Efficient Methods to Simulate Planar Free Surface in the 3D 4th-Order Staggered-Grid Finite-Difference Schemes

We numerically tested accuracy of two formulations of Levander's (1988) stress-imaging technique for simulating a planar free surface in the 4^th-order staggered-grid finite-difference schemes. We have found that both formulations (one with normal stress-tensor components at the surface, the other with shear stress-tensor components at the surface) require at least 10 grid spacings per minimum wavelength ( _min÷h = 10) if Rayleigh waves are to be propagated without significant grid dispersion in the range of epicentral distances up to 15 _dom ^S.Because interior 4^th-order staggered-grid schemes usually do not require more than 6 grid spacings per minimum wavelength, in the considered range of epicentral distances, it was desirable to find alternative techniques to simulate a planar free surface, which would not require denser spatial sampling than _min÷h = 6. Therefore, we have developed and tested new techniques: 1. Combination of the stress imaging (with the shear stress-tensor components at the surface) with Rodrigues' (1993) vertically refined grid near the free surface. 2. Application of the adjusted finite-difference approximations to the z-derivatives at the grid points at and below the surface that uses no virtual values above the surface and no stress imaging. The normal stress-tensor components are at the surface in one formulation, while the shear stress-tensor components are at the surface in the other formulation.The three developed formulations give for the spatial sampling _min÷h = 6 results very close to those obtained by the discrete-wavenumber method. Because, however, the technique with the vertically refined grid near the free surface requires 3 times smaller time step (due to the refined grid), the technique with adjusted finite-difference approximations is the most accurate and efficient technique from the examined formulations in the homogeneous halfspace.     

A Fourth Order Accurate SH-Wave Staggered Grid Finite-difference Algorithm with Variable Grid Size and VGR-Stress Imaging Technique

This article presents a new approach for the implementation of a planar-free surface boundary condition. It is based on a vertical grid-size reduction above the free surface during the explicit computation of a free surface boundary condition. This technique is very much similar to the well-known stress imaging technique. VGR-stress imaging technique name is proposed for this new free surface boundary condition (VGR stands for ‘vertical grid-size reduction’). To study the performance of the proposed VGR-stress imaging technique, it was implemented in a newly developed second order accurate in time and fourth-order accurate in space (2, 4) staggered grid SH-wave finite-difference (FD) algorithm with variable grid size. It was confirmed that the effective thickness (ETH) of first soil layer becomes less by one-half of vertical grid size than the assigned thickness (ATH), if stress imaging technique is used as a free surface boundary condition. The qualitative and quantitative results of various numerical experiments revealed that the proposed VGR-stress imaging technique is better than the stress imaging technique since it is free from the thickness discrepancy arising due to the use of images of stress components across the free surface. On the basis of iterative numerical experiments, it was confirmed that the stability condition for this FD scheme with variable grid size is It was also inferred that at least five to six grid points per shortest wavelength are required to avoid the grid dispersion. The maximum grid-spacing ratio up to 12.5 or even more did not affect the accuracy of (2,4) SH-wave algorithm. The obtained reduction of 10.46 and 5.38 folds in the requirement of computational memory and time for a particular basin-edge model, as compared with the homogeneous grid size, reflects the efficacy of the new FD algorithm.     

一种时空域优化的高精度交错网格差分算子与正演模拟

如何有效压制数值频散是有限差分正演模拟研究中的关键问题之一.近年来,许多学者对二阶声波方程的差分算子开展了大量的优化工作,在压制频散方面取得不错的效果.一阶压强-速度方程广泛用于研究地震波在地下变密度模型中传播规律,目前针对一阶方程的优化工作大多只是在空间差分算子上展开.本文在前人研究的基础上,推导出一阶声波方程中压强场与偏振速度场之间的解析关系,据此在传统交错网格基础上给出一种高精度的显式时间递推格式,该递推格式将时间差分与空间差分算子结合在一起,并采用共轭梯度法得到精确时间递推匹配系数,实现时空差分算子的同时优化.在编程实现算法的基础上,通过频散分析与三个典型模型测试表明：本文方法能够较为有效地压制时间频散与空间频散,提高数值计算精度;同时对复杂模型也有很好适用性.     

离散介质波场正演模拟与弱化性影响分析

从流变力学角度建立的离散介质本构关系同时考虑了介质的弹性、粘性与弱化性,与损伤力学建立的本构关系比较表明弱化因子具有损伤因子的力学意义。本文采用交错网格伪谱法正演模拟了离散介质中波的传播,并以平面波解分析了体波的频散和介质的吸收系数。高频和低频情况下波场数值模拟的结果是:饱和多孔介质中体波速度随弱化因子的增加而降低,介质吸收系数随弱化因子的增加而增加,弱化性对不同体波频散的影响程度不同。     

基于自适应网格的仿真型有限差分地震波数值模拟

在复杂山地和复杂海底条件下,地表和海底的剧烈起伏对地震波数值模拟提出了更高的要求.常规有限差分法采用矩形网格对模型进行网格剖分,由于矩形网格自身的限制,起伏地表或起伏海底只能由一系列阶梯状折线代替,从而引起人为虚假绕射波.此外,在模拟液-固界面的反射波时,如果界面与网格线不一致,则需要更密的网格才能得到精确的结果.为了解决上述问题,本文将自适应网格生成技术引入到起伏海底速度模型的网格剖分中,采用高阶仿真型有限差分法（MFD）对曲线坐标下的声波方程波进行了数值模拟.利用自适应网格生成技术对速度模型进行网格剖分不仅可以准确地描述模型边界,而且可以有效消除虚假绕射波.高阶仿真型有限差分法可以有效压制频散提高计算精度.模型试算结果表明,本文方法对复杂海底模型具有很好的适应性.     

波场模拟中的数值频散分析与校正策略

波动方程有限差分法正演模拟,对认识地震波传播规律、进行地震属性研究、地震资料地质解释、储层评价等,均具有重要的理论和实际意义.但有限差分法本身固有存在着数值频散问题,数值频散在正演模拟中是一种严重的干扰,会降低波场模拟的精度与分辨率.针对TI介质波场模拟的交错网格有限差分方法,本文从空间网格离散、时间网格离散和算子近似等三个方面对其产生的数值频散进行了分析,并结合其他学者的研究成果给出了TI介质波场模拟中压制数值频散的方法与策略：在已知介质频散关系时,对差分算子可实施算子校正;通过提高差分方程的阶数来提高波场模拟精度;采用流体力学中守恒式方程的通量校正传输方法来压制波场模拟中的数值频散;在实际正演模拟时,采用交错网格高阶有限差分方程,不仅在空间上采用高阶差分,而且在时间上也要采用高阶差分,否则只在单一方向上（空间或时间）提高方程的阶数对压制数值频散也不会取得理想的效果.     

起伏地表三维电阻率法有限差分数值模拟

有限差分法是地球物理数值模拟中最常用的方法之一,为了研究起伏地表对三维电阻率法的影响问题,本文基于网格变换方法将起伏地表映射成水平地表,推导出映射后坐标系下稳定电流场基本方程.采用有限差分法对映射后的控制方程进行数值模拟,通过对三维山谷、山脊地形进行数值模拟,分析不同测量装置的地形影响,结果表明:起伏地表对稳定电流场的影响很大.     

Evaluation of longitudinal and transverse dispersivities/distance ratios for tracer test in a radially convergent flow field with scale-dependent dispersion

This study presents a novel mathematical model for analysis of non-axisymmetrical solute transport in a radially convergent flow field with scale-dependent dispersion. A two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates is derived based on assuming that the longitudinal and transverse dispersivities increase linearly with the distance of the solute transported from its injected source. The Laplace transform finite difference technique is applied to solve the two-dimensional, scale-dependent advection–dispersion equation with variable-dependent coefficients. Concentration contours for different times, breakthrough curves of average concentration over concentric circles with a fixed radial distance, and breakthrough curves of concentration at a fixed observation point obtained using the scale-dependent dispersivity model are compared with those from the constant dispersivity model. The salient features of scale-dependent dispersion are illustrated during the non-axisymmetrical transport from the injection well into extraction well in a convergent flow field. Numerical tests show that the scale-dependent dispersivity model predicts smaller spreading than the constant-dispersivity model near the source. The results also show that the constant dispersivity model can produce breakthrough curves of averaged concentration over concentric circles with the same shape as those from the proposed scale-dependent dispersivity model at observation point near the extraction well. Far from the extracting well, the two models predict concentration contours with significantly different shapes. The breakthrough curves at observation point near the injection well from constant dispersivity model always produce lesser overall transverse dispersion than those from scale-dependent dispersivity model. Erroneous dimensionless transverse/longitudinal dispersivity ratio may result from parametric techniques which assume a constant dispersivity if the dispersion process is characterized by a distance-dependent dispersivity relationship. A curve-fitting method with an example is proposed to evaluate longitudinal and transverse scale-proportional factors of a field with scale-dependent dispersion.     

平面P-SV波入射时非均匀饱和土 自由场地的响应

基于Biot多孔介质波动模型,研究了非均匀饱和土层对平面P-SV波入射时的动力响应.考虑饱和土地基的物理力学特性沿厚度方向连续变化,利用亥姆霍兹矢量分解原理和动力刚度法,分析了平面入射P-SV波在非均匀饱和土层中的反射和透射,并给出了基岩表面和自由表面处反射系数和透射系数的计算表达式.基于理论推导结果,数值分析了平面SV波入射下非均匀饱和土自由场地的动力响应,其中假设饱和土地基的物理力学性质沿土层深度按幂律梯度变化.数值结果表明,平面SV波入射所引起的地面位移与基岩位移之比均随土层厚度和土体的非均匀程度、波的入射角和入射频率的增加而减小,且其竖向位移比的减小更为显著,厚土层对地震波的耗散作用尤为明显.      

基于WNAD方法的非一致网格算法及其弹性波场模拟

加权近似解析离散化(WNAD) 方法是近年发展的一种在粗网格步长条件下能有效压制数值频散的数值模拟技术. 在地震勘探的实际应用中, 不是所有情况都适合使用空间大网格步长. 为适应波场模拟的实际需要, 本文给出了求解波动方程的非一致网格上的WNAD算法. 这种方法在低速区、介质复杂区域使用细网格, 在其他区域采用粗网格计算. 在网格过渡区域, 根据近似解析离散化方法的特点, 采用了新的插值公式, 使用较少的网格点得到较高的插值精度. 数值算例表明, 非一致网格上的WNAD方法能够有效压制数值频散, 显著减少计算内存需求量和计算时间, 进一步提高了地震波场的数值模拟效率.     

Dispersion attenuation structure of the crust around the Weifang-Jiashan segment of the Tanlu fault zone in North China

On the condition that the velocity ratio of compressive wave to shear wave is stable during the propagating process of seismic wave, this paper develops an estimation method for medium quality factor based on single station's travel time difference between direct S and P waves and the first period signal of direct P wave. 8 774 high SNR wave data altogether recorded by 75 stations are analyzed. The results show that: (1) under the normal regional stress field, the quality factors Q_mSP in the stable tectonic area are higher than that in the active tectonic area around the Weifang-Jiashan section and its surrounding area in the Tanlu fault zone; (2) in the Juxian-Tancheng section the seismic wave attenuation is relatively quick, and the media is relatively broken, suggesting no tectonic stress accumulation; (3) the Xinyi-Sihong section is currently locking and in accumulating elastic strain energy stage, which has the deep environment and conditions of strong earthquake generation similar to those of the 1668 M8.5 Tancheng strong earthquake.     

三角网格有限元法声波与弹性波模拟频散分析

本文对声波与弹性波方程进行有限元法离散,构造有限元法频散关系的一般特征值问题,分析了时间离散格式为中心差分的三角网格有限元法声波与弹性波模拟的频散特性. 比较了三种质量矩阵即分布式质量矩阵、集中质量矩阵和混合质量矩阵对有限元法频散的影响;选取四种典型三角网格,分析了混合质量矩阵有限元（MFEM）频散的方向各向异性;数值频散、方向各向异性随插值阶数的增加逐渐减弱,当空间为三阶插值时,频散主要表现为随采样率的变化而几乎无明显方向各向异性, 其频散幅值也较小. 控制其他影响因素不变的情况下,研究了不同波速比介质中弹性波的数值频散. 最后给出了三角网格MFEM的数值耗散性.     

Linear and nonlinear computations of the 1992 Nicaragua earthquake tsunami

Numerical computations of tsunamis are made for the 1992 Nicaragua earthquake using different governing equations, bottom frictional values and bathymetry data. The results are compared with each other as well as with the observations, both tide gauge records and runup heights. Comparison of the observed and computed tsunami waveforms indicates that the use of detailed bathymetry data with a small grid size is more effective than to include nonlinear terms in tsunami computation. Linear computation overestimates the amplitude for the later phase than the first arrival, particularly when the amplitude becomes large. The computed amplitudes along the coast from nonlinear computation are much smaller than the observed tsunami runup heights; the average ratio, or the amplification factor, is estimated to be 3 in the present case when the grid size of 1 minute is used. The factor however may depend on the grid size for the computation.     

考虑应变软化的边坡稳定分析

在密砂、坚硬黏土及原状土的强度试验中,土试样常表现为应变软化,随着应变的增加其抗剪强度降低,并且发生渐进破坏。应用传统的极限平衡法,采用峰值强度作为计算参数进行稳定分析验算时,通常忽略土材料的渐进破坏过程,这可能会对边坡稳定评价带来不利影响。基于有限元极限平衡法,提出考虑应变软化的边坡稳定分析方法,并通过算例分析证明该方法的合理性。     

陕西重力测网起算基准稳定性分析

采用经典平差方法处理重力网数据时,判断起算基准是否稳定是一个关键性问题。本文在精细化处理陕西重力测网观测资料基础上,采用线性回归法,对1992—2011年陕西重力测网起算基准进行了稳定性分析。并以泾阳M_S 4.8地震为例,分析了重力起算基准稳定性对重力网计算的影响及线性回归方法的有效性,结果表明:(1)起算基准重力值随时间变化明显;(2)起算基准扰动影响改正后,地震前后重力场及跨断裂重力段差变化特征更加符合实际情况;(3)处理重力数据及分析重力场变化特征时,必须考虑起算基准稳定性的影响。     

危岩体在地震作用过程中的失稳模式及稳定性评价

地震作用过程中地震加速度通常呈先增大后减小的特征。利用拟静力法对危岩的稳定性进行分析时,考虑地震过程中地震加速度的变化,对山西太原天龙山危岩体加固工程中的同一危岩体分别以滑塌式和倾倒式破坏模式进行计算,发现地震作用过程中危岩体可能在两种破坏失稳模式之间相互转化。将此问题扩展至一般情况进行计算并讨论,得出如下结论:地震力对危岩体破坏作用的贡献大小不同,通常情况下,地震作用力对危岩的倾覆力矩贡献相对较大;进行稳定性评价时应考虑地震作用过程,以安全系数最先达到1.0的破坏模式作为危岩体的可能破坏模式进行计算;对危岩体进行抗震加固设计时应对加固设计进行多种工况下的校核,保证其在地震作用过程中不同危险状态的稳定性。     

Stability and accuracy analysis of the central difference method for real‐time substructure testing

The central difference method (CDM) that is explicit for pseudo‐dynamic testing is also believed to be explicit for real‐time substructure testing (RST). However, to obtain the correct velocity dependent restoring force of the physical substructure being tested, the target velocity is required to be calculated as well as the displacement. The standard CDM provides only explicit target displacement but not explicit target velocity. This paper investigates the required modification of the standard central difference method when applied to RST and analyzes the stability and accuracy of the modified CDM for RST. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic,petrologic, and geodetic analyses of the 1999 dome-forming eruption of Guagua Pichincha volcano,Ecuador

Guagua Pichincha, located 14 km west of Quito, Ecuador, is a stratovolcano bisected by a horseshoe-shaped caldera. In 1999, after some months of phreatic activity, Guagua Pichincha entered into an eruptive period characterized by the extrusion of several dacitic domes, vulcanian eruptions, and pyroclastic flows. We estimated the three-dimensional (3-D) P-wave velocity structure beneath Guagua Pichincha using a tomographic inversion method based on finite-difference calculations of first-arrival times. Hypocenters of volcano-tectonic (VT) earthquakes and long-period (LP) events were relocated using the 3-D P-wave velocity model. A low-velocity anomaly exists beneath the caldera and may represent an active volcanic conduit. Petrologic analysis of eruptive products indicates a magma storage region beneath the caldera, having a vertical extent of 7–8 km with the upper boundary at about sea level. This zone coincides with the source region of deeper VT earthquakes, indicating that a primary magma body exists in this region. LP swarms occurred in a cyclic pattern synchronous with ground deformation during magma extrusions. The correlation between seismicity and ground deformation suggests that both respond to pressure changes caused by the cyclic eruptive behavior of lava domes.     

Three-dimensional structure of the crust and upper mantle beneath the south China area from long period surface waves

In the present study the long period surface wave records of 238 wave-paths from 79 earthquakes within China and its adjacent regions received by 30 seismic network stations are measured by using the improved match-filtering frequency-time analysis technique and the grid dispersion inversion method to obtain the rayleigh pure-path dispersion values for 147 slant grids of 4° × 4° in this area, then a three-dimensional shear wave velocity model of the crust and upper mantle beneath south China area to a depth of 170 km is inversed. It is found that there are obvious differences among the main structural units, and there are also certain differences among the subordinate elements even in the individual unit. The crustal thickness of this area is ranging from 30 to 43 km, and is getting thicker gradually from the east to the west. The average shear velocity of crust is ranging form 3.48 to 3.68 km/s with the lowest in the northeast part and highest in the west part. No obvious crustal low velocity layer of large scale is detected. There exist upper mantle low velocity zones in the most of south China area with the starting depth ranging from 75 to 106 km. The lowest shear velocity within the low velocity zones is about 4.28–4.38 km/s. Despite of the existing of upper mantle low velocity zones beneath the most of south China area, the interfaces between the important layers are quite clear, the variation of the bedding surfaces is very gentle, and the lateral changes measured in a larger scale of the underground structure are rather small. It may indicate that the crustal and upper mantle structure of the main part of south China area belongs to the relatively stable structure of the continental blocks except for the fringe areas such as the fold-faulted region in the west part and the fault system along the southeastern coast which may belong to the tectonically active area. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 159–167, 1993. This subject is supported by the National Science Foundation of China.     

强震作用下超高桥墩动力稳定性理论研究

根据平截面假定,考虑超高桥墩大位移变形产生的几何非线性影响,建立超高桥墩的振动控制微分方程,利用变步长的龙格-库塔法进行求解,结合B-R运动判定准则,对超高桥墩在地震作用下的动力失稳机理进行研究。理论分析表明,超高桥墩的动力失稳与桥墩的几何尺寸、质量分布、边界条件有密切关系;桥墩动力失稳时刻随地震波加速度峰值的增大而减小;失稳时刻与失稳加速度荷载有对应关系。算例结果表明:本文方法正确,利用本文理论能够准确计算超高桥墩的失稳时刻及失稳加速度,对超高桥墩动力失稳的理论分析及工程实践有重要指导意义。