Effects of scattering and resonance on energy dissipation of an internal tide in a narrow shelf

The effects of scattering and resonance on the energy dissipation of an internal tide were investigated using a two-dimensional model which is a reassembled version of the theoretical generation model devised by Rattray et al. (1969) for internal tide. The basic character of the scattering process at the step bottom was first investigated with a wide shelf model. When the internal wave incited from a deep region (Region II) into the shallow shelf region (Region I), a passing wave into the shallow region, a reflected wave into the deep region, and a beam-like wave, i.e. a scattered wave (SW), emanated at the step bottom. The SW, which consists of the superposition of numerous internal modes, propagated upward/downward into both regions. The general properties of the SW were well expressed around the shelf edge, even in the present model with viscosity effect. The amplitude of the SW decreased dramatically when the depth of the velocity maximum of the incident internal wave in Region II corresponded with the depth of the shelf edge. In the narrow shelf model, where the decay distance of the internal wave in Region I is longer than the shelf width, the incident internal wave reflected at the coast to form a standing wave. When the internal wave in Region I is enhanced by the resonance, the energy of the SW in Region II is also intensified. Furthermore, the energy of the modes in Region II predominated when the velocity maximum is identical to that of the dominant mode in Region I. These results suggest that the spatial scale of shelf region is a very important factor governing the energy dissipation of the internal tide through reflection and scattering in a narrow shelf.     

外差激光雷达测量水体布里渊散射可行性研究

该文分析外差激光雷达测量水体布里渊散射的可行性。借助测量水体布里渊散射的频移 ,可得到水体声速或温度。文中利用两条 12 7I2 吸收线锁定激光输出频率 ,产生稳定的频差约为7.5 GHz发射激光和激光本振。通过对 12 7I2 吸收线稳定度、激光频率稳定度、系统信噪比和反演精度的分析和计算机模拟 ,得出水体深度 2 5 m以内水体布里渊散射频移的测量误差可以控制在2 .5 MHz以内 ,达到水中声速 0 .6 m/ s或温度 0 .1℃的测量精度。     

Laser probe Ar/Ar dating: History and development from a technical perspective

The ⁴⁰Ar/³⁹Ar method using a laser probe opened the door to microscale measurements and diffusion profiles frozen in samples. In the first decade since the initial application of a laser for ⁴⁰Ar/³⁹Ar dating in 1973, practical applications have been few. This is due not only to the fact that the laser and vacuum technologies were immature but that mass spectrometry was also in its infancy. In those days, the sensitivity of a mass spectrometer was generally insufficient to measure the small amount of argon degassed from a geological sample by a laser. These problems have subsequently been solved by new technologies. To understand their current status, a brief history of their development is outlined. This outline focuses on the required detection limit in micro scale measurement, practical approaches for accurate measurement are explained through examples in our laboratory specifically relating to the technical aspects of ⁴⁰Ar/³⁹Ar dating.     

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.