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A hint to the origin of the discrepancy is found in Aki and Richard's
textbook (1980), section 3.4, where eq. (2) is derived with the
specification that
is the ``transformational'', i.e.
hypothetical
isobaric, volume change. Actually the material in the source does
not experience isobaric conditions because it must displace the
surrounding medium, which counteracts with additional forces and
moments. The transformational and the actual change of volume are
in general different. This has apparently escaped some readers of
the textbook. The two volumes coincide only for cracks, as we
shall see in a moment.
Another complication is that the displacement field
of a seismic
source is in general not divergence-free (
),
so the volume
change depends on where we measure it. As the interface between
the "source" and the "medium" is to some extent arbitrary, so is
the volume change.

Being cautioned against these two pitfalls, we can now proceed
to a quantitative discussion of some simple sources. **We consider
only the permanent displacement field associated with the final
value of the moment tensor, and only homogeneous and isotropic media.**

** Next:** Definition of source and
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*Erhard Wielandt *

2003-05-30