The first arrival travel times and amplitudes have various geophysical applications for near sub-surface characterization, such as refraction tomography. Many works have been done to estimate these components using finite-difference schemes to solve the Eikonal and transport equations. In most of these studies, the local finite-difference operator assumes plane wave fronts, that is not accurate near the source position. We propose here to use the perturbation method in order to overcome this difficulty. Travel times and amplitudes are decomposed into two terms: a homogeneous term computed analytically and an additive perturbation computed with finite-differences. This approach mimics better the spherical behavior of wave fronts in the source neighborhood resulting in better travel time gradients and thus in better amplitudes. Classical methods consider travel times and amplitudes as a separated problem and compute amplitudes a posteriori. In this study we introduce a new method to compute these components jointly. Results show that we improve the amplitude for high contrast velocity models by adapting a joint computation of both travel times and amplitudes.


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