| Function type | Instantaneous velocity is a function of a velocity map and time. |
| Definition of parameters |
A = constant factor. V0 map = velocity map. α = constant acceleration factor. T = bottom seismic time of the layer. |
| Operational applications |
Same as V0 + α T model, introducing an additional V0map parameter. You may consider α to be relatively constant for a considered layer, and V0 to be variable. Introducing a V0map with possible spatial variation, linked with seismic information, enables to minimize well depth mismatches. |
$$
V_{inst} = V0 + α \times t
$$
$$
DZ = \int_{t_0}^{t_0+DT} V_{inst}dt = \int_{t_0}^{t_0+DT} (V0+α \times t) \times dt
$$
$$
DZ = \left( V0 + α \times t_0 + \frac{α}{2} \times DT \right) \times DT
$$
$$
V_{int} = V0 + α \times t_0 + \frac{α}{2} \times DT
$$