Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

Scattering of elastic waves by a fracture zone containing randomly distributed cracks

We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena.We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ ^–1 peaks aroundka1, the phase velocity is almost independent ofk in the rangeka<1 and it increases monotonically withk in the rangeka>1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ ^–1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ ^–1 is proportional tok ^–1 independently of model parameters and the wave modes. If the seismological observation thatQ ^–1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.     

A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite

The purpose of this paper is to present a model for the radiation pressure acceleration of a spherical satellite, due to the radiation reflected by a planet with a uniform albedo. A particular choice of variables allows one to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimensional integrals. Exact analytical expressions are found for the integrals corresponding to the case where the spacecraft does not "see" the terminator. The other integrals can be computed either numerically, or analytically in an approximate form. The results are compared with those of Lochry (1966). The model is applied to Magellan, a spacecraft orbiting Venus.     

等截面单桩抗拔承载性状试验研究

在基坑中对等截面单桩进行了抗拔静载试验，在桩身设置应变式钢筋计，成功测得桩身各截面的应变数据。分析试验所得数据，对试验抗拔桩抗拔系数的取值、侧摩阻力的发挥、混凝土桩身的开裂等进行了探讨，相应给出了抗拔桩的设计建议。     

Centrifuge modelling-based verification of response spectra design methods for some vulnerable structures

Residential RC framed structures suffered heavily during the 2001 Bhuj earthquake in Gujarat, India. These types of structures also saw severe damage in other earthquakes such as the 1999 Kocaeli earthquake in Turkey and 921 Ji-Ji earthquake in Taiwan. In this paper the seismic response of residential structures was investigated using physical modelling. Idealised soft storey and top heavy, two degrees of freedom (2DOF) portal frame structures were developed and tested on saturated and dry sand models at 25 g using the Schofield Centre 10-m Beam Centrifuge. It was possible to recreate observed field behaviour using these models. As observed in many of the recent earthquakes, soft storey structures were found to be particularly vulnerable to seismic loads. Elastic response spectra methods are often used in the design of simple portal frame structures. The seismic risk of these structures can be significantly increased due to modifications such as removal of a column or addition of heavy water tanks on the roof. The experimental data from the dynamic centrifuge tests on such soft storey or top-heavy models was used to evaluate the predictions obtained from the response spectra. Response spectra were able to predict seismic response during small to moderate intensity earthquakes, but became inaccurate during strong earthquakes and when soil structure interaction effects became important. Re-evaluation of seismic risk of such modified structures is required and time domain analyses suggested by building codes such as IBC, UBC or NEHRP may be more appropriate.