Local interpolation of coseismic displacements measured by InSAR

Coseismic displacements play a significant role in characterizing earthquake causative faults and understanding earthquake dynamics. They are typically measured from InSAR using pre- and post-earthquake images. The displacement map produced by InSAR may contain missing coseismic values due to the decorrelation of ASAR images. This study focused on interpolating missing values in the coseismic displacement map of the 2003 Bam earthquake using geostatistics with the aim of running a slip distribution model. The gaps were grouped into 23 patches. Variograms of the patches showed that the displacement data were spatially correlated. The variogram prepared for ordinary kriging (OK) indicated the presence of a trend and thus justified the use of universal kriging (UK). Accuracy assessment was performed in 3 ways. First, 11 patches of equal size and with an equal number of missing values generated artificially, were kriged and validated. Second, the four selected patches results were validated after shifting them to new locations without missing values and comparing them with the observed values. Finally, cross validation was performed for both types of patch at the original and shifted locations. UK results were better than OK in terms of kriging variance, mean error (ME) and root mean square error (RMSE). For both OK and UK, only 4 out of 23 patches (1, 5, 11 and 21) showed ME and RMSE values that were substantially larger than for the other patches. The accuracy assessment results were found to be satisfactory with ME and RMSE values close to zero. InSAR data inversion demonstrated the usefulness of interpolation of the missing coseismic values by improving a slip distribution model. It is therefore concluded that kriging serves as an effective tool for interpolating the missing values on a coseismic displacement map.