A direct inversion method for non-uniform quasi-random point sequences

2013 ◽  
Vol 19 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Colas Schretter ◽  
Harald Niederreiter
Keyword(s):  
Random Point ◽  
Inversion Method ◽  
Direct Inversion

APPLICATIONS OF TWO NON-CENTRAL HYPERGEOMETRIC DISTRIBUTIONS OF BIASED SAMPLING STATISTICAL MODELS

2021 ◽  
Vol 4 (4) ◽  
pp. 415-424
Author(s):  
A. A. Issa ◽  
K. O. Adetunji ◽  
T. Alanamu ◽  
E. J. Adefila ◽  
K. A. Muhammed
Keyword(s):  
Statistical Models ◽  
Research Work ◽  
Hypergeometric Distribution ◽  
Biased Sampling ◽  
Inversion Method ◽  
Urn Model ◽  
Fisher Distribution ◽  
Direct Inversion ◽  
Mean And Variance ◽  
Hypergeometric Distributions

Statistical models of biased sampling of two non-central hypergeometric distributions Wallenius' and Fisher's distribution has been extensively used in the literature, however, not many of the logic of hypergeometric distribution have been investigated by different techniques. This research work examined the procedure of the two non-central hypergeometric distributions and investigates the statistical properties which includes the mean and variance that were obtained. The parameters of the distribution were estimated using the direct inversion method of hyper simulation of biased urn model in the environment of R statistical software, with varying odd ratios (w) and group sizes (mi). It was discovered that the two non - central hypergeometric are approximately equal in mean, variance and coefficient of variation and differ as odds ratios (w) becomes higher and differ from the central hypergeometric distribution with ω = 1. Furthermore, in univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, although central hypergeometric is more consistent than any of them. Also, in multinomial situation, it was observed that Fisher distribution is more consistent at (ω = 0.2, 0.5), Wallenius distribution at (ω = 0.7, 0.9) and central hypergeometric at (ω = 0.2)    

A Comparative Study of Direct and Iterative Inversion Approaches to Determine the Spatial Shear Modulus Distribution of Elastic Solids

2019 ◽  
Vol 11 (10) ◽  
pp. 1950097 ◽  
Author(s):  
Zhi Liu ◽  
Yanli Sun ◽  
Jianwei Deng ◽  
Dongmei Zhao ◽  
Yue Mei ◽  
...  
Keyword(s):  
Shear Modulus ◽  
Comparative Study ◽  
Inversion Method ◽  
Noise Levels ◽  
Elastic Solids ◽  
Direct Inversion ◽  
Advantages And Disadvantages ◽  
Iterative Inversion ◽  
Very High ◽  
Selection Of

This paper presents a comparative study of two typical inverse algorithms, i.e., direct and iterative inversion methods, to reconstruct the shear modulus distribution of linearly elastic solids. Both approaches are based on the finite element framework and compared utilizing both the simulated and experimental data. The reconstruction results demonstrate that both approaches are capable of identifying the nonhomogeneous shear modulus distribution of solids well. It can also be found that the direct inversion method is much faster than the iterative inversion method, whereas the iterative inversion method is capable of yielding better shear modulus ratio between the stiff inclusion and the soft background even with very high noise levels. Afterwards, a thorough comparison on the advantages and disadvantages of these two approaches has been performed. This comparative study provides useful information on the selection of the proper inverse scheme in estimating nonhomogeneous elastic property distribution of soft solids nondestructively.

Perturbation method of analysis of crystal truncation rod data

2005 ◽  
Vol 38 (2) ◽  
pp. 299-305 ◽  
Author(s):  
I. K. Robinson ◽  
M. Tabuchi ◽  
S. Hisadome ◽  
R. Oga ◽  
Y. Takeda
Keyword(s):  
Perturbation Method ◽  
Diffraction Pattern ◽  
Model Calculation ◽  
Lattice Strain ◽  
Inversion Method ◽  
Layered Semiconductor ◽  
Direct Inversion ◽  
Crystal Truncation Rod ◽  
Semiconductor Heterostructure ◽  
Perturbation Approximation

A new method of direct inversion of crystal truncation rod (CTR) data is demonstrated for the analysis of layered semiconductor heterostructure materials. This method is based on approximations that are valid when the electron density deviations and lattice strain are small in the regions of the sample close to a well defined surface. The CTR diffraction pattern can then be regarded as a perturbation with respect to that of an ideal surface. The direct inversion method is shown to work for the analysis of a series of InP/GaInAs/InP heterostructures. The ability to recover strain information is demonstrated with a model calculation. The beginning of breakdown of the perturbation approximation is seen and explained in both cases.

Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media

2016 ◽  
Vol 20 (2) ◽  
pp. 353-373 ◽  
Author(s):  
Jie Yao ◽  
Anne-Cécile Lesage ◽  
Fazle Hussain ◽  
Donald J. Kouri
Keyword(s):  
Scattering Theory ◽  
Incidence Angle ◽  
Neumann Series ◽  
Forward Scattering ◽  
Acoustic Medium ◽  
Inversion Method ◽  
Angle Of Incidence ◽  
Direct Inversion ◽  
Reference Medium ◽  
Density Perturbations

AbstractWe extend the full wavefield modeling with forward scattering theory and Volterra Renormalization to a vertically varying two-parameter (velocity and density) acoustic medium. The forward scattering series, derived by applying Born-Neumann iterative procedure to the Lippmann-Schwinger equation (LSE), is a well known tool for modeling and imaging. However, it has limited convergence properties depending on the strength of contrast between the actual and reference medium or the angle of incidence of a plane wave component. Here, we introduce the Volterra renormalization technique to the LSE. The renormalized LSE and related Neumann series are absolutely convergent for any strength of perturbation and any incidence angle. The renormalized LSE can further be separated into two sub-Volterra type integral equations, which are then solved noniteratively. We apply the approach to velocity-only, density-only, and both velocity and density perturbations. We demonstrate that this Volterra Renormalization modeling is a promising and efficient method. In addition, it can also provide insight for developing a scattering theory-based direct inversion method.

scholarly journals Direct inversion of the apparent complex‐resistivity spectrum

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1399-1404 ◽  
Author(s):  
J. Xiang ◽  
N. B. Jones ◽  
D. Cheng ◽  
F. S. Schlindwein
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Optimal Parameter ◽  
Geophysical Methods ◽  
Inversion Method ◽  
Model Parameters ◽  
Complex Resistivity ◽  
Direct Inversion ◽  
Optimal Parameter Estimation ◽  
Cole Model

Cole‐Cole model parameters are widely used to interpret electrical geophysical methods and are obtained by inverting the induced polarization (IP) spectrum. This paper presents a direct inversion method for parameter estimation based on multifold least‐squares estimation. Two algorithms are described that provide optimal parameter estimation in the least‐squares sense. Simulations demonstrate that both algorithms can provide direct apparent spectral parameter inversion for complex resistivity data. Moreover, the second algorithm is robust under reasonably high noise.

scholarly journals Direct Inversion Method of Fault Slip Analysis to Determine the Orientation of Principal Stresses and Relative Chronology for Tectonic Events in Southwestern White Mountain Region of New Hampshire, USA

Geosciences ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 464 ◽  
Author(s):  
Christopher C. Barton ◽  
Jacques Angelier
Keyword(s):  
New Hampshire ◽  
Fault Slip ◽  
Mountain Region ◽  
Inversion Method ◽  
Hubbard Brook Experimental Forest ◽  
Principal Stresses ◽  
White Mountains ◽  
Direct Inversion ◽  
Tectonic Events ◽  
Relative Chronology

The orientation and relative magnitudes of paleo tectonic stresses in the western central region of the White Mountains of New Hampshire is reconstructed using the direct inversion method of fault slip analysis on 1–10-m long fractures exposed on a series of road cuts along Interstate 93, just east of the Hubbard Brook Experimental Forest in North Woodstock, NH, USA. The inversion yields nine stress regimes which identify five tectonic events that impacted the White Mountain region over the last 410 Ma. The inversion method has potential application in basin analysis.

scholarly journals Improved Magnetotelluric Zohdy-Oldenburg Direct Inversion

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Hui Cao ◽  
Yun Liu ◽  
Kun Peng Wang
Keyword(s):  
Jacobian Matrix ◽  
Least Square ◽  
Ratio Method ◽  
Inversion Method ◽  
Model Parameters ◽  
Sparse Linear Systems ◽  
Linear Inversion ◽  
Direct Inversion ◽  
Rugged Topography ◽  
Linear Systems Of Equations

Based on researches of Baiyao (1995) and Zhang and Xu (2001), this paper proposes an improved 2D MT Zohdy-Oldenburg direct inversion method, in the least-square sense, embodying the features of Zohdy’s ratio method and Oldenburg’s difference method, in the condition of rugged topography, with phase information. It bypasses large calculations of the Jacobian matrix and large sparse linear systems of equations and enables direct modifications and comparisons of the model parameters. According to the calculation and analysis of examples, it shows faster convergence and higher precision. In contrast with the conventional linear inversion, the calculation speed of this new method can be increased by more than 10 times.

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