Abstract: The change of landslide displacement in Zhongxian area of the Three Gorges reservoir area shows step deformation characteristics. Because rainfall as the main influencing factor, the high energy frequency point of amplitude is obtained by fast Fourier transform, and a Fourier series fitting function based on high energy frequency is proposed by using the fast Fourier transform method of signal processing. The monthly rainfall in the Zhongxian region of the Three Gorges Reservoir area is fitted, and the fitting model of high correlation and acceptable mean square error is obtained. In the research area with similar geological model and landslide mechanism, the influence of landslide inclination on horizontal displacement is greater. By defining the influence weight of landslide inclination angle, the total weight displacement in the study area is calculated, which can better reflect the effect of the dip angle. By setting the rainfall Fourier series fitting function as the rainfall factor term, and the step function as the step factor term, the least square method is used to fit the step process of the three-stage deformation in the study area, a mathematical statistical model consisting of a combination of rainfall impact control and rainfall items is obtained. The method is applied to the 11-month monthly monitoring data of 9 step deformation landslides in the Zhongxian area of the Three Gorges reservoir area, which shows that the fitting accuracy obtained by the method is better, the correlation is higher, the mean square error is smaller, and it can accurately reflect the step deformation characteristics of horizontal displacement in this region at different time and different deformation stages. This method can be used as a new idea for regional landslide spatial prediction.

Key words: fast fourier transform, high energy frequency point, step deformation, rainfall and horizontal displacement, mathematical statistical model