Travel time estimation is a very challenging problem in seismology. This seismic attribut is highly important to understand the Earth's interior and the wave propagation. In order to estimate a multi-value travel time field, by tracking the wavefront, the eikonal equation must be solved. However, solving a non-linear Partial Differential Equation, which solution implies a discontinuity propagating (wavefront), is not an easy task. \cite{cheng2007}, \cite{boka2011} and \cite{boka2011} showed that the Discontinuous
Galerkin Finite Element Method (DG-FEM) is suitable for wavefront propagation problems. In this work, some assumptions are supplied in order to treat the eikonal equation as a 1D advection, and the DG-FEM is implemented to solve our formulation. Three different numerical examples of wavefront tracking along different media, homogeneous and heterogeneous, are provided to show applications of this methodology. Requirements to extend this work to 2D and 3D are also included.
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