Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media

Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation attenuating media, where real imaginary parts function capture dispersion effects amplitude attenuation seismic waves, respectively. Conventionally, such mainly computed either by tracing rays exactly complex space or approximately so that resulting distributed irregularly space. However, data processing methods, as prestack depth migration tomography, require uniformly eikonals. Therefore, we have developed unified framework to Eulerianize several popular approximate real-space ray-tracing methods eikonals satisfy classic equation novel advection equation, respectively, dub method Eulerian partial-differential-equation method. We further develop highly efficient high-order solve these two equations using factorization idea Lax-Friedrichs weighted essentially nonoscillatory schemes. Numerical examples demonstrate our yields accurate eikonals, analogous those from methods. Our can be useful tomography media.