A level set based Eulerian method for paraxial multivalued traveltimes

We apply the level-set methodology to compute multivalued solutions of the paraxial eikonal equation in both isotropic and anisotropic metrics. This paraxial equation is obtained from 2D stationary eikonal equations by using one of the spatial directions as the artificial evolution direction. The advection velocity field used to move level sets is obtained by the method of characteristics; therefore, the motion of level sets is defined in a phase space, and the zero level set yields the location of bicharacteristic strips in the reduced phase space. The multivalued traveltime is obtained from solving another advection equation with a source term. The complexity of the algorithm is O(N3logN) in the worst case and O(N3) in the average case, where N is the number of the sampling points along one of the spatial directions. Numerical experiments including the well-known Marmousi synthetic model illustrate the accuracy and the efficiency of the Eulerian method.