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Applicable Analysis
An International Journal
Volume 71, 1998 - Issue 1-4
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Original Articles

New results in the classical travel-time inversion problem

Pages 253-270 | Received 01 Jun 1998, Published online: 20 Jan 2011

References

  • Gerver , M.L. 1997 . Advances in the classical travel-time inversion problem , Vol. 16 , Moscow : MITP RAS, Preprint . Computational seismology. 30, Moscow: Nauka (to appear in 1998) (Russian)
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  • Gerver , M.L. and Markushevich , V.M. 1965 . An investigation of the ambiguity in the determination of the velocity of propagation of seismic waves from the travel-time curve . Dokl. Akad. Nauk SSSR , 163 ( 6 ) : 1377 – 1380 . English transl. in Dokl. Acad. Sci. USSR. Earth Sci. Sect. 163 (1965)
  • Gerver , M.L. and Markushevich , V.M. 1966 . Determination of seismic wave velocity from the traveltime curve . Geophys. J. Royal Astr. Soc , 11 ( 6 ) : 165 – 173 .
  • Gerver , M.L. and Markushevich , V.M. 1967 . “ Determination of the velocity of propagation of seismic waves from the travel-time curve ” . In Methods and programs for the analysis of seismic observations , 3 – 51 . Moscow : Nauka . (Computational seismology. 3) (Russian). English transl., Consultants Bureau, New York 1972, pp. 148-171
  • Gerver , M.L. and Kudryavtseva , E.A. 1996 . On the boundary of the set of solutions in the travel-time inversion problem . Dokl. Akad. Nauk , 346 ( 5 ) : 672 – 674 . (Russian). English transl. in Trans. Dokl. Russian Acad. Sci. Earth Sci. Sect. V.347 (1996)
  • Gerver , M.L. and Kudryavtseva , E.A. 1997 . On extremal properties of waveguides with finitely many layers in the travel-time inversion problem . Dokl. Akad. Nauk , 356 ( 1 ) : 25 – 28 . (Russian). English transl. in Doklady Mathematics. 1997. V. 56. N. 2, pp. 777-780
  • Gerver , M.L. and Kudryavtseva , E.A. 1997 . A universal sequence in the classical travel-time inversion problem . Mat. Sb , 188 ( 4 ) : 3 – 56 . (Russian). English transl. in Sbornik: Mathematics 1997. V. 188. N. 4, pp. 483-536
  • Gerver , M.L. and Kudryavtseva , E.A. 1997 . New proof of theorems on universal sequence and on extremal properties of discrete measures . Uspekhi Mat. Nauk , 52 ( 6 ) : 153 – 154 . (Russian). English transl. in Russian Math Surveys 52 (1997)
  • Gerver , M.L. and Kudryavtseva , E.A. 1997 . “ Extremal properties of discrete measures, universal sequence and duality principle ” . Vol. 23 , Moscow : MITP RAS, Preprint . Mat. Sb. (to appear in 1998) (Russian)
  • Kronrod , A.S. 1964 . “ Nodes and weights of quadrature formulae ” . In Sixteen-place tables , 144 Moscow : Nauka . (Russian). English transl., Consultants Bureau, New York 1965
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  • Bernstein , I.N. and Gerver , M.L. 1978 . “ On the problem of integral geometry for a family of geodesies and on inverse kinematic problem ” . In Institute of Physics of the Earth, Akad Nauk SSSR , 4 Moscow : Preprint . Dokl. Akad. Nauk. SSSR, 1978. V. 243. N. 2, pp. 302-305 (Russian). English transl. in Dokl. Acad. Sci. USSR. Earth Sci. Sect. V. 243 (1978)
  • Romanov , V.G. 1978 . Integral geometry on geodesies of isotropic Riemannian metric . Dokl. Akad. Nauk. SSSR , 241 ( 2 ) : 290 – 293 . (Russian). English transl. in Dokl. Acad. Sci. USSR. V. 241 (1978).
  • Mukhometov , R.G. and Romanov , V.G. 1978 . On the problem of finding an isotropic Riemannian metric in n-dimensional space . Dokl. Akad. Nauk. SSSR , 243 ( 1 ) : 41 – 44 . (Russian). English transl in Dokl. Acad. Sci. USSR. V. 243 (1978)
  • Bernstein , I.N. and Gerver , M.L. 1980 . “ A condition of distinguishability metrics by travel-time curves ” . In Methods and algorithms of interpretation of seismological data , 50 – 73 . Moscow : Nauka . (Computational seismology, 13) (Russian). English transl. in Computational seismology. V. 13 (1981), pp.48-72
  • Polya , G. and Sctgö , G. 1978 . “ Problems and theorems in analysis ” . In Grundleheren Math. Wiss , Vol. 11 , Berlin : Springer-Verlag .
  • Gerver , M.L. 1996 . Some simple theorems on the distribution of roots . Uspekhi Mat. Nauk , 51 ( 3 ) : 191 – 192 . (Russian). English transl, in Russian Math Surveys 51 (1996)
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