Fuzzy Uncertainty Representations of Coseismic Displacement Measurements Issued From SAR Imagery

An emerging way to reduce the geodetic parameter uncertainty is to combine the large numbers of data provided by satellite synthetic aperture radar (SAR) images. However, the measurements by radar imagery are subject to both random and systematic uncertainties. Thus, mathematical theories that are adequate for each type of uncertainty representation and handling have to be selected. Probability theory is known as the adequate theory for uncertainties corresponding to random variables, but questionable for systematic uncertainties, arising from information incompleteness. Fuzzy theory, being a generalization of interval mathematics, is more adapted to such uncertainty. Moreover, it provides a bridge with probability theory by its ability to represent a family of probability distributions. Therefore, we consider here the conventional probability and the fuzzy approaches for handling the random and systematic uncertainties of displacement measurements derived from differential SAR interferometry (D-InSAR) and SAR amplitude image correlation. The applications are performed on the measurement of the displacement field due to the 2005 Kashmir earthquake. The fuzzy approach, being free from distribution and independence hypotheses, gives the most pessimistic uncertainty assessment, while the conventional probability approach gives the most optimistic uncertainty assessment. As confirmed by the Monte Carlo simulation applied to an earth deformation model, the actual uncertainty should be situated between the fuzzy and conventional uncertainties.