We present approximate nonhyperbolic P-wave moveout formula applicable to horizontally layered, weakly or moderately anisotropic media of arbitrary anisotropy symmetry and orientation. Symmetry and orientation may differ from layer to layer. Instead of commonly used Taylor series expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. Resulting formula yields the square of traveltime as a function of the square of the offset along a surface profile. It depends, in each layer, on the thickness of the layer, on the reference P-wave velocity used for the construction of a reference ray, and on three weak-anisotropy (WA) parameters specified in the global Cartesian coordinate system. These three parameters can be expressed in terms of local WA parameters specifying anisotropy of a given layer, specified in a local coordinate system, and on directional cosines specifying the orientation of the local coordinate system with respect to the global one. The number of local WA parameters may vary from three for transverse isotropy, six for orthorhombic symmetry to fifteen for triclinic symmetry. Tests of the accuracy of the more accurate of the approximate formulae indicate that maximum relative errors do not exceed 0.5% or 2.5% for weak or moderate P-wave anisotropy, respectively.
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