scholarly journals Tectonics from fluvial topography using formal linear inversion: Theory and applications to the Inyo Mountains, California

2014 ◽  
Vol 119 (8) ◽  
pp. 1651-1681 ◽  
Author(s):  
L. Goren ◽  
Matthew Fox ◽  
Sean D. Willett
Keyword(s):  
Linear Inversion ◽  
Inversion Theory

Refinements to the linear velocity inversion theory

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 112-118 ◽  
Author(s):  
Frank G. Hagin ◽  
Jack K. Cohen
Keyword(s):  
Synthetic Data ◽  
Scattered Wave ◽  
Scattering Data ◽  
Inversion Method ◽  
Impedance Change ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Velocity Inversion ◽  
Linear Algorithm ◽  
Inversion Theory

The linear inversion method presented by Cohen and Bleistein in 1979 gives seriously degraded results when large reflectors are encountered. Obviously there is an irrecoverable loss of information when such a linear algorithm is applied to a nonlinear world. However, in many cases, excellent results can be achieved by suitable postprocessing of the output of the basic linear inversion algorithm. Although a certain degree of helpful postprocessing can be and has been performed by straightforward consideration of the linearization process, we present here a substantially improved postprocessing algorithm. The basis for these improvements is a more accurate scattering model due to Lahlou et al where, among other things, a WKB analysis of the wave equation led to a much more accurate accounting of the geometric spreading of the scattered wave. These notions plus an effective use of traveltime are used in the new algorithm to improve both the estimate of the reflector locations and the estimate of amplitude (velocity or acoustic impedance) change across the reflectors. The basic idea is to insert this idealized scattering data into the original linear algorithm, and then use the result of this computation as a guide in the interpretation of the numerical output of the algorithm. We demonstrate the result of computer implementation of this algorithm on synthetic data, with and without noise, and verify that the postprocessing algorithm produces dramatically improved reflector locations and speed estimates. Moreover, the new algorithm adds only very modest cost to the basic processing, which is, in turn, very competitive in cost to other multidimensional algorithms.

Analysis of Electromagnetic Inverse Model of Resistance Spot Welding

2010 ◽  
Vol 160-162 ◽  
pp. 974-979
Author(s):  
Nai Feng Fan ◽  
Zhen Luo ◽  
Yang Li ◽  
Wen Bo Xuan
Keyword(s):  
Resistance Spot Welding ◽  
Regularization Method ◽  
Spot Welding ◽  
Influence Factors ◽  
Great Influence ◽  
Welding Process ◽  
Inverse Model ◽  
Resistance Spot ◽  
Inversion Theory

Resistance spot welding (RSW) is an important welding process in modern industrial production, and the quality of welding nugget determines the strength of products to a large extent. Limited by the level of RSW quality monitor, however, RSW has rarely been applied to the fields with high welding quality requirements. Associated with the inversion theory, in this paper, an electromagnetic inverse model of RSW was established, and the analysis of influence factors, such as the layout of the probes, the discrete program and the regularization method, was implemented as well. The result shows that the layout of the probe and the regularization method has great influence on the model. When the probe is located at the y direction of x-axis or the x direction of y-axis and Conjugate Gradient method is selected, a much better outcome can be achieved.

Linear inversion

2016 ◽  
Vol 35 (12) ◽  
pp. 1085-1087 ◽  
Author(s):  
Matt Hall
Keyword(s):  
Linear Algebra ◽  
Linear Inversion ◽  
The World

As a student geologist, I was never inducted into the world of linear algebra. Later, as a professional, I remained happily ignorant of Hessian matrices and Hermitian adjoints. But ever since reading Brian Russell's Don't neglect your math essay (Russell, 2012), I've wanted to put things right. In particular, I have wanted to understand the well-known geophysical equation at the heart of every inversion: d = Gm. It's only an equation — how hard can it be?

A Heuristic Approach to use Sparseness in Linear Inversion Problems

2013 ◽  
Author(s):  
Adelson S. de Oliveira ◽  
José L. Carbonesi ◽  
Paulo Casañas Gomes ◽  
Thiago S. F. X. Teixeira
Keyword(s):  
Heuristic Approach ◽  
Linear Inversion
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