Shear Trough Depth and Geometry Relation Determined from Satellite Radar Images from One or Two Orbits

Abstract—The subsidence of the Earth’s surface, calculated from the theoretical model of a shear trough above a longwall developed by pillar and room caving are compared with displacements that can be estimated from trough monitoring using satellite images acquired from a single and two orbits. It is shown that the transverse and longitudinal axes of the trough do not shift when subsidence is calculated using data from descending and ascending orbits together. The maximum subsidence magnitude is determined almost without error. Errors in the reconstruction of the trough geometry appear where there is a significant northern displacement component, which, due to the characteristics of satellite radar imaging, is usually neglected. For the north‒south and west‒east trending troughs, these are their northern and southern boundaries; and for a trough trending from northwest to southeast, these are its northernmost and southernmost corners. In the maps of displacements in the direction towards the satellite (Line-of-Sight displacements, LOS), as well as in the subvertical displacement maps U_subv calculated using images from a single orbit, assuming that horizontal surface displacements are much smaller than vertical ones, the subsiding and uplifting areas are always shifted towards the satellite. Namely, in the displacement maps based on satellite images acquired from ascending and descending orbits these areas are always shifted to the west and east, respectively. The displacement magnitude is 50–60 m. The displacement direction of the longitudinal and transverse axes of the trough in the maps of subvertical displacements U_subv depends on their strike. The displacements of the trough axes relative to their real ground position should be taken into account when estimating the location of a shear trough from the maps U_subv of subvertical displacements derived from images from one orbit. In these maps, the maximum subsidence magnitude is approximately 10% larger than the displacements calculated from the trough model.