| Function type | Instantaneous velocity is a function of a velocity map and time isopach. |
| Definition of parameters |
A = constant rescaling factor. V0map = velocity map. 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 × DT, introducing an additional V0map parameter. You may consider alpha 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. For example, you can introduce a seismic V0 map based on your available seismic velocity map. |
$$
V_{inst} = V0 + α \times (t-t_0)
$$
$$
DZ = \int_{t_0}^{t_0+DT} V_{inst}dt = \int_{t_0}^{t_0+DT} (V0+α \times (t-t_0)) \times dt
$$
$$
DZ = \left( V0 + ( α – 1) \times t_0 + \frac{α}{2} \times DT \right) \times DT
$$
$$
V_{int} = V0 + ( α – 1) \times t_0 + \frac{α}{2} \times DT
$$