Stochastic Modeling And Identification Of Seismic Records Based On Established Deterministic Formulations

. Stochastic modeling on the basis of established deterministic formulations is stressed and some examples from seismology are presented. Using well‐known deterministic models for a source time function, a single parameter stochastic difference equation (autoregressive model) is derived for seismic records of P‐waves from nuclear explosions and natural earthquakes. A model‐evaluation technique other than statistical goodness‐of‐fit is considered, and its application is illustrated using available data. The interdependency between the characteristic polynomial of the difference equation, its complementary solution (signal), its particular integral (noise) and some physical variables are explained. Variables included in the discussion are duration, intensity and the so‐called corner frequency. Utilizing these dependencies, the signal‐generated character of noise is also illustrated. To fit the model an estimation procedure is described, and its statistical properties are derived. It is shown that the proposed model fits the records of P‐waves from underground nuclear explosions and natural earthquakes as well as the records of Rayleigh waves from atmospheric explosions. Applications of the model to depth‐ and reflection‐parameter estimation and to event discrimination are discussed, and some representative numerical examples are presented.