Ray Method for Volume Waves in Anisotropic Media

Elastic Waves ◽  
2018 ◽  
pp. 191-205
Author(s):  
Vassily M. Babich ◽  
Aleksei P. Kiselev
Keyword(s):  
Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 308-319 ◽  
Author(s):  
Ivan Pšenčík ◽  
Joe A. Dellinger

In inhomogeneous isotropic regions, S-waves can be modeled using the ray method for isotropic media. In inhomogeneous strongly anisotropic regions, the independently propagating qS1- and qS2-waves can similarly be modeled using the ray method for anisotropic media. The latter method does not work properly in inhomogenous weakly anisotropic regions, however, where the split qS-waves couple. The zeroth‐order approximation of the quasi‐isotropic (QI) approach was designed for just such inhomogeneous weakly anisotropic media, for which neither the ray method for isotropic nor anisotropic media applies. We test the ranges of validity of these three methods using two simple synthetic models. Our results show that the QI approach more than spans the gap between the ray methods: it can be used in isotropic regions (where it reduces to the ray method for isotropic media), in regions of weak anisotropy (where the ray method for anisotropic media does not work properly), and even in regions of moderately strong anisotropy (in which the qS-waves decouple and thus could be modeled using the ray method for anisotropic media). A modeling program that switches between these three methods as necessary should be valid for arbitrary‐strength anisotropy.


Author(s):  
T. V. Nefedkina ◽  
P. A. Lykhin ◽  
G. A. Dugarov

In this paper, we investigate optimization algorithm of joint nonlinear AVOA inversion of PP+PS reflections in anisotropic media. Algorithm is based on the exact solution for PP and PS waves reflection coefficients in anisotropic HTI medium. The PP and PS wave’s reflections from the top of the anisotropic layer are examined. We use synthetic seismograms generated by ray method for the algorithm testing. We show that joint compressional and converted wave’s inversion allows increasing the robustness of the method and the accuracy of medium-parameter estimates. Coefficients of anisotropy are determined with better accuracy if signal-to-noise ratio is bigger than 5 for PP wave and bigger than 2 for PS wave.


Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Dirk Gajewski ◽  
Ivan Pšenčík

The ray method is used to compute high‐frequency seismic vector wavefields in weakly attenuating layered anisotropic structures. The attenuating effects are introduced by substituting the real elastic parameters for perfectly elastic media by complex frequency dependent elastic parameters with small imaginary parts. The imaginary parts are formally considered to be of the order of [Formula: see text] for [Formula: see text]. Under this assumption, it is possible to work with real rays, only the eikonal is complex. The approximate computations based on this algorithm are only a few percent slower than those for perfectly elastic anisotropic media. The range of applicability of the weak attenuation concept is investigated by comparison of ray computations with results of the reflectivity method for an isotropic, constant gradient model. The study indicates that the region of applicability of the weak attenuation concept may be broader than expected. The combined effects of anisotropy and attenuation on the propagation of seismic waves in a three‐dimensional model of the uppermost crust with an anisotropic attenuating layer are then studied. The anisotropy as well as the attenuation are supposed to be caused by aligned partially liquid‐filled cracks. Hudson’s formulas to compute complex effective elastic parameters are used. Frequency responses and VSP synthetic seismograms for different degrees of viscosity of the liquid, and, thus, different degree of attenuation, show the effects of attenuation on the propagating waves. Nine‐component VSP vector wavefields are computed for two different source‐borehole directions along the strike of the cracks and 45 degrees off the strike of the cracks. The seismograms for the attenuating model are compared with seismograms for the corresponding perfectly elastic model.


Author(s):  
S. Fujishiro

The mechanical properties of three titanium alloys (Ti-7Mo-3Al, Ti-7Mo- 3Cu and Ti-7Mo-3Ta) were evaluated as function of: 1) Solutionizing in the beta field and aging, 2) Thermal Mechanical Processing in the beta field and aging, 3) Solutionizing in the alpha + beta field and aging. The samples were isothermally aged in the temperature range 300° to 700*C for 4 to 24 hours, followed by a water quench. Transmission electron microscopy and X-ray method were used to identify the phase formed. All three alloys solutionized at 1050°C (beta field) transformed to martensitic alpha (alpha prime) upon being water quenched. Despite this heavily strained alpha prime, which is characterized by microtwins the tensile strength of the as-quenched alloys is relatively low and the elongation is as high as 30%.


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