断層モデルに基づく地震動応答スペクトル予測法と予測結果のばらつきに関する検討

The green's function method in quantum statistics

A common goal of dynamic structural analysis is to predict the response of a structure subjected to ground motions having a specified spectral acceleration at a given period. This is important, for example, when coupling ground-motion hazard curves from probabilistic seismic hazard analysis (PSHA) with results from dynamic structural analysis. The prediction is often obtained by selecting ground motions that match a target response spectrum and using those ground motions as input to dynamic analysis. The commonly used uniform hazard spectrum (UHS) is shown here to be an unsuitable target for this purpose, as it conservatively implies that large-amplitude spectral values will occur at all periods within a single ground motion. An alternative, termed a conditional mean spectrum (CMS), is presented here. The CMS provides the expected (i.e., mean) response spectrum, conditioned on occurrence of a target spectral acceleration value at the period of interest. It is argued that this is the appropriate target response spectrum for the goal described above and is thus a useful tool for selecting ground motions as input to dynamic analysis. The CMS is described, its advantages relative to the UHS are explained, and practical guidelines for use in ground-motion selection are presented. Recent work illustrating the impact of this change in target spectrum on resulting structural response is briefly summarized.

Simulations that are meant to determine the steady-state distribution of a diffusible solute such as oxygen in tissues have typically used finite difference methods to solve the diffusion equation. Finite difference methods require a tissue mesh with enough points to resolve oxygen gradients near and between discrete blood vessels. The large number of points that are typically required can make these calculations very slow. In this paper, we investigate a numerical method known as the Green's function method which is not bound by the same constraint. The Green's function method is expected to yield an accurate oxygen distribution more quickly by requiring fewer mesh points. Both methods were applied to calculate the steady state oxygen distribution in a model simulation region. When the Green's function calculation used meshes with 1/2, 1/4 and, 1/8 of the resolution required for the finite-difference mesh, there was good agreement with the finite difference calculation in all cases. When the volume of the domain was increased 8-fold the Green's function method was able to calculate the O2 field in 22 minutes, whereas the finite difference calculation is expected to take approximately 1 week. The number of steps required for the Green's function calculation increases quadratically with the number of points in the tissue mesh. As a result, small meshes are calculated very quickly using Green's functions, while for larger mesh sizes this method experiences a significant decrease in efficiency.

The aim of this study is to investigate the strong ground motion generation of destructive earthquake in Kermanshah with the moment magnitude of 7.3 using Empirical Green’s function (EGF) method. To simulate the ground-motion can be helpful for understanding seismic hazard and reduce fatalities due to lack of real ground motion. We collected the seismograms recorded at seven strong motion stations with good quality to estimate the source parameters at frequencies between 0.1 and 10.0 Hz. By minimizing the root-mean-square (rms) errors to obtain the best source parameters for the earthquake. The earthquake fault was divided into seven sub-faults along the strike and seven sub-faults along the slope. The asperity of 21×10.5 km was obtained. The rupture starting point has been located in the northern part of the strong motion seismic area. The coordinates of the rupture starting point indicate that the rupture propagation on the fault plan was unilateral from north to south. The simulated ground motions have a good correlation with observed records in both frequency and time domain. The results are in well agreement with the Iranian code of practice for seismic resistant design of buildings, however, the calculated design spectrum of Sarpol-e Zahab station is higher than the design spectrum of the Iranian code which suggest that the Iranian code may need to be re-evaluated for this area.

Strong motion records for earthquakes epicentred in the Gulf of Aqaba during swarms in August 1993 and November 1995 are studied. These recordings are made at two sites in the City of Aqaba, one near the seashore and the other inland. The former site has deep alluvial profile with low shear-wave velocity, while the latter's soil profile is constituted of shallow stiff alluvium overlaying rock. The magnitudes of these events range from 4·8 to 6·2 on the Richter scale. Ground motion on the seashore site is much greater than the inland site. Response spectra are derived for each of the available accelerograms. Thirteen records at the inland site are statistically treated to arrive at mean response spectrum using 5 per cent damping. The derived spectra are found to be sharp with small plateau, this is associated with small peak displacement. Empirical site-dependent response spectra are also derived based on recent research and on recommendations of the UBC'97. Comparison is made between the empirical and measured spectra. These were found to be quite close for the inland site but data are not sufficient for the seashore site to make a conclusive comparison. Copyright © 1999 John Wiley & Sons, Ltd.

The elastic response of a vacancy in a semi-infinite fcc copper lattice containing a free surface is calculated by using a new multiscale Green's function method. The method treats the lattice distortion near the vacancy at the atomistic level and the free surface at the macroscopic continuum level in the same formalism. The lattice is modeled using the lattice statics Green's function that fully accounts for the discrete atomistic structure of the lattice and can model a large crystallite containing a million atoms without excessive CPU effort. The method is especially useful for modeling the elastic response of nanocrystals containing point defects in which surfaces and interfaces play important roles. The method bridges the length scales seamlessly by relating the microscopic lattice distortion near a point defect to measurable macroscopic parameters of the solid such as the strain and the displacement field at a free surface. Using the interatomic potential derived by Cleri and Rosato, the lattice distortion, relaxation energy, and relaxation volume due to a vacancy are calculated in an otherwise perfect copper lattice for a million-atom model containing a free (100) surface. The calculated value of the relaxation volume is in excellent agreement with the observed value. Numerical results are also presented for the strain and the displacement fields at the free surface due to a vacancy and the interaction energy between a vacancy and the free surface in anisotropic semi-infinite copper.

The M 5.0 earthquake that occurred near Au Sable Forks, New York on 20 April 2002 is the first moderate event in eastern North America (ENA) to be well recorded on modern regional broadband seismographic stations, and is thus important in refining our understanding of source and propagation processes of moderate ENA earthquakes. We analyze the available seismographic recordings to obtain the source spectrum of the Au Sable Forks earthquake, comparing the results obtained using two methods. In the direct method, the Fourier spectra of the records from each station are corrected back to the source by using an empirical regional attenuation model for ENA. In the empirical Green's function method, aftershocks are used as empirical Green's functions to remove path and site effects. Results from these two methods agree closely and are in agreement with a two-corner source model for ENA. A pronounced sag in the source spectrum at a frequency near 2 Hz is suggestive of significant source complexity. Observed response spectral amplitudes agree well with the predictions of several ground-motion relations for ENA for an event of M 5.0. It is concluded that ground motions from this earthquake were “typical” for ENA earthquakes of this magnitude.

Resonance plays a key role in the formation of many physical phenomena. The complex-scaled Green's function method provides a powerful tool for exploring resonance. In this paper, we combine this method with the theory describing deformed nuclei with the formalism presented. Taking $^{45}\text{S}$ as an example, we elaborate numerical details and demonstrate how to determine the resonance parameters. The results are compared with those obtained by the complex scaling method and the coupled-channel method and satisfactory agreement is obtained. In particular, the present scheme focuses on the advantages of the complex scaling method and the Green's function method and is more suitable for the exploration of resonance.

The formulation of the Green's-function method, recently suggested by Ziman, for solving the energy-band problem in a so-called "muffin-tin" potential (zero outside spheres representing the various atoms, and spherically symmetrical within each sphere) is transformed to a form very much like that of the Augmented-plane-wave (APW) method, but cannot be transformed exactly into the APW formulation. The wave function set up by the Green's-function method is a superposition of plane waves satisfying the wave equation inside as well as outside the spheres representing the atoms, having a discontinuity of slope at the surfaces of the atomic spheres, enough to produce the correct solution of the Schr\"odinger problem outside the spheres. To get correct wave functions inside the atoms, one would have to construct augmented plane waves from these plane waves.

In recent seismic design codes, accelerograms recorded in areas with similar conditions to the target site are required for seismic analysis. When there are no available recorded ground motions of sufficiently large intensities, small intensity ground motions need to be appropriately amplified. In this study, the Empirical Green’s Functions (EGF) method by finite earthquake fault modeling was used for this purpose. The high frequency filter according to the distance between earthquake source to site was applied. The regression analysis of spectral acceleration amplifications by magnitude and hypocentral distance was performed. Finally, the methodology to determine an optimum condition for converting the recorded accelerogram into ground motion time histories compatible with the Design Response Spectrum (DRS) was suggested.

In order to develop site-specific response spectra from strong ground motion recordings appropriate for Eastern United States (EUS) sites, it is necessary to perform extrapolations from response spectra appropriate in other areas due to the scarcity of strong ground motion recordings available in the EUS. Recordings obtained from the more abundant Western United States (WUS) database are typically chosen to perform these extrapolations. The extrapolations require knowledge of how differences in tectonic and geologic conditions between EUS and WUS translate into differences in recorded ground motions. One of the most widely accepted tectonic differences between EUS and WUS is the observed depth of earthquake rupture for magnitudes 4 and greater. This report documents, using sophisticated three-dimensional numerical modeling techniques, how spectral shapes extrapolated from the WUS database must be scaled to account for differences in earthquake rupture shallowness. Using sophisticated three-dimensional numerical modeling techniques, the potential ground motions from small shallow events are estimated and the spectral shapes compared to those calculated for larger magnitude earthquakes occurring at more typical depths in the EUS. The possible effects of local soil conditions on the seismic response spectra are demonstrated. Earthquake ruptures of various magnitudes, site distances and fault types are compared as a function of rupture shallowness for a generic rock site and a generic soil site and do not include the possible effects of site-specific soil properties present in the upper fifty meters. Comparisons are also made among four earth models to demonstrate the effects of local soil conditions on the calculated response spectra.

We have calculated the Debye-Waller factor (DWF) of Cu from a model that was used successfully in earlier calculations of anharmonicity by Cowley and Shukla. The present calculation has been carried out using quasiharmonic theory, the lowest-order (λ2) anharmonic perturbation theory, and a Green's function (GF) method which sums an infinite series of the λ2−type anharmonic terms. The static approximation ω → 0 in the cubic contribution to the self-energy of the GF, introduced in the earlier work on the DWF by Shukla and Hubschle is further justified by showing that in the high-temperature limit the exact results for the λ2 anharmonic contributions (cubic and quartic) to the Helmholtz free energy are given in this approximation. Results for the DWF are also obtained for a modified version of the Morse potential with λ2 perturbation theory (PT) and the GF method. The GF results are in excellent agreement with the experimental Mossbauer and X-ray data in the entire temperature range, 300 K  T  120...

The fracture behaviors of nanoscale sp-bonded materials have been studied using the molecular dynamics and lattice Green's function methods. The initial atomic structures of the crack are determined both from the elastic solutions as well as from those by lattice Green's function method for the infinite systems. Firstly, we calculate the Green function for the defective lattice, with dislocation and crack, by solving the Dyson equation, appropriate for absolute zero temperature, After the lattice Green functions of the absolute zero temperature have been determined, the lattice parameters and interatomic force constants are adjusted to fit to materials at temperature T. In general, we have found that the lattice trapping and stress intensity factors for dislocation emission K Ile , The fracture and strength properties are also investigated for the nanocrystailine materials like semiconductor quantum wire and nanotubes. The O(N) tight-binding molecular dynamics (TBMD) method is used to analyze the reconstruction of atomic bonding near the crack tip as well as the cleaved surface. We compare the fracture behavior of nanoscale materials with those of corresponding bulk-size materials.

<sec><p indent="0mm">Exotic nuclei far from the β stability line have become important scientific goals in the studies of experimental physics at large scientific facilities and theoretical research due to the rich new physics. In these exotic nuclei, the neutron or proton Fermi level is close to the continuum threshold. The pairing correlation could scatter the valence neutrons or protons into the continuum. This leads to the extended neutron or proton density distributions in these exotic nuclei. Therefore, properly describing the pairing correlation and continuum is crucial for studying the structures and properties of these exotic nuclei. The Hartree-Fock-Bogoliubov (HFB) theory is one of the promising tools for describing exotic nuclei. In this theory, people usually solve the HFB equation directly in the coordinate space or the Woods-Saxon basis. In the coordinate space, when employing box boundary conditions to discretize the continuum, the behavior of the wave functions at the boundaries will be affected by the size of the box. Meanwhile, one could not obtain the energy and width of the resonant states directly from the discretized continuum states. The Green’s function (GF) is a simple and effective tool for handling the continuum, which has been widely used in nuclear structure research. The GF can be established by using the wave functions that satisfy the equation of motion and the proper bound boundary conditions for the bound and continuum states. Then one can use the loop integral of the GF on the complex energy plane to construct the particle density and level density. In this way, the continuum states can be included in the density with proper boundary conditions, and thus the extended density distribution can be properly described. Furthermore, the GF on the complex energy plane and the level density can be used to identify the resonant states directly. </sec><sec> This paper briefly reviews the development of the GF method in the continuum density functional theory, focusing on its application in describing halo phenomena and single-particle resonance states in exotic nuclei. For the description of the halo phenomena, this review takes the neutron-rich Zr as examples to show the results given by Skyrme HFB calculations with the GF method. The extended neutron particle and pair density distributions can be more properly described by the GF method, compared to the box-discretized method. The self-consistency to deal with the pairing correlation and the continuum is important to determine the asymptotic neutron particle and pair density distributions. Furthermore, with the level density obtained by the loop integral of the GF on the complex energy plane, one can describe both the bound and resonant states on the same footing. Recently, in the relativistic mean field theory, a new method to obtain precise information for the resonant energy and width is proposed by using directly the poles of the GF on the complex energy plane. This helps explain the conservation and breaking of pseudospin symmetry in the nucleon single-particle levels. Additionally, Green’s function method is easily compatible with various theoretical models, thus in the future it can be further applied to describe the exotic nuclear collective resonances and nuclear reaction processes. </sec>

An analytic and numerical solution with spectral Green's function method for transport equation in spherical geometry