6th COSPAR Capacity Building Workshop, Sinaia, 4-16 June 2007

Basic Analysis Techniques and Multi-Spacecraft Data
Computer Session

Joachim Vogt


The computer session on Basic Analysis Techniques and Multi-Spacecraft Data is supposed to provide an introduction to the computer environment at Hotel Cota 1400 using some selected data analysis tools. The session will take advantage of the IDL installation on the workshop Linux PCs (note that special knowledge of Linux is not required to work on the assignments). Depending on your experience with IDL and your prior knowledge in data analysis you should make your choice among the following information sheets which contain instructions and worked examples.

Getting started with IDL

If so far you have not yet had experience with IDL, you are encouraged to go through the instructions on this sheet to become acquainted with key language elements and the syntax of IDL. The sheet provides a quick start and will help you to understand more complex IDL programs presented later.

For further information and instructions, see sheet 1.

Probability density estimation using the kernel method

There is more to the estimation of probability density functions (p.d.f.'s) than the histogram technique. The second information sheets guides you through a worked example using the so-called kernel method. The method not only produces smooth p.d.f. estimates but is also independent of the chosen origin of the bin array.

For further information and instructions, see sheet 2.

Multipoint gradient estimation in model magnetic fields

The estimation of spatial derivatives (curl, divergence, gradient) is a key issue in Cluster data analysis. Here you make use of the reciprocal vector method to estimate the spatial derivative matrix along simplified spacecraft orbits in given model magnetic fields. The inter-spacecraft distance can be varied as well as the magnetic field model and the imposed noise level. Since this exercise is meant to help assessing the imperfections of the gradient estimation method, the model magnetic fields are chosen to be curl-free (and, of course, divergence-free).

For further information and instructions, see sheet 3.

Multipoint gradient estimation in measured magnetic fields

The reciprocal vector method is applied to estimate electrical currents using FGM measurements of the Cluster-II spacecraft. We look at cases previously analysed by Dunlop et al. using a slightly different but equivalent method (the so-called curlometer technique).

For further information and instructions, see sheet 4.

Magnetospheric boundary analysis

Fundamental (single-spacecraft) boundary analysis techniques based on the minimum variance principle are addressed in a small programming exercise. The AMPTE/IRM data set used in chapter 8 (by B. Sonnerup and M. Scheible) of the ISSI Cluster data analysis book should serve as a reference case. Since IDL provides a number of modules like EIGENQL, PCOMP, or the family of SVD routines that can be used for an eigenvector analysis of the (co)variance matrix, the actual programming effort can be kept small.

A genuine multi-spacecraft approach to boundary analysis takes the crossing times and locations to estimate boundary parameters such as the boundary normal vector and the boundary velocity (in the spacecraft frame of reference).

For further information and instructions, see sheet 5.


Last modified: Tue May 29 12:33:39 CEST 2007