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Time history responses of the surface were obtained for a linear elastic half-plane including regularly distributed enormous embedded circular cavities, subjected to propagating obliquely incident plane SH-waves. An advanced numerical approach named half-plane time-domain boundary element method (BEM), which only located the meshes around the cavities, was used to create the model. By establishing the modified boundary integral equation (BIE) independently for each cavity and forming the matrices, the final coupled equation was solved step-by-step in the time-domain to obtain the boundary values. The responses were developed for a half-plane with five hundred twelve cavities. The amplification patterns were also obtained to illustrate the frequency-domain responses for some cases. According to the results, the presence of enormous cavities affects the scattering and diffraction of the waves arrived to the surface. The introduced method can be recommended for geotechnical/mechanical engineers aimed at modeling the structures in the fields of earthquake engineering as well as composite materials.
Techniques for soil property estimation can be categorized into two main groups, in-situ and laboratory methods. Previous investigations indicated that strong ground motions record provides a very useful tool to estimating the in-situ characteristics of soil. The main objective of the present work is to utilize the particle swarm optimization algorithm (PSOA) integrated with linear site response method to obtain the equivalent soil profile characteristics from the available surface and bedrock earthquake motion records. To demonstrate the numerical efficiency and the validity of this approach, the procedure is validated against an available case. Then this procedure is utilized to identify the soil properties profiles of the site by using strong ground motions data recorded during the Bam earthquake of December 26, 2003. The magnitude and PGA of Bam earthquake were MW 6.6 and 0.8 g respectively.
Numerical simulation in transverse isotropic media with tilted symmetry axis (TTI) using the standard staggered-grid finite-difference scheme (SSG) results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme (RSG) is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme (CSG) is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme (RSGC). The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.
Topographic effect study is a very important research topic in seismology, seismic engineering, earthquake engineering, engineering earthquake construction and engineering seismology. This paper focuses on its present development status. Post-earthquake investigation has found that the existence of topography caused more serious earthquake damage. The actual seismographs also recorded the topographic amplification effect of 6 to 7 times and even more than 10 times. Numerical simulation is an important technique to study topographic effect, which complements the lack of observed records. However researches on 3-D topographic effect are not enough and need to be studied deeper. To find the main influence factors and the quantitative relationship between topography and ground motion are required very urgently. Obviously the achievements not only can be applied in the earthquake resistant design, but also can provide the quantitative pre-earthquake disaster prediction and quantitative post-earthquake disaster evaluation.
A closed-form wave equation analytic solution of two-dimensional scattering and diffraction of out-of-plane (SH) waves by an almost semi-circular shallow cylindrical hill on a flat, elastic and homogeneous half space is proposed by applying the discrete Fourier series expansions of sine and cosine functions. The semi-circular hill problem is discussed as a special case for the new formulated equation. Compared with the previous semi-circular cases solutions, the present method can give surface displacement amplitudes which agrees well with previous results. Although the proposed equation can only solve the problem of SH-waves diffracted by almost semi-circular shallow hills, the stress and displacement residual amplitudes are numerical insignificantly everywhere. Moreover, the influences of the depth-to-width ratio (a parameter defined in this paper to evaluate the shallowness of the topography of hills) on ground motions are presented and summarized. The limitations and errors of truncation from Graf’s addition theorem and Fourier series equations in the present paper are also discussed.
It is now common practice to perform simultaneous traveltime inversion for the velocity field and the reflector geometry in reflection/refraction tomography, or the velocity field and the hypocenter locations in regional earthquake tomography, but seldom are all three classes of model parameters updated simultaneously. This is mainly due to the trade-off between the different types of model parameters and the lack of different seismic phases to constrain the model parameters. Using a spherical-coordinate ray tracing algorithm for first and later (primary reflected) arrival tracing algorithm in combination with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model parameters in regional or global tomographic studies. In this paper we incorporate the multistage irregular shortest-path ray tracing algorithm (in a spherical coordinate system) with a subspace inversion solver to formulate a simultaneous inversion algorithm for triple model parameters updating using direct and later arrival time information. Comparison tests for two sets of data (noise free and added noise) indicate that the new triple-class parameter inversion algorithm is capable of obtaining nearly the same results as the double-class parameter inversion scheme. Furthermore, the proposed multi-parameter type inversion method is not sensitive to a modest level of picking error in the traveltime data, and still performs well with a relatively large uncertainty in earthquake hypocentral locations. Thisshows it to be a feasible and promising approach in regional or global tomographic applications.
The conventional pseudo-acoustic wave equations (PWEs) in vertical transversely isotropic (VTI) media may generate SV-wave artifacts and propagation instabilities when anisotropy parameters cannot satisfy the pseudo-acoustic assumption. One solution to these issues is to use pure acoustic anisotropic wave equations, which can produce stable and pure P-wave responses without any SV-wave pollutions. The commonly used pure acoustic wave equations (PAWEs) in VTI media are mainly derived from the decoupled P-SV dispersion relation based on first-order Taylor-series expansion (TE), thus they will suffer from accuracy loss in strongly anisotropic media. In this paper, we adopt arbitrary-order TE to expand the square root term in Alkhalifah’s accurate acoustic VTI dispersion relation and solve the corresponding PAWE using the normalized pseudo-analytical method (NPAM) based on optimized pseudo-differential operator. Our analysis of phase velocity errors indicates that the accuracy of our new expression is perfectly acceptable for majority anisotropy parameters. The effectiveness of our proposed scheme also can be demonstrated by several numerical examples and reverse-time migration (RTM) result.
Vertical records are critically important when determining the rupture model of an earthquake, especially a thrust earthquake. Due to the relatively low fitness level of near-field vertical displacements, the precision of previous rupture models is relatively low, and the seismic hazard evaluated thereafter should be further updated. In this study, we applied three-component displacement records from GPS stations in and around the source region of the 2013 MW 6.6 Lushan earthquake to re-investigate the rupture model. To improve the resolution of the rupture model, records from both continuous and campaign GPS stations were gathered, and secular deformations of the GPS movements were removed from the records of the campaign stations to ensure their reliability. The rupture model was derived by the steepest descent method (SDM), which is based on a layered velocity structure. The peak slip value was about 0.75 m, with a seismic moment release of 9.89 × 1018 N·m, which was equivalent to an MW6.60 event. The inferred fault geometry coincided well with the aftershock distribution of the Lushan earthquake. Unlike previous rupture models, a secondary slip asperity existed at a shallow depth and even touched the ground surface. Based on the distribution of the co-seismic ruptures of the Lushan and Wenchuan earthquakes, post-seismic relaxation of the Wenchuan earthquake, and tectonic loading process, we propose that the seismic hazard is quite high and still needs special attention in the seismic gap between the two earthquakes.
A new source location method using wave-equation based traveltime inversion is proposed to locate microseismic events accurately. With a source-independent strategy, microseismic events can be located independently regardless of the accuracy of the source signature and the origin time. The traveltime-residuals-based misfit function has robust performance when the velocity model is inaccurate. The new Fréchet derivatives of the misfit function with respect to source location are derived directly based on the acoustic wave equation, accounting for the influence of geometrical perturbation and spatial velocity variation. Unlike the mostly used traveltime inversion methods, no traveltime picking or ray tracing is needed. Additionally, the improved scattering-integral method is applied to reduce the computational cost. Numerical tests show the validity of the proposed method.
Finite difference methods have been widely employed in solving the eikonal equation so as to calculate traveltime of seismic phase. Most previous studies used regular orthogonal grid. However, much denser grid is required to sample the interfaces that are undulating in depth direction, such as the Moho and the 660 km discontinuity. Here we propose a new finite difference algorithm to solve the eikonal equation on non-orthogonal grid (irregular grid). To demonstrate its efficiency and accuracy, a test was conducted with a two-layer model. The test result suggests that the similar accuracy of a regular grid with ten times grids could achieve with our new algorithm, but the time cost is only about 0.1 times. A spherical earth model with an undulant 660 km discontinuity was constructed to demonstrate the potential application of our new method. In that case, the traveltime curve fluctuation corresponds to topography. Our new algorithm is efficient in solving the first arrival times of waves associated with undulant interfaces.