The model value is a key parameter of Udomore® Depth conversion computations; it enables to properly handle uncertainties on the time picking and interval velocity model, and maximize the confidence in the depth model. The model value is derived from the Bayesian kriging model of all layers at the layer considered as follows :
$$
{\huge \sigma}_{RZ_l} = \left( \frac{{\Large 1}}{Nw_l} \sum\limits_{i=1}^{Nw_l} \left( \sum\limits_{j=1}^l {\Large \Delta t_j (x_i)^2 \cdot } {\huge \sigma}^{\Large 2}_{RV_j} {\Large (x_i) + \overline{V_l} (x_i)^2 \cdot } {\huge \sigma}^{\Large 2}_{RV_l} {\Large(x_i) } \right) \right)^{\Large {\frac{1}{2}}}
$$
Where:
- \(V\) is the mean velocity at the wells and t the mean of time at the wells
- \({\huge \sigma}_{RZ_l}\) is the average standard deviation of the modeled residual depth of the layer \(l\)
- \( Nw_l\) is the number of well-tops corresponding to the layer \(l\)
- \(\Delta t_j (x_i)\) is the one-way time interval of the layer \(j\) at the \(i^{th}\) welltop