Abstract
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).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Berryman JG (1991) Lectures notes on nonlinear inversion and tomography. Borehole seismic tomography. Technical report, Lawrence Livermore National Laboratory
Dines KA, Lytle RJ (1979) Computerized geophysical tomography. IEEE Proc 67(7):1065–1073
Fernández-Martínez JL, Pedruelo-González LM (2008) Anisotropic mean traveltime curves: a method to estimate anisotropic parameters from 2D transmission tomographic data. Math Geosci 41(2):163–192. doi:10.1007/s11004-008-9202-4
Fernández-Martínez JL, Fernández-Álvarez JP, Pedruelo-González LM (2006) Mean traveltime curves analysis: a method to improve understanding of data behaviour in 2-D transmission tomography at the pre-inversion stage. Math Geol 38(3):343–374
Fernández-Martínez JL, Fernández-Alvarez JP, Pedruelo-González LM (2008) MTCLAB: a MATLAB®-based program for traveltime quality analysis and preinversion velocity tuning in 2-D transmission tomography. Comput Geosci 34(3):213–225. doi:10.1016/j.cageo.2007.03.008
Fernández-Martínez JL, Pedruelo-González LM, García-Gonzalo E (2009a) AMTCLAB: a MATLAB®-based program for traveltime analysis and velocity tuning in 2D elliptical anisotropic media. Comput Geosci 35(10):2057–2064. doi:10.1016/j.cageo.2008.11.013
Fernández-Martínez JL, Pedruelo-González LM, DeParis J, Mangriotis MD, Rector JW (2009b). Application of the mean traveltime curves to GPR and VSP data. In: Annual meeting, EEGS, SAGEEP
Gelbke C, Miranda F, Sattel G (1989) The results of a seismic transmission tomography survey at the Grimsel rock laboratory. Log Anal 243–260
Gordon R (1974) A tutorial on ART. IEEE Trans Nucl Sci NS-21:78–93
Ivansson S (1986) Seismic borehole tomography. Theory and computational methods. IEEE Proc 74(2):328–338
Scales JA (1987) Tomographic inversion via the conjugate gradient method. Geophysics 52:179–185
Scales JA, Gersztenkorn A (1988) Robust methods in inverse theory. Inverse Probl 4:1071–1091
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Fernández Martínez, J.L., Pedruelo González, L.M. & Rector, J.W. Robust Mean Traveltime Curves in 2D Transmission Tomographic Surveys. Math Geosci 42, 377–400 (2010). https://doi.org/10.1007/s11004-010-9272-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-010-9272-y