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Time-Distance Detailed Specifications

Team Coordinator: Tom Duvall

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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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