Interpreting non‐orthogonal split shear waves for seismic anisotropy in multicomponent VSPS

Abstract

There are two main sources of non‐orthogonality in multicomponent shear‐wave seismics: inherent non‐orthogonal split shear waves arising from substantial ray deviation in off‐symmetry planes due to strong anisotropy or complex overburden, and apparent non‐orthogonal split shear waves in the horizontal plane due to variation of the angle of incidence even if the two shear waves along the raypath are orthogonal. Many techniques for processing shear‐wave splitting in VSP data ignore these kinds of non‐orthogonality of the split shear waves. Assuming inherent non‐orthogonality in zero‐offset VSPs, and apparent non‐orthogonality in offset VSPs, we derive equations for the four‐component data matrix. These can be solved by extending the linear‐transform technique (LTT) to determine the shear‐wave polarizations in zero‐offset and offset VSPs. Both full‐wave synthetic and field data are used to evaluate the technique and to examine the effects of non‐orthogonal polarized split shear waves. If orthogonality is incorrectly assumed, errors in polarization measurements increase with the degree of non‐orthogonality, which introduces a consistent decreasing trend in the polarization measurements. However, the effect of non‐orthogonality on the estimation of geophone orientation and time delays of the two split shear waves is small and negligible in most realistic cases. Furthermore, for most cases of weak anisotropy (less than 5% shear‐wave anisotropy) apparent non‐orthogonality is more significant than inherent non‐orthogonality. Nevertheless, for strong anisotropy (more than 10% shear‐wave anisotropy) with complicated structure (tilted or inclined symmetry axis), inherent non‐orthogonality may no longer be negligible. Applications to both synthetic and real data show that the extended linear‐transform techniques permit accurate recovery of polarization measurements in the presence of both significant inherent and apparent non‐orthogonality where orthogonal techniques often fail.

Spatiotemporal Properties of Seismicity and Variations of Shear-Wave Splitting Parameters in the Western Gulf of Corinth (Greece)

“…This is due to the significant scatter in ϕ measurements (Figure S16), while a secondary ϕ maximum at a SW-NE direction, that would be in agreement with previous studies, is also observed. The existence of two groups of ϕ measurements at stations PYRG and HELI indicates either a strong spatial dependence or that shear-waves propagate through two distinct media with different anisotropic properties [21,77,78].…”

Discussions on the Processing of the Multi-Component Seismic Vector Field

“…The abovementioned vector wavefield separation methods all imply that the P-waves and S-waves are orthogonally polarized, and this assumption is generally not valid for an anisotropic medium [82]. For the wavefield separation problem of non-orthogonal P-waves and S-waves in an anisotropic medium, Lei [33] and Lu et al [34] discussed this problem from the perspective of natural earthquakes and exploration seismology and provided a solution.…”

A method for non-orthogonal seismic polarization-vector separation

“…is general in that it can represent cases with fewer than three non‐orthogonal vectors, reducing to of Li et al (1998) in the case of two vectors in horizontal plane.…”

“…Seismic anisotropy exists almost everywhere in the earth medium (Crampin & Booth 1985; Crampin 1987, 1989; Yao et al 1992; Bouin et al 1996; Song & Richards 1996; Lei et al 1997; Wolfe & Silver 1998; Fouch et al 2000; Christensen et al 2001). While polarizations in homogeneous isotropic medium are mutually orthogonal, polarizations of body waves in anisotropic medium are usually not (Crampin & Booth 1985; Crampin 1991; Li et al 1998). Progress in dealing with non‐orthogonal shear‐waves on horizontal components under some special conditions in anisotropic medium has been made (Li & Crampin 1993; Li et al 1998).…”

“…While polarizations in homogeneous isotropic medium are mutually orthogonal, polarizations of body waves in anisotropic medium are usually not (Crampin & Booth 1985; Crampin 1991; Li et al 1998). Progress in dealing with non‐orthogonal shear‐waves on horizontal components under some special conditions in anisotropic medium has been made (Li & Crampin 1993; Li et al 1998). However, the impact of P on the horizontal components, caused by the non‐orthogonal relationship between P and S waves in anisotropic media, has been ignored.…”