Adaptive local kriging to retrieve slant-range surface motion maps of the Wenchuan earthquake

Abstract

Kriging is a widely used technique for raster data interpolation from point samples, such as in the generation of digital elevation models and geochemical maps. The quality of the result depends on both spatial distribution of the sampled values and nature of the semivariogram model, which fits an empirical global function to the sample data set to predict values at the unknown locations. However, such a semivariogram model may not be suitable for data sets with complex local trends in spatial distribution, such as those observed in differential interferometric synthetic aperture radar (DInSAR) data of the Wenchuan earthquake. Here we propose a modified kriging method, adaptive local kriging (ALK), for the retrieval of data lost through decoherence in Advanced Land Observing Satellite (ALOS) phased array L-band synthetic aperture radar (PALSAR) DInSAR data, within the intensely deformed fault zone of the 2008 Wenchuan earthquake. In ALK, a series of dynamic linear local semivariogram models is used rather than a global semivariogram for the whole data set. The localized adaptive approach ensures accurate interpolation in the areas of good DInSAR data with small decoherence gaps and avoids drastic errors in the extensive decoherence gaps; the overall value prediction is thus significantly improved, as confirmed by comparison with the original DInSAR data and fidelity verification experiments.