Influencing InSAR Spatial Sampling: Where should Reflectors or Transponders be Deployed?
Mahapatra, Pooja; Hanssen, Ramon

Several studies have shown that applying InSAR to monitor ground deformation in vegetated non-urbanised areas leads to a low spatial persistent scatterer (PS) measurement density. Furthermore, PS are inhomogeneously distributed at unpredictable locations. This makes it difficult to determine a priori, i.e. before acquiring SAR images for at least a year, whether the area in question can be reliably monitored. Algorithmic improvements can extract additional information from resolution cells subject to temporal and geometrical decorrelation (distributed scatterers). However, there may still be areas that heavily decorrelate between SAR acquisitions, such as forests, from which no coherence information can be extracted.

In this work, we determine the required density and locations of deliberately-introduced PS (e.g. passive corner reflectors, low-cost active transponders) in areas where the existing PS network alone is insufficient to adequately capture the ground deformation signal. By doing so, there is also some a priori control over the location of measurements, especially in critical areas. The availability of existing PS can be estimated roughly by inspection of the surface characteristics (e.g. vegetation, degree of urbanization) of the region. Determining if additional PS are necessary, and if so, their optimal positioning in terms of spatial extent, density and relative positioning, is a third-order network design problem, defined as the problem of improving, extending or densifying an existing geodetic network in an optimal way by introducing additional points/observations. As an aside, zero-, first- and second-order problems deal with datum definitions, starting configurations and precision requirements, respectively.

A key requirement for network design is the (implicit) a priori knowledge of the deformation process. This knowledge can be the expected subsidence or uplift characteristics, such as the magnitude of the deformation, its temporal behaviour, spatial gradients, extent and homogeneity. There is also an inherent trade-off between sampling density and cost; the higher the spatial sampling, the better the signal reconstruction, but the higher the investment required in terms of additional hardware. An optimal configuration would require the least number of additional PS of a known measurement precision for the best possible deformation signal reconstruction (up to a certain precision requirement), while taking into account redundancy in case some of the critically-located additional PS are disturbed or fail to operate, or if the deformation signal behaves differently from prior expectation.

We present here a scheme by which a priori knowledge of the expected deformation process is translated into requirements on the density of deliberately-introduced PS, taking into account the existing PS in the region as well as reflector/transponder precision. The density requirements and the existing PS locations are input to a third order network design algorithm that determines the optimal locations for the deliberately-introduced PS. This optimal network configuration would aim to satisfy a preset measurement quality (e.g. precision) with minimum cost. Simulation and real-world examples are shown as applications of this scheme.