Problems are encountered during the course of one’s research on related topics. These are put on a list with promises made that one day, they will be revisited. The one discussed here was put on such a list four decades ago. It was visited a number of times during that time. However, there was always the problem of being unable rederive the results presented in the paper. The specific work dealt with in this report is: [ Section (4.3) Computation of the Coefficients of Elasticity, Using the w Surface (Gassmann, 1964) ]. As noted in the title, using ray travel times (the w surface) the phase velocity is used to invert for the anisotropic parameters in a transversely isotropic ( TI ) medium. The exact phase velocities may be used to this end, given that the measured ray travel times have been acquired with reasonable accuracy. Apart from the exact phase velocities, the problem is set up so that approximate and linearized forms of the phase velocity may also be used. It should be further mentioned that the author is now able to derive the equations in the abovementioned section of the paper. As this is a fairly complex and lengthily undertaking, it will not be included here. A proper resolution with the formulae in the above paper was achieved. Consequently the equations given in that paper will be used in a moderately modified form. Only P- wave travel times are considered, as the qP and qSv wave fronts are coupled so that the anisotropic medium parameters for both may be obtained using only P- wave data.
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