2‐D DMO for a medium with constant vertical velocity gradient

1991 ◽  
Author(s):  
Matthias Schwab ◽  
Gerald H. F. Gardner
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Vertical Velocity Gradient

scholarly journals Brief Communication: On the influence of vertical velocity profiles on the combined power output of two model wind turbines in yaw

2017 ◽  
Author(s):  
Jannik Schottler ◽  
Agnieszka Hölling ◽  
Joachim Peinke ◽  
Michael Hölling
Keyword(s):  
Wind Turbines ◽  
Vertical Velocity ◽  
Velocity Gradient ◽  
Power Output ◽  
Velocity Profiles ◽  
Total Power ◽  
Misalignment Angle ◽  
Velocity Gradients ◽  
Total Power Output ◽  
Vertical Velocity Gradient

Abstract. The effect of vertical velocity gradients on the total power output of two aligned model wind turbines as a function of yaw misalignment of the upstream turbine is studied experimentally. It is shown that asymmetries of the power output of the downstream turbine and the combined power of both with respect to the upstream turbine's yaw misalignment angle can be linked to the vertical velocity gradient of the inflow.

A constrained parametric inversion for velocity analysis based on CFP technology

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1210-1222 ◽  
Author(s):  
M. M. Nurul Kabir ◽  
D. J. Verschuur
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Fluid Pressure ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Parametric Inversion ◽  
Layer Velocity ◽  
Vertical Velocity Gradient

A method of velocity analysis based on the common focusing point (CFP) method is presented. The two important aspects of the method are the use of the CFP domain and the use of a new parameterization—a vertical velocity gradient to describe the lateral velocity variation within a layer. The layer velocity is defined with only two parameters: an average velocity [Formula: see text]and a vertical velocity gradient (β). Layer velocity parameterization using [Formula: see text] and β assumes that the lithology of the layer is constant and that the overburden and fluid pressure increase linearly with depth. This type of parameterization is suitable for areas with gross changes in lithology (clastic‐carbonate‐salt) and for rock in hydrostatic equilibrium. A layer‐based model is required for these areas. The salt dome data example presented belongs to this type of area, so the layer‐based model with the defined parameterization produced a very good subsurface velocity model. The method is based on the principle of equal traveltime between the focusing operator and the corresponding focus point response. The velocity estimation problem is formulated as a constrained parametric inversion process. The method of perturbation is applied where linear assumptions are made; the velocity inversion, however, is a nonlinear problem, and the model parameter updates are computed iteratively using Newton’s method. The velocity model is built by layers in a top‐down approach, which makes the problem quasi‐linear.

scholarly journals Inclusion of velocity gradients in the Unno solution for magnetic field diagnostic from spectropolarimetric data

2010 ◽  
Vol 6 (S274) ◽  
pp. 291-294
Author(s):  
Guillaume Molodij ◽  
Véronique Bommier
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Vertical Velocity ◽  
Velocity Gradient ◽  
Coming Out ◽  
The Sun ◽  
Velocity Gradients ◽  
Vertical Velocity Gradient

AbstractWe present an extension of the Unno-Rachkovsky solution that provides the theoretical profiles coming out of a Milne-Eddington atmosphere imbedded in a magnetic field, to the additional taking into account of a vertical velocity gradient. Thus, the theoretical profiles may display asymmetries as do the observed profiles, which facilitates the inversion based on the Unno-Rachkovsky theory, and leads to the additional determination of the vertical velocity gradient. We present UNNOFIT inversion on spectropolarimetric data performed on an active region of the Sun with the french-italian telescope THEMIS operated by CNRS and CNR on the island of Tenerife.

Migration velocity analysis in factorized VTI media

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 708-718 ◽  
Author(s):  
Debashish Sarkar ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Migration Velocity ◽  
P Wave ◽  
Velocity Analysis ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Wave Migration ◽  
Vti Media

One of the main challenges in anisotropic velocity analysis and imaging is simultaneous estimation of velocity gradients and anisotropic parameters from reflection data. Approximating the subsurface by a factorized VTI (transversely isotropic with a vertical symmetry axis) medium provides a convenient way of building vertically and laterally heterogeneous anisotropic models for prestack depthmigration. The algorithm for P‐wave migration velocity analysis (MVA) introduced here is designed for models composed of factorized VTI layers or blocks with constant vertical and lateral gradients in the vertical velocity VP0. The anisotropic MVA method is implemented as an iterative two‐step procedure that includes prestack depth migration (imaging step) followed by an update of the medium parameters (velocity‐analysis step). The residual moveout of the migrated events, which is minimized during the parameter updates, is described by a nonhyperbolic equation whose coefficients are determined by 2D semblance scanning. For piecewise‐factorized VTI media without significant dips in the overburden, the residual moveout of P‐wave events in image gathers is governed by four effective quantities in each block: (1) the normal‐moveout velocity Vnmo at a certain point within the block, (2) the vertical velocity gradient kz, (3) the combination kx[Formula: see text] of the lateral velocity gradient kx and the anisotropic parameter δ, and (4) the anellipticity parameter η. We show that all four parameters can be estimated from the residual moveout for at least two reflectors within a block sufficiently separated in depth. Inversion for the parameter η also requires using either long‐spread data (with the maximum offset‐to‐depth ratio no less than two) from horizontal interfaces or reflections from dipping interfaces. To find the depth scale of the section and build a model for prestack depth migration using the MVA results, the vertical velocity VP0 needs to be specified for at least a single point in each block. When no borehole information about VP0 is available, a well‐focused image can often be obtained by assuming that the vertical‐velocity field is continuous across layer boundaries. A synthetic test for a three‐layer model with a syncline structure confirms the accuracy of our MVA algorithm in estimating the interval parameters Vnmo, kz, kx, and η and illustrates the influence of errors in the vertical velocity on the image quality.

Wave boundary layers in a stratified fluid

2017 ◽  
Vol 833 ◽  
pp. 512-537 ◽  
Author(s):  
G. M. Reznik
Keyword(s):  
Exact Solutions ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Velocity Gradient ◽  
Initial Perturbation ◽  
Stratified Fluid ◽  
Horizontal Velocity ◽  
Asymptotic Solutions ◽  
Linear Evolution ◽  
Wave Boundary

We study so-called wave boundary layers (BLs) arising in a stably stratified fluid at large times. The BL is a narrow domain near the surface and/or bottom of the fluid; with increasing time, gradients of buoyancy and horizontal velocity in the BL grow sharply and the BL thickness tends to zero. The non-stationary BL can arise both as a result of linear evolution of the initial perturbation and under the action of an external force (tangential stress exerted on the fluid surface in our case). We analyse both the variants and find that the ‘forced’ BLs are much more intense than the ‘free’ ones. In the ‘free’ BLs all fields are bounded and the gradients of buoyancy and horizontal velocity grow linearly in time, whereas in the ‘forced’ BL only the vertical velocity is bounded and the buoyancy and horizontal velocity grow linearly in time. As to the gradients in the ‘forced’ BL, the vertical velocity gradient grows in time linearly and the gradients of buoyancy and horizontal velocity grow quadratically. In both of the cases we determine exact solutions in the form of expansions in the vertical wave modes and find asymptotic solutions valid at large times. The comparison between them shows that the asymptotic solutions approximate the exact ones fairly well even for moderate times.

Rheotaxis of spermatozoa

1961 ◽  
Vol 153 (953) ◽  
pp. 490-502 ◽  
Keyword(s):  
Fluid Flow ◽  
Specific Gravity ◽  
Vertical Velocity ◽  
Velocity Gradient ◽  
Linear Velocity ◽  
Direction Parallel ◽  
Unknown Mechanism ◽  
Velocity Gradients ◽  
Stream Lines ◽  
Do So

1. The response of human and bull spermatozoa to vertical velocity gradients has been examined, the fluid flow being in horizontal planes. 2. Dead human and bull spermatozoa point downstream (negative rheotaxis) in the top half of a parabolic velocity gradient and upstream (positive rheotaxis) in the bottom half. Although spermatozoa point preferentially in one or other direction, parallel to the stream ­ lines, in linear velocity gradients, this cannot be described as positive or negative rheotaxis because the direction in which the spermatozoa point is determined by the direction of shear. 3. The response of dead human and bull spermatozoa to velocity gradients is due to the head of the spermatozoon having a higher specific gravity than the tail, which causes the spermatozoon to sink head first in a medium of lower specific gravity than that of the spermatozoon. 4. Live human and bull spermatozoa exhibit positive rheotaxis, i.e. they swim up stream, in both halves of a parabolic velocity gradient. 5. The behaviour of previously flow-orientated spermatozoa in a just-reversed velocity gradient has been photographed and analysed. Though the mechanism whereby dead spermatozoa re-orientate in such conditions is understood, live spermatozoa, which also re-orientate in these conditions, may do so by a different and, at present, unknown mechanism.

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