Application to SOHO/MDI dataset

Figure  shows a cube of raw velocity data from the MDI instrument. The data have been transformed to Cartesian coordinates by projecting high-resolution data from an area approximately 18$^\circ$ square onto a tangent plane. The object in the center of the time-slice (top of cube) is a sun-spot (irrelevant to this study). The sample spacing is 1 minute on the time-axis and approximately 825 km on the two spatial axes.

 

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Figure 2 Cube of MDI data.

Time-variable features of Figure  fall into two distinct spectral windows. The low temporal frequency events (<1.5 mHz) are related to solar convection, while the higher frequency events are related to acoustic wave propagation. We were interested in studying acoustic wave phenomena; so as a preprocessing step, we removed the lower frequency spectral window by applying a low-cut filter to the data.

Figure  shows the impulse response derived by multi-dimensional spectral factorization. Due to the lack of coherent reflectors within the solar interior, no reflection events are visible. The strong vertical velocity gradient causes the first arrival to be a diving wave. Later arrivals are the multiple events of increasing order (PP, PPP etc.) illustrated in Figure .

 

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Figure 3 Three-dimensional minimum phase impulse response.

 

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Figure 4 Schematic showing some of the raypaths visible in helioseismic time-distance plots.