scholarly journals SEISMIC TOMOGRAPHY USING METROPOLIS METHOD OF VELOCITY FIELDS PARAMETERIZED BY HAAR WAVELET SERIES

2016 ◽  
Vol 34 (2) ◽  
Author(s):  
Alexsandro Guerra Cerqueira ◽  
Wilson Mouzer Figueiró ◽  
Paulo Eduardo Miranda Cunha
Keyword(s):  
Velocity Field ◽  
Seismic Tomography ◽  
Seismic Waves ◽  
Seismic Velocity ◽  
Haar Wavelet ◽  
Velocity Fields ◽  
Metropolis Method ◽  
Geological Models ◽  
Qualitative Models ◽  
Wavelet Series

ABSTRACT. The representation of compressional seismic waves velocity fields from geological models through numerical parameters has a strong geophysical importance, because, it makes possible to quantify such qualitative models, allowing its mathematical manipulation. In this way, the parameterization by Haar wavelet series may be seen as an attractive alternative.Keywords: parameterization, Haar wavelet series, pyramid algorithm, seismic tomography, seismic velocity field, traveltime data, Metropolis method. RESUMO. A representação de campos de velocidades sísmicas compressionais, através de parâmetros numéricos, é de importância básica na geofísica, pois torna possível a quantificação de modelos, antes qualitativos, permitindo assim que sejam matematicamente manipulados. A parametrização por série ondaleta Haar pode ser vista como uma alternativa atrativa para quantificar tais modelos...Palavras-chave: parametrização, série ondaleta Haar, inversão sísmica tomográfica, campo de velocidade sísmica, dados de tempo de trânsito, método Metropolis.

Seismic tomography inversion of velocity field parameterized by Haar wavelet series

2017 ◽  
Author(s):  
Alexsandro G. Cerqueira ◽  
Wilson M. Figueiró ◽  
Paulo E.M. Cunha
Keyword(s):  
Velocity Field ◽  
Seismic Tomography ◽  
Haar Wavelet ◽  
Tomography Inversion ◽  
Wavelet Series

scholarly journals Experimental Validation of Falling Liquid Film Models: Velocity Assumption and Velocity Field Comparison

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1205
Author(s):  
Ruiqi Wang ◽  
Riqiang Duan ◽  
Haijun Jia
Keyword(s):  
Experimental Data ◽  
Particle Image Velocimetry ◽  
Velocity Field ◽  
Experimental Validation ◽  
Particle Image ◽  
Velocity Fields ◽  
Number Range ◽  
Comparison Results ◽  
Image Velocimetry ◽  
Experimental Particle

This publication focuses on the experimental validation of film models by comparing constructed and experimental velocity fields based on model and elementary experimental data. The film experiment covers Kapitza numbers Ka = 278.8 and Ka = 4538.6, a Reynolds number range of 1.6–52, and disturbance frequencies of 0, 2, 5, and 7 Hz. Compared to previous publications, the applied methodology has boundary identification procedures that are more refined and provide additional adaptive particle image velocimetry (PIV) method access to synthetic particle images. The experimental method was validated with a comparison with experimental particle image velocimetry and planar laser induced fluorescence (PIV/PLIF) results, Nusselt’s theoretical prediction, and experimental particle tracking velocimetry (PTV) results of flat steady cases, and a good continuity equation reproduction of transient cases proves the method’s fidelity. The velocity fields are reconstructed based on different film flow model velocity profile assumptions such as experimental film thickness, flow rates, and their derivatives, providing a validation method of film model by comparison between reconstructed velocity experimental data and experimental velocity data. The comparison results show that the first-order weighted residual model (WRM) and regularized model (RM) are very similar, although they may fail to predict the velocity field in rapidly changing zones such as the front of the main hump and the first capillary wave troughs.

Solutions for Non-Newtonian Flow Into Elliptical Openings

1991 ◽  
Vol 58 (3) ◽  
pp. 820-824 ◽  
Author(s):  
A. Bogobowicz ◽  
L. Rothenburg ◽  
M. B. Dusseault
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Steady State ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Velocity Fields ◽  
Newtonian Flow ◽  
Element Analysis ◽  
Elliptical Opening ◽  
Elliptical Coordinates

A semi-analytical solution for plane velocity fields describing steady-state incompressible flow of nonlinearly viscous fluid into an elliptical opening is presented. The flow is driven by hydrostatic pressure applied at infinity. The solution is obtained by minimizing the rate of energy dissipation on a sufficiently flexible incompressible velocity field in elliptical coordinates. The medium is described by a power creep law and solutions are obtained for a range of exponents and ellipse eccentricites. The obtained solutions compare favorably with results of finite element analysis.

scholarly journals A 4D continuous representation of myocardial velocity fields from tissue phase mapping magnetic resonance imaging

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0247826
Author(s):  
Bård A. Bendiksen ◽  
Gary McGinley ◽  
Ivar Sjaastad ◽  
Lili Zhang ◽  
Emil K. S. Espe
Keyword(s):  
Velocity Field ◽  
Velocity Fields ◽  
Tissue Phase Mapping ◽  
Continuous Representation ◽  
Resonance Imaging ◽  
Limits Of Agreement ◽  
B Splines ◽  
End Point ◽  
Tissue Phase ◽  
Linear B

Myocardial velocities carry important diagnostic information in a range of cardiac diseases, and play an important role in diagnosing and grading left ventricular diastolic dysfunction. Tissue Phase Mapping (TPM) Magnetic Resonance Imaging (MRI) enables discrete sampling of the myocardium’s underlying smooth and continuous velocity field. This paper presents a post-processing framework for constructing a spatially and temporally smooth and continuous representation of the myocardium’s velocity field from TPM data. In the proposed scheme, the velocity field is represented through either linear or cubic B-spline basis functions. The framework facilitates both interpolation and noise reducing approximation. As a proof-of-concept, the framework was evaluated using artificially noisy (i.e., synthetic) velocity fields created by adding different levels of noise to an original TPM data. The framework’s ability to restore the original velocity field was investigated using Bland-Altman statistics. Moreover, we calculated myocardial material point trajectories through temporal integration of the original and synthetic fields. The effect of noise reduction on the calculated trajectories was investigated by assessing the distance between the start and end position of material points after one complete cardiac cycle (end point error). We found that the Bland-Altman limits of agreement between the original and the synthetic velocity fields were reduced after application of the framework. Furthermore, the integrated trajectories exhibited consistently lower end point error. These results suggest that the proposed method generates a realistic continuous representation of myocardial velocity fields from noisy and discrete TPM data. Linear B-splines resulted in narrower limits of agreement between the original and synthetic fields, compared to Cubic B-splines. The end point errors were also consistently lower for Linear B-splines than for cubic. Linear B-splines therefore appear to be more suitable for TPM data.

scholarly journals Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

2011 ◽  
Vol 4 (3) ◽  
pp. 1569-1610
Author(s):  
J. J. Fürst ◽  
O. Rybak ◽  
H. Goelzer ◽  
B. De Smedt ◽  
P. de Groen ◽  
...  
Keyword(s):  
Velocity Field ◽  
Finite Difference ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Higher Order ◽  
Velocity Fields ◽  
Force Balance ◽  
Staggered Grid ◽  
Comparison Results ◽  
Resultant Velocity

Abstract. We present a novel finite difference implementation of a three-dimensional higher-order ice sheet model that performs well both in terms of convergence rate and numerical stability. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, an existing discretisation that operates exclusively on the regular grid serves as a reference. Participation in the ISMIP-HOM benchmark indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This allows a direct comparison not only of the resultant velocity fields but also of the solver's convergence behaviour which holds main differences. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the precision for the resultant velocity field can be chosen higher in the novel finite difference implementation. For high precisions, the old discretisation experiences difficulties to converge due to large variation in the velocity fields of consecutive Picard iterations. Finally, changing discretisation prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher precision and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented. Transient applications also benefit from the increased computational efficiency.

JOINT 3D TRAVELTIME INVERSION OF P, S AND CONVERTED WAVES

2001 ◽  
Vol 09 (04) ◽  
pp. 1407-1416 ◽  
Author(s):  
GIULIANA ROSSI ◽  
ALDO VESNAVER
Keyword(s):  
Linear System ◽  
Seismic Waves ◽  
Velocity Fields ◽  
Traveltime Inversion ◽  
S Waves ◽  
The Earth ◽  
Converted Waves

Converted waves can play a basic role in the traveltime inversion of seismic waves. The sought velocity fields of P and S waves are almost decoupled, when considering pure P and S arrivals: their only connection are the possible common reflecting interfaces in the Earth. Converted waves provide new equations in the linear system to be inverted, which directly relates the two velocity fields. Since the new equations do not introduce additional unknowns, they increase the system rank or its redundancy, so making its solutions better constrained and robust.

scholarly journals Analysis of Convective Thunderstorm Split Cells in South-Eastern Romania

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Daniel Carbunaru ◽  
Sabina Stefan ◽  
Monica Sasu ◽  
Victor Stefanescu
Keyword(s):  
Velocity Field ◽  
Velocity Fields ◽  
Severe Weather ◽  
Doppler Velocity ◽  
Doppler Weather Radar ◽  
Dynamic Features ◽  
South Eastern ◽  
Wind Profiles ◽  
Convective Cells ◽  
Splitting Process

The mesoscale configurations are analysed associated withthesplitting process of convective cells responsible for severe weather phenomena in the south-eastern part of Romania. The analysis was performed using products from the S-band Doppler weather radar located in Medgidia. The cases studied were chosen to cover various synoptic configurations when the cell splitting process occurs. To detect the presence and intensity of the tropospheric jet, the Doppler velocity field and vertical wind profiles derived from radar algorithms were used. The relative Doppler velocity field was used to study relative flow associated with convective cells. Trajectories and rotational characteristics associated with convective cells were obtained from reflectivity and relative Doppler velocity fields at various elevations. This analysis highlights the main dynamic features associated with the splitting process of convective cells: the tropospheric jet and vertical moisture flow associated with the configuration of the flow relative to the convective cells for the lower and upper tropospheric layers. These dynamic characteristics seen in the Doppler based velocity field and in the relative Doppler velocity field to the storm can indicate further evolution of convective developments, with direct implications to very short range forecast (nowcasting).

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