# Accession Number:

## AD0633604

# Title:

## A MATHEMATICAL APPROXIMATION TO THE GEOMAGNETIC FIELD.

# Descriptive Note:

## Master's thesis,

# Corporate Author:

## AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING

# Personal Author(s):

# Report Date:

## 1966-03-01

# Pagination or Media Count:

## 101.0

# Abstract:

An attempt was made to form a mathematical model for calculating the geomagnetic field using fewer terms than presently used in spherical harmonic expansion models. The model was to be made up of pairs of magnetic monopoles. It was found that at least four pairs of monopoles would be needed to produce a satisfactory model. The initial data used for fitting the four pair of monopoles was the geomagnetic field as calculated by a spherical harmonic expansion using the Jensen and Cain coefficients. Emphasis was given to fitting the South Atlantic Anomaly. The root-mean-square error for this region was 1.3 x 10 to the -2 gauss while the overall root-mean-square error was 3.4 x 10 to the -2 gauss. Comparison of the errors of the monopole model with the errors of the Jensen and Cain coefficients indicates that the root-mean-square error for the monopole model is larger than that of the Jensen and Cain coefficients. Additionally, it was found that the monopole model calculations were only 13 faster than the spherical harmonic expansion instead of the desired 12 or more reduction in calculation time. Author

# Descriptors:

# Subject Categories:

- Geomagnetism
- Statistics and Probability