scholarly journals An analysis of deconvolution: Modeling reflectivity by fractionally integrated noise

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1093-1107 ◽  
Author(s):  
M. M. Saggaf ◽  
M. Nafi Toksöz
Keyword(s):  
White Noise ◽  
Well Logs ◽  
Noise Model ◽  
Reflection Coefficients ◽  
Deconvolution Method ◽  
Spectral Character ◽  
White Noise Process ◽  
Process Study ◽  
Using Data ◽  
Special Case

Reflection coefficients are observed in nature to have stochastic behavior that departs significantly from the white‐noise model. Conventional deconvolution methods, however, assume reflectivity to be a white‐noise process. In this paper we analyze the deconvolution process, study the implications of the assumption of white noise, and show that the conventional operator can recover only the white component of reflectivity. A new stochastic model, fractionally integrated noise, is proposed for modeling reflectivity—a model that more closely approximates its spectral character and that encompasses white noise as a special case. We discuss different techniques to generalize the conventional deconvolution method based on the new model in order to handle reflectivity that is not white and compare the results of the conventional and generalized filters using data derived from well logs.

scholarly journals STOCHASTIC MODEL OF THE BRAZILIAN GPS NETWORK COORDINATES TIME SERIES

2018 ◽  
Vol 24 (4) ◽  
pp. 545-563
Author(s):  
Christian Gonzalo Pilapanta Amagua ◽  
Claudia Pereira Krueger ◽  
Alfonso Rodrigo Tierra Criollo
Keyword(s):  
Time Series ◽  
Random Walk ◽  
White Noise ◽  
Power Law ◽  
Fractional Power ◽  
Noise Model ◽  
Coastal Zones ◽  
White Noise Process ◽  
Noise Process ◽  
Stochastic Properties

Abstract It is well known that daily estimates of GPS coordinates are highly temporally correlated and that the knowledge and understanding of this correlation allows to establish more realistic uncertainties of the parameters estimated from the data. Despite this, there are currently no studies related to the analysis and calculation of the noise sources in geodetic time series in Brazil. In this context, this paper focuses on the investigation of the stochastic properties of a total of 486 coordinates time series from 159 GPS stations belonging to the Brazilian Network for Continuous Monitoring of GNSS (RBMC) using the maximum likelihood estimation approach. To reliably describe the GPS time series, we evaluate 4 possible stochastic models as models of each time series: 3 models with integer spectral indices (white noise, flicker plus white noise and random-walk plus white noise model) and 1 with fractional spectral index (fractional power-law plus white noise). By comparing the calculated noise content values for each model, it is possible to demonstrate a stepwise increase of the noise content, being the combination of a fractional power-law process and white noise process, the model with smaller values and the combination of random walk process with white noise process, the model with greater values. The analysis of the spatial distribution of the noise values of the processes allow demonstrate that the GPS sites with the highest accumulated noise values, coincide with sites located in coastal zones and river basins and that their stochastic properties can be aliased by the occurrence of different physical signals typical of this type of zones, as the case of the hydrological loading effect.

A unified framework for the deconvolution of traces of nonwhite reflectivity

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1660-1676 ◽  
Author(s):  
M. M. Saggaf ◽  
Enders A. Robinson
Keyword(s):  
White Noise ◽  
Gaussian Noise ◽  
Moving Average ◽  
Noise Model ◽  
Reflection Coefficients ◽  
Unified Framework ◽  
Deconvolution Problem ◽  
White Noise Model ◽  
Alternative Processes ◽  
Stochastic Properties

One of the fundamental assumptions of conventional deconvolution methods is that reflection coefficients follow the white‐noise model. However, analysis of well logs in various regions of the world confirms that in the majority of cases, reflectivity tends to depart from the white‐noise behavior. The assumption of white noise leads to a conventional deconvolution operator that can recover only the white component of reflectivity, thus yielding a distorted representation of the desired output. Various alternative processes have been suggested to model reflection coefficients. In this paper, we will examine some of these processes, apply them, contrast their stochastic properties, and critique their use for modeling reflectivity. These processes include autoregressive moving average (ARMA), scaling Gaussian noise, fractional Brownian motion, fractional Gaussian noise, and fractionally integrated noise. We then present a consistent framework to generalize the conventional deconvolution procedure to handle reflection coefficients that do not follow the white‐noise model. This framework represents a unified approach to the problem of deconvolving signals of nonwhite reflectivity and describes how higher‐order solutions to the deconvolution problem can be realized. We test generalized filters based on the various stochastic models and analyze their output. Because these models approximate the stochastic properties of reflection coefficients to a much better degree than white noise, they yield generalized deconvolution filters that deliver a significant improvement on the accuracy of seismic deconvolution over the conventional operator.

scholarly journals Empirical Bayes scaling of Gaussian priors in the white noise model

2013 ◽  
Vol 7 (0) ◽  
pp. 991-1018 ◽  
Author(s):  
B. T. Szabó ◽  
A. W. van der Vaart ◽  
J. H. van Zanten
Keyword(s):  
White Noise ◽  
Empirical Bayes ◽  
Noise Model ◽  
White Noise Model

scholarly journals Empirical White Noise Processes and the Subjective Probabilistic Approaches

2019 ◽  
Vol 48 (1) ◽  
pp. 19-30
Author(s):  
András Rövid ◽  
László Palkovics ◽  
Péter Várlaki
Keyword(s):  
White Noise ◽  
Random Number ◽  
White Noise Process ◽  
Random Number Generators ◽  
Noise Process ◽  
Complementary Approach ◽  
Fuzzy Random

The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis.

scholarly journals On the Basel Liquidity Formula for Elliptical Distributions

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 92
Author(s):  
Janine Balter ◽  
Alexander McNeil
Keyword(s):  
Risk Factor ◽  
White Noise ◽  
Gaussian White Noise ◽  
General Assumption ◽  
Elliptical Distributions ◽  
Risk Capital ◽  
White Noise Process ◽  
Gaussian White Noise Process ◽  
Loss Distributions ◽  
Symmetric Loss

A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L (profit-and-loss) are linear in the risk-factor changes. A generalization of the formula is derived under the more general assumption that risk-factor changes are multivariate elliptical. It is shown that the Basel formula tends to be conservative when the elliptical distributions are from the heavier-tailed generalized hyperbolic family. As a by-product of the analysis, a Fourier approach to calculating expected shortfall for general symmetric loss distributions is developed.

Sign in / Sign up

Export Citation Format

Share Document