Seismic traveltime inversion for transverse isotropy

Geophysics ◽  
1990 ◽  
Vol 55 (2) ◽  
pp. 192-200 ◽  
Author(s):  
B. S. Byun ◽  
D. Corrigan
Keyword(s):  
Field Experiments ◽  
Seismic Anisotropy ◽  
Transverse Isotropy ◽  
Quantitative Measure ◽  
Transversely Isotropic ◽  
Velocity Anisotropy ◽  
Additional Information ◽  
Stiffness Coefficients ◽  
Anisotropy Parameters ◽  
Low Degrees

Quantitative measurements of seismic anisotropy can provide a valuable clue to the lithology and degree of stratification in sedimentary rocks with hydrocarbon potential. We present a practical technique for obtaining anisotropy parameters (i.e., five stiffness coefficients A, C, F, L, and M) from seismic traveltime measurements for horizontally layered, transversely isotropic media. The technique is based on the construction of ray‐velocity surfaces in terms of five measurement parameters. An iterative model‐based optimization scheme is then used to invert the traveltime parameters for the five stiffness coefficients in a layer‐stripping mode. Both model and field experiments are performed to demonstrate the feasibility of the method. The model experiment shows that inversion errors (especially in stiffness coefficients A, F, and M) increase with increasing number of layers. Despite these errors, the proposed method does provide a quantitative measure of velocity anisotropy as additional information that cannot be obtained readily from conventional methods. A field VSP data example shows the correlation between the anisotropy parameters and lithology: Chalk and shale exhibited high degrees of anisotropy, and sands showed low degrees of anisotropy.

Relationships between the anisotropy parameters for transversely isotropic mudrocks

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. MR195-MR203
Author(s):  
Fuyong Yan ◽  
Lev Vernik ◽  
De-Hua Han
Keyword(s):  
Elastic Properties ◽  
Seismic Anisotropy ◽  
Measurement Data ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
The Other ◽  
Quality Analysis ◽  
Directional Bias ◽  
Empirical Relations ◽  
Anisotropy Parameters

Studying the empirical relations between seismic anisotropy parameters is important for the simplification and practical applications of seismic anisotropy. The elastic properties of mudrocks are often described by transverse isotropy. Knowing the elastic properties in the vertical and horizontal directions, a sole oblique anisotropy parameter determines the pattern of variation of the elastic properties of a transversely isotropic (TI) medium in all of the other directions. The oblique seismic anisotropy parameter [Formula: see text], which determines seismic reflection moveout behavior, is important in anisotropic seismic data processing and interpretation. Compared to the other anisotropy parameters, the oblique anisotropy parameter is more sensitive to the measurement error. Although, theoretically, only one oblique velocity is needed to determine the oblique anisotropy parameter, the uncertainty can be greatly reduced if multiple oblique velocities in different directions are measured. If a mudrock is not a perfect TI medium but it is expediently treated as one, then multiple oblique velocity measurements in different directions should lead to a more representative approximation of [Formula: see text] or [Formula: see text] because the directional bias can be reduced. Based on a data quality analysis of the laboratory seismic anisotropy measurement data from the literature, we found that there are strong correlations between the oblique anisotropy parameter and the principal anisotropy parameters when data points of more uncertainty are excluded. Examples of potential applications of these empirical relations are discussed.

Analytic study of the effective parameters for determination of the NMO velocity function in transversely isotropic media

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1855-1866 ◽  
Author(s):  
Jack K. Cohen
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Velocity Function ◽  
Transversely Isotropic Media ◽  
Wave Phase Velocity ◽  
Isotropic Media ◽  
Anisotropy Parameters ◽  
Vti Media ◽  
Ray Parameter

In their studies of transversely isotropic media with a vertical symmetry axis (VTI media), Alkhalifah and Tsvankin observed that, to a high numerical accuracy, the normal moveout (NMO) velocity for dipping reflectors as a function of ray parameter p depends mainly on just two parameters, each of which can be determined from surface P‐wave observations. They substantiated this result by using the weak‐anisotropy approximation and exploited it to develop a time‐domain processing sequence that takes into account vertical transverse isotropy. In this study, the two‐parameter Alkhalifah‐Tsvankin result was further examined analytically. It was found that although there is (as these authors already observed) some dependence on the remaining parameters of the problem, this dependence is weak, especially in the practically important regimes of weak to moderately strong transverse isotropy and small ray parameter. In each of these regimes, an analytic solution is derived for the anisotropy parameter η required for time‐domain P‐wave imaging in VTI media. In the case of elliptical anisotropy (η = 0), NMO velocity expressed through p is fully controlled just by the zero‐dip NMO velocity—one of the Alkhalifah‐ Tsvankin parameters. The two‐parameter representation of NMO velocity also was shown to be exact in another limit—that of the zero shear‐wave vertical velociy. The analytic results derived here are based on new representations for both the P‐wave phase velocity and normal moveout velocity in terms of the ray parameter, with explicit expressions given for the cases of vanishing onaxis shear speed, weak to moderate transverse isotropy, and small to moderate ray parameter. Using these formulas, I have rederived and, in some cases, extended in a uniform manner various results of Tsvankin, Alkhalifah, and others. Examples include second‐order expansions in the anisotropy parameters for both the P‐wave phase‐velocity function and NMO‐velocity function, as well as expansions in powers of the ray parameter for both of these functions. I have checked these expansions against the corresponding exact functions for several choices of the anisotropy parameters.

Focal mechanisms produced by shear faulting in weakly transversely isotropic crustal rocks

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. D145-D151 ◽  
Author(s):  
Václav Vavryčuk
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Focal Mechanisms ◽  
Crustal Rocks ◽  
Linear Vector ◽  
Double Couple ◽  
Anisotropic Rocks ◽  
Anisotropy Parameters ◽  
Anisotropy Strength

Shear faulting in anisotropic rocks produces non-double-couple (non-DC) mechanisms. The non-DC mechanisms can comprise the isotropic (ISO) and compensated linear vector dipole (CLVD) components. The formulas for percentages of the ISO and CLVD are simplified under the assumption of weak transverse isotropy and can be expressed advantageously in terms of Thomsen’s anisotropy parameters. Shear faulting in crustal rocks with anisotropy strength of 10% can produce an ISO of up to 10% and a CLVD of up to 30%. Such values are significant and detectable in carefully determined focal mechanisms.

Causes of compressional‐wave anisotropy in carbonate‐bearing, deep‐sea sediments

Geophysics ◽  
1984 ◽  
Vol 49 (5) ◽  
pp. 525-532 ◽  
Author(s):  
R. L. Carlson ◽  
C. H. Schaftenaar ◽  
R. P. Moore
Keyword(s):  
Deep Sea ◽  
Transversely Isotropic ◽  
Compressional Wave ◽  
Carbonate Content ◽  
Velocity Anisotropy ◽  
Acoustic Anisotropy ◽  
Transversely Isotropic Media ◽  
Deep Sea Sediments ◽  
Isotropic Media ◽  
Low Degrees

Forty indurated sediment samples from DSDP site 516 were studied with the principle objective of determining which of several proposed mechanisms is the cause of acoustic anisotropy in carbonate‐bearing deep‐sea sediments. Recovered from sub‐bottom depths between 388 and 1222 m, the samples have properties exhibiting the following ranges: wet‐bulk density, 1.90 to [Formula: see text]; fractional porosity, 0.46 to 0.14; carbonate content, 34 to 88 percent; compressional‐wave velocity (at 0.1 kbar), 1.87 to 4.87 km/sec; anisotropy, 1 to 13 percent. Velocities were measured in three mutually perpendicular directions through the same specimen in 29 of the 40 samples studied. Calcite fabric has been estimated by x‐ray pole figure goniometry. The major findings of this study are. (1) Carbonate‐bearing deep‐sea sediments may be regarded as transversely isotropic media with symmetry axes normal to bedding. (2) Calcite c‐axes are weakly concentrated in a direction perpendicular to bedding, but the preferred orientation of calcite does not contribute significantly to velocity anisotropy. (3) The properties of bedded and unbedded samples are distinctly different. Unbedded sediments exhibit low degrees of acoustic anisotropy (1 to 5 percent). By contrast, bedded samples show higher degrees of anisotropy (to 13 percent), and anisotropy increases markedly with depth of burial. Thus, bedding must be regarded as the principal cause of acoustic anisotropy in calcareous, deep‐sea sediments.

Effects of transverse isotropy on P‐wave AVO for gas sands

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 883-888 ◽  
Author(s):  
Ki Young Kim ◽  
Keith H. Wrolstad ◽  
Fred Aminzadeh
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Velocity Anisotropy ◽  
Special Cases ◽  
Class 1 ◽  
Zero Offset ◽  
Ti Media

Velocity anisotropy should be taken into account when analyzing the amplitude variation with offset (AVO) response of gas sands encased in shales. The anisotropic effects on the AVO of gas sands in transversely isotropic (TI) media are reviewed. Reflection coefficients in TI media are computed using a planewave formula based on ray theory. We present results of modeling special cases of exploration interest having positive reflectivity, near‐zero reflectivity, and negative reflectivity. The AVO reflectivity in anisotropic media can be decomposed into two parts; one for isotropy and the other for anisotropy. Zero‐offset reflectivity and Poisson’s ratio contrast are the most significant parameters for the isotropic component while the δ difference (Δδ) between shale and gas sand is the most important factor for the anisotropic component. For typical values of Tl anisotropy in shale (positive δ and ε), both δ difference (Δδ) and ε difference (Δε) amplify AVO effects. For small angles of incidence, Δδ plays an important role in AVO while Δε dominates for large angles of incidence. For typical values of δ and ε, the effects of anisotropy in shale are: (1) a more rapid increase in AVO for Class 3 and Class 2 gas sands, (2) a more rapid decrease in AVO for Class 1 gas sands, and (3) a shift in the offset of polarity reversal for some Class 1 and Class 2 gas sands.

Analysis of seismic anisotropy parameters for sedimentary strata

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D495-D502 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Samik Sil ◽  
Xue-Lian Chen
Keyword(s):  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Measurement Data ◽  
Transversely Isotropic ◽  
Theoretical Expression ◽  
Strong Correlations ◽  
Backus Averaging ◽  
Anisotropy Parameters ◽  
Intrinsic Anisotropy ◽  
Gas Bearing

Based on a large quantity of laboratory ultrasonic measurement data of sedimentary rocks and using Monte Carlo simulation and Backus averaging, we have analyzed the layering effects on seismic anisotropy more realistically than in previous studies. The layering effects are studied for different types of rocks under different saturation conditions. If the sedimentary strata consist of only isotropic sedimentary layers and are brine-saturated, the [Formula: see text] value for the effective transversely isotropic (TI) medium is usually negative. The [Formula: see text] value will increase noticeably and can be mostly positive if the sedimentary strata are gas bearing. Based on simulation results, [Formula: see text] can be determined by other TI elastic constants for a layered medium consisting of isotropic layers. Therefore, [Formula: see text] can be predicted from the other Thomsen parameters with confidence. The theoretical expression of [Formula: see text] for an effective TI medium consisting of isotropic sedimentary rocks can be simplified with excellent accuracy into a neat form. The anisotropic properties of the interbedding system of shales and isotropic sedimentary rocks are primarily influenced by the intrinsic anisotropy of shales. There are moderate to strong correlations among the Thomson anisotropy parameters.

Anisotropy signatures in the Cooper Basin of Australia: Stress versus fractures

2016 ◽  
Vol 4 (2) ◽  
pp. SE51-SE61 ◽  
Author(s):  
Stephanie Tyiasning ◽  
Dennis Cooke
Keyword(s):  
Seismic Data ◽  
Oil And Gas ◽  
Seismic Anisotropy ◽  
Transverse Isotropy ◽  
Ground Truth ◽  
Tectonic Stress ◽  
Reverse Fault ◽  
Stress Regime ◽  
Velocity Anisotropy ◽  
Cooper Basin

Theoretically, vertical fractures and stress can create horizontal transverse isotropy (HTI) anisotropy on 3D seismic data. Determining if seismic HTI anisotropy is caused by stress or fractures can be important for mapping and understanding reservoir quality, especially in unconventional reservoirs. Our study area was the Cooper Basin of Australia. The Cooper Basin is Australia’s largest onshore oil and gas producing basin that consists of shale gas, basin-centered tight gas, and deep coal play. The Cooper Basin has unusually high tectonic stress, with most reservoirs in a strike-slip stress regime, but the deepest reservoirs are interpreted to be currently in a reverse-fault stress regime. The seismic data from the Cooper Basin exhibit HTI anisotropy. Our main objective was to determine if the HTI anisotropy was stress induced or fracture induced. We have compared migration velocity anisotropy and amplitude variation with offset anisotropy extracted from a high-quality 3D survey with a “ground truth” of dipole sonic logs, borehole breakout, and fractures interpreted from image logs. We came to the conclusion that the HTI seismic anisotropy in our study area is likely stress induced.

Seismic anisotropy in sedimentary rocks, part 1: A single‐plug laboratory method

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1415-1422 ◽  
Author(s):  
Zhijing Wang
Keyword(s):  
Seismic Anisotropy ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Cylindrical Sample ◽  
Laboratory Method ◽  
Piezoelectric Transducers ◽  
Low Permeability ◽  
Seismic Velocities ◽  
Fluid Displacement ◽  
Fluid Saturation

A single‐plug method for measuring seismic velocities and transverse isotropy in rocks has been rigorously validated and laboratory tested. The method requires only one sample to measure the velocities needed to derive the five independent elastic constants for transversely isotropic materials. In this method, piezoelectric transducers are fitted to the top, bottom, and sides of the cylindrical sample. Laboratory velocity and anisotropy can be measured as functions of pressure, temperature, fluid saturation, and fluid displacement. Because this method uses a horizontal core plug that has much higher permeability than a vertical core plug, it is especially suitable for low‐permeability shale measurements. It reduces the sample preparation and velocity measurement time by more than two‐thirds.

Seismic critical-angle anisotropy analysis in the τ -p domain

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. A53-A57 ◽  
Author(s):  
Samik Sil ◽  
Mrinal K. Sen
Keyword(s):  
Critical Angle ◽  
Seismic Anisotropy ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Seismic Line ◽  
Full Wave ◽  
Current Implementation ◽  
Approximation Errors ◽  
Anisotropy Parameters ◽  
Axis Of Symmetry

Seismic critical-angle reflectometry is a relatively new field for estimating seismic anisotropy parameters. The theory relates changes in the critical angle with azimuth of the seismic line to the principal axis and anisotropy parameters. Current implementation of the critical-angle reflectometry process has certain shortcomings in that the critical angle is determined from critical offset and the process is vulnerable to different approximation errors. Seismic critical-angle analysis in the plane-wave [Formula: see text] domain can handle these issues and has the potential to become an independent tool for estimating anisotropy parameters. The theory of seismic critical-angle reflectometry is modified to make it suitable for [Formula: see text] domain analysis. Then using full-wave synthetic seismograms at three different azimuths for a transversely isotropic medium with a horizontal axis of symmetry (HTI), the effectiveness of anisotropy parameter estimation is demonstrated.

Plane-wave propagation in attenuative transversely isotropic media

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. T17-T30 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Wave Attenuation ◽  
Transversely Isotropic ◽  
Attenuation Coefficients ◽  
The Real ◽  
Velocity Anisotropy ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy ◽  
Ti Media

Directionally dependent attenuation in transversely isotropic (TI) media can influence significantly the body-wave amplitudes and distort the results of the AVO (amplitude variation with offset) analysis. Here, we develop a consistent analytic treatment of plane-wave properties for TI media with attenuation anisotropy. We use the concept of homogeneous wave propagation, assuming that in weakly attenuative media the real and imaginary parts of the wave vector are parallel to one another. The anisotropic quality factor can be described by matrix elements [Formula: see text], defined as the ratios of the real and imaginary parts of the corresponding stiffness coefficients. To characterize TI attenuation, we follow the idea of the Thomsen notation for velocity anisotropy and replace the components [Formula: see text] by two reference isotropic quantities and three dimensionless anisotropy parameters [Formula: see text], and [Formula: see text]. The parameters [Formula: see text] and [Formula: see text] quantify the difference between the horizontal- and vertical-attenuation coefficients of P- and SH-waves, respectively, while [Formula: see text] is defined through the second derivative of the P-wave attenuation coefficient in the symmetry direction. Although the definitions of [Formula: see text], and [Formula: see text] are similar to those for the corresponding Thomsen parameters, the expression for [Formula: see text] reflects the coupling between the attenuation and velocity anisotropy. Assuming weak attenuation as well as weak velocity and attenuation anisotropy allows us to obtain simple attenuation coefficients linearized in the Thomsen-style parameters. The normalized attenuation coefficients for P- and SV-waves have the same form as the corresponding approximate phase-velocity functions, but both [Formula: see text] and the effective SV-wave attenuation-anisotropy parameter [Formula: see text] depend on the velocity-anisotropy parameters in addition to the elements [Formula: see text]. The linearized approximations not only provide valuable analytic insight, but they also remain accurate for the practically important range of small and moderate anisotropy parameters — in particular, for near-vertical and near-horizontal propagation directions.

Sign in / Sign up

Export Citation Format

Share Document