A P waves’ automatic picking by detecting the changes of seismic signals’ stationary random process through similarity analysis

2018 ◽  
Vol 115 ◽  
pp. 225-231 ◽  
Author(s):  
Xu Wang ◽  
Jihua Fu ◽  
Chengpei Tang ◽  
Zhitao Li ◽  
Jianjun Wang
Keyword(s):  
Random Process ◽  
Stationary Random Process ◽  
Similarity Analysis ◽  
Seismic Signals ◽  
P Waves ◽  
Automatic Picking

Induced transformations of recurrent a.m.s. dynamical systems

2015 ◽  
Vol 15 (02) ◽  
pp. 1550010
Author(s):  
Sheng Huang ◽  
Mikael Skoglund
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Random Process ◽  
Ergodic Theorem ◽  
Finite Measure ◽  
Stationary Random Process ◽  
Finite State ◽  
Ratio Ergodic Theorem

This note proves that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon–McMillan–Breiman theorem, as well as the Shannon–McMillan theorem, holds for all reduced processes of any finite-state recurrent asymptotically mean stationary random process. As a by-product, a ratio ergodic theorem for asymptotically mean stationary dynamical systems is presented.

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