Some Research Issues in Remote Sensing of Solid Earth

We show that a large optical geostationary telescope would be a breakthrough instrument to measure geophysical deformations of surfaces, including seismic waves. Techniques include motion detection and photoclinometry of transient topography. The design of such an instrument depends mainly on the photometric budget of the scenes at 1Hz and beyond. Application to simulated seisms in California shows that the space seismometer would recover most of the detailed pattern of ground motion, including the Mac cone characteristic of debated supershear earthquakes. 3D (x,y,t) complex path integral on a graph (phase unwrapping) is a key issue in differential SAR interferometry. Phase unwrapping allows to estimate the spatio-temporal evolution of the deformation from a pile of radar images. We suggest that, because of the noise and the plethora of data, the fundamental hypothesis according to which the interferograms are well sample is statistically incorrect. Undersampling yields limitation in the use of Cauchy's Integral Theorem. Statistical approaches using random walk are suggested. Imagery of tectonics and of ground deformation in shallow coastal water seems to become of interest in the tectonic group at IPGP. We discuss the potential of available satellite images (e.g. MERIS onboard ENVISAT) for a monitoring of deformation on the basis of results derived from Hyperspectral imagery of the Sumatran mega-earthquake. The probability p that an image derived from a distribution of colored pixels is a natural scene is difficult to estimate because of combinatoric explosion. While some authors investigate second order correlation procedures to estimate the entropy of natural scenes in this context, we rather propose a procedure to reduce the dimensionality using closed collars of colored pixels. A preliminary estimate of p derived from a set of hyperspectral images is discussed.