Tomography advancements for large datasets and complex velocity
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
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 GeoDepth Tomography solution addresses the computational, interpretational, and acquisitional challenges of updating large and complex velocity
models for critical seismic assets.
RTM overcomes the compromising assumptions of other depth migration methods by properly propagating acoustic wave fields through the most complex velocity
regimes, including sub-salt, for structures having dips in excess of 90 degrees, and in the presence of reflection boundaries that may generate internal multiples.