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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. [ABSTRACT FROM AUTHOR]

The evolution of seismo-ionospheric disturbances accompanied strong destructive earthquakes in the region of Kuril and Japan Islands on October 4, 1994, September 25, 2003, and November 15, 2006 is studied in the paper. For determination of the dynamics of spatial-temporal and amplitude parameters of disturbances in the total electron content (TEC) on the basis of the Japan network of receiving GPS stations GEONET and Korean network KGN, the method of drawing 'distance-time' diagrams and quasi-optimal algorithm of spatial-temporal processing of the GPS network data was used. The ionospheric response was detected at a distance D from the epicenter up 2500 km. The maximal value of the disturbance amplitude is observed at D = 400-600 km. For the September 25, 2003 and November 15, 2006 earthquakes, the velocity V of propagation of the dominant disturbance mode is independent of the distance and equal to 850 and 1100 m/s, respectively. At a distance D ∼ 600 km, the wave disturbance from the main shock of the October 4, 1994 earthquake is split into two modes: the velocity of the 'fast mode' of the disturbance increases with distance from 1500 to 2400 m/s, while the velocity of the 'slow mode' V = 600 m/s does not depend on D. Possible interpretation of the obtained results is given. [ABSTRACT FROM AUTHOR]