Shear‐wave polarizations and subsurface stress directions at Lost Hills field

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1331-1348 ◽  
Author(s):  
D. F. Winterstein ◽  
M. A. Meadows
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Data Matrix ◽  
Wave Polarization ◽  
Polarization Direction ◽  
S Wave ◽  
Near Surface ◽  
Polarization Technique ◽  
The Matrix ◽  
Vertical Travel

2 × 2 S-wave data matrix, accomplished by computationally rotating sources and receivers. Although polarization directions obtained by assuming a homogeneous subsurface were moderately consistent with depth, considerable improvement in consistency resulted from analytically stripping off a thin near‐surface layer whose fast S-wave polarization direction was about N 6°E. S-wave birefringence for vertical travel averaged 3 percent in two zones, 200–700 ft and 1200–2100 ft (60–210 m and 370–640 m), which had closely similar S-wave polarizations. Between those zones, the polarization direction changed and the birefringence magnitude was not well defined. S-wave polarizations from two concentric rings of offset VSPs were consistent in azimuth with one another and with polarizations of the near offset VSP. This consistency argues strongly for the robustness of the S-wave polarization technique as applied in this area. The S-wave polarization pattern in offset data fits a model of vertical cracks striking N 55°E in a weakly transversely isotropic matrix, where the infinite‐fold symmetry axis of the matrix is tilted 10 degrees from the vertical towards N 70°E. Such a model is of monoclinic symmetry.

Geometrical spreading in a layered transversely isotropic medium with vertical symmetry axis

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2082-2091 ◽  
Author(s):  
Bjørn Ursin ◽  
Ketil Hokstad
Keyword(s):  
Ray Tracing ◽  
Seismic Data ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Analytical Approximation ◽  
Geometrical Spreading ◽  
S Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
Amplitude Versus

Compensation for geometrical spreading is important in prestack Kirchhoff migration and in amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of seismic data. We present equations for the relative geometrical spreading of reflected and transmitted P‐ and S‐wave in horizontally layered transversely isotropic media with vertical symmetry axis (VTI). We show that relatively simple expressions are obtained when the geometrical spreading is expressed in terms of group velocities. In weakly anisotropic media, we obtain simple expressions also in terms of phase velocities. Also, we derive analytical equations for geometrical spreading based on the nonhyperbolic traveltime formula of Tsvankin and Thomsen, such that the geometrical spreading can be expressed in terms of the parameters used in time processing of seismic data. Comparison with numerical ray tracing demonstrates that the weak anisotropy approximation to geometrical spreading is accurate for P‐waves. It is less accurate for SV‐waves, but has qualitatively the correct form. For P waves, the nonhyperbolic equation for geometrical spreading compares favorably with ray‐tracing results for offset‐depth ratios less than five. For SV‐waves, the analytical approximation is accurate only at small offsets, and breaks down at offset‐depth ratios less than unity. The numerical results are in agreement with the range of validity for the nonhyperbolic traveltime equations.

Changes in shear‐wave polarization azimuth with depth in Cymric and Railroad Gap oil fields

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1349-1364 ◽  
Author(s):  
D. F. Winterstein ◽  
M. A. Meadows
Keyword(s):  
Shear Wave ◽  
Lower Layer ◽  
Oil Fields ◽  
Data Consistency ◽  
Data Matrix ◽  
Wave Polarization ◽  
S Wave ◽  
Polarization Azimuth ◽  
Uppermost Layer ◽  
Vsp Data

Shear‐wave [Formula: see text]-wave) polarization azimuths, although consistent over large depth intervals, changed abruptly and by large amount of various depths in nine-component vertical seismic profiling (VSP) data from the Cymric and Railroad Gap oil fields of the southwest San Joaquin basin. A simple layer‐stripping technique made it possible to follow the polarization changes and determine the [Formula: see text]-wave birefringence over successive depth intervals. Because the birefringence and polarization azimuth are related to in‐situ stresses and fracture, information from such analysis could be important for reservoir development. Near offset VSP data from Cymrix indicated that the subsurface could be appproximated roughly as two anisotropic layers. The upper layer, from the surface to 800 ft (240 m), had vertical [Formula: see text]-wave birefringence as large was about 6 percent down to 1300 ft (400 m). In the upper layer the polarization azimuth of the fast [Formula: see text]-wave was N 60°E, while in the lower layer it was about N 10°E. Refinement of the layer stripping showed that neither layer was anisotropically homogenous, and both could be subdivided into thinner layers. Near offset [Formula: see text]-wave VSP data from the Railroad Gap well also show high birefringence near the surface and less birefringence deeper. In the uppermost layer, which extends down to 1300 ft (400 m), the [Formula: see text]-wave birefringence was 9 percent, and the lag between the fast and slow [Formula: see text]-waves exceeded 60 ms at the bottom of the layer. Seven layers in all were needed to accommodate [Formula: see text]-wave polarization changes. The most reliable azimuth angle determination as judged from the data consistency were those of the uppermost layer, at N 46°E, and those from depths 2900–3700 ft (880–1130 m) and 3900–5300 ft (1190–1610 m), at N 16°E and N 15°W, respectively. Over those intervals the scatter of calculated azimuths about the mean was typically less than 4 degrees. The largest birefringence at both locations occurred in the same formation, the Pliocene Tulare sands and Pebble Conglomerate. In those formations the azimuth of the fast [Formula: see text]-wave polarization was roughly orthogonal to the southwest. In the deeper Antelope shale, [Formula: see text]-wave polarization directions in both areas were close to 45 degrees from the fault. Confidence in the layer stripping procedure was bolstered by major improvement in data quality that resulted from stripping. Before stripping, wavelets of the two [Formula: see text]-waves sometimes had very different waveforms, and it was often impossible to come close to diagonalizing the 2 × 2 S‐wave data matrix by rotating sources and receivers by the same angle. After stripping, wavelets were more similar in shape, and the S‐wave matrix was more nearly diagonalizable by rotating with a single angle.

Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part 2 — Dipping TTI layer

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. D123-D134 ◽  
Author(s):  
Pawan Dewangan ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Vertical Plane ◽  
Transversely Isotropic ◽  
Estimation Algorithm ◽  
Velocity Model ◽  
Inversion Algorithm ◽  
S Wave ◽  
Weak Anisotropy ◽  
Symmetry Direction ◽  
Tti Media

Dipping transversely isotropic layers with a tilted symmetry axis (TTI media) cause serious imaging problems in fold-and-thrust belts and near salt domes. Here, we apply the modified [Formula: see text] method introduced in Part 1 to the inversion of long-offset PP and PS reflection data for the parameters of a TTI layer with the symmetry axis orthogonal to the bedding. The inversion algorithm combines the time- and offset-asymmetry attributes of the PSV-wave with the hyperbolic PP- and SS-wave moveout in the symmetry-axis plane (i.e., the vertical plane that contains the symmetry axis). The weak-anisotropy approximations for the moveout-asymmetry attributes, verified by numerical analysis, indicate that small-offset (leading) terms do not contain independent information for the inversion. Therefore, the parameter-estimation algorithm relies on PS data recorded at large offsets (the offset-to-depth ratio has to reach at least two), which makes the results generally less stable than those for a horizontal TTI layer in Part1. The least-resolved parameter is Thomsen’s coefficient [Formula: see text]that does not directly influence the moveout of either pure or converted modes. Still, the contribution of the PS-wave asymmetry attributes helps to constrain the TTI model for large tilts [Formula: see text] of the symmetry axis [Formula: see text]. The accuracy of the inversion for large tilts can be improved further by using wide-azimuth PP and PS reflections. With high-quality PS data, the inversion remains feasible for moderate tilts [Formula: see text], but it breaks down for models with smaller values of [Formula: see text] in which the moveout asymmetry is too weak. The tilt itself and several combinations of the medium parameters (e.g., the ratio of the P- and S-wave velocities in the symmetry direction), however, are well constrained for all symmetry-axis orientations. The results of Parts 1 and 2 show that 2D measurements of the PS-wave asymmetry attributes can be used effectively in anisotropic velocity analysis for TTI media. In addition to providing an improved velocity model for imaging beneath TTI beds, our algorithms yield information for lithology discrimination and structural interpretation.

Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. T75-T95 ◽  
Author(s):  
Stéphane Operto ◽  
Jean Virieux ◽  
A. Ribodetti ◽  
J. E. Anderson
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Wave Mode ◽  
Absorbing Boundary Conditions ◽  
P Wave ◽  
Domain Modeling ◽  
S Wave ◽  
Absorbing Boundary

A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen’s anisotropic parameters [Formula: see text] and [Formula: see text], and the tilt angle. The finite-difference discretization relies on a parsimonious mixed-grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at the source or at seismic discontinuities when [Formula: see text]. In frequency-domain modeling with absorbing boundary conditions, the unstable S-wave mode is not excited when [Formula: see text], allowing stable simulations of the P-wave mode for such anisotropic media. Some S-wave instabilities are seen in the PMLs when the symmetry axis is tilted and [Formula: see text]. These instabilities are consistent with previous theoretical analyses of PMLs in anisotropic media; they are removed if the grid interval is matched to the P-wavelength that leads to dispersive S-waves. Comparisons between seismograms computed with the frequency-domain acoustic TTI method and a finite-difference, time-domain method for the vertical transversely isotropic elastic equation show good agreement for weak to moderate anisotropy. This suggests the method can be used as a forward problem for viscoacoustic anisotropic full-waveform inversion.

PS-wave moveout inversion for tilted TI media: A physical-modeling study

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. D135-D143 ◽  
Author(s):  
Pawan Dewangan ◽  
Ilya Tsvankin ◽  
Mike Batzle ◽  
Kasper van Wijk ◽  
Matthew Haney
Keyword(s):  
Physical Modeling ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Pure Mode ◽  
Velocity Analysis ◽  
S Wave ◽  
Reflection Data ◽  
Modeling Data ◽  
Modified Formula ◽  
Ti Media

Mode-converted PS-waves can provide critically important information for velocity analysis in transversely isotropic (TI) media. We demonstrate, with physical-modeling data, that the combination of long-spread reflection traveltimes of PP- and PS-waves can be inverted for the parameters of a horizontal TI layer with a tilted symmetry axis. The 2D multicomponent reflection data are acquired over a phenolic sample manufactured to simulate the effective medium formed by steeply dipping fracture sets or shale layers. The reflection moveout of PS-waves in this model is asymmetric with respect to the source and receiver positions, and the moveout-asymmetry attributes play a crucial role in constraining the TI parameters. Applying the modified [Formula: see text] method to the PP and PS traveltimes recorded in the symmetry-axis plane, we compute the time and offset asymmetry attributes of the PS-waves along with the traveltimes of the pure SS reflections. The algorithm of Dewangan and Tsvankin is then used to invert the combination of the moveout attributes of PP-, SS-, and PS-waves for the medium parameters and the thickness of the sample. It should be emphasized that the pure-mode (PP and SS) traveltimes alone are insufficient for the inversion, even if 3D wide-azimuth data are available. Our estimates of the symmetry axis tilt and layer thickness almost coincide with the actual values. The inverted model is also validated by reproducing the results of transmission experiments with both P- and S-wave sources. The transmitted SV wavefield exhibits a prominent cusp (triplication) accurately predicted by the parameter-estimation results.

Seismic vertical transversely isotropic parameter inversion from P- and S-wave cross-borehole measurements in an aquifer environment

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D101-D116
Author(s):  
Julius K. von Ketelhodt ◽  
Musa S. D. Manzi ◽  
Raymond J. Durrheim ◽  
Thomas Fechner
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Perturbation Equation ◽  
S Wave ◽  
P Waves ◽  
Data Set ◽  
Near Surface ◽  
S Waves ◽  
Wave Measurements ◽  
Wave Splitting

Joint P- and S-wave measurements for tomographic cross-borehole analysis can offer more reliable interpretational insight concerning lithologic and geotechnical parameter variations compared with P-wave measurements on their own. However, anisotropy can have a large influence on S-wave measurements, with the S-wave splitting into two modes. We have developed an inversion for parameters of transversely isotropic with a vertical symmetry axis (VTI) media. Our inversion is based on the traveltime perturbation equation, using cross-gradient constraints to ensure structural similarity for the resulting VTI parameters. We first determine the inversion on a synthetic data set consisting of P-waves and vertically and horizontally polarized S-waves. Subsequently, we evaluate inversion results for a data set comprising jointly measured P-waves and vertically and horizontally polarized S-waves that were acquired in a near-surface ([Formula: see text]) aquifer environment (the Safira research site, Germany). The inverted models indicate that the anisotropy parameters [Formula: see text] and [Formula: see text] are close to zero, with no P-wave anisotropy present. A high [Formula: see text] ratio of up to nine causes considerable SV-wave anisotropy despite the low magnitudes for [Formula: see text] and [Formula: see text]. The SH-wave anisotropy parameter [Formula: see text] is estimated to be between 0.05 and 0.15 in the clay and lignite seams. The S-wave splitting is confirmed by polarization analysis prior to the inversion. The results suggest that S-wave anisotropy may be more severe than P-wave anisotropy in near-surface environments and should be taken into account when interpreting cross-borehole S-wave data.

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