DIP-MOVEOUT ERROR IN TRANSVERSELY ISOTROPIC MEDIA WITH LINEAR VELOCITY VARIATION IN-DEPTH

Levin modeled the moveout, within common-midpoint (CMP) gathers, of reflections from plane-dipping reflectors beneath homogeneous, transversely isotropic media. For some media, when the axis of symmetry for the anisotropy was vertical, he found departures in stacking velocity from predictions based upon the familiar cosine-of-dip correction for isotropic media. Here, I do similar tests, again with transversely isotropic models with vertical axis of symmetry, but now allowing the medium velocity to vary linearly with depth. Results for the same four anisotropic media studied by Levin show behavior of dip-corrected stacking velocity with reflector dip that, for all velocity gradients considered, differs little from that for the counterpart homogeneous media. As with isotropic media, traveltimes in an inhomogeneous, transversely isotropic medium can be modeled adequately with a homogeneous model with vertical velocity equal to the vertical rms velocity of the inhomogeneous medium. In practice, dip-moveout (DMO) is based on the assumption that either the medium is homogeneous or its velocity varies with depth, but in both cases isotropy is assumed. It turns out that for only one of the transversely isotropic media considered here-shale-limestone-would v(z) DMO fail to give an adequate correction within CMP gathers. For the shale-limestone, fortuitously the constant-velocity DMO gives a better moveout correction than does the v(z) DMO.