Abstract
The total inversion algorithm and some elements of Mathematical Information Theory are used in the treatment of travel-time data belonging to a seismic refraction experiment from the southern segment (Sardinia Channel) of the European Geotraverse Project. The inversion algorithm allows us to improve a preliminary propagating model obtained by means of usual trial and error procedure and to quantify the resolution degree of parameters defining the crust and upper mantle of such a model. Concepts related to Mathematical Information Theory detect some seismic profiles of the refraction experiment which give the most homogeneous coverage of the model in terms of number of trajectories crossing it. Finally, the efficiency of the inversion procedure is quantified and the uncertainties regarding knowledge of different parts of the model are also evaluated.
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References
Ash, R.,Information Theory (Interscience Publishers, New York 1965).
Auzende, J. M., Olivet, J. L., andBonnin, J. (1974), Le détroit Sardano-Tunisien et la zone de fracture nord-tunissienne, Tectonophys.21, 357–374.
Banda, E., Ansorge, J., Boloix, M., andCórdoba, D. (1980),Structure of the Crust and Upper Mantle Beneath the Balearic Islands (Western Mediterranean), Earth Plan. Sci. Lett.49, 219–230.
Banda, E., Egger, A., Demartin, M., Maistrello, M., andAnsorge, J.,Crustal structure under Sardinia. InSecond EGT Workshop. The Southern Segment (European Science Foundation, Strasbourg, France 1985).
Ben-Menahem, A., andSingh, S. J.,Seismic Waves and Sources (Springer-Verlag, Berlin 1981).
Brioullin, L.,Science and Information Theory (Academic Press, New York 1962).
Dantz, D. (1978),Ray-tracing Method, Ph.D. Thesis, Freie Universität, Berlin.
Finetti, I., andMorelli, G. (1972),Wide Scale Digital Seismic Exploration of the Mediterranean Sea, Bolletino di Geofisica Teor. ed Appl.14, 291–342.
Finetti, I., andMorelli, G. (1973),Geophysical Exploration of the Mediterranean Sea, Boll. Geofis. Teor. Appl.15, 263–341.
Firbas, P.,Tomography from seismic profiles. InSeismic Tomography (Reidel Publishing Co., Holland 1987).
Hatzfeld, D. (1978),Etude sismotectonique de la zone de collision Ibero-Maghrebine, These Univ. Scient. Med., Grenoble, France.
Ivansson, S.,Crosshole transmission tomography. InSeismic Tomography (Reidel Publishing Co., Holland 1987).
Kintchin, R. T.,Mathematical Foundations of Information Theory (Dover, New York 1957).
Lana, X., andMartínez, M. D. (1990),Joint Inversion of Travel Times and Waveforms by Means of Annealing Algorithms. Application to a Seismic Refraction Experiment, Pure Appl. Geophys.134 (1), 117–133.
Lana, X., Martínez, M. D., andde Miguel, F. (1990),Efficiency of a Seismic Network from the Viewpoint of Mathematical Information Theory: Application to the Andalusia (Spain) Seismic Network, Tectonophys.176, 377–386.
Nicolich, R.,EGT Southern Segment reflection seismics in the offshore areas. InSecond EGT Workshop. The Southern Segment (European Science Foundation, Strasbourg 1985).
Nolet, G.,Waveform tomography. InSeismic Tomography (Reidel Publishing Co., Holland 1987).
Shannon, C. E. (1948),A Mathematical Theory of Communication, Bell Systems Tech. J.27, 379–423 and 623–656.
Tarantola, A., andValette, B. (1982),Generalized Nonlinear Inverse Problem Solved using the Least Square Criterion, Rev. Geophys. Space Phys.20 (2), 219–232.
Tarantola, A.,Inversion Problem Theory (Elsevier, New York 1987a).
Tarantola, A.,Inversion of travel time and seismic waveforms, InSeismic Tomography (Reidel Publishing Co., Holland 1987b).
Torelli, L., Cornini, S., andMarchetti, F.,Seismic stratigraphy and tectonic-structural setting of the Sardinia Channel (Western Central Mediterranean). InSecond EGT Workshop. The Southern Segment (European Science Foundation, Strasbourg, France 1985).
Yogomida, K.,Surface waves in weakly heterogeneous media. InMathematical Geophysics (Reidel Publishing Co. Holland, 1988).
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Martínez, M.D., Lana, X. Some elements of mathematical information theory and total inversion algorithm applied to travel time inversion. PAGEOPH 137, 113–132 (1991). https://doi.org/10.1007/BF00876892
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DOI: https://doi.org/10.1007/BF00876892