Helioseismic Ring Analyses of Artificial Data Computed for Two‐dimensional Shearing Flows

Abstract

The local helioseismological technique of ring analysis has been crucial in the discovery of complex large-scale flows in the Sun's near-surface shear layer. However, current implementations of ring-analysis procedures assume that the flow field is horizontally homogeneous over the analysis region. This assumption is certainly incorrect, and in the present paper we assess the significance of this approximation by analyzing artificial data sets computed from models of horizontal shear flows. We consider the simple case of purely horizontal and unidirectional flow that varies solely in the horizontal direction orthogonal to the flow in a piecewise-constant manner. An ensemble of plane waves is incident on the flow, and the scattered wave field produced by the prescribed two-dimensional flow is computed to generate an artificial helioseismic power spectrum. The artificial spectrum is processed in a manner similar to standard ring analysis, and the flow field that is thereby inferred is compared with the known imposed flow. We find that the inferred flow velocity is essentially an average of the true flow velocity over the region of the analysis, weighted by the square of the spatial apodization function used in processing the oscillation signal. Furthermore, the shape of a p-mode line profile is determined by the distribution of speeds across the analysis region.