Calibration of a Land Subsidence Model Using InSAR Data via the Ensemble Kalman Filter

Abstract

The application of interferometric synthetic aperture radar (InSAR) has been increasingly used to improve capabilities to model land subsidence in hydrogeologic studies. A number of investigations over the last decade show how spatially detailed time-lapse images of ground displacements could be utilized to advance our understanding for better predictions. In this work, we use simulated land subsidences as observed measurements, mimicking InSAR data to inversely infer inelastic specific storage in a stochastic framework. The inelastic specific storage is assumed as a random variable and modeled using a geostatistical method such that the detailed variations in space could be represented and also that the uncertainties of both characterization of specific storage and prediction of land subsidence can be assessed. The ensemble Kalman filter (EnKF), a real-time data assimilation algorithm, is used to inversely calibrate a land subsidence model by matching simulated subsidences with InSAR data. The performance of the EnKF is demonstrated in a synthetic example in which simulated surface deformations using a reference field are assumed as InSAR data for inverse modeling. The results indicate: (1) the EnKF can be used successfully to calibrate a land subsidence model with InSAR data; the estimation of inelastic specific storage is improved, and uncertainty of prediction is reduced, when all the data are accounted for; and (2) if the same ensemble is used to estimate Kalman gain, the analysis errors could cause filter divergence; thus, it is essential to include localization in the EnKF for InSAR data assimilation.