不连续走时曲线的反演
ON THE INVERSION PROBLEM FOR A DISCONTINUOUS TRAVEL-TIME CURVE
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摘要: 本文系统地求解了不连续走时曲线的反演问题.所得到的解答表明,除了在低速层(若存在)内,其余各处的速度分布以及低速层的厚度均可唯一地确定.本文指出Slichter(1932)关于低速层厚度上界的推导和Gerver-Markushevich(1966)的反演公式是不合理的.Abstract: A complete solution of the inversion problem has been aihieved for a discontinuous travel-time curve. The solutions show that, except in the LVL (if exists), the velocity structure and the thickness of the LVL can be uniquely determined. Finally, we point out that the Gerver-Markushevichs formula (1966) is incorrect.
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[1] Herglotz, G,1907. Phys. Zeits, 8, 145——147.
[2] Baseman, H.1910. Phys. Mag., 19, 576.
[3] Wiechert and Geiger, 1910. Phys. Zcits., 11, 294.
[4] Aki,K.,and P. G. Richards, 1980. Ozrantitative Scisnzology——theory and methods, 641——659. San Fran——ciso: Freeman
[5] Bocher, M., 1909. An introduction to the study of integral equations, 9. Cambridge University press.
[6] Slichter, L, B., 1932. The theory of the interpretation of seismic traveltime curve in horizontal structures.Physics, 3, 273——295.
[7] Gerver, M. L., and V. Markushevich, 1966. Determination if a Seismic Wave Velocity from the travel——time curve. Geophys. J., 165——173.
[8] Lanczos, C,1961. Linear Differential Operators. 140. London: Van Nostrand.[1] Herglotz, G,1907. Phys. Zeits, 8, 145——147.
[2] Baseman, H.1910. Phys. Mag., 19, 576.
[3] Wiechert and Geiger, 1910. Phys. Zcits., 11, 294.
[4] Aki,K.,and P. G. Richards, 1980. Ozrantitative Scisnzology——theory and methods, 641——659. San Fran——ciso: Freeman
[5] Bocher, M., 1909. An introduction to the study of integral equations, 9. Cambridge University press.
[6] Slichter, L, B., 1932. The theory of the interpretation of seismic traveltime curve in horizontal structures.Physics, 3, 273——295.
[7] Gerver, M. L., and V. Markushevich, 1966. Determination if a Seismic Wave Velocity from the travel——time curve. Geophys. J., 165——173.
[8] Lanczos, C,1961. Linear Differential Operators. 140. London: Van Nostrand.
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