Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea volcano

Abstract

An elastic point source model proposed by Mogi for magma chamber inflation and deflation has been applied to geodetic data collected at many volcanoes. The volume of ground surface uplift or subsidence estimated from this model is closely related to the volume of magma injection into or withdrawal from the reservoir below. The analytical expressions for these volumes are reviewed for a spherical chamber and it is shown that they differ by the factor 2(1-v), where v is Poisson's ratio of the host rock. For the common estimate v=0.25, as used by Mogi and subsequent workers, the uplift volume is 3/2 the injection volume. For highly fractured rocks, v can be even less and the uplift volume can approach twice the injection volume. Unfortunately, there is no single relation between the inflation of magma reservoirs and the dilation or contraction of host rocks. The inflation of sill-like bodies, for instance, generates no overall change in host rock volume. Inflation of dike-like bodies generates contraction such that, in contrast with Mogi's result, the uplift volume is generally less than the injection volume; for v=0.25, the former is only 3/4 of the latter. Estimates of volumes of magma injection or withdrawal are there-fore greatly dependent on the magma reservoir configuration. Ground surface tilt data collected during the 1960 collapse of Kilauea crater, one of the first events interpreted with Mogi's model and one of the largest collapses measured at Kilauea, is not favored by any one of a variety of deformation models. These models, however, predict substantially different volumes of both magma withdrawal and ground surface subsidence.