Least‐squares deconvolution of apparent resistivity pseudosections

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1682-1690 ◽  
Author(s):  
M. H. Loke ◽  
R. D. Barker
Keyword(s):  
Least Squares ◽  
Apparent Resistivity ◽  
Least Squares Method ◽  
Random Noise ◽  
Electrode Array ◽  
Earth Model ◽  
Damping Factor ◽  
Data Set ◽  
Single Data ◽  
Starting Model

A fast technique for the inversion of data from resistivity tomography surveys has been developed. This technique is based on the smoothness‐constrained, least‐squares method, and it produces a 2-D subsurface model that is free of distortions in the apparent resistivity pseudosection caused by the electrode array geometry used. A homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. Tests with a variety of models and data from field surveys show that this technique is insensitive to random noise, provided a sufficiently large damping factor is used, and that it can resolve structures that cause overlapping anomalies in the pseudosection. On a 33 MHz 80486DX microcomputer, it takes about 5 s to process a single data set.

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.

Incorrect least-squares regression coefficients in method-comparison analysis.

1979 ◽  
Vol 25 (3) ◽  
pp. 432-438 ◽  
Author(s):  
P J Cornbleet ◽  
N Gochman
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Least Squares Method ◽  
Regression Line ◽  
Method Comparison ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Data Set ◽  
Data Points ◽  
Regression Slopes

Abstract The least-squares method is frequently used to calculate the slope and intercept of the best line through a set of data points. However, least-squares regression slopes and intercepts may be incorrect if the underlying assumptions of the least-squares model are not met. Two factors in particular that may result in incorrect least-squares regression coefficients are: (a) imprecision in the measurement of the independent (x-axis) variable and (b) inclusion of outliers in the data analysis. We compared the methods of Deming, Mandel, and Bartlett in estimating the known slope of a regression line when the independent variable is measured with imprecision, and found the method of Deming to be the most useful. Significant error in the least-squares slope estimation occurs when the ratio of the standard deviation of measurement of a single x value to the standard deviation of the x-data set exceeds 0.2. Errors in the least-squares coefficients attributable to outliers can be avoided by eliminating data points whose vertical distance from the regression line exceed four times the standard error the estimate.

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.

scholarly journals Effective fault detection in structural health monitoring systems

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987323 ◽  
Author(s):  
Marwa Chaabane ◽  
Majdi Mansouri ◽  
Kamaleldin Abodayeh ◽  
Ahmed Ben Hamida ◽  
Hazem Nounou ◽  
...  
Keyword(s):  
Fault Detection ◽  
Least Squares ◽  
Partial Least Squares ◽  
Least Squares Method ◽  
Random Noise ◽  
Ratio Test ◽  
Multiscale Representation ◽  
Kernel Partial Least Squares ◽  
Partial Least Squares Model ◽  
Partial Least Squares Method

A new fault detection technique is considered in this article. It is based on kernel partial least squares, exponentially weighted moving average, and generalized likelihood ratio test. The developed approach aims to improve monitoring the structural systems. It consists of computing an optimal statistic that merges the current information and the previous one and gives more weight to the most recent information. To improve the performances of the developed kernel partial least squares model even further, multiscale representation of data will be used to develop a multiscale extension of this method. Multiscale representation is a powerful data analysis way that presents efficient separation of deterministic characteristics from random noise. Thus, multiscale kernel partial least squares method that combines the advantages of the kernel partial least squares method with those of multiscale representation will be developed to enhance the structural modeling performance. The effectiveness of the proposed approach is assessed using two examples: synthetic data and benchmark structure. The simulation study proves the efficiency of the developed technique over the classical detection approaches in terms of false alarm rate, missed detection rate, and detection speed.

scholarly journals Calibration for Parameter Estimation of Signals with Complex Noise via Nonstationarity Measure

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhiming Zhou ◽  
Zhengyun Zhou ◽  
Liang Wu
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Least Squares Method ◽  
Random Noise ◽  
Calibration Method ◽  
Numerical Studies ◽  
Chaotic Signals ◽  
Inaccurate Estimation ◽  
Non Gaussian ◽  
First Time

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex (such as non-Gaussian noise, strong noise, and chaotic noise). This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of the stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types (including random noise and chaotic noise) and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations.

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.

Comparison of the least‐squares criterion and the Cauchy criterion in frequency‐wavenumber inversion

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2027-2035 ◽  
Author(s):  
Lasse Amundsen
Keyword(s):  
Lower Bound ◽  
Least Squares ◽  
Scale Parameter ◽  
Least Squares Method ◽  
Random Noise ◽  
Synthetic Data ◽  
Error Criterion ◽  
Numerical Examples ◽  
Wavenumber Domain ◽  
Weather Noise

One alternative to the least‐squares inversion technique is the use of a Cauchy error criterion. We show how inversion algorithms of the Gauss‐Newton type based on the least‐squares method can be modified to handle the Cauchy norm. A criterion for the lower bound of the scale parameter in the Cauchy norm is given. We compare the least‐squares and Cauchy error criteria by inverting synthetic data corrupted by random noise and weather noise. The data are transformed to the frequency‐wavenumber domain before the inversion starts. The numerical examples show that the algorithm based on the Cauchy criterion is more robust in the presence of the noise tested here. Per iteration, the computer costs of the two algorithms are approximately the same.

Multicomponent Spectrophotometric Analysis of Metal Ions Based on Simultaneous or Consecutive Application of Several Reagents

1994 ◽  
Vol 59 (9) ◽  
pp. 1951-1963
Author(s):  
Jiří Perůtka ◽  
Josef Havel ◽  
Luděk Jančář
Keyword(s):  
Metal Ions ◽  
Least Squares Method ◽  
Spectrophotometric Analysis ◽  
Experimental Conditions ◽  
Data Set ◽  
Single Data ◽  
Relative Errors ◽  
Partial Least Squares Method ◽  
Absorbance Data

This paper deals with nonconventional approaches to multicomponent spectrophotometric analysis consisting of (i) simultaneous or consecutive addition of several nonselective reagents in the multicomponent determination of metal ions, and (ii) the use of absorbance data which have been measured at different pH values or in different experimental conditions and subsequently combined into a single data set, evaluated by the partial least squares method. The following multicomponent mixtures of metal ions with reagents were examined: Co2+ and Fe3+ with nitroso-R-salt and 1,10-phenanthroline; Co2+, Cu2+ and Fe3+ with nitroso-R-salt and zincon; Co2+, Cu2+ and Zn2+ with nitroso- R-salt and zincon; and Cu2+, Zn2+ and Ni2+ with zincon and PAR. The average relative error of determination was 2% (two metal ions) and 5% (three metal ions). Cu2+, Zn2+ and Ni2+ were also quantitated in ALPAKA alloy with relative errors of 4 - 9%.

scholarly journals EFEITO DO MEIO E DA IDADE DA VACA SOBRE O GANHO DE PESO NA FASE DE CRIA, RECRIA E OS DIAS PARA SE OBTER 160 KG EM ANIMAIS DA RAÇA GUZERÁ

2004 ◽  
Vol 9 (1) ◽  
Author(s):  
E. GEMIN ◽  
J.C. SOUZA ◽  
L.O.C. SILVA ◽  
C.H.M. MALHADO ◽  
P.B. FERRAZ FILHO
Keyword(s):  
Environmental Factors ◽  
Statistical Model ◽  
Least Squares ◽  
Random Effects ◽  
Environmental Effects ◽  
Fixed Effects ◽  
Least Squares Method ◽  
Data Set ◽  
Quadratic Effect ◽  
Daily Gain

O objetivo deste trabalho foi avaliar a influência dos efeitos de meio e da idade da vaca sobre os ganhos de peso do nascimento ao desmame (GPD), período pós-desmame (GPS) e sobre o número de dias para se obter 160 kg (D160). O rebanho avaliado continha 1.747 animais, sendo os dados analisados pelo método dos quadrados mínimos utilizando-se um modelo estatístico contendo os efeitos fixos de mês, ano e sexo do bezerro, o efeito aleatório de touros na fazenda, e como covariável a idade da vaca ao parto. As médias ajustadas para ganho de peso pré e pós-desmame, e para dias para a obtenção 160 kg foram 0,604 ± 0,01 kg; 0,399 ± 0,01 kg; em 285 ± 5,3 dias, respectivamente. Os machos foram superiores às fêmeas relativo ao GPD = 6,0%; D160 = 5,8 %, GPS = 20,1%. Quanto ao mês, as maiores médias de ganho de peso no pré-desmame recaiu nos animais nascidos no mês de agosto. Com relação aos dias para se obter 160 kg, os melhores resultados foram dos animais nascidos nos meses julho a setembro. A idade da vaca influenciou as caracteristicas ganho de peso pré-desmame e no D160. Environmental effects and age of dam on pre- and post-weaning daily gain, and on number of days to gain 160 kg from birth to weaning on guzerath breed cattle Abstract The objective of this study was to evaluate the effects of environmental factors and age of dam on pre- (GPD) and post-weaning (GPS) daily gain, and on the were number of days to gain 160 kg (D160) from birth to weaning. The data set contained 1,747 animals, and were analyzed by the least squares method. The statistical model included the fixed effects of month and year of birth, and sex of the calf and age of the dam at calving. Sire nested within farm and the error were random effects. The pre- and post-weaning average daily gains, and days to gain 160 kg least squares means were 0.604 ± 0.01 kg, 0.399 ± 0.01 kg, and 285.0 ± 5.3 days, respectively. The males were 6.0, 21.1 and 5.8% superior to the females for GPD, GPS and D160, respectively. The highest pre-weaning gain was for the animals born August. Regarding D160, the best results were for the animals born from July to September. Age of the cow showed a significant quadratic effect on the traits. The best cows were the 94-month-old ones. First calving cows produced the lightest calves. The results showed the importance of the environmental effects on the traits studied, evidencing the need for them to be corrected.

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