Abstract:Seismic activity is a random natural phenomenon. When variables of basic elements of seismic activity are taken as temporal and spatial functions they are found to have basic random field features. This paper discusses the statistical features of energy and frequency fields of seismic activity under certain conditions, in addition to stationary problems found within the seismic activity field. Results show that it is rational to use the random field method to study seismic activity. Through a discussion of the energy distribution of seismic activity and statistical characteristics of the time distribution of earthquakes, the following conclusions are drawn: (1) Seismic activity has random field distribution characteristics and can be seen as a type of random field; therefore, it is possible to conduct quantitative mathematical studies of seismic activity using the random field method. (2) The logarithmic values of energy released by seismic activity obey the distribution law of the exponential function expressed in the paper; however, the distribution laws differ in different regions due to influence of the b value. (3) Under the condition of stationary activity, the temporal distribution of small earthquake activity in a certain region obeys the poisson distribution. (4) In most cases, the statistical characteristics of seismic activity can be basically maintained, as long as the regional stress distribution has not subversively changed, and seismic activity in this region can be considered to be in a stable state.
