Anisotropic kriging to derive missing coseismic displacement values obtained from synthetic aperture radar images

Coseismic displacements play a vital role in the characterization of geological faults and understanding earthquake dynamics. We demonstrate the utility of anisotropic geostatistics to interpolate their missing values. These were due to noncoherence of pre- and post-earthquake advanced synthetic aperture radar images obtained from the earthquake affected area around the city of Bam in Iran. A spherical function was used for modeling the variograms. Directional variograms revealed geometric and zonal anisotropy. The geometric anisotropy was reduced to isotropy by applying a linear transformation of the coordinates, whereas the complexity of zonal anisotropy is discussed. Results from the geometric anisotropy model indicated a continuation of the geological fault towards the north underneath the city of Bam. Cross-validation gave a mean error close to zero, whereas the root mean square error value was approximately 0.1 m, well below the detection limit of pixel-tracking technique. We conclude that ordinary kriging using a variogram model corrected for geometric anisotropy produced more accurate interpolation results than an isotropic model.