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fault. Due to the combined effects of fling and directivity in the vicinity of the surface fault, the directions of the maximum velocities and displacements are inclined with respect to the fault plane. On the other hand, when softer surface layers are added to the medium, the directivity effects become more significant than the fling effects, because the dynamic Green's functions are more pronounced than the static ones.

A theoretical model for constructing the x-squared model is proposed by modifying the k-squared model of Bernard et al. (1996). The k-squared model provides a theoretical basis for the empirical x-squared model under the assumptions that (1) the spatial wavenumber spectrum of the slip distribution falls off as the inverse of the wavenumber squared (k-squared), (2) the Fourier amplitudes of the slip velocity are independent of x at high frequencies, and (3) the rupture velocity is constant. In this study, a more realistic model is proposed by modifying the last two assumptions. First, a Kostrov-type slip velocity model is proposed by superposing equilateral triangles, in which a source-controlled fmax is imposed by the minimum duration among the triangles. The Fourier amplitude of our slip velocity model falls off as the inverse of x at high frequencies less than fmax. Next, in order to model variable rupture velocities, the incoherent rupture time (Dt r), namely, the difference between the actual rupture time and the coherent (average) rupture time, is introduced. After checking various models for Dt r distributions, the k-squared model for Dt r , similar to that for the slip distributions of the k-squared model, is found to be the most plausible. Finally, it is confirmed that the proposed source model (we call it as the x-inverse-squared model), which consists of the combination of the slip velocity proposed here and the k-squared distributions for both slip and Dt r , not only is consistent with the empirical x-squared model, but also provides the theoretical basis for constructing realistic source models at broadband frequencies.

SummaryWe succeeded in plan-view dynamic observation of the initial formation process of carbon nanotubes from b-SiC(1 1 1) surfaces by time-resolved high resolution transmission electron microscopy. At 1360 8C, the flakes of graphite layers of a fibre orientation were formed on the SiC(1 1 1) surfaces. From the graphite layers, carbon nanotubes were formed perpendicular to the (1 1 1) plane of the SiC. A scanning tunnelling microscopy observation showed that the end of carbon nanotube was closed. These results indicate that the caps of the carbon nanotubes are formed by a lift of a part of the graphene along the [1 1 1] direction of the SiC through generation of pentagons and heptagons. Two types of carbon nanotube, single-wall and double-wall, were observed in plan-view images. Different image intensity between an outer ring and an inner ring in double-wall nanotubes suggests that the inner layers of multiwall nanotubes are formed after the outer ones.

The theoretical basis of the x-squared model and the characteristics of near-source broadband strong ground motions are investigated using a 2D source model with spatial variations in slip and rupture velocity. This is an extension of a study by Hisada (2000a), who used 1D source models for the same purpose. First, Hisada's slip-velocity function (2000a) is modified by superposing scalene triangles to construct Kostrov-type slip-velocity functions with arbitrary combinations for the source-controlled f max and the slip duration. Then, it is confirmed that the Fourier amplitudes of these slip velocities fall off as the inverse of x at frequencies lower than f max (Hisada, 2000a). Next, the effects of 2D spatial distributions of slip and rupture time on the source spectra are investigated. In order to construct a realistic slip distribution, the hybrid slip model is proposed, which is the combination of the asperity model at lower wavenumbers and the k-squared model (Herrero and Bernard, 1994) at higher wavenumbers. The source spectra of the proposed 2D models, which have the k-squared distribution for slip and rupture time, fall off as the inverse of x, when the slip is instantaneous. This result also agrees with Hisada (2000a). Therefore, the x-inverse-squared model, which consists of the combination of the Kostrov-type slip velocity proposed here and the k-squared distributions for both slip and rupture time, is not only consistent with the empirical x-squared model, but also provides the theoretical basis for constructing realistic 2D source models at broadband frequencies. In addition, it is confirmed that the proposed source model successfully simulates most of the well-known characteristics of the near-fault strong ground motions at broadband frequencies, that is, permanent offsets in displacements, longperiod pulses in velocities, and complex randomness in accelerations. The nearsource directivity effects are also confirmed; the fault-normal components are dominant over the fault-parallel components, especially at the forward rupture direction. However, the ratio between the fault-normal and fault-parallel components is roughly independent of frequency, which is contradictory to empirical models. This suggests that a 3D faulting model is necessary to represent more realistic near-source strong motions at broadband frequencies.