QUARTIC MOVEOUT COEFFICIENT FOR A DIPPING AZIMUTHALLY ANISOTROPIC LAYER

Abstract

Interpretation and inversion of azimuthally varying nonhyperbolic reflection moveout requires accounting for both velocity anisotropy and subsurface structure. Here, our previously derived exact expression for the quartic moveout coefficient A 4 is applied to P‐wave reflections from a dipping interface overlaid by a medium of orthorhombic symmetry. The weak‐anisotropy approximaton for the coefficient A 4 in a homogeneous orthorhombic layer is controlled by the anellipticity parameters η ⁽¹⁾ , η ⁽²⁾ , and η ⁽³⁾ , which are responsible for time processing of P‐wave data. If the dip plane of the reflector coincides with the vertical symmetry plane [x 1 , x 3 ], A 4 on the dip line is proportional to the in‐plane anellipticity parameter η ⁽²⁾ and always changes sign for a dip of 30○. The quartic coefficient on the strike line is a function of all three η–parameters, but for mild dips it is mostly governed by η ⁽¹⁾ —the parameter defined in the incidence plane [x 2 , x 3 ]. Whereas the magnitude of the dip line A 4 typically becomes small for dips exceeding 45○, the nonhyperbolic moveout on the strike line may remain significant even for subvertical reflectors. The character of the azimuthal variation of A 4 depends on reflector dip and is quite sensitive to the signs and relative magnitudes of η ⁽¹⁾ , η ⁽²⁾ , and η ⁽³⁾ . The analytic results and numerical modeling show that the azimuthal pattern of the quartic coefficient can contain multiple lobes, with one or two azimuths of vanishing A 4 between the dip and strike directions. The strong influence of the anellipticity parameters on the azimuthally varying coefficient A 4 suggests that nonhyperbolic moveout recorded in wide‐azimuth surveys can help to constrain the anisotropic velocity field. Since for typical orthorhombic models that describe naturally fractured reservoirs the parameters η (1,2,3) are closely related to the fracture density and infill, the results of azimuthal nonhyperbolic moveout analysis can also be used in reservoir characterization.