Backscattering from spherical elastic inclusions and accuracy of the Kirchhoff approximation for curved interfaces

The Kirchhoff (or tangent plane) approximation, derived from the theoretically complete Kirchhoff–Helmholtz integral representation for the seismic wavefield, has been used extensively for the analysis of seismic-wave scattering from irregular interfaces; however, the accuracy of this method for curved interfaces has not been rigorously established. This paper describes an efficient Kirchhoff algorithm to simulate scattered waves from an arbitrarily curved interface in an elastic medium. Synthetic seismograms computed using this algorithm are compared with exact synthetics computed using analytical formulae for scattering of plane P waves by a spherical elastic inclusion. A windowing technique is used to remove strong internal reverberations from the analytical solution. Although the Kirchhoff method tends to underestimate the total scattering intensity, the accuracy of the approximation improves with increasing value of the wavenumber-radius product, kR . The arrival times and pulse shapes of primary reflections from the sphere are well approximated using the Kirchhoff approach regardless of curvature of the scattering surface, but the amplitudes are significantly underestimated for kR ≤ 5. The results of this work provide some new guidelines to assess the accuracy of Kirchhoff-synthetic seismograms for curved interfaces.     

The Theory of Coda Wave Interferometry

Coda waves are sensitive to changes in the subsurface because the strong scattering that generates these waves causes them to repeatedly sample a limited region of space. Coda wave interferometry is a technique that exploits this sensitivity to estimate slight changes in the medium from a comparison of the coda waves before and after the perturbation. For spatially localized changes in the velocity, or for changes in the source location, the travel-time perturbation may be different for different scattering paths. The coda waves that arrive within a certain time window are therefore subject to a distribution of travel-time perturbations. Here I present the general theory of coda wave interferometry, and show how the time-shifted correlation coefficient can be used to estimate the mean and variance of the distribution of travel-time perturbations. I show how this general theory can be used to estimate changes in the wave velocity, in the location of scatterer positions, and in the source location.     

Attenuation, transport and diffusion of scalar waves in textured random media

Most theoretical investigations of seismic wave scattering rely on the assumption that the underlying medium is statistically isotropic. However, deep seismic soundings of the crust as well as geological observations often reveal the existence of elongated or preferentially oriented scattering structures. In this paper, we develop mean field and radiative transfer theories to describe the attenuation and multiple scattering of a scalar wavefield in an anisotropic random medium. The scattering mean free path is found to depend strongly on the propagation direction. We derive a radiative transfer equation for statistically anisotropic random media from the Bethe–Salpeter formalism and propose a Monte Carlo method to solve this equation numerically. At longer times, the energy density is shown to obey a tensorial diffusion equation. The components of the diffusion tensor are obtained in closed form and excellent agreement is found between Monte Carlo simulations and analytical solutions of the diffusion equation. The theory has important potential implications for lithospheric models where scatterers are for example flat structures preferentially aligned along the surface. In this simple geometry, analytical expressions of the Coda Q parameter can be given explicitly in the diffusive regime. Our results suggest that pulse broadening and coda decay are controlled by different parameters, related to the eigenvalues of the diffusion tensor. These eigenvalues can differ by more than one order of magnitude. This theory could be applied to probe the anisotropy of length scales in the lithosphere.     

Solar system observations by the Wisconsin Ultraviolet Photopolarimeter Experiment– III. The first ultraviolet linear spectropolarimetry of the Moon

Portions of the Moon were observed by the Wisconsin Ultraviolet Photopolarimeter Experiment ( WUPPE ) on 1995 March 12, 14 and 17, and represent the first ultraviolet (UV) spectropolarimetric observations of the Moon. The polarimetric observations confirm that a change in the dominant scattering process occurs in the UV, changing from volume scattering in the near-UV to surface scattering in the far-UV. The data are investigated empirically. It is found that Umov's relationship holds when the polarization is perpendicular to the scattering plane. It is also found that the degree of polarization can be modelled by a phase-angle-dependent polarization modified by a wavelength-dependent depolarization factor. The scattering function for each observation is determined.     

On the polarization of Hα scattered by neutral hydrogen in active galactic nuclei

Raman scattering by atomic hydrogen converts the UV continuum around Lyβ into optical continuum around Hα, and the basic atomic physics has been discussed in several works on symbiotic stars. We propose that the same process may operate in active galactic nuclei (AGN) and calculate the linear polarization of the broad emission lines Raman-scattered by high-column neutral hydrogen component. The conversion efficiency of the Raman scattering process is discussed and the expected scattered flux is computed using the spectral energy distribution of an AGN given by a typical power law. The high-column H  i component in AGN is suggested by many observations, encompassing the radio through UV and X-ray ranges.   When neutral hydrogen component with a column density ∼10²² cm⁻² is present around the active nucleus, it is found that the scattered Hα is characterized by a very broad width ∼20 000 km s⁻¹ and that the strength of the polarized flux is comparable to that of the electron-scattered flux expected from a conventional unified model of narrow-line AGN. The width of the scattered flux is mainly determined by the column density of the neutral scatterers where the total scattering optical depth becomes of order unity. The asymmetry in the Raman scattering cross-section around Lyβ introduces red asymmetric polarized profiles around Hα. The effects of the blended Lyβ and O  vi 1034 doublet are also investigated.   We briefly discuss the spectropolarimetric observations performed on the Seyfert galaxy IRAS 110548-1131 and the narrow line radio galaxy Cyg A. Several predictions regarding the scattering by the high-column neutral hydrogen component in AGN are discussed.     

地下目标瞬时散射的时域有限差分法数值模拟

采用时域有限差分（ＦＤＴＤ）法数值模拟电磁脉冲波的入地传输，以及地下二维目标的瞬时散射，详细讨论了ＦＤＴＤ法中主要参数的取值原则．在稳定条件下所取时间间隔随波进入不同煤质而不同，以满足因果律．通过数值计算证明，在无耗空间得到的吸收边界条件也适用于有耗媒质．数值模拟在地面接收到的地下目标的回波响应与有关文献的结果一致．     

Frequency dependent characteristics of coda wave quality factor in central and southcentral Alaska

Coda wave quality factor (Q _c ) was investigated by using digital data (100 sample sec^–1) recorded by a vertical component short-period station installed for this study. The station was located in the greater Fairbanks area in central Alaska. From several hundred earthquakes recorded by this station in about a year, 27 earthquakes were selected for the above study; 7 of these selected earthquakes were located along the Alaska Wadati-Benioff zone (Pacific plate). The other 20 earthquakes were located in the area of intraplate seismicity (North American plate). The data was filtered using 9 pass-bands with center frequency varying from 1.5 Hz to 16 Hz with octave bandwidth. The values ofQ _c obtained from the coda amplitude decay rates measured on the filtered data after corrections due to the recording instrument and source-receiver separation show appreciable frequency dependence. The value ofQ _c varies in the range of 253 and 1190 corresponding to the frequency interval from 1.5 Hz to 16 Hz for the study area. This variation is close to that reported by others for the Kanto region of Japan. Moreover, the characteristics ofQ _c obtained in the present case seem to be independent of epicentral distance and hypocentral depth.