This is a collection of simple formulae describing the seismic signal from expansive or explosive spherical sources. Such sources can be characterized by the volume of displaced material, either as a function of time or as a final value. We call this the source volume. It is in general different from the total volume occupied by the source, which may depend on an arbitrarily defined interface between the source and the medium. Only changes of this volume are relevant in the present context.
A source that is defined by the time history of its volume changes will be called a volume source. It does not constitute a complete physical model for the generation of seismic signals in volcanoes since the cause of the volume changes remains unspecified. However, very simple relationships exist between the source volume and the seismic wavefield. The source volume can therefore directly be determined from seismic observations, and can serve as a constraint to any physical theory of the source itself.
Another interesting parameter of explosive sources is the total force that acts on real or virtual plane interfaces through or near the source. Simple formulae connecting the source volume, the force, and the seismic signal will also be given.
The ``radial'' direction is always understood as radial in space, outward from the source. In models with a free surface, the z axis points vertically downward from the source.