Equivalence of AR-representations in the light of the impulsive-smooth behaviour

2007 ◽  
Vol 17 (8) ◽  
pp. 769-785 ◽  
Author(s):  
A. C. Pugh ◽  
E. N. Antoniou ◽  
N. P. Karampetakis
Keyword(s):  
Ar Representations

scholarly journals Robust AR Representations of Ocean Spectra

1991 ◽  
Vol 117 (12) ◽  
pp. 2926-2930 ◽  
Author(s):  
Josep R. Medina ◽  
Carlos R. Sanchez‐Carratala
Keyword(s):  
Ar Representations

Fundamental Equivalence of Discrete-Time AR Representations

2001 ◽  
Vol 34 (13) ◽  
pp. 231-236
Author(s):  
A.I.G. Vardulakis ◽  
E.N. Antoniou
Keyword(s):  
Discrete Time ◽  
Ar Representations

scholarly journals NOTIONS OF EQUIVALENCE FOR DISCRETE TIME AR-REPRESENTATIONS

2002 ◽  
Vol 35 (1) ◽  
pp. 29-34
Author(s):  
N. Karampetakis ◽  
S. Vologiannidis ◽  
A.I. Vardulakis
Keyword(s):  
Discrete Time ◽  
Ar Representations

The generalized one‐dimensional synthetic seismogram

Geophysics ◽  
1987 ◽  
Vol 52 (5) ◽  
pp. 589-605 ◽  
Author(s):  
P. R. Gutowski ◽  
S. Treitel
Keyword(s):  
Moving Average ◽  
Normal Incidence ◽  
Synthetic Seismogram ◽  
Stratified Medium ◽  
Autoregressive Moving Average ◽  
Reflection Coefficients ◽  
Source Surface ◽  
Theoretical Treatment ◽  
Surface Source ◽  
Ar Representations

The normal‐incidence synthetic seismogram for an elastic and horizontally stratified medium has been thoroughly studied for a relatively restricted number of source and receiver locations. Most existing treatments are concerned with the special case in which the source as well as the receiver are situated at the surface; few attempts have dealt with completely arbitrary source and receiver geometries. Here we examine arbitrary geometries with the aid of the layer matrix approach, in which upgoing and downgoing wave motion at each interface is expressed in terms of z-transform polynomials. Such an approach brings to light a number of physically important relations that the model satisfies. For example, the synthetic seismograms generally have the familiar autoregressive‐moving average (ARMA) structure for the surface‐source, surface‐receiver case. For particular combinations of reflection coefficients, however, the seismograms reduce to purely autoregressive (AR) representations. In all cases, we work out the delay properties that the respective autoregressive and moving average components must obey. The present solutions are easily reduced to a useful form for practical computation. One application of particular current interest is the simulation of vertical seismic profiling (VSP) surveys, where we have extended the theoretical treatment to include expressions for the derivatives of the seismograms with respect to the reflection coefficients. The resulting time series, which we call Jacobograms, are indicative of the sensitivity of the seismogram to the various reflection coefficients and are thus diagnostic of the model’s behavior.

scholarly journals Fundamental equivalence of discrete-time AR representations

2003 ◽  
Vol 76 (11) ◽  
pp. 1078-1088 ◽  
Author(s):  
A. I. G. Vardulakis ◽  
E. Antoniou
Keyword(s):  
Discrete Time ◽  
Ar Representations
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