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Objectives: The Ripley' s K-function has been widely applied to test for spatial point patterns in many fields such as economic geography, plant geography, and epidemiology. Because of the mathematical confusion of spatial point processes, there are many errors in measuring the distributions of spatial point objects in the corresponding published papers. Methods: This paper discusses Monte Carlo simulation method in the application of Ripley's K-function from perspectives of dynamics of random point patterns, suitability of parameter definition, and reliability of edge correction algorithms. First, we introduce the estimation methods of spatial point pattern analysis based on Ripley's K-function. Second, the formula of Ripley's Kfunction is corrected by various edge effect correction methods and compared in the applications. Finally, the modified algorithm is employed for spatial point pattern analysis of the nutrient concentrations of orange plants in Xinping County, Yunnan Province, China. Results: The preliminary results indicated that the number of Monte Carlo simulations has a great influence on the analysis of the observed spatial point patterns. The significance tests of the observed spatial point patterns change in the process of running ArcGIS Ripley's K-function software package, showing some degree of uncertainty of the observed results. The edge effect correction of Ripley's K-function based on GIS techniques is greatly recommended due to its extension to an arbitrary polygon from a common rectangular shape. Conclusions: Considering the popularity of Monte Carlo simulation in statistics and spatial data analysis, this paper provides important insights on edge correction and significance tests in other spatial clustering methods. [ABSTRACT FROM AUTHOR]

Objectives: The position time series of global navigation satellite system (GNSS) contain rich tectonic and non-tectonic deformation information, and the complex components are difficult to accurately model and effectively separate non-tectonic information. It is very important to remove the non-tectonic de‐ formation information for the accurate and effective application of the observation data. Methods: Empirical mode decomposition （EMD） is an adaptive time-frequency processing method to correct the period term of time series at 24 GNSS continuous stations and 2 mobile stations in Sichuan Province and Yunnan Province. Results: The results show that the correction of the period term is necessary, and the EMD method can ex‐ tract the different frequency and amplitude period components adaptively according to its own characteristics of signal at each station. Compared with the original time series, the average root mean square error after correction is reduced significantly in N, E and U directions. And EMD method is more accurate and effective than harmonic model modification. We use the modified continuous station time series to simulate the mobile observations, and find that relatively reliable motion velocities can be obtained after an observation period of 5 ‐6 years. The stability and reliability of EMD method are verified by correcting the period term of the mobile station with the actual continuous observation station at a close distance. Conclusions: This paper provides a reference and theoretical basis for the implementation of mobile GNSS observation and the correction of observation data. [ABSTRACT FROM AUTHOR]