Interpolation using predictive painting

Time dip describes how a seismic event changes from one trace to the next. If available, the local dips could be used to interpolate log data along seismic structure and predict an expected log profile in a location with no well log data. Similar to Karimi et al. (2017), we generate log property volumes by weighting predictive painting. Predictive painting is defined using plane-wave destruction filters which measure the local slope of seismic events (Fomel, 2002). The local slope of seismic events is used to predict one trace from another trace and can be used to interpolate a reference well log through a seismic volume (Appendix B) (Fomel, 2010). The interpolation based on the distance between the reference well and any location is the seismic dataset, as defined in Equation 7. The RBF and log property volumes generated from data at each well location are combined to form a single log property volume using the following interpolant:

$$V(x,t) = \dfrac{\sum_{k}^{N}\phi(\vert x - x_k\vert)S_k(x,t)}{\sum_{k}^{N}\phi(\vert x - x_k\vert)}$$ (18)

where $\mathbf{S_{k}}$ is the volume created by spreading log data from location $x_k$ to the entire seismic data set using predictive painting and $N$ is the total number of wells used in the interpolation.