Comments on "An inversion procedure of the generalized Vandermonde matrix"

1973 ◽  
Vol 18 (3) ◽  
pp. 326-326 ◽  
Author(s):  
I. Goknar
Keyword(s):  
Vandermonde Matrix ◽  
Inversion Procedure

scholarly journals Implementation of Machine Learning Algorithms in Spectral Analysis of Surface Waves (SASW) Inversion

2021 ◽  
Vol 11 (6) ◽  
pp. 2557
Author(s):  
Sadia Mannan Mitu ◽  
Norinah Abd. Rahman ◽  
Khairul Anuar Mohd Nayan ◽  
Mohd Asyraf Zulkifley ◽  
Sri Atmaja P. Rosyidi
Keyword(s):  
Spectral Analysis ◽  
Surface Waves ◽  
Soil Profile ◽  
Field Tests ◽  
Iteration Process ◽  
Machine Learning Algorithms ◽  
Support Vector ◽  
Complex Processes ◽  
Inversion Procedure ◽  
Inversion Analysis

One of the complex processes in spectral analysis of surface waves (SASW) data analysis is the inversion procedure. An initial soil profile needs to be assumed at the beginning of the inversion analysis, which involves calculating the theoretical dispersion curve. If the assumption of the starting soil profile model is not reasonably close, the iteration process might lead to nonconvergence or take too long to be converged. Automating the inversion procedure will allow us to evaluate the soil stiffness properties conveniently and rapidly by means of the SASW method. Multilayer perceptron (MLP), random forest (RF), support vector regression (SVR), and linear regression (LR) algorithms were implemented in order to automate the inversion. For this purpose, the dispersion curves obtained from 50 field tests were used as input data for all of the algorithms. The results illustrated that SVR algorithms could potentially be used to estimate the shear wave velocity of soil.

A generalized maxentropic inversion procedure for noisy data

2002 ◽  
Vol 127 (2-3) ◽  
pp. 249-260 ◽  
Author(s):  
Amos Golan ◽  
Henryk Gzyl
Keyword(s):  
Noisy Data ◽  
Inversion Procedure

PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)

2004 ◽  
Vol 03 (01) ◽  
pp. 69-90 ◽  
Author(s):  
BEHZAD HAGHIGHI ◽  
ALIREZA HASSANI DJAVANMARDI ◽  
MOHAMAD MEHDI PAPARI ◽  
MOHSEN NAJAFI
Keyword(s):  
Potential Energy ◽  
Diffusion Coefficients ◽  
Potential Energy Function ◽  
Model Potential ◽  
Inversion Method ◽  
Low Density ◽  
Initial Model ◽  
Lennard Jones ◽  
Inversion Procedure ◽  
And Diffusion

Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

A lithospheric velocity anomaly beneath the Shagan river Test Site. Part 2. Imaging and inversion with amplitude transmission tomography

1992 ◽  
Vol 82 (2) ◽  
pp. 999-1017
Author(s):  
K. L. McLaughlin ◽  
J. R. Murphy ◽  
B. W. Barker
Keyword(s):  
Fourier Transforms ◽  
Test Site ◽  
Small Scale ◽  
Projection Operators ◽  
Order Partial Differential Equation ◽  
Linear Inversion ◽  
Discrete Fourier Transforms ◽  
Velocity Anomaly ◽  
Inversion Procedure ◽  
River Test

Abstract A linear inversion procedure is introduced that images weak velocity anomalies using amplitudes of transmitted seismic waves. Using projection operators from geometrical ray theory, an image of an anomaly is constructed from amplitudes recorded at arrays of receivers using arrays of sources. The image is related to the velocity anomaly by a second-order partial-differential equation that is inverted using 2-D discrete Fourier transforms. As an example of the inversion procedure, magnitude residuals for European stations recording Shagan River explosions are used to image the deep lithospheric anomaly beneath the Shagan River test site described in Part 1. This formal inversion analysis confirms the existence of a small-scale lateral heterogeneity located 50 km west-northwest of the test site at a probable depth between 80 and 100 km and indicates that it is consistent with a deterministic 1.5% peak-to-peak (or 0.5% rms) velocity anomaly with a scale length of about 3 km. 3-D dynamic raytracing is then used to verify that the inferred laterally varying structure produces amplitude fluctuations consistent with observations.

Simple inversion of time‐domain electromagnetic data

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 925-933 ◽  
Author(s):  
C. T. Barnett
Keyword(s):  
Time Domain ◽  
Eddy Currents ◽  
Early Time ◽  
Late Time ◽  
Current Filament ◽  
Equivalent Current ◽  
Time Domain Electromagnetic ◽  
Inversion Procedure ◽  
Current Filaments ◽  
Simple Inversion

The eddy currents induced in a thin confined conductor by a fixed‐loop time‐domain EM system can be represented by a single equivalent current filament. The equivalent current filament stays in the plane of the conductor at all times during the decay of the secondary field, but tends to migrate from a position of maximum primary field coupling at early time toward the center of the conductor at late time. This filament approximation is used in the design of a least‐squares inversion procedure which fits circular or rectangular current filaments to an observed eddy current distribution. The inversion procedure provides a rapid but precise means of estimating the position, size, and attitude of a conductor which has been detected by a time‐domain EM survey.

An inversion procedure from rotational total cross sections

1994 ◽  
Vol 101 (3) ◽  
pp. 2016-2022 ◽  
Author(s):  
J. C. Belchior ◽  
J. N. Murrell
Keyword(s):  
Cross Sections ◽  
Total Cross Sections ◽  
Inversion Procedure

scholarly journals A depolarisation lidar based method for the determination of liquid-cloud microphysical properties

2014 ◽  
Vol 7 (9) ◽  
pp. 9917-9992 ◽  
Author(s):  
D. P. Donovan ◽  
H. Klein Baltink ◽  
J. S. Henzing ◽  
S. R. de Roode ◽  
A. P. Siebesma
Keyword(s):  
Water Content ◽  
Multiple Scattering ◽  
Liquid Water ◽  
Cloud Droplet ◽  
Optimal Estimation ◽  
Liquid Water Content ◽  
Cloud Base ◽  
Base Region ◽  
Large Eddy Simulation Model ◽  
Inversion Procedure

Abstract. The fact that polarisation lidars measure a depolarisation signal in liquid clouds due to the occurrence of multiple-scattering is well-known. The degree of measured depolarisation depends on the lidar characteristics (e.g. wavelength and receiver field-of-view) as well as the cloud macrophysical (e.g. liquid water content) and microphysical (e.g. effective radius) properties. Efforts seeking to use depolarisation information in a quantitative manner to retrieve cloud properties have been undertaken with, arguably, limited practical success. In this work we present a retrieval procedure applicable to clouds with (quasi-)linear liquid water content (LWC) profiles and (quasi-)constant cloud droplet number density in the cloud base region. Thus limiting the applicability of the procedure allows us to reduce the cloud variables to two parameters (namely the derivative of the liquid water content with height and the extinction at a fixed distance above cloud-base). This simplification, in turn, allows us to employ a fast and robust optimal-estimation inversion using pre-computed look-up-tables produced using extensive lidar Monte-Carlo multiple-scattering simulations. In this paper, we describe the theory behind the inversion procedure and successfully apply it to simulated observations based on large-eddy simulation model output. The inversion procedure is then applied to actual depolarisation lidar data corresponding to a range of cases taken from the Cabauw measurement site in the central Netherlands. The lidar results were then used to predict the corresponding cloud-base region radar reflectivities. In non-drizzling condition, it was found that the lidar inversion results can be used to predict the observed radar reflectivities with an accuracy within the radar calibration uncertainty (2–3 dBZ). This result strongly supports the accuracy of the lidar inversion results. Results of a comparison between ground-based aerosol number concentration and lidar-derived cloud droplet number densities are also presented and discussed. The observed relationship between the two quantities is seen to be consistent with the results of previous studies based on aircraft-based in situ measurements.

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