FIRST-ARRIVAL TRAVEL-TIME CALCULATION FOR ATTENUATING TILTED TRANSVERSELY ISOTROPIC MEDIA USING A FAST SWEEPING METHOD

First-arrival traveltime plays an important role in many geophysical applications including static correction, seismic tomography and migration. Eikonal equation has been proven effective and accurate for calculating the first-arrival traveltime even in complex subsurface media. Eikonal equation in attenuating media can provide not only the information of phase arrival, but also the amplitude decay due to the introduction of complex-valued traveltime and medium parameters. By applying the rotation operator to the eikonal equation in attenuating VTI media, the equation in attenuating TTI media can be obtained directly. However, traditional numerical methods such as fast sweeping method and fast marching method, which update the traveltime in the grids along the direction of wave front expansion by selecting the minimum of traveltimes, cannot be applied to attenuating media since there is no minimum value between two complex numbers. In order to address this problem, the perturbation method has been introduced by factoring the complex-valued eikonal equation into real part and imaginary part, called zeroth- and first-order governing equations, respectively. The real part of the complex-valued traveltime corresponds to the phase of waves, while the imaginary part describes the amplitude decay associated with seismic attenuation. Thus, by applying numerical methods for these governing equations, the real and imaginary parts of traveltime can be solved successively. Additionally, the source-singularity problem results from finite-difference-based solutions of eikonal equation hinders the accuracy of travel-time in the whole computation domain. The factorization method can be used to tackle with source-singularity problem to improve accuracy. Numerical tests verify the validity and accuracy of the proposed algorithm.