Multiple-point geostatistics to derive missing surface displacement values of a glacier inferred from dinsar

Glacier displacements play a vital role in the monitoring and understanding of glacier dynamics. Glacier displacement fields are typically retrieved from pre- and post-event SAR images using DInSAR. The glacier displacement map produced by DInSAR contains missing values due to decorrelation of the SAR images. This study demonstrates the utility of direct sampling—a well-established multiple-point geostatistics method—for deriving those missing values. Univariate and bivariate implementations of direct sampling are employed. In the univariate implementation, missing values are derived in single displacement map, whereas in bivariate implementation gaps in two displacement maps are filled simultaneously. Evaluation is carried out by artificially generated missing values on the displacement map of different shapes and sizes at different locations with known values. Imposed missing values are then reconstructed and compared with the original values. Reconstruction results of both implementations were compared with ordinary kriging using qualitative and quantitative measures. The study shows that with an increase in the size of such discontinuities, ordinary kriging predictions deteriorate significantly, whereas only slight decrease in reconstruction accuracy is observed for direct sampling. The results of both implementations are similar with the univariate implementation performing slightly better over bivariate implementation because the information from ancillary data is only partly complementary for bivariate reconstructions. Direct sampling performed better than ordinary kriging with accuracy below the DInSAR detection limit. This study concludes that multiple-point geostatistics is an effective method for deriving missing values in DInSAR derived displacement maps. Direct sampling based reconstruction is fast and straightforward to implement.