Analytical model test of methods to find the geometry and velocity of magnetic structures

Abstract

It is important to determine the dimensionality and velocity information in the study of spatial magnetic structures. Many data analysis theories/techniques are based on the assumption of one or two dimensions. For example, the Grad-Shafranov (GS) reconstruction method assumes a dimensionality of two or less. The Minimum Direction Derivative (MDD) method provides an indication of the dimensionality. For the structure velocity, the components in each dimensionality can be calculated by Spatio-Temporal Difference analysis (STD). In order to improve the convenience of use of MDD method, a new parameter D m quantifying the dimensionality based on MDD eigenvalues is introduced in this paper. The influences of noise /turbulence, separation distance and tetrahedron configuration on MDD and the evaluation of D m are systematically tested using two analytical models for magnetic structures, representing a magnetic mirror and magnetic flux rope. We tested and gave the threshold values of three quality indicators for MDD results using the flux rope model. We also show that the error induced by turbulence is comparable to that of random noise when the turbulence scales are less than the spacecraft separation. Besides, the accuracy of STD velocity estimation will also be influenced by turbulence for cases with excessively high data time resolution. By using D m, we show that an ideal model of a mirror-like structure can be divided into one dimension (1-D) and three dimension (3-D) regions. This restricts the applicability of the GS method in mirror-like structures. For example, in a given reconstruction range, the GS error increased from less than 7% to more than 15% by using the data along trajectories in 1-D and 3-D regions as predicated by D m. Thus, it is important to estimate the structure dimensionality, which can be further used to estimate the reliability of the GS reconstruction map.