Synthetic data test

First of all, we extracted 3 traces from the Sigmoid model at lateral locations 0.09km, 0.64km, and 1.19km. The predictive painting of the trace sampled at 0.64km is shown in Figure 2. Then we compute the interpolation weighted by RBF according to conventional geometric distance $d(x_k,x_r)$, the result is shown in Figure 3a.

interpold,interp
Figure 3. Interpolation results with (a) conventional RBF coefficients without considering faults, and (b) proposed modified RBF coefficients using geologic distance.

Next, we incorporate the proposed $\tilde d(\mathbf{x}_k,\mathbf{x}_r)$ in the interpolation for comparison. We measure the fault attribute using plane-wave Sobel filter proposed by Phillips et al. (2016). In result Figure 3b, the recovery at the fault location is significantly improved, because geologic distance weights prevent the well log information from incorrectly spreading across the fault.