Seismic Signal and Data Analysis of Rock Media with Vertical Anisotropy

This paper is concerned with anisotropic effects on seismic data and signal analysis for transversely isotropic rock media with vertical anisotropy. It is understood that these effects are significant in many practical applications, e.g. earthquake forecasting, materials exploration inside the Earth’s crust, as well as various practical works in oil industry. Under the framework of the most accepted anisotropic media model (i.e. VTI media, transverse isotropy with a vertical axis symmetry), with applications of a set of available anisotropic rock parameters for sandstone and shale, we have performed numerical calculations of the anisotropic effects. We show that for rocks with strong anisotropy, the induced relative depth error can be significantly large. Nevertheless, with an improved understanding of the seismic-signal propagation and proper data processing, the error can be reduced, which in turn may enhance the probability of forecasting accurately the various wave propagations inside the Earth’s crust, e.g. correctly forecasting the incoming earthquakes from the center of the Earth.

The influence of rock anisotropy on elliptical-polarization state of inhomogenously refracted P-wave

This paper discusses the influence of the anisotropy parameters on elliptical-polarization of the inhomogenously refracted P-wave induced at VTI-media interface.For this refracted P-wave,we have derived,the equations of the elliptical-polarization trajectory.Following the elliptical-polarization trajectory,we calculated the effects of the rock anisotropic-parameters on the polarization state,with a Poincare-sphere-like representation,for several varying media parameters.It is noted that the size,shape and initial phase angle of the elliptical-polarization trajectory are all depending the anisotropy media,as well as on the incident-angle.We expect that the findings from this paper would be applied to practical applications of seismic exploration.

Acoustic Goos-H?nchen effect

We report two models of the lateral displacement of acoustic-wave scattering on a fluid-solid interface that reveal an acoustic analog of the Goos-H?nchen effect in optics. This acoustic analog is called the acoustic Goos-H?nchen effect. Using newly proposed models, we made numerical calculations for the system of a water-Perspex interface. Specifically, in the post-critical-angle region,we observed a lateral displacement(and transition time) of the reflected P-wave with respect to the incident P-wave. The first arrival of the acoustic signal from the interface is found to be a reflected P-wave rather than the sliding-refraction P-wave usually described in traditional acoustic-logging sliding P-wave theory. For both proposed models, the effective propagation speed of the reflected P-wave along the interface depends on not only the physical properties of the interfacial media but also the incident angle.These observations are intriguing and warrant further investigation.

Reflection and refraction of elastic wave at VTI-TTI media interface

We explore the physical phenomenon of acoustic waves induced at the interface between two different anisotropic rock media.Specifically,one medium is a transversely isotropic medium with a vertical axis of symmetry(VTI medium)and the other one is a transversely isotropic medium with a tilt axis of symmetry(TTI medium).By solving the Kelvin-Christoffel equation,an eighth-order polynomial is established for reflection and refraction angles,which is confirmed from SnelFs law.Three types of analytical expressions of the polarization coefficients of the induced waves are obtained corresponding to different incident angle regions.An effective algorithm has been developed for numerical analysis of the polarization coefficients.Applying characteristic anisotropic parameters reported in the literature,the influencing factors on reflection and refraction coefficients are analyzed,e.g.,the anisotropy,the tilt-angle of rock-layer,and the incident-angle.The calculated reflection and refraction coefficients have been rechecked for energy conservation.

An analysis of the rate of isomerization in molecules with an asymmetric double well potential

The classical theory of the rate of unimolecular isomerization developed by Gray and Rice as extended by Zhao and Rice is applied to the calculation of the rate of isomerization in model systems which have linear asymmetric double well potentials. We are interested in this system for two reasons. First, we are interested in the detailed dynamical processes for the mentioned system because it is widely related to practical chemical reactions. Second, the present model system has an asymmetric double well potential, which provides a different test of the accuracy of the approximations used in the Gray-Zhao-Rice theory than posed by previous applications. We have calculated relaxation rates and relaxation times for the model systems on different time scales. We find that for the systems under studies the Gray-Zhao-Rice version of the classical theory of isomerization rate yields values in good agreement with those generated from trajectory calculations and from the Reactive Island theory of De Leon et al.