Anisotropy in sedimentary rocks modeled as random media

Geophysics ◽  
1992 ◽  
Vol 57 (4) ◽  
pp. 564-576 ◽  
Author(s):  
Claudia Kerner
Keyword(s):  
Random Media ◽  
Transversely Isotropic ◽  
Anisotropic Behavior ◽  
S Wave ◽  
Elastic Parameters ◽  
Transversely Isotropic Medium ◽  
Long Wavelength ◽  
Wave Velocities ◽  
Wavelength Scale ◽  
Averaging Techniques

The anisotropic behavior to be expected from various types of sediments is investigated by considering them as laminated media, with randomly varying velocity depth distributions. Two different stochastic processes are used to model transitional and cyclic layering. The kinematics of waves propagating through the laminated media is studied by evaluating overall elastic parameters of the transversely isotropic medium in the long wavelength limit using averaging techniques. Models with strong velocity fluctuations and high correlation between P‐ and S‐wave velocities exhibit significant anisotropy, comparable in magnitude to field and laboratory measurements. Elastic wavefields for the stochastic models were computed and the results were compared with analytical and numerical results for homogeneous anisotropic media computed with the derived overall parameters. The wavefield modeling shows that anisotropy and scattering are not simply effects influencing waves on the opposite ends of the wavelength scale but that there is an intermediate range where both effects profoundly influence wave propagation.

Recovery of elastic parameters for a multi-layered transversely isotropic medium

2004 ◽  
Vol 1 (4) ◽  
pp. 327-335 ◽  
Author(s):  
Ruiping Li ◽  
Norman F Uren ◽  
John A McDonald ◽  
Milovan Urosevic
Keyword(s):  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Elastic Parameters ◽  
Transversely Isotropic Medium

scholarly journals To substantiate the high velocities of P- and S-waves in the upper mantle of Transbaikalia

2020 ◽  
Vol 2 (3) ◽  
pp. 22-33
Author(s):  
Victor Solovyev ◽  
Viktor Seleznev ◽  
Vladimir Chechelnitsky ◽  
Alexander Salnikov ◽  
Natalya Galyova
Keyword(s):  
Mineral Composition ◽  
Upper Mantle ◽  
High Speed ◽  
Orogenic Belt ◽  
S Wave ◽  
Elastic Parameters ◽  
S Waves ◽  
Wave Velocities ◽  
High Speeds ◽  
Experimental Values

The results of the analysis of geological, geophysical, and geodynamic studies in the South-East of Transbaikalia are presented in order to substantiate the high speeds of P-and S-waves along the Mohorovichich boundary established here by profile seismic and area seismological studies. The issues of possible anisotropy of the upper mantle were discussed, and the experimental values of Р-and S-wave velocities (according to the data of the GSS and seismology) were compared with the calculations of elastic parameters values based on the approximate mineral composition of probable upper mantle rocks (peridotites, percolates, pyroxenites and eclogites) and experimental values of Р - and S-wave velocities for these rocks obtained at pressures in the upper mantle (up to 10 kbar). By results of discussion of possible causes of increased speeds made the conclusion on the validity of assumptions about the nature of the high-speed block in the mantle of Transbaikalia as the plates eclogites (or eclogitic rocks) in the area of Mongol-Okhotsk orogenic belt.

Computation of synthetic seismograms for a thin layered periodic structure

1982 ◽  
Vol 19 (7) ◽  
pp. 1449-1453
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Seismic Data ◽  
Integration Method ◽  
Transversely Isotropic ◽  
Synthetic Seismograms ◽  
Transversely Isotropic Medium ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Reflectivity Method ◽  
Wavelength Approximation ◽  
Time Required

In the long-wavelength approximation it has been shown in several papers within the last 20 years that an elastic medium composed of alternating homogeneous isotropic layers of two different constituents is equivalent both kinematically and dynamically to a homogeneous transversely isotropic medium. Such a fact excludes uniqueness in inverting seismic data for these particular cases. A comparison of the seismic responses of the equivalent media is made by constructing synthetic seismograms using the reflectivity (numerical integration) method and the asymptotic ray approach. For the sake of simplicity the SH case only is considered. The preferable approach when considering media of this type is found to be the asymptotic ray approximation as the CPU time required is a fraction of that used in the reflectivity method for comparable results.

Exploitation of data-information content in elastic-waveform inversions

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. R105-R115 ◽  
Author(s):  
Edgar Manukyan ◽  
Sabine Latzel ◽  
Hansruedi Maurer ◽  
Stefano Marelli ◽  
Stewart A. Greenhalgh
Keyword(s):  
Information Content ◽  
Seismic Data ◽  
Data Sets ◽  
S Wave ◽  
Elastic Parameters ◽  
Waveform Data ◽  
Wave Velocities ◽  
Area Of Interest ◽  
Trade Offs ◽  
Free Data

Elastic-waveform inversions have the potential to provide detailed subsurface images of the elastic parameters (P- and S-wave velocities and density), but acquisition of suitable data sets and their inversion are nontrivial tasks. We explore the information content offered by elastic-waveform data by means of a 2D synthetic study. Comprehensive noise-free data sets that include recordings based on multicomponent (directed) sources and multicomponent (vector) receivers that fully surround the area of interest allow all elastic parameters to be reliably recovered. Results that are almost as good can be achieved with the more commonly used crosshole configuration. If only single-source components (e.g., those oriented perpendicular to the borehole walls) are used, then there is no significant quality degradation of the tomographic images. Crosshole experiments that include pressure sources and multicomponent receivers still allow P- and S-wave velocities to be recovered, but such data sets contain virtually no information about the density. Finally, seismic data collected with omnidirectional pressure sources and pressure receivers contain information about P- and S-wave velocities, but there are pronounced trade-offs between these parameters. This is demonstrated through formal model-resolution analyses. This study concludes that seismic data recorded with pressure sources and 2C receivers offer the best compromise between acquisition efficiency and data-information content.

scholarly journals Bounds of elastic parameters characterizing transversely isotropic media: Application to shales

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C243-C252 ◽  
Author(s):  
Rune M. Holt
Keyword(s):  
Elastic Moduli ◽  
Laboratory Data ◽  
Transversely Isotropic ◽  
S Wave ◽  
Elastic Parameters ◽  
Reliable Determination ◽  
Transversely Isotropic Media ◽  
Stress Changes ◽  
Isotropic Media ◽  
Engineering Parameters

Several rocks, and in particular shales, are often described as transversely isotropic (TI) materials. Geophysical data coverage does not always permit reliable determination of all five elastic parameters, neither in seismic and sonic data from the field nor in laboratory measurements. Data may, however, be constrained by the existence of bounds on elastic moduli, derived from the fundamental requirement of positive elastic energy. Conditioned bounds are described for engineering parameters such as Poisson’s ratios as well as anisotropy coefficients such as the moveout parameter [Formula: see text] and the anellipticity parameter [Formula: see text]. “Conditioned bounds” means bounds that in general depend on some of the other elastic moduli: The bounds we have evaluated are controlled primarily by P- and S-wave moduli obtained from wave propagation along a symmetry axis and to some extent by P- and S-wave anisotropies. Such data may be acquired more easily from geophysical measurements. We have inspected the laboratory data obtained with various types of shales under different testing conditions, and none of them failed to adapt to the bounds. The data indicate, for instance, clear distinctions between how the proximity to bounds is driven by stress changes for saturated versus nonsaturated shales.

Seismic velocities in transversely isotropic media, II

Geophysics ◽  
1980 ◽  
Vol 45 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Franklyn K. Levin
Keyword(s):  
Wave Velocity ◽  
Transversely Isotropic ◽  
P Wave ◽  
Seismic Velocities ◽  
Sh Wave ◽  
S Wave ◽  
Wave Velocities ◽  
P Wave Velocity ◽  
Surface Spread ◽  
Isotropic Solids

P‐wave, SV‐wave, and SH‐wave velocities are computed for transversely isotropic solids formed from two isotropic solids. The combinations are shale‐sandstone and shale‐limestone solids of an earlier paper (Levin, 1979), but one velocity of the nonshale component is allowed to vary over the range of Poisson’s ratios σ = 0 to σ = 0.45, i.e., from a rigid solid to a near‐liquid. When the S‐wave velocity of either the sandstone or limestone is varied, the ratio of horizontal P‐wave velocity to vertical P‐wave velocity goes through a maximum as σ increases and subsequently falls to values less than unity as σ approaches 0.5. The P‐wave velocity that would be found with a short surface spread also goes through a maximum and, at σ = 0.5, is less than the P‐wave velocity of either isotropic component. SV‐wave velocities found for data from a short spread are unreasonably large; SH‐wave velocities decrease monotonically as σ increases, but the ratio of horizontal SH‐wave velocity to vertical SH‐wave velocity goes through a minimum of unity.

Sonic logging in deviated boreholes penetrating an anisotropic formation: Laboratory study

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. E125-E134 ◽  
Author(s):  
Zhenya Zhu ◽  
Shihong Chi ◽  
M. Nafi Toksöz
Keyword(s):  
Transversely Isotropic ◽  
Body Waves ◽  
P Wave ◽  
Laboratory Model ◽  
Stoneley Wave ◽  
S Wave ◽  
Wave Velocities ◽  
Anisotropic Formation ◽  
Sonic Logging ◽  
Drill Holes

Development of deepwater fields requires drilling deviated or horizontal wells. Many formations are highly anisotropic, that is, the P- and S-wave velocities vary with propagation direction. Sonic logs acquired in these wells need to be corrected for anisotropy effects before the logs can be used in formation evaluation and seismic applications. In this study, we use a laboratory model made of an orthorhombic Phenolite block to study acoustic logging in deviated wells. We first measure the qP-, qSV-, and SH-wave group velocities by using body waves at angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90° relative to the slowest P-wave principal axis of the Phenolite block. We then drill holes at the same angles in the block. We record monopole and dipole sonic waveforms in these holes and extract the qP-, qSV-, SH-, and Stoneley-wave velocities by using the slowness-time semblance method. The velocities measured through the use of monopole logging and dipole logging vary with borehole deviations. We find that an equivalent transversely isotropic (TI) model can fit the measured qP-, qSV-, and Stoneley-wave velocities very well. The S-wave velocities at low to medium borehole deviations can be used to differentiate an orthorhombic material from a TI one.

Attenuation operators and complex wave velocities for scattering in random media

1996 ◽  
Vol 148 (1-2) ◽  
pp. 269-285 ◽  
Author(s):  
Y. Fang ◽  
G. M�ller
Keyword(s):  
Random Media ◽  
Wave Velocities ◽  
Complex Wave

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.

scholarly journals A new traveltime approximation for TI media

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. C37-C42 ◽  
Author(s):  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Power Series ◽  
Eikonal Equation ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Efficient Tool ◽  
Trade Off ◽  
Background Medium ◽  
The Common ◽  
Anisotropy Parameters ◽  
Ti Media

In a transversely isotropic (TI) medium, the trade-off between inhomogeneity and anisotropy can dramatically reduce our capability to estimate anisotropy parameters. By expanding the TI eikonal equation in power series in terms of the aneliptic parameter [Formula: see text], we derive an efficient tool to estimate (scan) for [Formula: see text] in a generally inhomogeneous, elliptically anisotropic background medium. For a homogeneous-tilted transversely isotropic medium, we obtain an analytic nonhyperbolic moveout equation that is accurate for large offsets. In the common case where we do not have well information and it is necessary to resolve the vertical velocity, the background medium can be assumed isotropic, and the traveltime equations becomes simpler. In all cases, the accuracy of this new TI traveltime equation exceeds previously published formulations and demonstrates how [Formula: see text] is better resolved at small offsets when the tilt is large.

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