Stratigraphic coordinates, a coordinate system tailored to seismic interpretation

Algorithm

In summary, our algorithm for transferring seismic images from the regular Cartesian coordinate system into the stratigraphic coordinate system consists of the following steps:

1. Extract the first axis of the stratigraphic coordinate system $Z_0\left(x,y,z\right)$ from seismic image $P\left( x,y,z \right)$ by predictive painting;

2. Start with $X_0$ at $\left(z = 0\right)$ as an initial value and solve equation 1 with boundary condition 3 numerically for $X_0$;

3. Start with $Y_0$ at $\left(z = 0\right)$ as an initial value and solve equation 2 with boundary condition 4 numerically for $Y_0$.

We solve equations 1 and 2 numerically with an explicit upwind finite-difference scheme (Li and Fomel, 2013; Franklin and Harris, 2001).