# complex velocity

## complex velocity

[′käm‚pleks və′läs·əd·ē]
(fluid mechanics)
In ideal aerodynamic flow, the derivative of the complex potential with respect to z = x + iy, where x and y are the chosen coordinates.
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In this work, it is shown that Full Waveform inversion has a great potential for estimating complex velocity models such as Marmousi Velocity Model when the acquisition parameters are as optimal as possible.
(b) Through the resetting potential at any place in the seepage plane of the karst tunnel, the potential function, flow function, and complex velocity of the seepage field in the karst tunnel are solved
The potential function, the flow function, and the complex velocity at any place in the infinite plane are solved.
[mathematical expression not reproducible], and [f.sub.e] are the complex acceleration vector, complex velocity vector, complex displacement vector, complex forces vector, respectively.
The complex velocity for two neighboring line sinks is
Combining the equations in (6) using the complex velocity F = u + iv, we get momentum equation in complex velocity
is the complex velocity, [V.sub.D] is the differentiable and resolution scale independent velocity, [V.sub.F] is the nondifferentiable and resolution scale dependent velocity, [??] x [nabla] is the convective term,
Applying the fractal operator (1) to the complex velocity (2) and accepting a generalized inertial principle (a generalization of Nottale's principle of scale covariance [12-14]), we obtain the geodesics in the form of the Navier-Stokes-type equations:
However the flow is three dimensional and all the perturbed variables have been obtained using boundary layer type equations, which reduce to two coupled differential equations for a complex velocity.
Our method yields, in particular, an algorithmic approach for deriving the fluid's complex velocity (Section 4).
Reverse time migration (RTM) is considered the benchmark in imaging due to its ability to handle complex velocity models with abrupt discontinuities typical of structures such as salt bodies, with which ray-based methods typically struggle.
Let us explicitly introduce the real and imaginary parts of the complex velocity V = V - iU,
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