Formal Quantification of Spatially Differential Characteristics of PSI-Derived Vertical Surface Deformation Using Regular Triangle Network: A Case Study of Shixi in the Northwest Xuzhou Coalfield

This study addresses the challenge of quantifying spatially differential vertical surface deformation (SDVSD). Traditional approaches using persistent scatterer interferometry (PSI) data often focus on bulk vertical surface deformation (VSD) but overlook directional variability and struggle with irregularly distributed persistent scatterer (PS) points, limiting comprehensive SDVSD analysis. This study proposes a regular triangle network (RTN)-based framework that tessellates the study area into uniform triangular units, enabling the systematic quantification of the SDVSD direction, magnitude and rate while mitigating spatial biases from uneven PS distributions. Applied to the Shixi area in China’s Northwest Xuzhou Coalfield, the RTN-based framework revealed that (1) the SDVSD directionality aligned with the coal strata dip and working face distribution, contrasting with VSD’s focus on the magnitude and rate alone; (2) SDVSD exhibited seasonal rate fluctuations suggesting environmental influences, and, unlike VSD, it has a non-additivity property in temporal evolution; (3) there was spatial divergence between SDVSD and VSD, i.e., high VSD rates did not necessarily correlate with high SDVSD rates, emphasizing the need for an independent spatial gradient analysis. This study demonstrates that the RTN-based framework effectively disentangles the directional and magnitude (rate) components of SDVSD, offering a robust tool for the identification of deformation hotspots and linking surface dynamics to subsurface processes. By formalizing the quantification of PSI-derived SDVSD, this study advances InSAR deformation monitoring, providing actionable insights for infrastructure risk mitigation and sustainable land management in mining regions and beyond.