azimuth.

 

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Figure 6 Two-dimensional amplitude spectra of impulse responses shown in Figure  above. The impulse responses were computed by (a) three-dimensional autocorrelation, and (b) three-dimensional Kolmogorov spectral factorization.