Strains of scattering of near-field of a point source

Three dimensional scattering of near-field is studied for dilatation and rotation in the time domain. The perturbation method is applied to solve the equation of motion for the first order scattering from a weak inhomogeneity in an otherwise homogeneous medium. The inhomogeneity is assumed close enough to the point source so that the near-field intermediate wave is dominating over the far-field sphericalP andS pulses. The integral expressions are derived to relate dilatation and rotation of scattering to the radial fluctuations of velocities and density in the inhomogeneity. These integrals are solved to calculate the strains of scattering from (a part of) an inhomogeneous spherical shell of arbitrary curvature. Variable curvature may allow the shape of inhomogeneity volume element to change uniformly from spherical to rectangular. Rotation of scattering from a spherical shell is independent ofP wave velocity inhomogeneity. Dilatation of scattering does not involveS wave velocity inhomogeneity but its gradient. The back scattering results are obtained as a special case. Strains are computed numerically, for hypothetical models to study the effects of various parameters viz., velocity inhomogeneity, distance of source from inhomogeneity and from receiver, and thickness of inhomogeneity. The curvature of the spherical shell is varied to study the effects of the shape of inhomogeneous volume element on scattering.     

Scattering of a spherical pulse from a small inhomogeneity: Dilatation and rotation

Perturbations in elastic constants and density distinguish a volume inhomogeneity from its homogeneous surroundings. The equation of motion for the first order scattering is studied in the perturbed medium. The scattered waves are generated by the interaction between the primary waves and the inhomogeneity. First order scattering theory is modified to include the source term generating the primary waves. The body force equivalent to the scattering source is presented in a convenient form involving the perturbations in wave velocities and gradient of density perturbation. A procedure is presented to study the scattering of a spherical pulse from a small inhomogeneity, in time domain. The size of inhomogeneity is assumed small as compared to its distance from source and receiver. No restrictions are placed on the positions of source, receiver and inhomogeneity. The dilatation and rotations are calculated for a pulse scattered from an arbitrary point in a spherical volume. The aggregate of the scattered phases from all the points of the inhomogeneity, reaching at a fixed receiver, gives the amount of scattering from the inhomogeneity. The interaction of bothP andS waves with inhomogeneity are considered. Dilatation and rotations for scattering are obtained as integral expressions over the solid angle of inhomogeneity. These expressions are computed numerically, for hypothetical models. The effects of source (unit force) orientations, velocity and density perturbations, and size of inhomogeneity, on the scattered phases, are discussed.     

Near-field ground motion during earthquake preparation process

Wave number discretization method is applied to study the near-field of seismic sources embedded in a cracked elastic solid. Near-field solutions are obtained for horizontal and vertical line forces. Effects of modifications in cracks of focal region on ground motion, in the near-field, are studied numerically for different

? values of crack density

? saturation of cracks

? width of cracks, and

? regimes of connection between cracks.

An earthquake process is assumed to be going through five major stages. These stages represent continuous accumulation of stress, interconnections between cracks leading to eventual failure and drainage of fluid from cracks after the major shock. Variations in the velocity ratio of waves noted from accelerograms verify the process of preparation of an earthquake.P wave contribution to vertical acceleration is negligible when the source is a vertical line force andS wave contributes only a little to horizontal acceleration when the source is a horizontal line force.     

Simultaneous inversion of the aftershock data of the 1993 Killari earthquake in Peninsular India and its seismotectonic implications

The aftershock sequence of the September 30th, 1993 Killari earthquake in the Latur district of Maharashtra state, India, recorded by 41 temporary seismograph stations are used for estimating 3-D velocity structure in the epicentral area. The local earthquake tomography (LET) method of Thurber (1983) is used. About 1500P and 1200S wave travel-times are inverted. TheP andS wave velocities as well asV _P/V_Sratio vary more rapidly in the vertical as well as in the horizontal directions in the source region compared to the adjacent areas. The main shock hypocentre is located at the junction of a high velocity and a low velocity zone, representing a fault zone at 6–7 km depth. The estimated average errors ofP velocity andV _P/V_Sratio are ±0.07 km/s and ±0.016, respectively. The best resolution ofP and S-wave velocities is obtained in the aftershock zone. The 3-D velocity structure and precise locations of the aftershocks suggest a ‘stationary concept’ of the Killari earthquake sequence.     

基于包络的汶川大地震高频地震波辐射区域反演及近场加速度合成

合理地估计汶川破坏区域的地震动有助于地震灾害的研究.通过利用芦山地震记录建立的加速度包络衰减关系和汶川地震近场30个台站的加速度包络,基于线源模型,采用差分进化方法反演了汶川地震断层面上高频 (＞1 Hz) 辐射区域分布.结果表明:断层面上高频辐射分布很不均匀,辐射较强的区域主要位于:(1) 产生较大地表破裂的映秀、北川和南坝区域;(2) 映秀和北川等凹凸体的周边区域,包括震中东北侧60~90 km区域、北川和南坝东北侧30 km处;(3) 断层破裂停止的东北端约30 km长的区域.其中,破裂贯穿到地表的映秀、北川和南坝是低频和高频辐射都很强的区域.对于无观测记录场点,选择其临近且场地条件类似的台站加速度提取平稳随机过程,结合高频辐射分布和衰减关系得到的包络,合成了加速度时程,可为汶川地震结构震害分析提供地震动输入.      

Dynamic response of an elastic and viscoelastic full-space to a spherical source

The dynamic response due to a spherical source of radius a embedded in an elastic and viscoelastic full-space is investigated at a distance R from the source. Previous solutions to the elastic case are extended to incorporate realistic source pressure functions. The elastic solution is then cast in a scale independent form in order to generalize the application. The results show that the near-field of the spherical source may be defined by R/a < 5. For this region the particle velocity and displacement decrease as R^?2, and the risetime decreases as R^?1. However. in the far-field region (R/a > 5) the particle velocity and displacement decrease as R^?1, and the risetime is independent of R. A non-constant Q model is developed to model viscoelastic attenuation and a complete analytical solution for wave propagation is obtained by cascading the separate mechanisms of geometric attenuation and viscoelastic attenuation. A comparison of our analytical model with the results of dynamic finite element modelling shows excellent agreement. This suggests that the method of cascading the separate transfer functions is a valid approach for wave propagation in viscoelastic media.     

A charge-consistent model for the acceleration of iron in the solar corona: Nonisothermal injection

A charge-consistent numerical model for the joint (regular and stochastic) acceleration of iron by a spherical shock wave propagating in the solar corona is proposed. Large-scale irregularities of the plasma density and the nonisothermal injection of ions are taken into account. For the case of iron, the energy dependence of the mean charge q_Fe(E) is determined by the relationships between the characteristic acceleration time, the charge-variation time for the accelerated ions, and the time for their trapping in regions of high plasma density. Due to the global inhomogeneity of the medium, these relationships depend on the shock speed. Our calculations indicate that photoionization by soft X-rays from flare regions can substantially change the charge states of heavy ions only in the most powerful solar events (both impulsive and gradual).     

Locating a point on a spherical surface relative to a spherical polygon of arbitrary shape

An algorithm for determining if any given point,P, on the surface of a sphere is located inside, outside, or along the border of an arbitrary spherical polygon,S, is described. The polygon is described by specifying coordinates of its vertices, and coordinates of some pointX which is known to lie withinS. The algorithm is based on the principle that an arc joiningX andP will cross the border ofS an odd number of times ifP lies outsideS, and an even number of times ifP lies withinS. The algorithm has been implemented as a set of FORTRAN subroutines, and a listing is provided. The algorithm and subroutine package can be used with spherical polygons containing holes, or with composited spherical polygons.     

Torsional wave propagation in non‐homogeneous layer between non‐homogeneous half‐spaces

The study of surface wave in a layered medium has their possible application in geophysical prospecting. In the present work, dispersion equation for torsional wave in an inhomogeneous isotropic layer between inhomogeneous isotropic half‐spaces has been derived. Two cases are discussed separately for torsional wave propagation in inhomogeneous layer between homogeneous and non‐homogeneous half‐spaces, respectively. Further, two possible modes for torsional wave propagation are obtained in case of inhomogeneous layer sandwiched between non‐homogeneous half‐spaces. Closed form solutions for displacement in the layer and half‐spaces are obtained in each case. The study reveals that the layer width, layer inhomogeneity, frequency of inhomogeneity, as well as inhomogeneity in the half‐space has significant effect on the propagation of torsional surface waves. Displacement and implicit dispersion equation for torsional wave velocities are expressed in terms of Heun functions and their derivatives. Effects of inhomogeneity on torsional wave velocity are also discussed graphically by plotting the dimensionless phase velocity against dimensionless and scaled wave number for different values of inhomogeneity parameter. Copyright © 2012 John Wiley & Sons, Ltd.     

The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain

By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave P_I, a slow compressional wave P_II, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane P_I and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity.     

SyntheticP wave seismograms from Longshot,Milrow and Cannikin explosions

The effect of spalling and other transfer functions is considered on the amplitude spectra and waveforms of telese mis short periodP wave seismograms generated due to Longshot. Milrow and Cannikin underground nuclear explosions. Source models of Haskell and Seggern were used for computingP wave seismograms from these events. Step-by-step variations of the amplitude spectra and waveforms ofP wave signal as is propagates from source to various seismometer array stations show that the source function, the source crust transfer function, the mantle transfer function and the spalling function are the most important factors that influence shaping of spectra and waveforms ofP seismograms. Comparison of computed and observedP wave seismograms at various seismometer array stations for Longshot explosion shows that computed seismograms do reproduce many of the features of observed seismograms. The results also support the conclusion that overburdenP wave velocity inferred from observed seismograms is less as compared to its value obtained from on-site measurements.     

Compressional and shear wave velocities at high temperature and confining pressure in basalts from the Faeroe Islands

Compressional (V_P) and shear (V_S) wave velocities and the dependent elastic constants have been determined by the pulse transmission technique to 6 kb confining pressure at room temperature and to 700° C at 6 kb confining pressure for eleven basalts from the Faeroe Islands. The Faeroe basalts investigated are tholeiitic, they clearly lie within the tholeiitic area, and display a pronounced trend of iron enrichment from rocks with an M/M + F ratio of 0.5 to rocks with an M/M + F ratio of about 0.25. The mean V_P and V_S for eleven specimens are 5.57 km/sec and 3.18 km/sec, respectively. Velocity—density relations for the basalts might be more appropriately described by non-linear solutions than by linear relations commonly used for basalts. In general, V_P and V_S remain unaffected by temperature up to 300° C. At higher temperature the changes in wave velocities are influenced by metamorphic processes and are, therefore, somewhat erratic. In zeolite-bearing specimens an abrupt velocity decrease around 350°C is observed, which correlates well with a drastic compaction of bulk volume. Additional experiments on cold-pressed zeolite powder clearly indicate that the sharp velocity decrease in the basalts is related to dehydration of zeolite minerals. Partial-melting processes, which occur within vesicules and pore-spaces at distinctly higher temperatures have no additional effect on wave velocity. Comparison with field data reveals that, without exception, the velocities at 0.5 kb confining pressure display the same range that has been commonly noted in refraction data for Layer 2. There are no significant differences in wave velocities and the pressure—temperature dependence in samples recovered from the upper, middle, and lower basalt series in the Faeroe Islands.     

Lower crustal fluid distribution in the northeastern Japan arc revealed by high-resolution 3D seismic tomography

The Ou Backbone Range strikes northwards through the central northeastern Japan arc and is bounded on both sides by the active reverse Uwandaira and Sen'ya faults. We have applied a traveltime inversion method (seismic tomography) with spatial velocity correlation to active and passive seismic data in order to investigate a three-dimensional (3-D) velocity structure. The data set contains 33,993 P- and 18,483 S-wave arrivals from 706 natural sources and 40 blasts, as well as 2803 P-wave traveltime data from 10 explosions detonated during the 1997 controlled source experiment. The traveltime inversion reveals a zone beneath the Ou Backbone Range in which P-wave velocities (V_P) are approximately 6–8% lower than the average velocity at equivalent depths. The low V_P and a low V_P to S-wave velocity (V_S) ratio (V_P/V_S) of about 1.65 suggest the presence of aqueous fluids in the middle crust.     

半无限介质内异质体方位探测数值研究

用数值模拟方法研究了地下异质体对波散射,分析了散射波对表面波相速度影响,结果表明：由相速度曲线扰动难以有效确定异质体方位。在表面波场中,散射波能量相对较小,不易辨别,以振源为中心,在测线上对称布置一组测点,通过两侧测点质点响应曲线比较,得到表面散射波场。在表面散射波场中,散射瑞利波是主要的,由散射瑞利波走时随测点位置变化可判断地下异质体的方位。最后,给出地下异质体方位测试方案。     

Estimation of high-frequency seismic wave radiation on fault plane of 2008 Wenchuan earthquake based on improved empirical Green’s function

A new strategy for inversion of high-frequency wave radiation condition on the fault plan is exhibited. One-dimensional source model of large earthquake was divided into subfaults, each subfault contains a series of subsources to express high-frequency wave radiation. Envelope of large earthquakes can be expressed as a root-mean-squared with combination of envelope attenuation relationship from all subsources. The envelope attenuation relationship is considered as the empirical Green’s function. Distribution of subsources is estimated by envelope inversion. According to this method, the high-frequency (>?1 Hz) wave radiation areas of 2008 Wenchuan earthquake are generally inverted by the differential evolution using acceleration data from 27 near-field stations, while acceleration waveforms of the Lushan earthquake from 43 near-field stations were utilized to create attenuation envelope. High-frequency waves radiated in: (1) surface rupture areas, including Yingxiu and Beichuan areas; (2) close to the boundaries of asperities near Yingxiu, Yuejiashan, Beichuan and Nanba areas; (3) within 30 km length near the fault northeastern tip; (4) around Qingchuan area.

     

透射边界-地基-风电结构地震响应与破坏模式

近海风力发电结构是由无限域地基、基础及上部结构组成的体系,有限域透射人工边界和地震动输入模式直接影响结构体系的动力响应。首先,建立透射人工边界-地基-基础-塔筒结构和固定边界-地基-基础-塔筒结构的有限元模型;然后,简要澄清了透射边界地震动输入之所以采用外力而不采取地震动物理量（加速度、速度和位移）的原因所在;最后,对给出的3种作用模式：（1）固定边界地震动输入,（2）只考虑外源输入波作用,（3）同时考虑外源输入波和内源振动的散射波作用,分别进行计算分析和比较。通过数值计算并结合理论分析,（1）澄清了对透射边界采用外力进行地震激励输入的方法的原因,这种输入方法合理可靠,符合实际情况;（2）在地震波等效荷载的生成中,针对圆形横截面地基提出了一种阻尼力、刚度力的便捷性生成方法,大大减小了工作量;（3）从自身振动特点及阻尼设置角度,解释了地震作用下采用透射边界比采用固定边界时风电结构响应减小的原因;（4）指出了地震作用下透射边界地基模型在结构动力响应与倒塌计算中内源振动反射的不容忽视性。     

Wave propagation in an inhomogeneous cross‐anisotropic medium

Analytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross‐anisotropic medium, in which Young's moduli (E, E′) and shear modulus (G′) varied exponentially as depth increased. However, for the rest moduli in cross‐anisotropic materials, ν and ν′ remained constant regardless of depth. We assume that cross‐anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain–displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi‐wave velocities, V_P, V_SV, and V_SH, and the wave vectors, $\mathop{\mathop{l}\limits^{\rightharpoonup}}\nolimits_{P}$ $\mathop{\mathop{l}\limits^{\rightharpoonup}}\nolimits_{\mathit{SV}}$, and $\mathop{\mathop{l}\limits^{\rightharpoonup}}\nolimits_{{\mathit{SH}}}$, can be generated for the inhomogeneous cross‐anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E′, G′/E′, and ν/ν′); and (3) the phase angle, θ. Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross‐anisotropic medium. Copyright © 2009 John Wiley & Sons, Ltd.     

充分考虑振动台实验滑移特征的地震滑坡基本单元体永久位移估算方法研究

充分考虑振动台实验揭示出来的基本地震滑坡单元体震动滑移特征,总结得到其永久位移的估算方法:（1）考虑地震动惯性力和重力的联合作用,计算相应向上和向下滑移的屈服加速度,以反应其可能向上和向下滑移的行为;（2）在适度简化斜坡岩土体动力学模型的基础上,考虑斜坡岩土体自振特性和滑体所在高度对地震波的放大效应,得到滑体附近的局部地震加速度;（3）考虑滑体附近局部加速度和滑移屈服加速度的控制作用,计算每一地震波的周期内滑体相对滑床所能达到的最大滑移速度（向上和向下）,进而得到相对动能;（4）考虑到滑体的动能基本耗散在滑带上,基于能量守恒原理,将相对动能除以滑带上的摩擦力,即可估算出每一周期内的永久位移;（5）将每一地震波周期内产生的永久位移相累加,即可得到总体的滑动位移。经与实验结果对比,本估算方法具有较高的精度与可靠性,虽只考虑了水平向地震动作用的影响,但对于存在竖向地震动的情况,其思路同样适用,只是需要计入竖向地震动惯性作用力的影响。     

Modeling of strong motion generation areas of the 2011 Tohoku,Japan earthquake using modified semi-empirical technique

Modification in the semi-empirical technique for the simulation of strong ground motion has been introduced to incorporate the strong motion generation areas (SMGA) in the modeled rupture plane. Strong motion generation areas identified within the rupture plane of the Tohoku earthquake of March 11, 2011 (M _w = 9.0), have been modeled using this modified technique. Two different source models having four and five SMGAs, respectively, are considered for modeling purpose. Strong motion records using modified semi-empirical technique have been simulated at two near-field stations located at epicentral distance of 137 and 140 km, respectively, using two different source models. Comparison of the observed and simulated acceleration waveforms is made in terms of root mean square error (RMSE) at both stations. Minimum root mean square error of the waveform comparison has been obtained at both the stations for source model having five SMGAs. Simulations from same rupture model have been made at other four stations lying at epicentral distance between 154 and 249 km. Comparison of observed and simulated records has been made in terms of RMSE in acceleration records, velocity records and response spectra at each six station. Simulations have been made at six other stations to obtain distribution of peak ground acceleration and peak ground velocity with hypocentral distance. Peak ground acceleration and velocity from simulated and observed records are compared at twelve stations surrounding the source of Tohoku earthquake. Comparison of waveforms and parameters extracted from observed and simulated strong motion records confirms the efficacy of the developed modified technique to model earthquake characterized by SMGAs.     

Equivalent-linear seismic analyses of MSW landfills using DEEPSOIL

Responses of municipal solid waste (MSW) landfills during earthquakes are gaining worldwide importance due to the devastating nature of earthquake on landfills. Apart from the post-earthquake safety and serviceability issues which pose environmental and public health problems, other important concerns are related to the behavior of closed landfills during and after earthquake. In present study, one dimensional (1-D) equivalent-linear analysis was carried out to model the behaviour of MSW landfills subjected to seismic base accelerations using the DEEPSOIL software. Influence of foundation types, height and stiffness of MSW landfills and seismic base accelerations on the seismic responses in terms of surface accelerations, normalized stresses (i.e., shear stress/effective vertical stress) and spectral amplification are evaluated. The results showed that height and stiffness of landfills, type of foundation and amount of seismic base acceleration and period play important role in evaluating the seismic responses of MSW landfills. Assumption of constant unit weight and shear wave velocity for landfills underestimates maximum horizontal acceleration (MHA), normalized shear stresses and spectral amplification at the top of landfills. Landfill models with smaller heights (up to 40 m high) showed higher amplification ratio for low seismic base accelerations with mean period near to that of soil and landfill resonance for all sites. A complex behavior was observed at higher seismic base accelerations due to non-linear behavior of landfill materials.