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Prolate sources

For a LVD (linear vector dipole) type source that is prolate in the direction of the forces, most of the moment is required to deform the outer medium, and only a small fraction remains to expand the source itself. The medium counteracts the lengthwise expansion of a thin and long body very strongly. The ratio between the moment and the volume change of the source can be arbitrarily large, as is apparent from the following model: Two colinear forces of opposite direction act at some finite distance d from each other. To avoid singularities of the displacement field, we distribute each force over a small sphere with a radius $r \ll d$. The source volume is defined as comprising the two spheres and a narrow tube connecting them. Obviously, the volume change within the source can be made arbitrarily small. Most of the volume change occurs outside the source. Thus, the ratio of moment to source-volume change can be arbitrarily large.

Erhard Wielandt