Seismic horizon reconstruction on polygonal domains using the Schwarz-Christoffel transformation
Methods of seismic horizon reconstruction based on the solution of a partial derivative equation are generally robust to noise. However, they can only reconstruct horizons on rectangular domains when using fast iterative methods which is inconvenient in regions of uncertainty or irrelevant data in the seismic image. In this paper, we propose a method to reconstruct seismic horizons on any polygonal domain based on a succession of Schwarz-Christoffel transformations which conserve the angles locally. Since these are conformal transformations, the form of the equation is preserved and the solution on the polygonal domain corresponds to the solution on the rectangular domain using the grid data transformed from the rectangular into the polygonal domain.