Representation of complex geological velocity model based on level set method

The difficulties in the expression of geological velocity model are the accurate description of complex geological phenomena and the effective support for the forward and inverse applications. We presented a novel representation method for describing velocity models. Velocity discontinuity was embedded into model in the form of zero-value contour of an implicit function. Multi-copy strategy was to properly handle the contradictory interpolation of velocity value at the boundary of discontinuities. The representation method can be applied to describe very complicated velocity models such as the faulted interface with non-manifold nature and multiple value surfaces. In applications based on the ray theory, signed distance field and velocity discontinuity binary tree enable fast access to velocity information of arbitrary point and easy detection of ray-interface intersection. The model can make the ray propagate positively and honor Snell's law strictly when facing velocity interface and thus improve the accuracy of ray path. Two groups of ray tracing examples verify the effectiveness of the method.