Single pass eikonal solver in tilted transversely anisotropic media

We present a numerical scheme to solve the eikonal equation in a Tilted Transversely Isotropic (TTI) medium. The solution to this equation corresponds to the first arrival time of seismic pressure waves in the high frequency asymptotic regime, whose propagation speed is neither isotropic nor elliptic. Instead, the speed profile is characterized by a fourth degree polynomial equation in a rotated frame, defined in terms of the Thomsen or Hooke elasticity coefficients of the geophysical medium. We show that TTI eikonal equations can be expressed as the maximum or minimum of a family of Riemannian eikonal equations, for which efficient discretizations are known. Based on this observation, we propose an original scheme that is causal, thus solvable in a single pass over the domain, and Eulerian, hence also mapping well to massively parallel architectures. Numerical experiments illustrate the method's accuracy, speed and robustness, on both a problem with analytical solution and a realistic synthetic instance, and compare a CPU with a GPU implementation, with the GPU being fifty times faster than the CPU implementation.