Non‐hyperbolic moveout inversion of wide‐azimuth P‐wave data for orthorhombic media

Abstract

A B S T R A C TThe azimuthally varying non-hyperbolic moveout of P-waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long-spread, wide-azimuth P-wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry-plane NMO velocities, V (1) nmo and V (2) nmo , and the anellipticity parameters, η (1) , η (2) and η (3) . The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah-Tsvankin non-hyperbolic moveout equation.The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise-contaminated data for a single orthorhombic layer show that the best-constrained parameters are the azimuth ϕ of one of the symmetry planes and the velocities V (1) nmo and V (2) nmo , while the resolution in η (1) and η (2) is somewhat compromised by the trade-off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter η (3) , which influences only long-spread moveout in off-symmetry directions. For stratified orthorhombic models with depth-dependent symmetry-plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term.The algorithm was successfully tested on wide-azimuth P-wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long-offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetryplane directions are close to the azimuths of the off-trend fracture sets determined from borehole data and shear-wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P-wave time imaging and geometricalspreading correction in layered orthorhombic media.

Application of perturbation theory to a P-wave eikonal equation in orthorhombic media

“…For both models, the relative error in traveltime is less than 0.1% regardless to the choice of parameterization. To compare the accuracy, we also perform the computation with the traveltime approximation proposed by Vasconcelos and Tsvankin (2006). The results are shown in Figure 7.…”

“…where η 3 is an anelliptic parameter defined in horizontal symmetry plane [x; y] (Vasconcelos and Tsvankin, 2006). Note that indices (1,2) for NMO velocities and anellipticity parameters are different from those defined by Tsvankin (1997).…”

“…Assuming a homogeneous ORT medium, the perturbation coefficients can be computed analytically, and the perturbation series results in simple and accurate moveout approximation based on the Shanks transform (Bender and Orszag, 1978). The accuracy of the proposed approximation for both parameterizations is tested against the traveltime approximation proposed by Vasconcelos and Tsvankin (2006) using two ORT models. The results show superior accuracy of proposed approximation.…”

The offset-midpoint traveltime pyramid of P-waves in homogeneous orthorhombic media

“…We slightly modify Alkhalifah's (2003) notation by introducing the anellipticity parameter η 3 ≡ ðε 1 − ε 2 − δ 3 ð1 þ 2ε 2 ÞÞ∕ðð1 þ 2δ 3 Þð1 þ 2ε 2 ÞÞ (Vasconcelos and Tsvankin, 2006) defined in the [x, y] plane instead of the anisotropy parameter δ 3 (Appendix B). The similar modifications on Alkhalifah's (2003) notation may also be seen in Stovas (2016a, 2016b) and Stovas (2015).…”

Traveltime approximations and parameter estimation for orthorhombic media

“…The first and most important step in a successful processing sequence for P-wave data is to estimate the medium parameters. Existing work on orthorhombic traveltime inversion for reflection data has been done mainly through nonhyperbolic moveout description of the traveltimes (Al-Dajani et al, 1998;Xu et al, 2005;Vasconcelos and Tsvankin, 2006). Despite the improvements to handle large offsets, the accuracy of these approximations degrades at far offsets.…”