In his paper, Tuman found that, surprisingly, in all cases studied the minimum travel time of acoustic waves was along a curved path in a formation surrounding a borehole. The curvature resulted from velocity variations around the borehole in formations which show a nonlinear stress-strain relationship. However, the results of these calculations may be in error due to the use of incorrect stresses selected for the determination of the local acoustic wave velocity. In particular, the use of the radial stress distribution for this purpose is doubtful for the calculation of a curved travel path which in general does not deviate much from the vertical direction.

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