Plan for Time-Distance Analysis Tom Duvall 1. When: During any time when full-disk or high-res velocity and/or intensity are available for 8 hours. 2. Data: Map observed images into azimuthal equidistant coordinates with fixed position angle. The field covered can be up to the size of the observed hemisphere or more confined. Solar rotation can be tracked with either a constant rotation with latitude or with a differential rotation. The three-dimensional file of data (two space dimensions and one time) will be rearranged with time along the first axis to facilitate the crosscorrelations. The length of time and the spatial extent of the region tracked are a function of the purpose of the study. On the one hand, a longer sequence of observations will lead to a better signal to noise ratio but on the other hand this will lead to less time resolution of changing phenomena. For example, to study supergranulation, with a lifetime of order one day, the length of a sequence should be less than eight hours. To study giant cells with a much longer lifetime, several days of continuous observations could be used. We normally have to average together a number of crosscorrelations to get enough signal to adequately measure the time-distance features. This has been done at the expense of spatial resolution. So temporal and spatial resolutions can be traded off. A quantitative model of the noise will be developed. 3. Analysis: For each cube of data, crosscorrelations will be computed between each point and all points within small ranges of distance about the point. These crosscorrelations will be analyzed with a Hilbert transform to separate an envelope and phase function. An appropriate zero crossing of the phase function will be identified as the travel time. The travel time from the center point to the annulus and vice versa will be measured separately. Physically this separation is of waves going outward from the origin or inward to the origin. By taking the difference between these two, the signature of flows can be isolated. The travel times will be inverted to yield the wave speed and flows in the convection zone.This page last reviewed 14 Aug 1995
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