Nonstationary phase estimation using regularized local kurtosis maximization

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. A75-A80 ◽  
Author(s):  
Mirko van der Baan ◽  
Sergey Fomel
Keyword(s):  
Statistical Estimation ◽  
Phase Estimation ◽  
Time Varying ◽  
Seismic Wavelet ◽  
Optimization Framework ◽  
Phase Rotation ◽  
Seismic Sections ◽  
The Stability ◽  
Kurtosis Maximization ◽  
Zero Phase

Phase mismatches sometimes occur between final processed seismic sections and zero-phase synthetics based on well logs — despite best efforts for controlled-phase acquisition and processing. Statistical estimation of the phase of a seismic wavelet is feasible using kurtosis maximization by constant-phase rotation, even if the phase is nonstationary. We cast the phase-estimation problem into an optimization framework to improve the stability of an earlier method based on a piecewise-stationarity assumption. After estimation, we achieve space-and-time-varying zero-phasing by phase rotation.

Time-varying wavelet estimation and deconvolution by kurtosis maximization

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. V11-V18 ◽  
Author(s):  
Mirko van der Baan
Keyword(s):  
Field Measurements ◽  
Phase Changes ◽  
Data Driven ◽  
Wiener Filtering ◽  
Time Varying ◽  
Seismic Wavelet ◽  
Phase Rotation ◽  
Physical Laws ◽  
Kurtosis Maximization ◽  
Zero Phase

Phase mismatches sometimes occur between final processed sections and zero-phase synthetics based on well logs, despite best efforts for controlled-phase acquisition and processing. The latter are often based on deterministic corrections derived from field measurements and physical laws. A statistical analysis of the data can reveal whether a time-varying nonzero phase is present. This assumes that the data should be white with respect to all statistical orders after proper deterministic corrections have been applied. Kurtosis maximization by constant phase rotation is a statistical method that can reveal the phase of a seismic wavelet. It is robust enough to detect time-varying phase changes. Phase-only corrections can then be applied by means of a time-varying phase rotation. Alternatively, amplitude and phase deconvolution can be achieved using time-varying Wiener filtering. Time-varying wavelet extraction and deconvolution can also be used as a data-driven alternative to amplitude-only inverse-[Formula: see text] deconvolution.

Sensitivity of the dispersion correction to Q error

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 288-290 ◽  
Author(s):  
Richard E. Duren ◽  
E. Clark Trantham
Keyword(s):  
Amplitude Spectrum ◽  
Careful Attention ◽  
Dispersion Correction ◽  
Event Time ◽  
Seismic Wavelet ◽  
Reflection Time ◽  
Seismic Image ◽  
Time Zones ◽  
Seismic Sections ◽  
Zero Phase

A controlled‐phase acquisition and processing methodology for our company has been described by Trantham (1994). He pointed out that it is careful attention to wavelet phase that leads to improved well ties and a more geologically accurate seismic image. In addition, we prefer zero‐phase wavelets on our seismic sections. For a given amplitude spectrum they have the simplest shape and the highest peak; further, the peak occurs at the reflection time of the event. This alignment is important since the seismic wavelet generally broadens with increasing depth with a zero‐phase wavelet remaining symmetrical about the event time. Our experience has been that a true zero‐phase section can be tied over the entire length of a synthetic trace without having to slide the synthetic trace to tie different time zones.

Ghosting and marine signature deconvolution: A prerequisite for detailed seismic interpretation

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1468-1485 ◽  
Author(s):  
Dushan B. Jovanovich ◽  
Roger D. Sumner ◽  
Sharon L. Akins‐Easterlin
Keyword(s):  
Gulf Coast ◽  
Seismic Line ◽  
Near Surface ◽  
Seismic Wavelet ◽  
Phase Errors ◽  
Air Gun ◽  
Statistical Hypotheses ◽  
Seismic Sections ◽  
Sonic Logs ◽  
Zero Phase

Detailed lithologic interpretation of seismic sections and/or pseudo‐sonic logs generated from seismic data requires that the seismic trace can be modeled as a reflection series convolved with a zero‐phase broadband wavelet. Ghosting and marine signature deconvolution processing is a prerequisite for assuring that the seismic wavelet on a marine CDP section will be zero phase. A deterministic approach to deconvolution is centered around the concept of abandoning the purely statistical method of wavelet estimation and actually measuring the seismic wavelet. A proper signature recording for marine data is, therefore, a crucial component of deterministic deconvolution. Another important element in the deterministic deconvolution sequence is the application of a deghosting filter to remove near‐surface reflections. Proper application of a deghosting filter significantly improves the correlation between log synthetics and the seismic trace. It has been found that statistical deconvolution schemes, because of the number of statistical hypotheses required to produce a deconvolution filter, produce residual wavelets that are highly variable in character and whose average phases cover the entire phase spectrum, modulo 2π. Examples of a Gulf Coast marine line which was shot with Aquapulse™, air gun, and Maxipulse™ sources by the RV Hollis Hedberg are presented to demonstrate the differences between statistical and deterministic deconvolution processing sequences. It will be shown, using sonic logs from wells adjacent to the seismic line, that the deterministic deconvolution sections for all three sources are close to zero phase while the statistical deconvolution sections have residual average phase errors between 180 and 270 degrees. The deterministic deconvolution sections have a high degree of correlation among themselves and to the wells adjacent to the line, while the statistical deconvolution sections correlate poorly to each other and to the wells. Synthetic seismograms and their impedance logs, and the seismic sections and their corresponding pseudo‐sonic logs, are used to demonstrate how deconvolution influences lithologic interpretation. ™Western Geophysics Co.

LEAST‐SQUARES INVERSE FILTERING AND WAVELET DECONVOLUTION

Geophysics ◽  
1977 ◽  
Vol 42 (7) ◽  
pp. 1369-1383 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Seismic Data ◽  
Broad Band ◽  
Detailed Comparison ◽  
Inverse Filtering ◽  
Borehole Data ◽  
Seismic Wavelet ◽  
Phase Property ◽  
Seismic Sections ◽  
Phase Spectra ◽  
Zero Phase

Detailed comparison between borehole data and seismic data has taught that, in general, conventional seismic inverse filtering is not effective enough to produce desirable deconvolution results, i.e., seismic sections with broad‐band zero‐phase wavelets. Application of conventional seismic reverse filters has the advantage that very little information is needed from the user. However, as is shown in this paper, the phase spectra of these filters may be seriously in error, even if the seismic wavelet has the minimum‐phase property. In wavelet deconvolution the phase spectrum of the filter is correct, provided a good estimate of the seismic wavelet is available. In this paper, wavelet deconvolution is compared with Wiener filtering. The main conclusions are illustrated by examples.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

A parametric family of Massey-type methods: inference, prediction, and sensitivity

2020 ◽  
Vol 16 (3) ◽  
pp. 255-269
Author(s):  
Enrico Bozzo ◽  
Paolo Vidoni ◽  
Massimo Franceschet
Keyword(s):  
Quantitative Analysis ◽  
Control Theory ◽  
Dynamic Systems ◽  
Parametric Family ◽  
Time Varying ◽  
Multi Agent ◽  
Key Features ◽  
The Stability ◽  
Agent Coordination ◽  
Time Aware

AbstractWe study the stability of a time-aware version of the popular Massey method, previously introduced by Franceschet, M., E. Bozzo, and P. Vidoni. 2017. “The Temporalized Massey’s Method.” Journal of Quantitative Analysis in Sports 13: 37–48, for rating teams in sport competitions. To this end, we embed the temporal Massey method in the theory of time-varying averaging algorithms, which are dynamic systems mainly used in control theory for multi-agent coordination. We also introduce a parametric family of Massey-type methods and show that the original and time-aware Massey versions are, in some sense, particular instances of it. Finally, we discuss the key features of this general family of rating procedures, focusing on inferential and predictive issues and on sensitivity to upsets and modifications of the schedule.

The Corduneanu-Popov Approach to the Stability of Nonlinear Time-Varying Systems

1970 ◽  
Vol 18 (2) ◽  
pp. 267-281 ◽  
Author(s):  
James H. Taylor ◽  
Kumpati S. Narendra
Keyword(s):  
Time Varying ◽  
Time Varying Systems ◽  
The Stability

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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