## 1 Introduction  
Landslides constitute a predominant geological hazard in open-pit mines. Approximately 80% of major disasters documented in the past two decades were attributed to landslides, underscoring the critical need for advanced landslide prediction research [1]. Among diverse landslide prediction methodologies, the inverse velocity method (INV), pioneered by [PERSON] [2], has gained prominence due to its conceptual simplicity and robust applicability in time-prediction scenarios [3, 4, 5]. This method derives predicted failure times by extrapolating the intersection of fitting inverse velocity and time curves during the accelerated creep phase of slopes.  
[PERSON] et al. [6] examined the movement histories of a number of landslides that occurred in a variety of materials in a range of settings and demonstrated that the evaluation of plots of inverse velocity against time for landslides is a useful technique for forecasting movement styles and rates, and for interpreting ongoing deformation processes in real time. [PERSON] et al. [7] conducted comparative case studies to systematically evaluate the INV's advantages and limitations, particularly emphasizing its efficacy in imminent landslide prediction. [PERSON] et al. [8] applied the INV to radar displacement monitoring of open-pit mine slopes and suggested linear time prediction should be performed if a trend update point appears. [PERSON] et al. [9] demonstrated through rheological experiments that INV parameters exhibit remarkable stability under varying loads and moisture conditions. [PERSON] et al. [10] enhanced prediction accuracy by selectively utilizing deformation acceleration data for INV calculations. [PERSON] et al. [11] proposed a method for landslide prediction by combining three parameters--extent of change (EOC), extent of stability (EOS), and extent of mutation (EOM)--with the inverse velocity method, and the effectiveness of the method was verified by the measured data of a landslide in Yunnan Province, China. [PERSON] et al. [12] divided the landslide time uncertainty into observation uncertainty and model uncertainty and constructed a landslide time forecast method based on the principle of probability. [PERSON] et al. [13] developed a dynamic accelerated point identification method using normal distribution confidence intervals, establishing a logarithmic time-prediction model. Recent studies by [PERSON] et al. [14] and [PERSON] et al. [5] systematically investigated filtering algorithms' impacts on INV performance, while [PERSON] et al. [15] conducted a comparative examination of the INV and three other methods on a comprehensive database of 75 historical landslides.  
The above studies all indicate that the INV can obtain relatively accurate prediction results but does not emphasize the spatial position of the point used relative to the landslide body, which means that the displacement velocity data of all points within the landslide body can be considered for landslide time prediction. A key point addressed in this work is improving the accuracy and stability of landslide time prediction through the advanced utilization of displacement velocity measurements obtained from multiple monitoring points. This study proposes a multi-point collaborative inverse velocity landslide time prediction methodology for the case of \(\alpha=2\) using nonlinear least squares, which is based on slope radar multi-point group displacement monitoring data. The effectiveness and robustness of the proposed method are tested by comparing the results with those of single-point prediction and using different numbers of point clusters. It is hoped that this method can provide some reference for landslide time prediction in open-pit mines.