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Power-law attenuation in acoustic and isotropic anelastic media 总被引：1，自引：0，他引：1
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When comparing solutions for the propagation of SH waves in plane parallel layered elastic and viscoelastic (anelastic) media, one of the first things that becomes apparent is that in the elastic case the location of the saddle points required to obtain a high frequency approximation are located on the real p axis. This is true of the branch points also. In a viscoelastic medium this is not typical. The saddle point corresponding to an arrival lies in the first quadrant of the complex p-plane as do the branch points. Additionally, in the elastic case the saddle point and branch points lie on a straight line drawn through the origin (the positive real axis in the complex p-plane), while in the viscoelastic case this is generally not the case and the saddle point and branch points lie in such a manner as to indicate the degree of their complex values.In this paper simple SH reflected and transmitted particle displacement arrivals due to a point torque source at the surface in a viscoelastic medium composed of a layer over a half space will be considered. The path of steepest descent defining the saddle point in the first quadrant will be parameterized in terms of a real variable and the high frequency solutions and intermediate analytic results obtained will be used to formulate more specific constraints and observations regarding saddle point location relative to branch point locations in the complex p-plane.As saddle point determination for an arrival is, in general, the solution of a non-linear equation in two unknowns (the real and imaginary parts of the complex saddle point p
0), which must be solved numerically, the use of analytical methods for investigating this problem type is somewhat limited.Numerical experimentation using well documented solution methods, such as Newton's method, was undertaken and some observations were made. Although fairly basic, they did provide for the design of algorithms for the computation of synthetic traces that displayed more efficient convergence and accuracy than those previously employed. This was the primary motivation for this work and the results from the SH problem may be used with minimal modifications to address the more complicated subject of coupled P-SV wave propagation in viscoelastic media.Another reason for revisiting a problem that has received some attention in the literature was to approach it in a fairly comprehensive manner so that a number of specific observations may be made regarding the location of the saddle point in the complex p-plane and to incorporate these into computer software. These have been found to result in more efficient algorithms for the SH wave propagation and a significant enhancement of the comparable software in the P-SV problem. 相似文献
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基于简正模扰动理论和勒夫数扰动方法,采用Zschau 的地幔流变模型,在假设Chandler摆动的能量全部耗散于地幔滞弹性摩擦的条件下,导出Chandler 摆动Q(Q_w)的理论值.还考虑了滞弹地球的平衡极潮对摆动的影响,所得结果与绝大部分天文实测值非常一致.分析表明.平衡部分的影响大,地幔滞弹性很可能是Chandler 摆动最主要的能量耗散源,Q_w 的理论值约为71.还推算了吸收带模型参数α,研究了该模型的适用性,并讨论了Q_w 与地幔Q(Q_m)的关系. 相似文献
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We present an efficient scheme to compute high-frequency seismograms (up to 10 Hz) forSH-waves in a horizontally stratified medium with the mode summation method. The formalism which permits the computation of eigenvalues, eigenfunctions and related integral quantities is discussed in detail. Anelasticity is included in the model by using the variational method. Phase velocity, group velocity, energy integral and attenuation spectra of a structure enable the computation of complete strong motion seismograms, which are the basic tool for the interpretation of near-source broad-band data.Different examples computed for continental structures are discussed, where one example is the comparison between the observed transversal displacement recorded at station IVC for the November 4, Brawley 1976 earthquake and synthetic signals. In the case of a magnitudeM
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=5.7 earthquake in the Friuli seismic area we apply the mode summation method to infer from waveform modeling of all three components of motion of observed data some characteristics of the source.On leave from Institute of Geophysics, ETH, Zürich, Switzerland. 相似文献
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David Al-Attar 《Geophysical Journal International》2007,171(2):755-760
A formal solution to the elastodynamic equation in an anelastic earth model is presented. The derivation also incorporates the effects of aspherical structure, rotation, self-gravitation, and pre-stress. It is found that the solution can be expressed as a sum of the normal modes of the earth model along with additional terms accounting for anelastic relaxation processes. However, the derivation does not assume that such an eigenfunction expansion is possible, and so avoids difficulties previously encountered due to the non self-adjointness of the problem. 相似文献
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Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically. 相似文献
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An accurate model of the rotation of the Moon, constructed by numerical integration, has been presented in a previous paper. All direct perturbations capable of producing at least 10–4 seconds of arc on the Moon's rotational motion have been included, and the physical librations resulting from planetary effects and Earth-Moon figure-figure interactions have been presented. The present study deals with the Moon's physical librations resulting from the non-rigidities of the Moon and the Earth. The effects of the Moon's elasticity and of a lunar phase lag are analyzed. Physical librations due to lunar tides and those due to terrestrial tides are presented and described. 相似文献
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