A Spatial Resampling Minimum Variance beamforming technique based on diagonal reduction

2016 ◽  
Author(s):  
Bin Zhou ◽  
Jie Yu ◽  
Shibiao Mao ◽  
Wei Sun
Keyword(s):  
Minimum Variance ◽  
Spatial Resampling ◽  
Beamforming Technique ◽  
Diagonal Reduction

Accurate diffraction imaging for detecting small-scale geologic discontinuities

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. S447-S457 ◽  
Author(s):  
Peng Lin ◽  
Suping Peng ◽  
Jingtao Zhao ◽  
Xiaoqin Cui ◽  
Wenfeng Du
Keyword(s):  
Signal To Noise Ratio ◽  
Migration Velocity ◽  
Minimum Variance ◽  
Seismic Interpretation ◽  
Small Scale ◽  
Imaging Method ◽  
Velocity Analysis ◽  
Diffraction Imaging ◽  
Correlation Properties ◽  
Beamforming Technique

Seismic diffractions contain valuable information regarding small-scale inhomogeneities or discontinuities, and therefore they can be used for seismic interpretation in the exploitation of hydrocarbon reservoirs. Velocity analysis is a necessary step for accurate imaging of these diffractions. A new method for diffraction velocity analysis and imaging is proposed that uses an improved adaptive minimum variance beamforming technique. This method incorporates the minimum variance, coherence factor, and correlation properties to improve the signal-to-noise ratio and enhance correlations. Our method can make seismic diffractions become better focused in semblance panels, allowing for the optimal migration velocity for diffractions to be accurately picked. Synthetic and field examples demonstrate that the migration velocity for the diffractions can differ from that for the reflections. The results suggest that the diffraction velocity analysis and imaging method is feasible for accurately locating and identifying small-scale discontinuities, which leads to the possibility of using this approach for practical application and seismic interpretation.

scholarly journals Beamforming of Joint Polarization-Space Matched Filtering for Conformal Array

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Lutao Liu ◽  
Yilin Jiang ◽  
Liangtian Wan ◽  
Zuoxi Tian
Keyword(s):  
Energy Loss ◽  
Data Model ◽  
Signal To Noise Ratio ◽  
Minimum Variance ◽  
Matched Filtering ◽  
Conformal Array ◽  
Linearly Constrained ◽  
Polarization Sensitive Array ◽  
Array Beamforming ◽  
Beamforming Technique

Due to the polarization mismatch of the antenna, the received signal suffers from energy loss. The conventional beamforming algorithms could not be applied to the conformal array because of the varying curvature. In order to overcome the energy loss of the received signal, a novel joint polarization-space matched filtering algorithm for cylindrical conformal array is proposed. First, the snapshot data model of the conformal polarization sensitive array is analyzed. Second, the analytical expression of polarization sensitive array beamforming is derived. Linearly constrained minimum variance (LCMV) beamforming technique is facilitated for the cylindrical conformal array. Third, the idea of joint polarization-space matched filtering is presented, and the principle of joint polarization-space matched filtering is discussed in detail. Theoretical analysis and computer simulation results verify that the conformal polarization sensitive array is more robust than the ordinary conformal array. The proposed algorithm can improve the performance when signal and interference are too close. It can enhance the signal-to-noise ratio (SNR) by adjusting the polarization of the elements of the conformal array, which matches the polarization of the incident signal.

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

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