Effective orthorhombic anisotropic models for wavefield extrapolation

Abstract

Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models to reproduce wave propagation phenomena in the Earth's subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, we generate effective isotropic inhomogeneous models that are capable of reproducing the firstarrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, we develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic ones, is represented by a sixth order polynomial equation with the fastest solution corresponding to outgoing P waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, and using them to explicitly evaluate the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. We extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.