Robust Mean Traveltime Curves in 2D Transmission Tomographic Surveys

Acoustic tomography methods belong to the class of nondestructive inspection techniques and are used in engineering applications. One of the main issues for these methods is the direct arrival, which can be noisy or can be affected by scattering or other propagation effects. In this paper, we present the mathematical deduction and analysis of the so-called robust mean traveltime curves—the median, p-percentiles, inter-quartile range and minimum absolute deviation—for homogeneous isotropic or elliptical anisotropic media. Robust mean traveltime curves are a simple model used to describe the variation of the traveltime statistical descriptors for the different gathering subsets as a function of a gather index, and generalize the mean traveltime curves introduced in the past to the case of robust statistics. These curves admit analytical expression for zonal isotropic and elliptical anisotropic media explored via rectangular or irregular acquisition geometries, and thus, apply to 2D acoustic transmission tomography experiments conducted in relatively homogeneous blocks. The robust mean traveltime curves are more resistant to the presence of outliers, and thus they are preferred to infer background velocity models which can be taken into account in the resolution of the tomographic inverse problem. The property of robust descriptors to find blocky solutions in presence of velocity heterogeneities is also illustrated. Finally, we show the application of this methodology to a granitic medium (Febex Project, Nagra, Switzerland).