The effect of heterogeneity on the relatonship (10) between the source volume and the seismic displacement field is hard to predict. If there are cavities in the medium they might be expected to absorb some of the expansion of the source, but if they are more or less evenly distributed they would simply reduce the effective stiffness of the medium, and not affect the displacement vs. volume relationship. Unless there are specific reasons to assume that the material around the source is being compressed or dilated, eq. 10 seems to remain useful as a first guess for the near-field.
Heterogeneity has a marked effect on the tilt because of local strain-tilt coupling, as discussed in Wielandt & Forbriger (1999). Locally measured tilts may not represent the regional tilt at all. The latter can however be calculated from the differential vertical displacement between two broadband seismometers installed at a mutual distance in the order of 100 m.
The effect of topography on the displacements in a Mogi-type model has been investigated by Kirchdörfer (1999) with FE computations, using a conical model for the volcano. His results can be summarized as follows: