Summary
Standard methods of interpolating the velocity-depth distribution v=v(z) do not guarantee the continuity of the first and second derivatives of velocity and generate false interfaces of a higher order. These false interfaces cause anomalies in the amplitude-distance curves. It is suggested to apply the smoothed spline approximation to the depth-velocity distribution z=z(v). In this case, the ray integrals can be evaluated in a closed form. The amplitude-distance curves become quite smooth and stable. All necessary formulae and numerical examples are presented.
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References
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Červený, V., Pretlová, V. Computation of ray amplitudes of seismic body waves in vertically inhomogeneous media. Stud Geophys Geod 21, 248–255 (1977). https://doi.org/10.1007/BF01613252
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DOI: https://doi.org/10.1007/BF01613252