Fusion of D-InSAR and sub-pixel image correlation measurements for coseismic displacement field estimation: Application to the Kashmir earthquake (2005)

In geophysics, the uncertainty associated with model parameters or displacement measurements plays a crucial role in the understanding of geophysical phenomenon. An emerging way to reduce the geodetic parameter uncertainty is to combine a large number of data provided by SAR images. However, the measurements by radar imagery are subject to both random and epistemic uncertainties. Probability theory is known as the appropriate theory for random uncertainty, but questionable for epistemic uncertainty. Fuzzy theory is more adapted to epistemic uncertainty. Moreover, in a context of random and epistemic uncertainties, the conventional joint inversion in the least squares sense cannot be considered any more as the best scheme to reduce uncertainty. Therefore, in this article, in addition to joint inversion, two other fusion schemes, pre-fusion and post-fusion, are proposed. We consider here the conventional approach and an original fuzzy approach for handling random and epistemic uncertainties of D-InSAR and sub-pixel image correlation measurements. Joint inversion and pre-fusion are then applied to the measurement of displacement field due to the 2005 Kashmir earthquake by fusion of these data. The behaviours of these two fusion schemes versus uncertainty reduction are highlighted through comparisons of results.