| Function type | Instantaneous velocity is a function of time isopach. |
| Definition of parameters |
V0 = constant velocity factor. α = constant acceleration factor. DT = DT isopach time (automatically computed by UDOMORE® Depth as the difference between the time interpretation map at the top of the considered layer and the time interpretation map at the top of the layer immediately above). |
| Operational applications |
Same as V0 + α × T, except that V0 is linked to the top of the considered layer. Useful when you are in a layered model and the V0 at reference datum does not reflect a possible change of V0 values at the top of the layer. For example, when there is an important dip effect at the top of the layer. |
$$
V_{inst} = V0 + α \times (t-t_0)
$$
$$
DZ = \int_{t_0}^{t_0+DT} V_{inst}dt = \int_{t_0}^{t_0+DT} (V0+α \times (t-t_0)) \times dt
$$
$$
DZ = \left( V0 + (α – 1 ) \times t_0 + \frac{α}{2} \times DT \right) \times DT
$$
$$
V_{int} = V0 + (α – 1) \times t_0 + \frac{α}{2} \times DT
$$