scholarly journals One-dimensional constrained inversion study of TEM and application in coal goafs’ detection

2020 ◽  
Vol 12 (1) ◽  
pp. 1533-1540
Author(s):  
Si Yuanlei ◽  
Li Maofei ◽  
Liu Yaoning ◽  
Guo Weihong
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Data Interpretation ◽  
Volume Effect ◽  
Underground Space ◽  
Attenuation Curve ◽  
One Dimensional ◽  
Transient Electromagnetic ◽  
Geological Conditions ◽  
Geological Information

AbstractTransient electromagnetic method (TEM) is often used in urban underground space exploration and field geological resource detection. Inversion is the most important step in data interpretation. Because of the volume effect of the TEM, the inversion results are usually multi-solvable. To reduce the multi-solvability of inversion, the constrained inversion of TEM has been studied using the least squares method. The inversion trials were performed using two three-layer theoretical geological models and one four-layer theoretical geological model. The results show that one-dimensional least squares constrained inversion is faster and more effective than unconstrained inversion. The induced electromotive force attenuation curves of the inversion model indicate that the same attenuation curve may be used for different geological conditions. Therefore, constrained inversion using known geological information can more accurately reflect the underground geological information.

Spatial averaging of the vertical magnetic field in central‐loop configuration

Geophysics ◽  
1993 ◽  
Vol 58 (10) ◽  
pp. 1507-1510 ◽  
Author(s):  
Wei Qian ◽  
Laust B. Pedersen
Keyword(s):  
Tensor Decomposition ◽  
Data Interpretation ◽  
Impedance Tensor ◽  
Logarithmic Scale ◽  
Resistivity Structure ◽  
One Dimensional ◽  
Transient Electromagnetic ◽  
The Earth ◽  
Band Limited ◽  
Central Loop

Local resistivity heterogeneities can cause static shifts in the magnetotelluric (MT) impedance tensor that severely complicate data interpretation; the apparent resistivity is shifted on a logarithmic scale across the recorded frequency range while the phase has a band‐limited response. Different techniques such as electromagnetic array profiling (EMAP) (Torres‐Verdín and Bostick, 1992) and tensor decomposition (Zhang et al., 1987; Groom and Bailey, 1989; 1991) have been developed in the MT community to recognize and remove static shifts. Sternberg, et al. (1988) and Pellerin and Hohmann (1990) suggest that central‐loop transient electromagnetic (TEM) soundings can obtain an unbiased estimate of the regional resistivity structure of the earth and thereby correct for magnetotelluric static shifts. The regional resistivity structure of the earth must be one‐dimensional (1-D) for this method to work well.

scholarly journals Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Baiyu Wang
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
High Efficiency ◽  
Least Squares Method ◽  
Parabolic Problems ◽  
Moving Least Squares ◽  
One Dimensional ◽  
Moving Least Squares Method ◽  
The Stability

This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

Solution of problems in dynamic elasticity via a mixed least squares method

2015 ◽  
Vol 32 (3) ◽  
pp. 687-704 ◽  
Author(s):  
Maria Tchonkova
Keyword(s):  
Least Squares ◽  
Analytical Solutions ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Time Step ◽  
Theoretical Formulation ◽  
Content Type ◽  
One Dimensional ◽  
Dynamic Elasticity ◽  
Backward Euler

Purpose – The purpose of this paper is to present an original mixed least squares method for solving problems in dynamic elasticity. Design/methodology/approach – The proposed approach involves two different types of unknowns: velocities and stresses. The approximate solution to the dynamic elasticity equations is obtained via a minimization of a least squares functional, consisting of two terms: a term, which includes the squared residual of a weak form of the time rate of the constitutive relationships, expressed in terms of velocities and stresses, and a term, which depends on the squared residual of the equations of motion. At each time step the functional is minimized with respect to the velocities and stresses, which for the purpose of this study, are approximated by equal order piece-wise linear polynomial functions. The time discretization is based upon the backward Euler scheme. The displacements are computed from the obtained velocities in terms of a finite difference interpolation. The proposed theoretical formulation is given the general three-dimensional case and is tested numerically on the solution of one-dimensional wave equations. Findings – To test the performance of the method, it has been implemented in an original computer code, using object-oriented logic and written from scratch. Two one-dimensional problems from the mathematical physics, with well-known exact analytical solutions, have been solved. The numerical examples include a forced vibrating spring, fixed at its both ends and a rod, vibrating under its own weight, when one of its ends is fixed and the other is traction-free. The performed convergence study suggests that the method is convergent for both: velocities and stresses. The obtained results show excellent agreement between the exact and analytical solutions for displacement modes, velocities and stresses. It is observed that this method appears to be stable for the different mesh sizes and time step values. Originality/value – The mixed least squares formulation, described in this paper, serves as a basis for interesting future developments and applications to two and three-dimensional problems in dynamic elasticity.

The influence of selectable parameters in the element-free Galerkin method: A one-dimensional beam-in-bending problem

2009 ◽  
Vol 223 (7) ◽  
pp. 1579-1590 ◽  
Author(s):  
O F Valencia ◽  
F J Gómez-Escalonilla ◽  
J López-Díez
Keyword(s):  
Galerkin Method ◽  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Shape Functions ◽  
Element Free Galerkin Method ◽  
One Dimensional ◽  
Element Free Galerkin ◽  
Axially Loaded ◽  
Element Free

Continuing with the analysis performed for the one-dimensional axially loaded bar problem, a beam in bending is analysed to understand the influence of the characteristic parameters that have any influence in the solution of this problem using the element-free Galerkin method (EFGM), one of the most popular meshless methods. Both accuracy and time cost are considered as the evaluation functions to perform such an analysis. Both functions provide a reasonable idea to consider EFGM as an adequate method to solve the problem considered in this article. As in a one-dimensional axially loaded bar problem, the parameters to be considered will be those that affect the solution: number of nodes in which the domain is modelled, the nodes scatter, the order of the polynomial base to generate shape functions, the order of the quadrature to solve integrals, and the support radius. Besides, as in a one-dimensional axially loaded problem, some cases with different loading and stiffness conditions are considered. However, in this analysis a generalized moving least squares method is used to create shape functions instead of the moving least squares.

Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem

2016 ◽  
Vol 22 (2) ◽  
Author(s):  
Meisam Noei Khorshidi ◽  
Sohrab Ali Yousefi
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Control Parameter ◽  
Least Squares Method ◽  
Ritz Method ◽  
Source Control ◽  
Algebraic Equations ◽  
Least Squares Approximation ◽  
One Dimensional ◽  
Satisfier Function

AbstractAn inverse problem concerning a diffusion equation with source control parameter is considered. The approximation of the problem is based on the Ritz method with satisfier function. The Ritz method together with the least squares approximation (Ritz-least squares method) are utilized to reduce the inverse problem to the solution of algebraic equations. We extensively discuss the convergence of the method and finally present illustrative examples to demonstrate validity and applicability of the new technique.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method
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