Our method yields, in particular, an algorithmic approach for deriving the fluid's complex velocity (Section 4).

A rigorous analysis of (1) requires a detailed study of the complex velocity, the flow rate function and the velocity potential.

The complex velocity v(s) is further calculated based on the following equations:

We finally calculate the complex velocity values [w.

THE CALCULUS ALGORITHM OF THE FLUID'S COMPLEX VELOCITY

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,

Indeed, the imaginary part of the complex velocity field is given, in terms of the modulus of o, by the expression:

We shall express the energy equation in terms of the various equivalent variables which we use in scale relativity, namely, the wave function o, the complex velocity V or its real and imaginary parts V and -U.

Re-introducing the complex velocity field V = -2i[nabla] ln [psi] in this expression we finally obtain the correspondence:

The complex velocity field Va reads in terms of the wave function