Sequential data assimilation strategies for utilizing ground deformation data to assess rapidly evolving magma reservoirs

Abstract:

Classic inversion and joint inversion schemes for analyzing ground deformation data are limited in their ability to provide model forecasts and track the temporal dynamics of a volcano experiencing unrest. Sequential data assimilation techniques, such as the Ensemble Kalman Filter (EnKF; Evensen, 1994), estimate the instantaneous state of a dynamic system in a time-forward fashion by updating the model of a system whenever observations become available. The EnKF method uses a Markov Chain Monte Carlo approach to estimate the covariance matrix in the Kalman filter and also tracks model parameters concurrently at a fraction of the computational cost of the Kalman filter (Kalman, 1960) and Extended Kalman Filter (Schmidt, 1966). In this investigation, we build upon Gregg and Pettijohn (2015) to test the performance of the EnKF for assimilating multiple, disparate ground deformation datasets (InSAR, GPS, leveling, and EDM) to provide model forecasts of a volcano exhibiting rapid variations in surface deformation. Specifically, the EnKF is applied to a hypothetical volcano experiencing both inflation and deflation to determine how quickly the EnKF is able to respond to changes in the magma chamber source given a particular set of surface observations. Of interest is how the EnKF responds to limitations imposed by the spatial and temporal resolution of the observations as well as data uncertainties. A series of synthetic tests is run to compare EnKF functionality with individual and multiple dataset assimilation. As the EnKF is model-independent, we test the performance of the EnKF with both time-forward viscoelastic finite element models as well as classic elastic analytical models.

References:

Evensen, G. (1994), Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, JGR, doi:10.1029/94jc00572.

Gregg, P. M., and Pettijohn, J. C. (2015), A multi-data stream assimilation framework for the assessment of volcanic unrest, JVGR in Review.

Kalman, R. E. (1960), A new approach to linear filtering and prediction problems, J. Basic Eng., 82(1), 35-45.

Schmidt, S. F. (1966), Application of State-Space Methods to Navigation Problems, Advances in Control Systems, doi:10.1016/B978-1-4831-6716-9.50011-4.