A modified k-nearest-neighbors method is introduced that provides an efficient nonlinear estimate of the intensity of a point process (field) based on locations of events. The method is applied to perform a detailed statistical analysis of the spatial structure of the seismic intensity field (in the context of this paper, the term “intensity” refers to the intensity of the seismic field, and should not be mistaken for the intensity of ground motion caused by an earthquake). The proposed method requires neither a preliminarily delineated area nor a normalization procedure for the estimates. In contrast to many interpolation methods, estimates based on the proposed method are statistically justified. The “uncertainty relation” between the spatial smoothing effect and random errors is established for the method in an explicit form. A procedure for choosing the number of nearest neighbors k^* that controls the effective radius of smoothing is suggested. The proposed method is applied to analyze the seismic intensity field in two seismogenic regions surrounding the Kuril Islands and Japan during the period from 1904 to 2011. Spots of increased seismic activity in these regions are localized by the new method, and some quantitative statistical characteristics of these spots are determined and discussed.

修改后的k引入了最近邻法，该方法可根据事件的位置对点过程（场）的强度进行有效的非线性估计。该方法用于对地震烈度场的空间结构进行详细的统计分析（在本文中，术语“烈度”是指地震场的强度，不应将其理解为地震烈度的强度）。地震引起的地面运动）。所提出的方法既不需要估计的区域，也不需要归一化程序来进行估计。与许多插值方法相反，基于提出的方法的估计值在统计上是合理的。为该方法以显式形式建立了空间平滑效果和随机误差之间的“不确定性关系”。建议使用k ^*控制平滑的有效半径。将该方法用于分析1904-2011年千岛群岛和日本周边两个地震发生区的地震烈度场。采用新方法对这些地区地震活动增加的地点进行了定位，并给出了一些定量统计特征。这些地点已确定并讨论。