We offer approximate nonhyperbolic P-wave moveout formulae applicable to weakly or moderately anisotropic media of arbitrary anisotropy. Instead of commonly used Taylor expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the traveltime in terms of weak-anisotropy (WA) parameters. We specify the general formulae for the TI media with arbitrary tilt of the axis of symmetry. Resulting formulae depend on three WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. Tests of the accuracy of the more accurate of approximate formulae indicate that maximum relative errors are not greater than 2.5% for P-wave anisotropy of, approximately, 26%.
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