Magma compressibility and the missing source for some dike intrusions

Dike intrusions are often accompanied by localized deflation, interpreted as depressurizing magma chambers feeding the dike. In some cases the inferred volume decrease is a factor of 4 or 5 less than the volume increase of the dike. Here we explore whether this discrepancy can be explained by compressibility of the magma combined with the fact that cracks are much more compliant than equidimensional magma chambers. If pressure changes are small, the magma compressibility beta(m) is constant, and the dike ends up in hydrostatic equilibrium with an ellipsoidal magma chamber at the same depth, the ratio r(V) of the volume of the crack to the volume lost by the chamber is r(V) = 1 + 4 mu beta(m)/3 > 1, where mu is the host rock rigidity. For gas poor magmas, beta(m) = 0.6-2 center dot 10(-10) Pa-1 and mu = 3-25 GPa, we find 1.2 < r(V) < 7.7. Large changes in magma compressibility due to gas exsolution increase r(V).