1966
DOI: 10.1111/j.1365-246x.1966.tb03498.x
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Determination of a Seismic Wave Velocity from the Travel-Time Curve

Abstract: A solution of the following problem is presented: given a travel-time curve of a seismic wave, to determine the corresponding velocity distribution. This is a generalization of the Herglotz-Wiechert method to a medium with low-velocity zones.The velocity depends only on depth and is a piecewise double-smooth function with a finite number of waveguides. A complete mathematical description of this solution is presented. In the presence of wave-guides the solution is ambiguous. Necessary and sufficient conditions… Show more

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Cited by 113 publications
(60 citation statements)
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“…If a LVZ exists, this gap is the only possible shadow zone that could be caused by it. As described by Gerver [1966], the velocities in the LVZ cannot be found explicitly via inversion, however, the velocities above and below the LVZ can be calculated using Gerver's formula, and the maximum width of the LVZ can be estimated assuming a constant velocity within it [Aki and Richards, 1980 To discriminate between the two models obtained from the travel time inversions, waveforms are needed from epicentral distances of less than 2200 km. Since most of the waveforms from the TBSE are from distances greater than that, we cannot evaluate further structure above -300-km depth, and we are left with the possibility that a narrow LVZ might exist between a depth of 160 and 185 km in the P wave structure.…”
Section: Data and Travel Time Inversionmentioning
confidence: 99%
“…If a LVZ exists, this gap is the only possible shadow zone that could be caused by it. As described by Gerver [1966], the velocities in the LVZ cannot be found explicitly via inversion, however, the velocities above and below the LVZ can be calculated using Gerver's formula, and the maximum width of the LVZ can be estimated assuming a constant velocity within it [Aki and Richards, 1980 To discriminate between the two models obtained from the travel time inversions, waveforms are needed from epicentral distances of less than 2200 km. Since most of the waveforms from the TBSE are from distances greater than that, we cannot evaluate further structure above -300-km depth, and we are left with the possibility that a narrow LVZ might exist between a depth of 160 and 185 km in the P wave structure.…”
Section: Data and Travel Time Inversionmentioning
confidence: 99%
“…This is not the case. Gerver and Markushevitch (1966) showed that only the maximum thickness of the L VZ can be constrained from travel time data. Our approach will tend to estimate that a LVZ haa a thickness less than the maximum bound provided by the travel time data.…”
Section: Discussionmentioning
confidence: 99%
“…The lower amplitude first arrivals in this range result from the delay of the geometric arrivals due to the LVZ. For travel-time inversion studies the delayed geometric arrivals are the important phases for identification (SLICHTER, 1932;GERVER and MARKUSHEVITCH, 1966;AKI and RICHARDS, 1980). The incorrect identification of the geometric arrivals would pose interpreta tion problems for both I-D inversions and tomographic studies using travel times from this distance range.…”
Section: Discussionmentioning
confidence: 99%