We present an approach to separate the P- and S-waves in elastic displacement component data recorded at the earth’s surface by using the so-called pure mode wave propagators in anisotropic media. First, we reverse-time extrapolate the common-shot data in a vertically homogeneous computational model with elastic anisotropic wave equation to a reference depth close to the surface. Then we forward propagate these extrapolated wavefields using pseudo-pure mode wave equations to reconstruct the equivalent elastic wavefields within a narrow band near the surface. Finally, we project those wavefields onto the anisotropic polarization direction to extract pure P- or S-waves seismograms at the original recording surface. Synthetic data examples prove the feasibility of this approach.
We present a pure P-wave propagator for wavefield modeling and reverse time migration (RTM) in orthorhombic media. Projecting the original elastic anisotropic wave equation onto the propagation direction of P-wave yields an equivalent coupled second-order system. Further projecting the wavefield extrapolated using this system onto the anisotropic polarization direction produces pure mode P-wave data. Wavefield snapshots and impulse responses of RTM in 3D horizontal transversely isotropic and orthorhombic media prove the validity of this approach.
We present an approach of propagating pure wave-modes in general anisotropic media accurately. First we obtain pseudo-pure mode wave equations by projecting the elastic anisotropic wave equation onto isotropic polarization direction. Then we correct the projection error of the wavefield propagated with these equations. Pseudo-pure mode wave equation plus projection errors correction provide us accurate pure mode wave propagators. They have many advantages over the original elastic wave equation and the pseudo-acoustic wave equations in anisotropic media. Numerical examples demonstrate the applications to wavefield simulation and reverse-time migration (RTM) of P-wave in transversely isotropic (TI) media.
We present an approach of propagating pure wave modes in general anisotropic media accurately. In this part, we focus on the propagation of SV and SH wave in 3D anisotropic media. The eigenvalue (phase velocity) of SV and SH wave are the same at any wavenumber in isotropic media. We define each vector by their mutual orthogonality, and project the elastic wavefield onto isotropic polarization direction to obtain pseudo pure wave-mode equations. Then a correction method is applied after solving the equations to eliminate the error caused by anisotropy. Pseudo pure wave-mode equations plus projection correction provide us an accurate pure wave-mode propagator. Numerical examples demonstrate the applications to shear wave modeling in transversely isotropic (TI) and orthorhombic (ORT) media.
We present an approach to combine Bayesian viscoelastic AVA inversion with statistical rock physics to estimate petrophysical properties. Based on the approximate equations in week contrast and week attenuation media, we present a Bayesian viscoelastic AVA inversion method to obtain the elastic parameters including the attenuation coefficients. Except general rock physics models, the Dvokin and Mavko attenuation model is also used in statistical rock physics inversion for better estimation of petrophysical properties. Numerical examples on well log and synthetic seismic data demonstrate the feasibility of this approach.