May 10-13, 1994 | Tariq Alkhalifah and Ilya Tsvankin
This paper presents a method for velocity analysis in transversely isotropic (TI) media by inverting the dependence of P-wave moveout velocities on the ray parameter. The authors derive an exact analytic equation for the normal-moveout (NMO) velocity for dipping reflectors in anisotropic media, which is then inverted to recover the anisotropic parameters. The inversion technique is based on the NMO velocity equation for TI media derived by Tsvankin (1994). The authors show that the P-wave NMO velocity in homogeneous TI media with a vertical symmetry axis depends on the zero-dip value \( V_{\text{nmo}}(0) \) and a new effective parameter \( \eta \), which reduces to the difference between Thomsen parameters \( \epsilon \) and \( \delta \) in the limit of weak anisotropy. The inversion procedure allows the recovery of \( \eta \) and the reconstruction of the NMO velocity as a function of the ray parameter using moveout velocities for two different dips. The NMO velocity and \( \eta \) determine not only the NMO velocity but also the long-spread (nonhyperbolic) P-wave moveout for horizontal reflectors and time-migration impulse response. This means that the inversion of dip-moveout information allows for all time-processing steps in TI media using only surface P-wave data. The method is demonstrated on synthetic and field data from offshore Africa. Accurate time-to-depth conversion requires the resolution of the vertical velocity \( V_{P0} \) independently. If \( V_{P0} \) is known, the anisotropies \( \epsilon \) and \( \delta \) can be found by inverting two P-wave NMO velocities corresponding to a horizontal and a dipping reflector. If no well information is available, all three parameters can be obtained by combining the inversion results with shear-wave information. The paper also discusses the generalization of the NMO equation for layered anisotropic media and provides a Dix-type procedure to estimate the NMO velocity in any individual layer from surface reflection data.This paper presents a method for velocity analysis in transversely isotropic (TI) media by inverting the dependence of P-wave moveout velocities on the ray parameter. The authors derive an exact analytic equation for the normal-moveout (NMO) velocity for dipping reflectors in anisotropic media, which is then inverted to recover the anisotropic parameters. The inversion technique is based on the NMO velocity equation for TI media derived by Tsvankin (1994). The authors show that the P-wave NMO velocity in homogeneous TI media with a vertical symmetry axis depends on the zero-dip value \( V_{\text{nmo}}(0) \) and a new effective parameter \( \eta \), which reduces to the difference between Thomsen parameters \( \epsilon \) and \( \delta \) in the limit of weak anisotropy. The inversion procedure allows the recovery of \( \eta \) and the reconstruction of the NMO velocity as a function of the ray parameter using moveout velocities for two different dips. The NMO velocity and \( \eta \) determine not only the NMO velocity but also the long-spread (nonhyperbolic) P-wave moveout for horizontal reflectors and time-migration impulse response. This means that the inversion of dip-moveout information allows for all time-processing steps in TI media using only surface P-wave data. The method is demonstrated on synthetic and field data from offshore Africa. Accurate time-to-depth conversion requires the resolution of the vertical velocity \( V_{P0} \) independently. If \( V_{P0} \) is known, the anisotropies \( \epsilon \) and \( \delta \) can be found by inverting two P-wave NMO velocities corresponding to a horizontal and a dipping reflector. If no well information is available, all three parameters can be obtained by combining the inversion results with shear-wave information. The paper also discusses the generalization of the NMO equation for layered anisotropic media and provides a Dix-type procedure to estimate the NMO velocity in any individual layer from surface reflection data.