Selecting optimal displacement models using an improved stochastic model in InSAR arc-based time series analysis

In InSAR time series analysis for displacement studies, the essential parameter estimation part is performed on arcs between a reference point and an evaluation point. Usually, both points are scatterers that satisfy certain optimality conditions. The set of parameters to be estimated in the functional model can be different for each arc. Especially in the built environment, individual points may behave rather differently. Conventional approaches to estimate average displacement velocities for the entire time series length are therefore often sub-optimal. However, deviation from a single uniform parameterization for all arcs implies that for each arc the optimal model needs to be selected. Chang and Hanssen (2016) proposed a method to select the optimal functional model, i.e. parameterization, for each arc using multiple hypothesis testing (MHT). The selection was based on rejecting the conventional null hypothesis of linear steady-state displacement, satisfying Newton’s first law, in favor of an alternative hypothesis that is chosen from a library of canonical models. This procedure required the a priori selection of a significance level (related to the impact of the erroneous rejection of the null hypothesis), the discriminatory power (related to the impact of erroneously sustaining the null hypothesis), and the stochastic model of the arc observations. For the latter, a conservative uniform approximation was chosen. Recently, Brouwer and Hanssen (2023) developed a methodology to approximate the stochastic model for each scatterer in an InSAR time series analysis, based on amplitude behavior. By combining both approaches, i.e., applying the MHT approach for functional model selection using a point- and epoch-specific stochastic model, we significantly reduce both Type-1 and Type-2 errors, leading to the improved identification of dynamic mechanisms in a complex environment. We report on the mathematical background, the level of improvement in practical case studies as well as the numerical consequences of the approach. References: W.S. Brouwer, Y. Wang, F.J. van Leijen, and R.F. Hanssen. ”On the stochastic model for InSAR single arc point scatterer time series.” In IGARSS 2023-2023 IEEE International Geoscience and Remote Sensing Symposium, pp. 7902-7905. IEEE, 2023. L. Chang and R.F. Hanssen, ”A Probabilistic Approach for InSAR Time-Series Postprocessing,” in IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 1, pp. 421-430, Jan. 2016, doi: 10.1109/TGRS.2015.2459037.