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1.
地震自发破裂模拟是震源动力学研究的重要内容,了解复杂的断层动力学破裂过程对深入认识震源特征和解释运动学反演结果具有重要意义.基于边界积分方程方法的破裂模拟已经被广泛使用,大多采用的是平面断层模型的结构化网格划分.由于实际的断层往往具有较为复杂的几何特征,为了更为灵活地刻画断层几何复杂性,我们建立断层模型的三角形网格离散方案,通过精确的解析解形式来计算断层各个单元之间的应力格林函数,联立滑动弱化摩擦准则和非奇异边界积分方程,对断层的自发破裂过程进行了模拟.在简单的平面断层模型下,将计算结果与前人的结果进行了对比,验证了方法的正确性与有效性.对于几种常见的复杂断层模型,例如弯折、阶跃、含障碍体断层等,我们模拟了其破裂过程并对计算结果进行了比较与分析.模拟结果表明,非结构化网格划分的边界积分方程方法能够很好地模拟平面矩形断层或由其组成的规则断层,同时也能成功地模拟具有复杂几何形状的不规则断层上的动力学破裂过程.本研究的结果显示了边界积分方程方法在模拟复杂断层系统的动力学破裂问题上具有较广阔的应用前景. 相似文献
2.
本文利用边界积分方程方法,以基于三角形网格的全空间格林函数及离散积分核计算为基础,进行了最常见的弯折断层的破裂传播过程模拟.为了去除边界积分方程方法中格林函数计算存在的高度奇异性,研究采用分部积分等方法对动力学方程进行了重整化和离散化处理.地震力学过程可以被视为断层由静摩擦转为动摩擦的过程,对于震源破裂过程的动力学模拟,摩擦准则起着重要作用,本研究采用常用的滑动弱化摩擦准则.计算引入Courant-Friedrich-Lewy比值来表达场点的影响,并控制计算的收敛性和稳定性.通过与典型算例的比对,检验了方法的正确性和有效性.地震破裂能否穿越断层弯折部位继续传播是震源动力学研究的重要内容,基于此,本文建立了多种理论弯折断层模型,模拟了断层弯折对地震破裂传播的控制作用,并通过改变断层周边初始应力场、断层弯折角度大小以及滑动弱化距离大小等来分析各个因素对破裂传播的影响.模拟结果表明:断层面上初始破裂区域内外的应力越高,破裂越容易越过断层弯折部位继续传播;初始破裂区域半径越大,或滑动弱化距离越小,破裂也越容易发生,并越过弯折部位继续传播.同样的初始条件,断层弯折角度越大,断层弯折作为障碍体,对破裂传播的阻碍作用越显著.小的弯折角,其破裂传播过程与平面断层差别不明显,基本仍以椭圆方式对称向两侧传播. 相似文献
3.
震源动力学破裂过程数值模拟研究 总被引：2，自引：1，他引：1
首先阐述了震源动力学过程研究的重要意义, 在此基础上, 研究了复杂的断层几何形态及介质模型对动力学破裂过程的影响, 并对常用的有限元方法、 离散元方法、 有限差分方法和边界积分方程方法等进行了相应介绍. 讨论了这些数值模拟方法各自的优缺点, 建议在方法的选择上应视具体问题及计算的精度而定. 最后对动力学数值模拟的关键部分, 滑动摩擦准则进行了论述. 常用的滑动摩擦准则有滑动弱化准则、 速率弱化准则和速率-状态依赖摩擦准则. 在单纯考虑某个地震的动力学破裂传播过程时, 滑动弱化准则较为常用, 其中滑动弱化距离的选取至关重要. 但若考虑整个地震循环, 速率-状态依赖摩擦准则更为合适. 相似文献
4.
以格子法为基础,以声波方程为例研究非规则网格PML(Perfectly Matched Layer)方法.本方法的核心是建立局部坐标系下的分裂方程和基于积分近似的微分方程弱形式.该非规则网格模拟方法允许在计算域内设置任意形状的人工边界.对于二维半空间问题,与采用矩形人工边界相比,采用半圆形人工边界可减少计算量20%以上.采用光滑的曲边界,不仅可减少计算区域,还可避免常规的PML吸收边界在吸收带角点区域的特殊处理.本方法事先计算和存储边界单元的局部几何参数,在计算的每一时间步查表调用这些参数,与常规的直边界PML方法相比,不增加任何计算量. 相似文献
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从全球数字地震台网的长周期记录中，选择了震中距小于90的27个台站的54个P波震相和44个S波震相资料．首先，用波形反演方法确定了2001年1月26日印度古杰拉特(Gujarat)ＭS7.8地震的地震矩张量、震源机制、震源时间函数和时空破裂过程等震源参数．通过矩张量反演，并根据Kutch Mainland断层的走向、地震烈度的空间分布、余震震源的空间分布和震害的空间分布，确认2001年1月26日印度古杰拉特ＭS7.8地震的发震断层的走向为92、倾角为58、滑动角为62，即一走向近东-西向、断层面向南倾斜、以逆冲为主的左旋-逆断层．这次地震所释放的地震矩为3.51020 Nm，矩震级ＭW＝7.6．然后，借助合成地震图，采用频率域求谱商的方法，得到了依赖于台站方位的27个P波震源时间函数、22个S波震源时间函数以及平均的P波震源时间函数和S波震源时间函数．对震源时间函数的分析表明，这次地震是一次连续的破裂事件，开始比较急遽，但结束比较迟缓，总持续时间约19 s．最后，以所提取的P波和S波震源时间函数为资料，采用时间域的反演技术得到了断层面上滑动的时空分布．滑动量在断层面上的静态分布表明，断层面上的最大滑动量约为7 m．断层面上的最大应力降约为30 MPa，平均应力降约为7 MPa．滑动量大于0.5 m的区域在走向方向长85 km，在断层面倾斜方向宽约60 km(相应地，在深度方向约51 km)．破裂向东扩展约50 km，向西扩展约35 km．滑动量大于0.5 m的区域的主要部分呈椭圆形，其长轴取向与断层滑动方向一致．表明此区域破裂扩展的方向即是断层错动的方向．这种现象对于走滑断层情形是多见的，但对逆冲断层情形却少见．断层面上初始破裂点以东、以上部分面积大于初始破裂点以西、以下部分的面积，这是破裂非对称性的表现，表明破裂具有自西向东、自下向上单侧破裂的特征．从滑动率随时空变化的快照可以看出，滑动率在第4 s达到最大值，此时滑动率约为0.2 m/s，滑动基本上发生在破裂起始点及其周围．从第6 s开始，起始点的破裂基本结束，破裂开始向外围扩展．破裂向西的扩展速度明显小于向东的扩展速度．在第15 s，这种环形的扩展基本结束．自16 s以后，主要是一些零星的破裂点分布在破裂区的外围．从滑动量随时空变化的快照看，破裂自起始点开始后，逐渐向四周扩展．主要的破裂(滑动量大于5 m的区域)在6～10 s，具有明显的自西向东、向上的单侧破裂特征．在第11～13 s，破裂的西端向西、向下有所扩展．整个破裂过程持续约19 s．在整个破裂过程中的平均破裂速度约为3.3 km/s． 相似文献
8.
三维瞬变电磁正演算法作为研究处理与解释方法的重要基础,如何加速计算过程,减少计算机内存消耗尤为重要.为此,本文采用有限体积算法在八叉树(octree)网格上对时间域Maxwell方程组进行空间离散,相比于交错六面体网格,octree网格在局部区域网格细度相同的条件下可以显著减少细化区域外的网格数量,对复杂几何体边界的模拟更加灵活,而相比于非结构四面体网格,octree网格单元位置排列更加规律.通过octree网格离散三维正演模型使计算网格规模显著降低,减少了待求解方程的未知数,降低了物理内存消耗.空间离散后,瞬变电磁正演响应可以表示为关于初始磁场的矩阵指数函数,采用位移逆Krylov子空间模型降阶算法实现瞬变电磁场的求解,只需对系数矩阵进行一次矩阵分解和多次回代即可获得一系列时间序列的瞬变电磁场正演结果.本文算法在空间离散和方程求解两方面优化三维瞬变电磁正演过程,数值算例结果验证了本文算法的精度和高效性. 相似文献
9.
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. 相似文献
10.
推导出了分析二维粘及弹性场地地形对地震动影响的显式有限元-有限差分方法．这一方法中，首先利用人工边界及有限元离散方法，给出问题分析的有限元离散网格计算力学模型，并利用一种类似于差分方法的有限元方法，建立局部网格节点的动力方程，而后利用笔者提出的有阻尼体系动力方程求解的显式差分格式，及推广的多次透射边界公式，给出网格节点运动量计算的时域显式逐步积分公式．利用计算机程序实现这一方法的计算具有所需计算机内存量小及计算时间量小的优势，而且，这一方法适用于任意地形情况，具有较高的计算精度及较好的计算稳定性． 相似文献
11.
The choice of spatial grid size has been being a crucial issue in all kinds of numerical algorithms. By using BIEM (Boundary Integral Equation Method) to calculate the rupture process of a planar fault embedded in an isotropic and homogeneous full space with simple discretization scheme,this paper focuses on what grid size should be applied to control the error as well as maintaining the computing efficiency for different parameter combinations of (Dc,Te),where Dc is the critical slip-weakening dis-tance and Te is the initial stress on the fault plane. We have preliminarily found the way of properly choosing the spatial grid size,which is of great significance in the computation of seismic source rup-ture process with BIEM. 相似文献
12.
The staggered grid finite-difference method is a powerful tool in seismology and is commonly used to study earthquake source
dynamics. In the staggered grid finite-difference method stress and particle velocity components are calculated at different
grid points, and a faulting problem is a mixed boundary problem, therefore different implementations of fault boundary conditions
have been proposed. Viriuex and Madariaga (1982) chose the shear stress grid as the fault surface, however, this method has
several problems: (1) Fault slip leakage outside the fault, and (2) the stress bump beyond the crack tip caused by S waves
is not well resolved. Madariaga et al. (1998) solved the latter problem via thick fault implementation, but the former problem remains and causes a new issue;
displacement discontinuity across the slip is not well modeled because of the artificial thickness of the fault. In the present
study we improve the implementation of the fault boundary conditions in the staggered grid finite-difference method by using
a fictitious surface to satisfy the fault boundary conditions. In our implementation, velocity (or displacement) grids are
set on the fault plane, stress grids are shifted half grid spacing from the fault and stress on the fictitious surface in
the rupture zone is given such that the interpolated stress on the fault is equal to the frictional stress. Within the area
which does not rupture, stress on the fictitious surface is given a condition of no discontinuity of the velocity (or displacement).
Fault normal displacement (or velocity) is given such that the normal stress on the fault is continuous across the fault.
Artificial viscous damping is introduced on the fault to avoid vibration caused by onset of the slip. Our implementation has
five advantages over previous versions: (1) No leakage of the slip prior to rupture and (2) a zero thickness fault, (3) stress
on the fault is reliably calculated, (4) our implementation is suitable for the study of fault constitutive laws, as slip
is defined as the difference between displacement on the plane of z = + 0 and that of z = − 0, and (5) cessation of slip is achieved correctly. 相似文献
13.
Rudi Hessel 《水文研究》2005,19(15):3037-3049
With increasing computer power, process‐based models that use grids to discretize space have become increasingly popular. For such models, the simulation results might depend on both grid cell size and, in the case of dynamic models, on the time step length used in the model. In this study, the dynamic Limburg soil erosion model (LISEM) was applied to a small catchment on the Chinese Loess Plateau. To study the effect of grid cell size and time step length, simulations were performed for grid cell sizes ranging from 5 to 100 m for a single time step length, and for time step lengths ranging from 2 to 120 s for a single grid cell size. The results show that the LISEM results vary considerably as a function of both grid cell size and time step length. For both increase in cell size and increasing time step length, the trend was a decrease in predicted discharge and predicted soil loss. For discharge, the most important causes are likely to be a decrease in slope with increasing grid cell size, rainfall averaging for longer time step lengths, and numerical dispersion of the kinematic wave solution. For soil loss, the cause is less clear, reflecting the complexity of soil loss prediction, which depends on available water, transport capacity and sediment redistribution, all of which change in time and space. These results show that a choice for a certain grid cell size and a certain time step length should be made before calibration of the model. Similar erosion models are likely to have similar dependencies on grid size and time step length. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
14.
We examined seismic characteristics, b value and fractal dimension of the aftershock sequence of the January 26, 2001 Bhuj earthquake (Mw 7.7) that occurred in the Kutch failed rift basin, western margin of the Stable Continental Region (SCR) of India. A total of about 2,000 events (M?≥?2.0) were recorded within two and a half months, immediately after the main shock. Some 795 events were precisely relocated by simultaneous inversion. These relocated events are used for mapping the frequency-magnitude relation (b value) and fractal correlation dimension (Dc) to understand the seismic characteristics of the aftershocks and the source zone of the main shock. The surface maps of the b value and Dc reveal two distinct tectonic arms or zones of the V-shaped aftershock area, western zone and eastern zone. The b value is relatively higher (~1.6) in the western zone compared to a lower value (~1.4) in the eastern zone. The Dc map also shows a higher value (1.2–1.35) in the western zone compared to a lower Dc (0.80–1.15) in the eastern zone; this implies a positive correlation between Dc and b value. Two cross sections, E–W and N–S, are examined. The E–W sections show similar characteristics, higher b value and higher Dc in the western zone and lower in the eastern zone with depth. The N–S sections across the fault zones, however, show unique features; it imaged both the b and Dc characteristics convincingly to identify two known faults, the Kutch Mainland fault and the South Wagad fault (SWF), one stepping over the other with a seismogenic source zone at depth (20–35?km). The source zone at depth is imaged with a relatively lower b and higher Dc at the ‘fault end’ of the SWF showing a negative correlation. These observations, corroborated with the seismic tomography as well as with the proposed geological/tectonic model, shed a new light to our understanding on seismogenesis of the largest SCR earthquake in India in the recent years. 相似文献
15.
Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size 总被引：1，自引：1，他引：0
A non-hydrostatic terrain-following model in cross sectional form is applied to study the processes in the lee of a sill in
an idealized stratified fjord during super-critical tidal inflow. A sequence of numerical studies with horizontal grid sizes
in the range from 100 to 1.5625 m are performed. All experiments are repeated using both hydrostatic and non-hydrostatic versions
of the model, allowing a systematic study of possible non-hydrostatic pressure effects and also of the sensitivity of these
effects to the horizontal grid size. The length scales and periods of the internal waves in the lee of the sill are gradually
reduced and the amplitudes of these waves are increased as the grid size is reduced from 100 down to 12.5 m. With a further
reduction in grid size, more short time and space scale motions become superimposed on the internal waves. Associated with
the internal wave activity, there is a deeper separation point that is fairly robust to all parameters investigated. Another
separation point nearer to the top of the sill appears in the numerical results from the high-resolution studies with the
non-hydrostatic model. Associated with this shallower separation point, an overturning vortex appears in the same set of numerical
solutions. This vortex grows in strength with reduced grid size in the non-hydrostatic experiments. The effects of the non-hydrostatic
pressure on the velocity and temperature fields grow with reduced grid size. In the experiments with horizontal grid sizes
equal to 100 or 50 m, the non-hydrostatic pressure effects are small. For smaller grid sizes, the time mean velocity and temperature
fields are also clearly affected by the non-hydrostatic pressure adjustments. 相似文献
16.
Kenji Satake 《Pure and Applied Geophysics》1995,144(3-4):455-470
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. 相似文献
17.
Giovanni Battista Chirico Andrew W. Western Rodger B. Grayson Günter Blschl 《水文研究》2005,19(13):2539-2556
Specific catchment area (SCA) patterns are commonly computed on grids using flow direction algorithms that treat the flow as coming from a point source at the pixel centre. These algorithms are all ambiguous in the definition of the flow width to be associated with a pixel when computing the SCA. Different methods for computing the flow width have been suggested, without giving an objective reason. In the few cases where this issue has been specifically discussed, the flow width is derived from subjective analysis and incorrect conceptualizations. This paper evaluates alternative approaches for defining the flow width when computing SCA patterns using the D∞ and D8 algorithms, by comparing theoretical and computed SCA patterns on sloping planes, inward and outward cones. Two new methods of defining the flow width are also analysed for both the D∞ and D8 algorithms. The performances of the different methods are discussed in relation to two dimensionless parameters: (1) the global resolution, defined as the ratio of a characteristic length of the study area to the grid size and (2) the upslope area resolution, defined as the ratio of the theoretical SCA to the grid size. The optimal methods are identified by specific threshold values of these dimensionless parameters. We conclude that assuming the flow width invariant and equal to the grid size is generally the best approach in most practical circumstances, both for the D∞ and D8 algorithm. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
18.
Abstract A distributed eco-hydrological model based on soil—vegetation—atmosphere transfer processes is applied to estimate actual evapotranspiration (ET) and gross primary production (GPP) over the Wuding River basin, Loess Plateau, China, based on digital elevation model, vegetation and soil information between 2000 and 2003 over three grid sizes: 250 m, 1 km and 8 km. The spatial patterns of annual ET and GPP are related to precipitation variability and land-use/cover conditions. The grid size is shown to affect the spatial patterns of annual ET and GPP, the effect on GPP being more significant than that on ET. Geostatistical and regression analyses demonstrate that precipitation and vegetation influence the scaling effect of ET and GPP in a complex way. When precipitation is high, the scaling effect of ET is more dependent on precipitation. The scaling effect of ET and GPP from 1-km to 8-km grid size is much larger than that from 250-m to 1-km grid size, showing the 1-km grid size to be a feasible choice for simulation of their spatial patterns. Although the annual GPP is more sensitive to the grid size than annual ET, both daily ET and daily GPP averaged over the whole basin seem to be insensitive to the grid size, illustrating that the coarse grid size can be used to simulate spatially-averaged variables without losing much accuracy. 相似文献
19.
Digital elevation models (DEMs) at different resolutions (180, 360, and 720 m) are used to examine the impact of different levels of landscape representation on the hydrological response of a 690‐km2 catchment in southern Quebec. Frequency distributions of local slope, plan curvature, and drainage area are calculated for each grid size resolution. This landscape analysis reveals that DEM grid size significantly affects computed topographic attributes, which in turn explains some of the differences in the hydrological simulations. The simulations that are then carried out, using a coupled, process‐based model of surface and subsurface flow, examine the effects of grid size on both the integrated response of the catchment (discharge at the main outlet and at two internal points) and the distributed response (water table depth, surface saturation, and soil water storage). The results indicate that discharge volumes increase as the DEM is coarsened, and that coarser DEMs are also wetter overall in terms of water table depth and soil water storage. The reasons for these trends include an increase in the total drainage area of the catchment for larger DEM cell sizes, due to aggregation effects at the boundary cells of the catchment, and to a decrease in local slope and plan curvature variations, which in turn limits the capacity of the watershed to transmit water downslope and laterally. The results obtained also show that grid resolution effects are less pronounced during dry periods when soil moisture dynamics are mostly controlled by vertical fluxes of evaporation and percolation. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
20.
瞬变电磁三维时域有限差分（FDTD）正演的网格剖分受最小网格尺寸、时间步长、边界条件、目标尺寸、模型尺寸等的影响,结构化网格一直存在最小网格尺寸受限于异常目标尺寸的矛盾;尽管非均匀网格能够在保证模型尺寸的前提下尽可能的降低网格数量,但由于Yee网格结构的限制,非均匀网格不能无限制的扩大单一方向的尺寸,这是为了避免边界网格区域出现长宽比过大的畸形网格,影响计算精度甚至导致结果发散.在非均匀网格剖分的基础上,本文提出了瞬变电磁三维FDTD正演的多尺度网格方法,即首先使用较大尺寸的粗网格进行第一次剖分,然后在希望加密的区域进行二次剖分,使计算域中包含粗、细两套网格.尽管细网格包含在粗网格内部,但其具有Yee网格的全部属性,因而可以在网格中设置不同的电性参数模拟不同形状的目标.基于Maxwell方程组推导了细网格内电场和磁场的迭代公式,基于泰勒展开给出了设置粗、细网格后产生的内部边界条件,使电磁场的传播在粗、细网格和时间步进上得到统一.采用均匀半空间中包含三维低阻异常的经典模型和三维接触带复杂模型进行精度验证,发现多分辨网格方法计算结果满足精度要求.使用"L"型异常模型计算采用多分辨网格方法和不采用多分辨网格的传统FDTD方法对比计算效率,发现多分辨网格算法能够显著提高计算效率,并能够保证计算精度. 相似文献