On the accuracy of the vertical and eastern components of the Earth’s surface displacements calculated from SAR images obtained from two orbits

Satellite synthetic aperture radar (SAR) images make it possible to determine the change in the distance from the satellite to the reflecting object on the Earth’s surface over the time period between repeated imaging, i.e. determine the displacement of individual reflectors on the Earth’s surface or infrastructure in the direction to the satellite. Since the incidence angle of the radar emission for various satellites ranges from 30 to 50 degrees from the vertical, these displacements are the sum of the three components of the reflecting object displacement in the vertical, northern and eastern directions, multiplied by the sines and cosines of the sounding beam incidence angle and the azimuth of the satellite orbit. Because the satellite orbit is close to the polar one, the northern displacements are summed up with a coefficient significantly smaller than the vertical and eastern components. If it can be assumed that northern displacements do not exceed displacements in the other directions, then the contribution of the northern component can be neglected. Then, calculating displacement fields using images from the descending and ascending orbits, one can calculate the displacements along the vertical and to the east. If it can be assumed that the horizontal displacements do not exceed the vertical ones, then, neglecting both horizontal components, one can estimate the subvertical displacements using images from one orbit by dividing the displacements toward the satellite by the cosine of the incidence angle. Such assessments are often made when monitoring various natural and technogenic objects. The paper assesses the accuracy of such estimates on a theoretical model of an underground gas storage (UGS) facility. To solve the problem, we used a three-dimensional UGS model close to one of the underground storage facilities, for which we had previously performed calculations based on real data. Using the data on the boundary of the UGS facilities, the depth and thickness of the reservoir, we set a theoretical pressure change close to the real one during the period of gas withdrawal. This made it possible to calculate the synthetic fields of displacements on the Earth’s surface in vertical, northern and eastern directions, as well as displacements toward the satellite for imaging from ascending and descending orbits, using the real incidence angles of the satellite signal and azimuth of the orbits. After that, the subvertical displacements were calculated, assuming that the horizontal displacements are small. Then, using both the ascending and descending orbits, the vertical and eastern components were calculated, assuming that the northern displacements can be neglected. The amplitude of subvertical displacements is determined with good accuracy, but the regions of “uplift” and “subsidence” on line-of-sight displacement map turn out to be shifted towards the satellite. The errors in calculating the vertical and eastern displacements based on data from two orbits do not exceed a few percent. Therefore, the calculations of displacements based on data from two orbits should not lead to significant errors in estimating the vertical and eastern components of the displacement vector in real situations, at least for UGS’s and oil and gas fields.