A comparison of methods for propagating surface deformation uncertainties in model parameters

Two commonly utilized methods for propagating uncertainties in model parameters of surface deformation caused by underground mining are compared in this study. These methods enable estimation of standard uncertainties in indicators of surface deformation, specifically: subsidence, tilt, and horizontal strain, to be calculated. The first method is the law of propagation of uncertainty (LPU), based on a first-order Taylor series expansion without the use of higher-order derivatives. The second method is the Monte Carlo (MC) method. It relies on the calculation of many values of deformation indicator for random values of model parameters. It is noteworthy that in the previous research in this field no comparison of these methods was carried out. The calculations performed in this study based on both methods allow the verification of results and the features of both approaches to be compared. Calculations were performed applying the Knothe model, which assumes a normal distribution for the influence function. Both average values and model parameter uncertainties derived from hard coal mining across the entire Upper Silesian Coal Basin (USCB) region of Poland were used in this study. Model parameter uncertainties are high in this case, which is unfavorable for LPU, but results do indicate that this approach can be useful for propagating model parameter uncertainties for the surface deformation caused by underground mining. Keywords: Monte Carlo simulation Uncertainty propagation Mining deformation Indicators