Fuzzy vs probability uncertainty analysis of seismic displacement measurements issued from D-InSAR and SAR image correlation measurements: Application to the Kashmir earthquake (2005)

An emerging way to reduce the geodetic parameter uncertainty is to combine the large numbers of data provided by satellite radar images. However, the measurements by radar images are subjected both to random and epistemic uncertainties. Thus, mathematical theories which 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 epistemic uncertainties, arising from information incompleteness. Fuzzy theory being a generalization of interval mathematics, it 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 epistemic uncertainties of D-InSAR and SAR correlation measurements. The applications are performed on the measurement of displacement field due to the Kashmir earthquake (2005).