Ergodicity of stationary white Gaussian processes

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2091-2092
Author(s):  
Santi K. Ghosh
Keyword(s):  
Time Series ◽  
Signal Processing ◽  
Decomposition Theorem ◽  
Seismic Signal ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Predictive Deconvolution ◽  
Minimum Delay ◽  
Seismic Signal Processing ◽  
Noise Models

Stationary time series is an important concept in seismic signal processing. According to Robinson (1967), the method of predictive deconvolution is the minimum‐delay interpretation of the decomposition theorem of Wold (1938) for stationary time series. Stationary noise models have found use in geophysics as well (Robinson and Treitel, 1980).

scholarly journals On prediction and filtering problem of long-run stationary time series

2016 ◽  
Vol 8 (3) ◽  
pp. 8-18
Author(s):  
Phan Dang Cau
Keyword(s):  
Time Series ◽  
Wiener Filter ◽  
Seismic Signal ◽  
Stationary Time Series ◽  
Usual Sense ◽  
Seismic Signals ◽  
Stationary Time ◽  
The Earth ◽  
Long Run ◽  
Filtering Problem

Suppose by the  irregularity of the reflectivity of the earth a seismic signal is not always stationary in usual sense, but only long-run stationary (see [6,7]). Then  there arises a question: ‘why is wiener filter, which is  as well known is used in prediction and filtering of ergodic stationary time series, also applicable in processing seismic signals? In this paper we try to give answer to this question.

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