A new analytic procedure to determine hypocentral parameters of local seismic events

1984 ◽  
Vol 74 (2) ◽  
pp. 655-667
Author(s):  
D. Caccamo ◽  
G. Neri
Keyword(s):  
Least Squares ◽  
Iterative Process ◽  
Classical Method ◽  
Earth Model ◽  
Seismic Events ◽  
System Of Equations ◽  
Analytic Procedure ◽  
The Earth ◽  
The Matrix ◽  
Hypocentral Parameters

Abstract A new procedure for locating local earthquakes is proposed. Essentially, this procedure consists in solving—by means of least-squares technique—a system of equations which is formally analogous to that of Geiger (Ax = b) but different from his in the values of the matrix A and vector b elements. This difference makes our procedure more reliable than Geiger's because it significantly reduces the cases of both iterative process divergence and low precision. Among the factors contributing to this progress the lesser possibility that the matrix A contains columns proportional (or nearly proportional) one to another is considered of particular influence. More than 20,000 hypocentral calculations have been performed on simulated shocks: significant differences in the number of good locations were revealed between our procedure and the classical method of Geiger (1910). Ours is more precise, particularly when few stations were used or networks with an unsatisfactory geometry. The earth model also influences the observed differences as it contributes to generating those analytical conditions which make the calculation convergence more problematic when applying Geiger's method. Further applications are currently carried out in order to verify the procedure features for velocity laws and station configuration different from those used in this study.

scholarly journals Solving Separable Nonlinear Equations Using LU Factorization

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yun-Qiu Shen ◽  
Tjalling J. Ypma
Keyword(s):  
Nonlinear Equations ◽  
Iterative Process ◽  
Full Rank ◽  
Original System ◽  
System Of Equations ◽  
Lu Factorization ◽  
Numerical Implementation ◽  
Direct Solution ◽  
Differentiable Functions ◽  
The Matrix

Separable nonlinear equations have the form where the matrix and the vector are continuously differentiable functions of and . We assume that and has full rank. We present a numerical method to compute the solution for fully determined systems () and compatible overdetermined systems (). Our method reduces the original system to a smaller system of equations in alone. The iterative process to solve the smaller system only requires the LU factorization of one matrix per step, and the convergence is quadratic. Once has been obtained, is computed by direct solution of a linear system. Details of the numerical implementation are provided and several examples are presented.

Human Rights as Land Rights in the Pacific

1993 ◽  
Vol 6 (1) ◽  
pp. 61-80 ◽  
Author(s):  
John D'Arcy May
Keyword(s):  
Human Rights ◽  
Case Studies ◽  
Papua New Guinea ◽  
Land Rights ◽  
Human Community ◽  
The Earth ◽  
The Pacific ◽  
West Papua ◽  
The Matrix ◽  
The One

Do human rights in their conventional, Western understanding really meet the needs of Pacific peoples? This article argues that land rights are a better clue to those needs. In Aboriginal Australia, Fiji, West Papua and Papua New Guinea, case studies show that people's relationship to land is religious and implicitly theological. The article therefore suggests that rights to land need to be supplemented by rights of the land extending to the earth as the home of the one human community and nature as the matrix of all life.

TOTAL LEAST SQUARES FOR ESTIMATION OF THE GROSS OUTPUT VECTOR

2020 ◽  
Author(s):  
Dmitriy Vladimirovich Ivanov ◽  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Direct Costs ◽  
Total Least Squares ◽  
Test Cases ◽  
Output Vector ◽  
Final Consumption ◽  
The Matrix

The article proposes the estimation of the gross output vector in the presence of errors in the matrix of direct costs and the final consumption vector. The article suggests the use of the total least squares method for estimating the gross output vector. Test cases showed that the accuracy of the proposed estimates of the gross output vector is higher than the accuracy of the estimates obtained using the classical least squares method (OLS).

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 1. Kinematic and stress states of the billet

2021 ◽  
pp. 65-71
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Complete System ◽  
Shape Change ◽  
Plane Deformation ◽  
System Of Equations ◽  
Flow Rates ◽  
Die Forging ◽  
The Matrix ◽  
Stress States ◽  
Theory Of Plastic Flow

On the basis of the complete system of equations of the theory of plastic flow, the kinematic and stress states of the billet are determined when the channels are extruded under conditions of plane deformation of the misaligned position of the punch and the matrix. Keywords: die forging, extrusion, misaligned position, punch, matrix, plane deformation, plastic flow rates, stresses. [email protected]

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 2. Determination of the extrusion force, maximum pressure on the matrix wall and the heights of the walls, taking into account the elastic deformation jf the matrix

2021 ◽  
pp. 63-69
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Elastic Deformation ◽  
Shape Change ◽  
Plane Deformation ◽  
Maximum Pressure ◽  
Extrusion Force ◽  
System Of Equations ◽  
The Matrix ◽  
Theory Of Plastic Flow

On the basis of the system of equations of the theory of plastic flow, the forces, the maximum pressure on the wall of the matrix and the heights of the obtained walls when extruding channels are determined, taking into account the elastic deformation of the matrix. Keywords: die forging, extrusion, misalignment, punch, matrix, plane deformation, stresses. [email protected]

Some statistical aspects of the estimation of seismic travel times

1968 ◽  
Vol 58 (4) ◽  
pp. 1243-1260 ◽  
Author(s):  
William Tucker ◽  
Eugene Herrin ◽  
Helen W. Freedman
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Travel Time ◽  
Iterative Process ◽  
Iterative Technique ◽  
Absolute Minimum ◽  
Station Corrections ◽  
Monte Carlo Studies ◽  
Confidence Ellipses ◽  
Large Earthquakes

Abstract Some of the statistical aspects of estimating travel-time anomalies and station corrections are considered. In order to estimate these quantities using earthquake data the events themselves must first be located. We investigated the use of the Gauss-Newton iterative technique to obtain a least-squares epicenter location employing Monte Carlo methods. Results of these studies indicate that the Gauss-Newton process converges to an absolute minimum and that confidence ellipses computed by linear techniques are reliable for reasonable networks of well-distributed stations. Also the Monte Carlo studies indicate that a least-squares solution may be inaccurate if appreciable travel-time anomalies or station-error means exist. We then expanded the location procedure to include the estimation of travel-time anomalies and station corrections. In order to obtain these estimates data from some 278 large earthquakes were analyzed by using a modified Seidel iterative process.

Position Estimation of Single Camera Visual System Based on Total Least Squares Algorithm

2012 ◽  
Vol 239-240 ◽  
pp. 1352-1355
Author(s):  
Jing Zhou ◽  
Yin Han Gao ◽  
Chang Yin Liu ◽  
Ji Zhi Li
Keyword(s):  
Visual System ◽  
Least Squares ◽  
Total Least Squares ◽  
Position Estimation ◽  
Feature Points ◽  
Perspective Theory ◽  
Optical Feature ◽  
The Matrix ◽  
Least Squares Algorithm ◽  
Set Up

The position estimation of optical feature points of visual system is the focus factor of the precision of system. For this problem , to present the Total Least Squares Algorithm . Firstly , set up the measurement coordinate system and 3D model between optical feature points, image points and the position of camera according to the position relation ; Second , build the matrix equations between optical feature points and image points ; Then apply in the total least squares to have an optimization calculation ; Finally apply in the coordinate measuring machining to have a simulation comparison experiment , the results indicate that the standard tolerance of attitude coordinate calculated by total least squares is 0.043mm, it validates the effectiveness; Compare with the traditional method based on three points perspective theory, measure the standard gauge of 500mm; the standard tolerance of traditional measurement system is 0.0641mm, the standard tolerance of Total Least Squares Algorithm is 0.0593mm; The experiment proves the Total Least Squares Algorithm is effective and has high precision.

scholarly journals Earth pressure balance control of shield tunneling machine based on nonlinear least squares support vector machine model predictive control

2018 ◽  
Vol 52 (1-2) ◽  
pp. 3-10 ◽  
Author(s):  
Xuanyu Liu ◽  
Kaiju Zhang
Keyword(s):  
Support Vector Machine ◽  
Least Squares ◽  
Balance Control ◽  
Earth Pressure ◽  
Screw Conveyor ◽  
Support Vector ◽  
Pressure Balance ◽  
Machine Model ◽  
The Earth ◽  
Earth Pressure Balance

Background: Earth pressure balance shield machines are widely used in underground engineering. To prevent ground deformation even disastrous accidents, the earth pressure in soil chamber must be kept balance to that on excavation face during shield tunneling. Therefore, in this paper an advanced control strategy that a least squares support vector machine model-based predictive control scheme for earth pressure balance is developed. Methods: A prediction model is established to predict the earth pressure in chamber during the tunneling process by means of least squares support vector machine technology. On this basis, an optimization function is given which aims at minimizing the difference between the predicted earth pressure and the desired one. To obtain the optimal control actions, an improved ant colony system algorithm is used as rolling optimization for earth pressure balance control in real time. Results: Based on the field data the simulation experiments are performed. The results demonstrate that the method proposed is very effective to control earth pressure balance, and it has good stability. Conclusion: The screw conveyor speed and advance speed are the major factors affecting the earth pressure in chamber. The excavation face could be controlled balance better by adjusting the screw conveyor speed and advance speed.

scholarly journals ADA Solve the Cubic Equation in a New Method with Engineering Application

2020 ◽  
Vol 13 (3) ◽  
pp. 223-231
Author(s):  
Abdullah Dhayea Assi
Keyword(s):  
Classical Method ◽  
Engineering Application ◽  
Cubic Equation ◽  
A Value ◽  
Main Equation ◽  
The Matrix ◽  
Solution Equation ◽  
As Stress ◽  
Initial Root ◽  
Examination Room

         Up to date the cubic equation or matrix tensor is consisting of nine values ​​such as stress tensor that turns into the cubic equation which has been used for solving classic method. This is to impose an initial root several times to get it when achieves the equation and any other party is zero. Then dividing the cubic equation on the equation of the root. After that dividing the cubic equation on the equation of the root and using the classical method to find the rest of the roots. This is a very difficult issue, especially if the roots are secret or large for those who are looking in a difficult field or even for those who are in the examination room. In this research, two equations were reached, one that calculates the angle and the other that calculates the three roots at high accuracy without any significant error rate. By taking advantage of the traditional method, not by imposing a value to get the root of that equation, but by imposing an equation to get the solution equation that gives the value of that root. After imposing that equation, the general equation was derived from which that calculated the three roots directly and without any attempts. The angle that was implicitly derived during the derive of the main equation is calculated by taking advantage of the constants that do not change (invariants) for the matrix tensor (T).

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