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An Inversion Technique for the Determination of Velocity Fields from Spectral Line Profiles

Studies of solar absorption line profiles obtained at high spatial and spectral resolution have usually been content to extract one parameter (the frequency shift in the core of the line) from each profile to describe the velocity field. However, attempts have been made to obtain the variation of velocity with depth in the solar atmosphere either by simultaneous observation of the frequency shift in the cores of several lines with different excitation potentials or by measuring the bisector-shift in a single line profile as described by Kulander and Jefferies (1966). In the first method it is necessary to assign a depth of formation to the core of each line used while in the second method a depth of formation has to be assigned to each point in the line profile. Parnell and Beckers (1969) have discussed the problems involved in assigning a depth on formation and in particular they have shown that when a velocity field is present the concept of depth of formation is dependent of the velocity field. In this contribution we describe a method of determining the velocity field from a single line profile which does not suffer from the problems associated with methods based on the concept of depth of formation.