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Transformational and distributed volume changes

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 $\Delta V$ 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 $\vec u$ of a seismic source is in general not divergence-free ( $ \nabla \vec u \neq 0$), 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 up previous contents
Next: Definition of source and Up: Draft On the relationship Previous: The problem
Erhard Wielandt
2003-05-30