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For a given isotropic moment M, we can easily construct a mathematical
source model with any desired positive or negative volume change. We
simply let a linear vector dipole (LVD) with the moment 3M act in a
small sphere, either in its center or evenly distributed. (If the isotropic
moment equals zero, we may use a suitable scaled CLVD  a compensated
linear vector dipole  instead.) The displacement field outside the
source sphere has the divergence

(6) 
The volume integral of this divergence is zero over any spherical
shell enclosing the source, but since the divergence decays
as r^{3} in any given direction from the source, the integral
diverges to plus or minus infinity if taken over a suitable cone
in the polar or equatorial direction.
Our definition of the source permits to consider any part of
such a cone as part of the source. We can thus define the
boundary of the source
in such a way that its total volume change has any desired value.
Next: Acknowledgment
Up: Draft On the relationship
Previous: Source volume and moment
Erhard Wielandt
20030530