Magma-chamber volume changes associated with ring-fault initiation using a finite-sphere model: Application to the Aira caldera, Japan

We have derived an analytical solution expressing the magma-chamber volume change required for ring-fault (caldera) initiation in terms of a finite-sphere model. We consider the conditions by which magma-chamber contraction - volume reduction - could contribute to the initiation of a ring fault at the surface above the chamber, using the elastic-plastic theory of host-rock behaviour. The model does not consider “underpressure” (pressure less than lithostatic) in the chamber but only magma-chamber volume reduction or shrinkage. The model is heuristic in the sense that we do not explore the detailed mechanical condition for the volume reduction, apart from its being related to magma flow out of the chamber, but rather focus on the consequences of the reduction for ring-fault initiation and dip. The solution obtained for the finite-sphere model consists of a leading term that is proportional to the cube of the magma chamber depth and a second term that is proportional to the cube of the magma chamber radius. The second term reflects explicitly the effects of a finite source radius, whereas the first term corresponds to a solution for a point-source model. This follows because in a point-source model the magma chamber radius is zero so that the second term drops out. The equation that plays the key role in obtaining this solution is a linear function relating the radius of the caldera to the magma chamber depth. The proportionality coefficient of this equation is dimensionless and depends not only on the elastic constants of the medium but also on the depth (d) and radius (a) of the magma chamber, given by ε = a/d. In addition, because this coefficient controls a geometric parameter related to the overall form of the ring fault, our results indicate that the ring-fault shape and size is decided by the magma chamber depth and size, as well as by the host-rock elastic properties and angle of internal friction. The results indicate that the associated ring-fault is inward dipping and that the magma chamber radius can be estimated from the fault radius and dip. We applied the analytical solution to the ring-fault of the Aira caldera in southern Kyushu, Japan. The calculations indicate that the Aira ring-fault could have been initiated at the surface as a result of 2.8% reduction in the volume of a magma chamber with a radius of 4.7 km and at a depth of 9.1 km. These results agree with independent information on the Aira magma chamber. We conclude that the present solution yields useful first-order information on magma chambers associated with ring faults.