A physical model of shear‐wave propagation in a transversely isotropic solid

Geophysics ◽  
1994 ◽  
Vol 59 (3) ◽  
pp. 484-487 ◽  
Author(s):  
Chih‐Hsiung Chang ◽  
G. H. F. Gardner ◽  
John A. McDonald
Keyword(s):  
Wave Propagation ◽  
Physical Model ◽  
Shear Wave ◽  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Physical Property ◽  
Transversely Isotropic ◽  
Velocity Variation ◽  
Common Phenomenon ◽  
Isotropic Solid

It is now understood that seismic anisotropy is a comparatively common phenomenon in sedimentary layers. The elastic properties of most sedimentary rocks have been shown to be anisotropic. (Anisotropy means that the physical property of the material is a function of the measuring direction). Seismologists are generally concerned with velocity variation with the direction of propagation.

To: “A physical model of shear wave propagation in transversely isotropic solid,” by Chih‐Hsiung Chang, G. H. F. Gardner, and John A. McDonald (March 1994 GEOPHYSICS, 59, p. 484–487)

Geophysics ◽  
1994 ◽  
Vol 59 (8) ◽  
pp. 1311-1311
Keyword(s):  
Wave Propagation ◽  
Physical Model ◽  
Shear Wave ◽  
Transversely Isotropic ◽  
Isotropic Solid ◽  
Model Study

The title of this paper was incorrect. The title should be, “A physical model study of shear wave propagation in transversely isotropic solid.”

Numerical simulation of seismic wave propagation in viscoelastic-anisotropic media using frequency-independent Q wave equation

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. WA1-WA10 ◽  
Author(s):  
Tieyuan Zhu
Keyword(s):  
Numerical Modeling ◽  
Wave Propagation ◽  
Wave Equation ◽  
Inhomogeneous Medium ◽  
Seismic Anisotropy ◽  
Numerical Solutions ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Theoretical Formula ◽  
Frequency Independent

Seismic anisotropy is the fundamental phenomenon of wave propagation in the earth’s interior. Numerical modeling of wave behavior is critical for exploration and global seismology studies. The full elastic (anisotropy) wave equation is often used to model the complexity of velocity anisotropy, but it ignores attenuation anisotropy. I have presented a time-domain displacement-stress formulation of the anisotropic-viscoelastic wave equation, which holds for arbitrarily anisotropic velocity and attenuation [Formula: see text]. The frequency-independent [Formula: see text] model is considered in the seismic frequency band; thus, anisotropic attenuation is mathematically expressed by way of fractional time derivatives, which are solved using the truncated Grünwald-Letnikov approximation. I evaluate the accuracy of numerical solutions in a homogeneous transversely isotropic (TI) medium by comparing with theoretical [Formula: see text] and [Formula: see text] values calculated from the Christoffel equation. Numerical modeling results show that the anisotropic attenuation is angle dependent and significantly different from the isotropic attenuation. In synthetic examples, I have proved its generality and feasibility by modeling wave propagation in a 2D TI inhomogeneous medium and a 3D orthorhombic inhomogeneous medium.

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.

Laboratory results for the features of body‐wave propagation in a transversely isotropic media

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1921-1924 ◽  
Author(s):  
Young‐Fo Chang ◽  
Chih‐Hsiung Chang
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Elastic Anisotropy ◽  
Body Wave ◽  
Transversely Isotropic ◽  
Sedimentary Basins ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Much of the earth’s crust appears to have some degree of elastic anisotropy (Crampin, 1981; Crampin and Lovell, 1991; Helbig, 1993). The phenomena of elastic wave propagation in anisotropic media are more complex than those in isotropic media. Shear‐wave propagation in an orthorhombic physical model is most complex when the direction of the wave is close to the neighborhood of the cusp on the group velocity surfaces (Brown et al., 1991). The first identification of singularities in wave propagation through sedimentary basins occurred in the examination of shear‐wave splitting in multioffset vertical seismic profiles (VSPs) at a borehole site in the Paris Basin (Bush and Crampin, 1991), where large variations in shear‐wave polarizations in propagation directions close to point singularities were observed. Computation of synthetic seismograms for layer sequences showed that the shear‐wave polarizations and amplitudes were irregular near point singularities (Crampin, 1991).

Sign in / Sign up

Export Citation Format

Share Document