Objective function

With the definition in Equation (17), we can write the optimization function J as:

$$J\left(s\right) := \frac{1}{2}\sum_{z,\vec{m},\vec{h}} \left... ...- {\bf B}_z\left[\mathcal T_{z } \right] \right] \right\vert^2,$$ (18)

where s is the slowness function, and $z,\vec{m},\vec{h}$ stand respectively for depth, and the midpoint and offset vectors. In compact matrix form, we can write the objective function as:  

$$J\left(s\right):= \frac{1}{2} \left\vert{\bf I}\left(\AA \u - {\bf B}\mathcal T\right)\right\vert^2,$$ (19)

which takes special forms depending on our choice of the operators $\AA$ and ${\bf B}$:

WEMVA by TIF WEMVA by DSO

$$J\left(s\right)= \frac{1}{2} \left\vert{\bf I}\left(\u - \mathcal T\right)\right\vert^2 J\left(s\right)= \frac{1}{2} \left\vert{\bf I}\left({\bf D}\u \right)\right\vert^2$$