Volume Change of Seismic Sources from Moment Tensors
by Gerhard Müller
Abstract
In this note, the estimation of the volume change in the focal region of a seismic event from the isotropic part of the moment tensor is discussed. The moment tensor of a spherically symmetric source (explosion or implosion), as given in an earlier derivation, is supported with new arguments. The moment tensor of an explosion currently in use in studies of non-double-couple earthquakes is not confirmed. It turns out, however, that this moment tensor agrees with the isotropic part of the moment tensor of an arbitrarily shaped crack with tensile dislocation components, which is another realistic model of a source with volume change. If the moment M, representing the isotropic part of an observed moment tensor, is converted into a volume change with the model of a crack, 
Vcr = M/(
+ 2
/3) is obtained (, = Lamé parameters). The explosion or implosion model gives the spherical volume Vsph = M/( + 2), a significantly lower value. It is argued that the two values, which correspond to very different geometrical forms of a volume change (flat 2D versus compact 3D), approximately mark the range of possible volume changes of a seismic event. Earthquakes in volcanic and geothermal areas with significant isotropic moment-tensor parts should be interpreted by giving these limits until their source processes are better understood.