Interpretation and identification of minimum phase reflection coefficients

2001 ◽  
Vol 110 (6) ◽  
pp. 3003-3010 ◽  
Author(s):  
J. Gregory McDaniel ◽  
Cory L. Clarke
Keyword(s):  
Reflection Coefficients ◽  
Minimum Phase ◽  
Phase Reflection

Non‐Gaussian reflectivity, entropy, and deconvolution

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2862-2888 ◽  
Author(s):  
A. T. Walden
Keyword(s):  
Gaussian Distribution ◽  
Robust Statistics ◽  
Amplitude Distribution ◽  
Reflection Coefficients ◽  
General Description ◽  
Minimum Phase ◽  
Minimum Entropy ◽  
Highly Nonlinear ◽  
Non Gaussian ◽  
Deconvolution Techniques

Standard deconvolution techniques assume that the wavelet is minimum phase but generally make no assumptions about the amplitude distribution of the primary reflection coefficient sequence. For a white reflection sequence the assumption of a Gaussian distribution means that recovery of the true phase of the wavelet is impossible; however, a non‐Gaussian distribution in theory allows recovery of the phase. It is generally recognized that primary reflection coefficients typically have a non‐Gaussian amplitude distribution. Deconvolution techniques that assume whiteness but seek to exploit the non‐Gaussianity include Wiggins’ minimum entropy deconvolution (MED), Claerbout’s parsimonious deconvolution, and Gray’s variable norm deconvolution. These methods do not assume minimum phase. The deconvolution filter is defined by the maximization of a function called the objective. I examine these and other MED‐type deconvolution techniques. Maximizing the objective by setting derivatives to zero results in most cases in a deconvolution filter which is the solution of a highly nonlinear Toeplitz matrix equation. Wiggins’ original iterative approach to the solution is suitable for some methods, while for other methods straightforward iterative perturbation approaches may be used instead. The likely effects on noise of the nonlinearities involved are demonstrated as extremely varied. When the form of an objective remains constant with iteration, the most general description of the method is likelihood ratio maximization; when the form changes, a method seeks to maximize relative entropy at each iteration. I emphasize simple and useful link between three methods and the use of M-estimators in robust statistics. In attempting to assess the accuracy of the techniques, the choice between different families of distributions for modeling the distribution of reflection coefficients is important. The results provide important insights into methods of constructing and understanding the statistical implications and behavior of a chosen nonlinearity. A new objective is introduced to illustrate this, and a few particular preferences expressed. The methods are compared with the zero‐memory nonlinear deconvolution approach of Godfrey and Rocca (1981); for their approach, two distinctly different yet statistically comparable models for reflection coefficients are seen to give surprisingly similarly shaped nonlinearities. Finally, it is shown that each MED‐type method can be viewed as the minimization of a particular configurational entropy expression, where some suitable ratio plays the role of a probability.

Homomorphic deconvolution

Geophysics ◽  
1983 ◽  
Vol 48 (7) ◽  
pp. 1014-1016 ◽  
Author(s):  
D. J. Jin ◽  
J. R. Rogers
Keyword(s):  
Reflection Coefficient ◽  
Additive Noise ◽  
Critical Role ◽  
Minimum Phase ◽  
Integration Algorithm ◽  
The Public ◽  
Band Limited ◽  
Frequency Transformations ◽  
Analytical Expressions ◽  
Phase Reflection

The advantages of homomorphic deconvolution are that it does not require the assumptions of minimum‐phase wavelet and of a white random reflection coefficient series. Disadvantages of the method which have been recognized in the public domain are difficulties in unwrapping the phase, in dealing with band‐limited signals, and in handling mixed‐phase reflection coefficient series. These difficulties may be respectively overcome by using an “adaptive numerical integration algorithm” (Tribolet, 1977), frequency transformations (Tribolet, 1979), and exponential weighting of the signal (Tribolet, 1979). There seems to have been some understanding in the literature and among exploration researchers that additive noise would affect the performance of homomorphic deconvolution. However, to the best of our knowledge there have not appeared in the literature any analytical expressions or experiments conclusively showing how additive noise affects homomorphic deconvolution. Analytic and experimental analyses demonstrated that additive noise plays a critical role in homomorphic deconvolution such that homomorphic deconvolution is unreliable whenever the spectral amplitudes of the signal are very small over certain frequency bands and even a small amount of noise is present. This unreliability of the method overshadows its advantages.

Data-driven Controller Tuning for Non-minimum Phase Plants with Stability Constraints

2014 ◽  
Vol 134 (12) ◽  
pp. 1802-1808
Author(s):  
Ryota Matsuo ◽  
Kazuhiro Yubai ◽  
Daisuke Yashiro ◽  
Junji Hirai
Keyword(s):  
Data Driven ◽  
Minimum Phase ◽  
Controller Tuning

A UHF Compact Complex Impedance-transforming Balun with High Isolation

2020 ◽  
Vol 13 (8) ◽  
pp. 1135-1144
Author(s):  
Kittipong Nithiporndecha ◽  
Chatrpol Pakasiri
Keyword(s):  
Complex Impedance ◽  
Output Port ◽  
Reflection Coefficients ◽  
Coupled Line ◽  
High Isolation ◽  
Line Structure ◽  
Source Impedance ◽  
Phase Balance ◽  
High Output

Background: A compact complex impedance-transforming balun for UHF frequencies, which is based on a coupled-line structure that matched all ports and provided high output port isolation, was designed in this paper. Methods: A lumped component transformation was used to minimize circuit size. The implemented circuit operated at 433 MHz with the reflection coefficients less than -16 dB at all ports, 0.22 dB amplitude balance and 180° phase balance at the output ports. The signal coupling between the output ports was -16.8 dB. The circuit size is small at 0.032λ. Results: Complex impedance-transforming baluns were designed to operate at 433 MHz. The source impedance at port 1 was set at Zs = 12 - j12Ω and the load impedances at port 2 and 3 were set at ZL = 80 + j30Ω. Conclusion: A compact complex impedance-transforming balun at UHF frequency, with all ports matched and high isolations, was designed and illustrated in this paper.

Comparison of surface-wave reflection coefficients for different metals on quartz

1973 ◽  
Vol 9 (21) ◽  
pp. 495 ◽  
Author(s):  
R. Larosa ◽  
C.F. Vasile ◽  
D.V. Zagardo
Keyword(s):  
Surface Wave ◽  
Wave Reflection ◽  
Reflection Coefficients
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