L. Thomsen - Academia.edu (original) (raw)
Papers by L. Thomsen
SEG Technical Program Expanded Abstracts 2010, 2010
Understanding Seismic Anisotropy in Exploration and Exploitation, 2002
SEG Technical Program Expanded Abstracts 2014, 2014
GEOPHYSICS, 1986
Most bulk elastic media are weakly anisotropic. The equations governing weak anisotropy are much ... more 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 δ) controls most anisotropic phenomena of importance in exploration geophysics, some of which are nonnegligible even when the anisotropy is weak. The critical parameter δ 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.
GEOPHYSICS, 1995
In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mea... more In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mean‐square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short‐spread, common‐midpoint (CMP) gathers, even if both P‐ and S‐waves are recorded. Hence, we examine the feasibility of inverting long‐spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for [Formula: see text] curves for P‐ and SV‐waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate‐spread (i.e., spreads of about 1.5 times the reflector depth) P and SV moveouts. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector dept...
Geological Society of America Special Papers
GEOPHYSICS, 1994
The standard hyperbolic approximation for reflection moveouts in layered media is accurate only f... more 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 m...
GEOPHYSICS, 1999
Alford rotation analysis of 2C × 2C shear‐wave data (two source components, two receiver componen... more 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 ...
GEOPHYSICS, 1999
Converted‐wave processing is more critically dependent on physical assumptions concerning rock ve... more 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 [Formula: see text] (where [Formula: see text] is the ratio of average vertical velocities and γ2is 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 γ0instead of [Formula: see text] can result in suboptimal data collection. Com...
GEOPHYSICS, 2010
Recent advances in parameter estimation and seismic processing have allowed incorporation of anis... more 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 [Formula: see text] 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 technol...
The Leading Edge
I write to you again, near the middle of my term as your president. As I predicted last October i... more I write to you again, near the middle of my term as your president. As I predicted last October in these pages, this is a year of rapid change for SEG and of rapid realization of our global agenda. This has required extensive travel by your Executive Committee and business staff despite our resolve, as I described to you in October, that much of the international business of the Society should occur over the telephone and the Internet. This is perhaps inevitable, considering our rapidly growing membership (>28 000) and our global demographics (>60% non-U.S. members).
EAGE/SEG Research Workshop - Multicomponent Seismic - Past, Present and Future
SEG Technical Program Expanded Abstracts 2002, 2002
SEG Technical Program Expanded Abstracts 2010, 2010
Understanding Seismic Anisotropy in Exploration and Exploitation, 2002
SEG Technical Program Expanded Abstracts 2014, 2014
GEOPHYSICS, 1986
Most bulk elastic media are weakly anisotropic. The equations governing weak anisotropy are much ... more 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 δ) controls most anisotropic phenomena of importance in exploration geophysics, some of which are nonnegligible even when the anisotropy is weak. The critical parameter δ 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.
GEOPHYSICS, 1995
In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mea... more In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mean‐square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short‐spread, common‐midpoint (CMP) gathers, even if both P‐ and S‐waves are recorded. Hence, we examine the feasibility of inverting long‐spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for [Formula: see text] curves for P‐ and SV‐waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate‐spread (i.e., spreads of about 1.5 times the reflector depth) P and SV moveouts. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector dept...
Geological Society of America Special Papers
GEOPHYSICS, 1994
The standard hyperbolic approximation for reflection moveouts in layered media is accurate only f... more 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 m...
GEOPHYSICS, 1999
Alford rotation analysis of 2C × 2C shear‐wave data (two source components, two receiver componen... more 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 ...
GEOPHYSICS, 1999
Converted‐wave processing is more critically dependent on physical assumptions concerning rock ve... more 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 [Formula: see text] (where [Formula: see text] is the ratio of average vertical velocities and γ2is 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 γ0instead of [Formula: see text] can result in suboptimal data collection. Com...
GEOPHYSICS, 2010
Recent advances in parameter estimation and seismic processing have allowed incorporation of anis... more 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 [Formula: see text] 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 technol...
The Leading Edge
I write to you again, near the middle of my term as your president. As I predicted last October i... more I write to you again, near the middle of my term as your president. As I predicted last October in these pages, this is a year of rapid change for SEG and of rapid realization of our global agenda. This has required extensive travel by your Executive Committee and business staff despite our resolve, as I described to you in October, that much of the international business of the Society should occur over the telephone and the Internet. This is perhaps inevitable, considering our rapidly growing membership (>28 000) and our global demographics (>60% non-U.S. members).
EAGE/SEG Research Workshop - Multicomponent Seismic - Past, Present and Future
SEG Technical Program Expanded Abstracts 2002, 2002