Application of SBAS time series for spatial estimation of the time coefficient c in the Budryk–Knothe model

The Budryk–Knothe model is one of the fundamental tools used for predicting surface deformations induced by underground mining. Among the model parameters, the exploitation parameter a, describing the degree of deformation, and the time coefficient c, characterizing the temporal development of deformation, are of particular interest.

Both parameters show a strong dependence on geological and mining conditions, the mining system, and the mechanical properties of the rock mass. In practice, the time coefficient c is determined by fitting the time function to observed subsidence data, whereas the parameter a is derived from final deformations as a proportionality coefficient between the volume of extracted material and the size of surface deformation. Assuming constant values of both parameters throughout the entire mining period does not always allow for accurate representation of the temporal and spatial evolution of deformations, which may lead to reduced forecast accuracy.

The literature indicates that InSAR time series can provide information that is not available in classical measurements, particularly with regard to changes in the rate of subsidence and temporal variations in direct and secondary deformations. This creates the possibility of simultaneous analysis of c and a parameters based on observed displacements.

Despite the growing number of studies using InSAR time series to analyze mining-induced deformation, their application to the formal calibration of parameters c and a in the Budryk–Knothe model remains insufficiently recognized. The aim of this study is to assess whether the use of satellite-based InSAR time series can improve the accuracy and precision of surface deformation forecasts in this model.

We present the results of calculations performed for the Legnica–Głogów Copper Belt (LGOM) area using InSAR time series derived with the SBAS method. Observed vertical displacements were used to estimate local, spatially variable values of the time coefficient c, allowing an assessment of the variability of subsidence dynamics under different geological and mining conditions. The results indicate the potential of InSAR time series as a tool to support the calibration of Budryk–Knothe model parameters and improve the quality of surface deformation forecasts.