Converted‐wave reflection seismology over inhomogeneous, anisotropic media

Abstract

Converted-wave processing is more critically dependent on physical assumptions concerning rock velocities than is pure-mode processing, because not only moveout but also the offset of the imaged point itself depend upon the physical parameters of the medium. Hence, unrealistic assumptions of homogeneity and isotropy are more critical than for pure-mode propagation, where the image-point offset is determined geometrically rather than physically. In layered anisotropic media, an effective velocity ratio yeff -yz /yo (where yo -Vp /VS is the ratio of average vertical velocities and y2 is the corresponding ratio of short-spread moveout velocities) governs most of the behavior of the conversion-point offset. These ratios can be constructed from P-wave and converted-wave data if an approximate correlation is established between corresponding reflection events. Acquisition designs based naively on yo instead of yeff can Manuscript

Converted-wave seismology in anisotropic media revisited, Part I: Basic theory

“…Thomsen (1999) discussed various methods to account for the anisotropic effects using isotropic methods for conversion-point calculation, where the effects of anisotropy were only considered in the form of the effective velocity ratio v a ( S'e~. compensation).…”

“…Throughout the paper, Thomsen's (1999) notation is used. Subscripts P, S, and C denote P-, S-, and C-waves respectively.…”

“…Each layer in the model is homogeneous with the following interval parameters for the i-th layer (i=1,2 .... n): P-and Swave vertical velocities V~o i and Vsoi, P-and S-wave shortspread NMO velocities Ve2 i and Vs2 i, vertical one-way travel times /x tpoi and A tso: respectively, and Thomsen (1986) parameters e and ov i. Using the Thomsen's (1999) notation, the velocity ratios are defined as, Equations (9) and (10) are the exact definitions and appear to be complicated in terms of practical applications. (4) Alkhalifah (1997) found that the effects of the term Vso / Ve0 ~ in equation (9) is small and may be ignored for Pwave propagation.…”

“…Tessmer and Behle, 1988), and the other is based on the Taylor series expansion of the ray equation, including both asymptotic (first-order) and higher-order expansions (e.g. Thomsen, 1999). However, most of these equations have only been derived for layered isotropic media.…”

“…However, the existing theory (e.g. Thomsen 1999) is limited to the middle offsets approximately equal to the reflector depth (offset-depth ratio x/z= 1.0).…”