A new framework for simultaneous inversions of deformation and gravity data applied to the 1982-1999 inflation at the Long Valley caldera

The location and volume change of pressurized magma chambers can be constrained by inverse modelling of the surface displacements they cause. Through a joint inversion of surface displacements and gravity changes the chamber mass change during the pressurization period can also be inferred. Such inversions often start with constraining the deformation source parameters using the deformation data alone (step 1). Using these parameters the gravity data are then corrected for the effect of mass redistribution in the host rocks and surface uplift/subsidence associated with the chamber expansion (step 2). Next, the corrected gravity changes together with the source location from the deformation inversion are used to infer the intrusion mass (step 3). Provided that the intrusion compressibility is known, the intrusion density can be estimated from the intrusion mass and source volume change from step 1 and step 3, respectively (step 4).

We show that the original gravity data (only corrected for ambient effects) are directly related to the deformation source parameters through the deformation-induced gravity changes and the free-air effect. Thus, both of these effects, which have been mostly considered as nuisance, in fact can be harvested to provide better constraints on the deformation source parameters and the mass changes. We propose a Bayesian framework for the joint inversion of deformation and gravity data by which all the deformation source parameters and chamber mass change are constrained simultaneously. This way, steps 1 to 3 of the previous approach are carried out at once. The advantages of the suggested approach are: (a) this way the gravity data help constrain deformation source parameters with smaller uncertainties, (b) it leads to a smaller uncertainty for the inferred mass change, (c) the optimal relative weights of various deformation and gravity datasets can be estimated as hyper-parameters within the Bayesian inference, thus, they are estimated directly and in an objective way, (c) the gravity and deformation stations need not be co-located, (d) errors associated with interpolation of vertical displacements at gravity benchmarks are avoided, (e) the uncertainty of vertical displacements is no longer propagated into the reduced gravity changes, and thus, mass changes are estimated more accurately.  

We apply this approach to the deformation and gravity data associated with the 1982-1999 inflation period at Long Valley caldera. The results agree with those from earlier efforts; however, show a clear improvement in the constrained source parameters and the intrusion mass. We discuss the implications and benefits of this approach depending on the relative quality of the deformation and gravity data.