Leon Thomsen

Weak elastic anisotropy

Most bulk elastic media are weakly anisotropic. -The equations governing weak anisotropy are much simpler than those governing strong anisotropy, and they are much easier to grasp intuitively. These equations indicate that a certain anisotropic parameter (denoted 6) controls most anisotropic phenomena of importance in exploration geophysics. some of which are nonnegligible even when the anisotropy is weak. The critical parameter 6 is an awkward combination of elastic parameters, a combination which is totally independent of horizontal velocity and which may be either positive or negative in natural contexts.

Nonhyperbolic reflection moveout in anisotropic media

The standard hyperbolic approximation for reflection moveouts in layered media is accurate only for relatively short spreads, even if the layers are isotropic. Velocity anisotropy may significantly enhance deviations from hyperbolic moveout. Nonhyperbolic analysis in anisotropic media is also important because conventional hyperbolic moveout processing on short spreads is insufficient to recover the true vertical velocity (hence the depth). We present analytic and numerical analysis of the combined influence of vertical transverse isotropy and layering on long‐spread reflection moveouts. Qualitative description of nonhyperbolic moveout on “intermediate” spreads (offset‐to‐depth ratio x/z  < 1.7–2) is given in terms of the exact fourth‐order Taylor series expansion for P, SV, and P‐SV traveltime curves, valid for multilayered transversely isotropic media with arbitrary strength of anisotropy. We use this expansion to provide an analytic explanation for deviations from hyperbolic moveout, such as the strong...

Reflection seismology over azimuthally anisotropic media

Recent surveys have shown that azimuthal anisotropy (due most plausibly to aligned fractures) has an important effect on seismic shear waves. Previous work had discussed these effects on VSP data; the same effects are seen in surface recording of reflections at small to moderate angles of incidence. The anisotropic effects one different polarization components of vertically traveling shear waves permit the recognition and estimation of very small degrees of azimuthal anisotropy (of order 2 1 percent), as in an interferometer. Anisotropic effects on traveltime yield estimates of anisotropy which are averages over large depth intervals. Often, raw field data must be corrected for these effects before the reflectors may be imaged; two variations of a rotational algorithm to determine the “principal time series” are derived. Anisotropic effects on moveout lead to abnormal moveout unless the survey line is parallel to the fractures. Anisotropic effects on reflection amplitude permit the recognition and estimation of anisotropy (hence fracture intensity) differences at the reflecting horizon, i.e., with high vertical resolution,

Converted‐wave reflection seismology over inhomogeneous, anisotropic media

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 γeff≡γ22/γ0 (where γ0≡V¯p/V¯s is the ratio of average vertical velocities and γ2 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 γ0 instead of γeff can result in suboptimal data collection. Computer programs that implement algorithms for isotropi...

Understanding Seismic Anisotropy in Exploration and Exploitation

“All rock masses are seismically anisotropic, but we generally ignore this in seismic acquisition, processing, and interpretation. The anisotropy nonetheless does affect data, in ways that limit the effectiveness with which we can use it, as long as we ignore it. This book, produced for use with the 2002 SEG/EAGE Distinguished Instructor Short Course, helps us to understand why this inconsistency between reality and practice has been so successful in the past and why it will be less successful in the future as we acquire better seismic data (especially including vector seismic data) and correspondingly higher expectations of it. This book helps us to understand how we can modify our practice to more fully realize the potential inherent in data through algorithms which recognize the fact of seismic anisotropy. Sections include 1: Physical Principles, 2: P-waves (Subsurface Imaging), 3: P-waves (Subsurface Physical Characterization), 4: S-waves, and 5: C-waves. (DISC on DVD, 751A, is also available.)”

Seismic anisotropy in exploration and reservoir characterization: An overview

Recent advances in parameter estimation and seismic processing have allowed incorporation of anisotropic models into a wide range of seismic methods. In particular, vertical and tilted transverse isotropy are currently treated as an integral part of velocity fields employed in prestack depth migration algorithms, especially those based on the wave equation. We briefly review the state of the art in modeling, processing, and inversion of seismic data for anisotropic media. Topics include optimal parameterization, body-wave modeling methods, P-wave velocity analysis and imaging, processing in the τ-p domain, anisotropy estimation from vertical-seismic-profiling (VSP) surveys, moveout inversion of wide-azimuth data, amplitude-variation-with-offset (AVO) analysis, processing and applications of shear and mode-converted waves, and fracture characterization. When outlining future trends in anisotropy studies, we emphasize that continued progress in data-acquisition technology is likely to spur transition from t...

75-plus years of anisotropy in exploration and reservoir seismics: A historical review of concepts and methods

The idea that the propagation of elastic waves can be anisotropic, i.e., that the velocity may depend on the direction, is about 175 years old. The first steps are connected with the top scientists of that time, people such as Cauchy, Fresnel, Green, and Kelvin. For most of the 19th century, anisotropic wave propagation was studied mainly by mathematical physicists, and the only applications were in crystal optics and crystal elasticity. During these years, important steps in the formal description of the subject were made. At the turn of the 20th century, Rudzki stressed the significance of seismic anisotropy. He studied many of its aspects, but his ideas were not applied. Research in seismic anisotropy became stagnant after his death in 1916. Beginning about 1950, the significance of seismic anisotropy for exploration seismics was studied, mainly in connection with thinly layered media and the resulting transverse isotropy. Very soon it became clear that the effect of layer-induced anisotropy on data ac...

Reflection shear-wave data collected near the principal axes of azimuthal anisotropy

The presence of vertically oriented fractures and/or unequal horizontal stresses has created an azimuthally anisotropic earth, in which shear‐wave (SH) data collected along the principal axes of the anisotropy display time and reflection amplitude anomalies. Amoco shot two crossing shear‐wave (SH) lines that were approximately parallel to the orthogonal principal axes of the azimuthal anisotropy. At the tie point, these crossing SH lines display a time‐variant mis‐tie. The tie point also displays reflection‐coefficient anomalies, attributable to azimuthally dependent shear‐wave velocities. Field mapping documented a set of fractures striking N69E which are approximately parallel to the line that exhibited greater traveltimes. Time‐variant mis‐ties and reflection coefficient anomalies are two of the seismic responses theoretically expected of an azimuthally anisotropic earth, i.e., one in which the shear‐wave velocity depends upon the polarization azimuth of the shear wave.

Coarse-layer stripping of vertically variable azimuthal anisotropy from shear-wave data

Alford rotation analysis of 2C × 2C shear‐wave data (two source components, two receiver components) for azimuthal anisotropy is valid only when the orientation of that azimuthal anisotropy is invariant with depth. The Winterstein and Meadows method of layer stripping vertical seismic profiling (VSP) data relaxes this restriction for coarse‐layer variation of the orientation of the anisotropy. Here we present a tensor generalization of the conventional convolutional model of scalar wave propagation and use it to derive generalizations of Winterstein and Meadows layer stripping, valid for 2C × 2C data and for the restricted 2C-only case, in the VSP and reflection contexts. In the 2C × 2C VSP application, the result reduces to that of Winterstein and Meadows in the case where both fast and slow shear modes have the same attenuation and dispersion; otherwise, a balancing of mode spectra and amplitudes is required. The 2C × 2C reflection result differs from the 2C × 2C VSP result since two applications of the...

Microfracturing and deformation of westerly granite under creep condition

Abstract Three stages can be distinguished in the microfracturing radiation, and axial, transverse and volumetric strains ( Σ√ E , ϵ z , ϵ r and Δ V/V , respectively ) for Westerly granite under constant stress: (1) initial transient: rapid increase in ϵ r , Δ V/V , Σ√ E , and |ϵz|; (2) slow increase in ϵr and ΔV/V and |ϵz| but exponential increase in microfracturing radiation Σ√ E ; (3) supraexponential increase in Σ√ E and accelerated increase in ϵr and ΔV/V and |ϵz|. They can be interpreted in terms of closing and opening of cracks under stress and propagation of cracks as a result of stress-aided corrosion. At 150°C the drying effect overshadows any other effects of temperature on microfracturing and deformation. The rock is ‘strengthened’ as a result.