Prestack imaging of seismic data using Lp iterative reweighted least-squares wavefield extrapolation filters in the frequency-space domain

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. V243-V252
Author(s):  
Wail A. Mousa
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Least Squares Method ◽  
Filter Design ◽  
Finite Impulse Response ◽  
Weighted Least Squares ◽  
Data Set ◽  
Frequency Space ◽  
Wavefield Extrapolation ◽  
Iterative Reweighted Least Squares

A stable explicit depth wavefield extrapolation is obtained using [Formula: see text] iterative reweighted least-squares (IRLS) frequency-space ([Formula: see text]-[Formula: see text]) finite-impulse response digital filters. The problem of designing such filters to obtain stable images of challenging seismic data is formulated as an [Formula: see text] IRLS minimization. Prestack depth imaging of the challenging Marmousi model data set was then performed using the explicit depth wavefield extrapolation with the proposed [Formula: see text] IRLS-based algorithm. Considering the extrapolation filter design accuracy, the [Formula: see text] IRLS minimization method resulted in an image with higher quality when compared with the weighted least-squares method. The method can, therefore, be used to design high-accuracy extrapolation filters.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

Calibration of stormwater quality regression models: a random process?

2010 ◽  
Vol 62 (4) ◽  
pp. 875-882 ◽  
Author(s):  
A. Dembélé ◽  
J.-L. Bertrand-Krajewski ◽  
B. Barillon
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Regression Models ◽  
Linear Models ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Data Sets ◽  
Data Set ◽  
Urban Catchments

Regression models are among the most frequently used models to estimate pollutants event mean concentrations (EMC) in wet weather discharges in urban catchments. Two main questions dealing with the calibration of EMC regression models are investigated: i) the sensitivity of models to the size and the content of data sets used for their calibration, ii) the change of modelling results when models are re-calibrated when data sets grow and change with time when new experimental data are collected. Based on an experimental data set of 64 rain events monitored in a densely urbanised catchment, four TSS EMC regression models (two log-linear and two linear models) with two or three explanatory variables have been derived and analysed. Model calibration with the iterative re-weighted least squares method is less sensitive and leads to more robust results than the ordinary least squares method. Three calibration options have been investigated: two options accounting for the chronological order of the observations, one option using random samples of events from the whole available data set. Results obtained with the best performing non linear model clearly indicate that the model is highly sensitive to the size and the content of the data set used for its calibration.

scholarly journals Design of one‐way wavefield extrapolation operators, using smooth functions in WLSQ optimization

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 1037-1045 ◽  
Author(s):  
Jan W Thorbecke ◽  
Kees Wapenaar ◽  
Gerd Swinnen
Keyword(s):  
Least Squares ◽  
Recursive Algorithm ◽  
Weighted Least Squares ◽  
Convolution Operators ◽  
Smooth Functions ◽  
Exchange Method ◽  
Data Set ◽  
Depth Migration ◽  
Frequency Space ◽  
Small Depth

Many depth migration methods use one‐way frequency–space depth extrapolation methods. These methods are generally considered to be expensive, so it is important to find the most efficient way of implementing them. This usually means making spatial convolution operators that are as short as possible. Applying the extrapolation operators in a recursive way, using small depth steps, also demands that the operators do not amplify the wavefield at every depth step. Weighted least squares is an appropriate method to use for designing extrapolation operators that are accurate and efficient and that remain stable in a recursive algorithm. The extrapolated wavefields calculated with these operators are comparable with the extrapolation results obtained with other known operator design techniques as the Remez exchange method and nonlinear optimization. In this paper, the weighted least‐squares technique is refined by using different model functions. By smoothing the phase and amplitude transition at the evanescent cutoff, we can stabilize the resulting operators. The accuracy of the operators is shown in zero‐offset migration impulse responses in 2D and 3D media. The Sigsbee2A data set is used to illustrate the quality of the extrapolation operators in prestack depth migration in a complex medium.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

Intergenerational Earnings Mobility in Italy

2007 ◽  
Vol 7 (2) ◽  
Author(s):  
Sauro Mocetti
Keyword(s):  
Labor Market ◽  
Least Squares ◽  
Household Income ◽  
Intergenerational Mobility ◽  
Least Squares Method ◽  
Developed Countries ◽  
Data Set ◽  
Labor Market Success ◽  
Term Labor

Abstract This paper contributes to the growing number of studies on intergenerational mobility by providing a measure of earnings elasticity for Italy. The absence of an appropriate data set is overcome by adopting the two-sample two-stage least squares method. The analysis, based on the Survey of Household Income and Wealth, shows that intergenerational mobility is lower in Italy than it is in other developed countries. We also examine the reasons why the long-term labor market success of children is related to that of their fathers.

A Least-Squares Method for Computing Balance Corrections

1964 ◽  
Vol 86 (3) ◽  
pp. 273-277 ◽  
Author(s):  
Thomas P. Goodman
Keyword(s):  
Least Squares ◽  
Digital Computer ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Rotating Machinery ◽  
Residual Vibration ◽  
Computing Procedure ◽  
Balance Corrections

To compute final correction masses for multispeed, multiplane balancing of rotating machinery, a least-squares computing procedure has been developed. This procedure uses plain least squares to minimize the rms residual vibration of selected points on the machinery foundation, and then uses weighted least squares to reduce the maximum residual vibration. The computations have been programmed for a digital computer.

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