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.

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.

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.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

A Comparison of Accuracy Based on Data Imputation between Unconstrained Structural Equation Modeling and Weighted Least Squares Regression

2011 ◽  
Vol 130-134 ◽  
pp. 730-733
Author(s):  
Narong Phothi ◽  
Somchai Prakancharoen
Keyword(s):  
Structural Equation Modeling ◽  
Least Squares ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Equation Modeling ◽  
Data Imputation ◽  
Least Squares Regression ◽  
Waveform Generator ◽  
Data Set ◽  
Testing Group

This research proposed a comparison of accuracy based on data imputation between unconstrained structural equation modeling (Uncon-SEM) and weighted least squares (WLS) regression. This model is developed by University of California, Irvine (UCI) and measured using the mean magnitude of relative error (MMRE). Experimental data set is created using the waveform generator that contained 21 indicators (1,200 samples) and divided into two groups (1,000 for training and 200 for testing groups). In fact, training group was analyzed by three main factors (F1, F2, and F3) for creating the models. The result of the experiment show MMRE of Uncon-SEM method based on the testing group is 34.29% (accuracy is 65.71%). In contrast, WLS method produces MMRE for testing group is 55.54% (accuracy is 44.46%). So, Uncon-SEM is high accuracy and MMRE than WLS method that is 21.25%.

scholarly journals THE EFFECT OF URBAN GREEN SPACES ON HOUSE PRICES IN WARSAW

2018 ◽  
Vol 22 (5) ◽  
pp. 358-371 ◽  
Author(s):  
Radoslaw Trojanek ◽  
Michal Gluszak ◽  
Justyna Tanas
Keyword(s):  
Least Squares ◽  
Residential Buildings ◽  
House Prices ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Data Set ◽  
Urban Green ◽  
Urban Green Spaces ◽  
Green Area ◽  
The Impact

In the paper, we analysed the impact of proximity to urban green areas on apartment prices in Warsaw. The data-set contained in 43 075 geo-coded apartment transactions for the years 2010 to 2015. In this research, the hedonic method was used in Ordinary Least Squares (OLS), Weighted Least Squares (WLS) and Median Quantile Regression (Median QR) models. We found substantial evidence that proximity to an urban green area is positively linked with apartment prices. On an average presence of a green area within 100 meters from an apartment increases the price of a dwelling by 2,8% to 3,1%. The effect of park/forest proximity on house prices is more significant for newer apartments than those built before 1989. We found that proximity to a park or a forest is particularly important (and has a higher implicit price as a result) in the case of buildings constructed after 1989. The impact of an urban green was particularly high in the case of a post-transformation housing estate. Close vicinity (less than 100 m distance) to an urban green increased the sales prices of apartments in new residential buildings by 8,0–8,6%, depending on a model.

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.

Nonlinear 3D tomographic least-squares inversion of residual moveout in Kirchhoff prestack-depth-migration common-image gathers

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE13-VE23 ◽  
Author(s):  
Frank Adler ◽  
Reda Baina ◽  
Mohamed Amine Soudani ◽  
Pierre Cardon ◽  
Jean-Baptiste Richard
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Layer Velocity ◽  
Map Migration

Velocity-model estimation with seismic reflection tomography is a nonlinear inverse problem. We present a new method for solving the nonlinear tomographic inverse problem using 3D prestack-depth-migrated reflections as the input data, i.e., our method requires that prestack depth migration (PSDM) be performed before tomography. The method is applicable to any type of seismic data acquisition that permits seismic imaging with Kirchhoff PSDM. A fundamental concept of the method is that we dissociate the possibly incorrect initial migration velocity model from the tomographic velocity model. We take the initial migration velocity model and the residual moveout in the associated PSDM common-image gathers as the reference data. This allows us to consider the migrated depth of the initial PSDM as the invariant observation for the tomographic inverse problem. We can therefore formulate the inverse problem within the general framework of inverse theory as a nonlinear least-squares data fitting between observed and modeled migrated depth. The modeled migrated depth is calculated by ray tracing in the tomographic model, followed by a finite-offset map migration in the initial migration model. The inverse problem is solved iteratively with a Gauss-Newton algorithm. We applied the method to a North Sea data set to build an anisotropic layer velocity model.

scholarly journals Analysis of multicrystal pump–probe data sets. II. Scaling of ratio data sets

2016 ◽  
Vol 72 (2) ◽  
pp. 250-260 ◽  
Author(s):  
Bertrand Fournier ◽  
Jesse Sokolow ◽  
Philip Coppens
Keyword(s):  
Least Squares ◽  
Light Exposure ◽  
Weighted Least Squares ◽  
System Response ◽  
Data Sets ◽  
Data Set ◽  
Time Resolved ◽  
Pump Probe ◽  
Scaling Procedure ◽  
Ratio Data

Two methods for scaling of multicrystal data collected in time-resolved photocrystallography experiments are discussed. The WLS method is based on a weighted least-squares refinement of laser-ON/laser-OFF intensity ratios. The other, previously applied, is based on the average absolute system response to light exposure. A more advanced application of these methods for scaling within a data set, necessary because of frequent anisotropy of light absorption in crystalline samples, is proposed. The methods are applied to recently collected synchrotron data on the tetra-nuclear compound Ag2Cu2L4withL= 2-diphenylphosphino-3-methylindole. A statistical analysis of the weighted least-squares refinement residual terms is performed to test the importance of the scaling procedure.

scholarly journals ON THE MUTH DISTRIBUTION

2015 ◽  
Vol 20 (3) ◽  
pp. 291-310 ◽  
Author(s):  
Pedro Jodra ◽  
Maria Dolores Jimenez-Gamero ◽  
Maria Virtudes Alba-Fernandez
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Golden Ratio ◽  
Natural Extension ◽  
Real Data ◽  
Random Variable ◽  
Quantile Function ◽  
Lambert W Function ◽  
Data Set ◽  
Monte Carlo Simulation Study

The Muth distribution is a continuous random variable introduced in the context of reliability theory. In this paper, some mathematical properties of the model are derived, including analytical expressions for the moment generating function, moments, mode, quantile function and moments of the order statistics. In this regard, the generalized integro-exponential function, the Lambert W function and the golden ratio arise in a natural way. The parameter estimation of the model is performed by the methods of maximum likelihood, least squares, weighted least squares and moments, which are compared via a Monte Carlo simulation study. A natural extension of the model is considered as well as an application to a real data set.

Sign in / Sign up

Export Citation Format

Share Document