S波垂直入射下沉积盆地-凹陷耦合地形的地震动模拟

于彦彦, 陈宇嘉, 芮志良, 丁海平

于彦彦,陈宇嘉,芮志良,丁海平. 2025. S波垂直入射下沉积盆地-凹陷耦合地形的地震动模拟. 地震学报,47(3):422−437. DOI: 10.11939/jass.20240010
引用本文: 于彦彦,陈宇嘉,芮志良,丁海平. 2025. S波垂直入射下沉积盆地-凹陷耦合地形的地震动模拟. 地震学报,47(3):422−437. DOI: 10.11939/jass.20240010
Yu Y Y,Chen Y J,Rui Z L,Ding H P. 2025. Simulations of ground motion of canyon-basin coupled terrain under vertical incidence of S-wave. Acta Seismologica Sinica47(3):422−437. DOI: 10.11939/jass.20240010
Citation: Yu Y Y,Chen Y J,Rui Z L,Ding H P. 2025. Simulations of ground motion of canyon-basin coupled terrain under vertical incidence of S-wave. Acta Seismologica Sinica47(3):422−437. DOI: 10.11939/jass.20240010

S波垂直入射下沉积盆地-凹陷耦合地形的地震动模拟

基金项目: 

国家自然科学基金青年基金(51808371)和中国地震局工程力学研究所基本科研业务费专项(2021EEEVL0001)共同资助

详细信息
    通讯作者:

    于彦彦,博士,副教授,主要从事场地地震效应方面的研究,e-mail:yyy_usts@126.com

  • 中图分类号: P315.9

Simulations of ground motion of canyon-basin coupled terrain under vertical incidence of S-wave

  • 摘要:

    采用多次透射公式与三维谱元相结合的方法,研究了S波垂直入射下沉积盆地内耦合三维凹陷地形的地震响应,分析了无量纲宽度κ (凹陷宽度与盆地宽度之比)对地震动放大效应的影响。结果表明:① 无量纲宽度显著改变了盆地内地震动的分布特征、强度及强地震动的位置,凹陷地形对于波长与凹陷尺寸相当的入射波的散射效应更为显著,且此时最强烈地震动主要位于凹陷顶部区域;② 相较于单一盆地地形,盆地内存在凹陷的地形会放大紧邻凹陷顶部或距其一定距离的局部区域的地震动,放大系数介于1.1—1.3之间,地震动明显放大区域的位置随输入波的频域特性而改变,但凹陷底部始终为地震动削减区;③ 无量纲宽度和入射波偏振方向共同影响着地震动峰值位移及放大系数的分布特征,平行偏振方向剖面上放大系数曲线的起伏更为剧烈。

    Abstract:

    The seismic response of local sites is one of hot topics in the field of earthquake engineering. Currently, there have been many researches on the seismic effect of single basin site or local depression sites. However, studies about the basin-depression coupled sites are quite few. Actually, local lakes or deep foundation pits can be frequently found in the basins. So the studies of ground motion amplification characteristics of such a coupled terrain are of significance for earthquake prevention and disaster reduction in corresponding areas. In this paper, a numerical simulation method combining high-precision spectral element method and multiple transmission boundary is firstly introduced, which are used for the wave motion simulation of the interior nodes and boundary nodes, respectively. The accuracy of the method is validated by comparison with the analytical solution for seismic response of a hemisphere basin under SV wave incidence. Then, by using this method, the seismic responses of coupled three-dimensional depression terrain in sedimentary basins under vertical S-wave incidence are investigated considering different input waves, and the impacts of dimensionless width (defined as the ratio of depression width to basin’s radius, abbreviated as κ in the following) on the amplification effect of ground motion are analyzed. The distributions of peak ground displacement (PGD) and the corresponding amplification coefficients (defined as the ratio of the PGDs of basin-canyon coupled model to the single basin model), the displacement time histories along characteristic profiles and their amplification factor distributions are used for the study. Finally, influence of the depression shapes (three-dimensional rectangle and three-dimensional trapezoid) on the seismic amplification features is comparatively studied. The results indicate that:

    1) When no concave is contained in the basin, the incident waves on the semisphere surface are focused at the center of the basin, resulting in the strongest shaking in this region, which is the so called “focusing effect” . But the focusing areas varies significantly with the input wave, with the largest area for the Ninghe wave, and the smallest area for the pulse wave.

    2) The dimensionless width of the depression significantly changes the distribution characteristics, intensities, and locations of strong ground motions inside the basin. For the pulse wave incidence case, excepting for the κ=0.4 model, the ground motion amplitudes of the concave-coupled terrain are always larger than those of the only-basin model. While for the Ninghe and Kobe wave incidence case, the opposite happens.

    3) The scattering effect of concave terrain on incident wave components with wavelengths equivalent or close to their sizes is more significant, and the strongest ground motion is mainly located in the top area of the concave. In contrary, the ground motion amplification effects are insignificant for incident waves with wavelengths greatly longer than the size of depression, when the strong ground motion are still located at the center area of the basin.

    4) Compared to a single basin terrain, the concave terrain within the basin can cause amplification of ground motion in local areas adjacent to the top of the depression or at a certain distance from it, with amplification coefficients ranging from 1.1 to 1.3. Its position changes with the input wave and the dimensionless width, but the bottom of the depression is always a ground motion reduction zone. The amplification effect of the ground motions near the top of the concave or the basin edge is probably caused by the interference between the basin-edge induced surface wave, the directly input wave and the scattering wave on the concave surface.

    5) The dimensionless width of the depression and the polarization direction of the incident wave jointly affect the distribution characteristics of the peak ground displacement and amplification coefficient. In this study, the input ground motion is polarized in the plane for the left-right sides, and out-of-plane for the front-back sides. Then different wave mode conversion phenomenon occurred when waves impinge on the basin basement. The interference with the directly input wave gives rise to the significant difference in wave propagation behavior and ground motion distribution features along the two axis of the basin, which cannot be considered for the two-dimensional model. In addition, the amplification coefficient curve on the profile parallel to the polarization direction fluctuates more violently.

    6) The shape of the depression has certain influence on the distribution of simulated amplification coefficient. The ground motion distribution characteristics of trapezoidal depression on slope surface and bottom of depression are significantly different from those of rectangular depression. The effect of ground motion intensity on the depressed slope is greater than that on the top of both slopes when the slope angle is small. The PGD and amplification coefficient of the three-dimensional trapezoid concave site are a little smaller than the results of three-dimensional rectangle models. But the general distribution feature is comparable, the most affected area is always concentrated in the region of depression and the area adjacent to the edge of it.

    Therefore, for the basin-depression coupled site, the ground motion amplification effect caused by the canyon should be considered, especially when the predominant wavelength of the input wave is close to or smaller compared to the canyon scale. If the predicted ground motion values are obviously larger than the designed basic seismic acceleration of the corresponding area, the seismic fortification level of important engineering structures in the area should be appropriately raised. The results of this study can provide theoretical reference for the seismic damage defense work of sedimentary basin-depression coupling sites.

  • 地震波的震相在地震学发展及地球结构研究中起着重要的作用。随着数值计算方法的发展和观测技术水平的提高,逐渐可以利用地震波形中尽可能多的信号来研究地球结构(崇加军,2013)。地震波是源自震源和震中区的弹性波,震相是地震波显示在地震记录图上的信号(赵荣国,1999)。震相分析对深入研究地球的内部构造和探查地震活动规律具有极为重要的意义,地震震相识别也是省级地震分析和编目工作的一项常规工作。地震震相识别中,人工识别的成分占较大比例,而且由于震源机制和传播介质的复杂性,同一种震相在不同地震中的形态均不相同(杨配新等,2004),因此常见的震相Pn,Pg,Sn,Sg较易识别,但非常见的震相识别难度较大。而康拉德面是不连续面,地震波速度在深度变化的过程中均匀变化,因此Pb震相不易被发现,难以得到地震分析人员的关注。

    1923年,奥地利研究人员康拉德发现,大陆地壳内部还存在这样一个界面(Conrad,1925):该界面以上,岩石密度较低,为硅铝层,由中酸性岩石组成;该界面以下,岩石密度较高,为硅镁层(铁镁层),由基性岩石组成。该界面被称为康拉德(Conrad)不连续面,简称康氏面或康拉德面(刘瑞丰等,2014)。此后许多地震学研究人员在大陆地壳内不同区域和不同尺度上也探测到了该界面(Berry,Fuchs,1973胡德昭等,1989郭杰等,2013),并对其进行了相关研究。胡德昭等(1989)在中国东南部地壳内探查到康拉德面;1970—1994年期间,苏联的超深钻井项目研究显示康拉德界面上的地震波速度跃变非常大(Richard,1989Pavlenkova,1993)。但康拉德界面是否普遍存在仍有争议。相关研究认为,康拉德界面与研究区的地壳结构及其演化历史密切相关,在海洋地壳内或者有时在构造活动比较强烈的大陆地壳内,康拉德界面可能是缺失的(Litak,Brown,1989Richard,1989Pavlenkova,1993)。近期研究已在有些地质构造活动比较强烈的区域记录到的地震波形中发现有来自康拉德界面的强振幅震相(刘赛君等,2011郭杰等,2013),且焦煜媛等(2017)已在青藏高原东北缘找到康拉德面存在的直接地震学证据。郭杰等(2013)在位于豫北东的濮阳市地震台的观测中发现了康拉德界面的反射波震相。

    关于海南地区Pb震相的研究,也有一些相关的研究成果。范玉兰等(1990)在研究华南地区近震走时表时,描述到海口台、文昌台、定安台、那大台、琼中台等海南省台站在震中距大于151 km时,可记录到清晰的Pb震相;刘赛君等(2011)在海南岛西南海域地壳剖面海陆联合探测研究中提到Pb震相在50—130 km偏移距范围内可被追踪到。

    这样看来,有些地区不仅有康拉德面存在的证据,而且前人已记录到海南地区存在Pb震相,因此有必要进一步研究海南地区的Pb震相,故本文一方面以云南省地震台网和广东省地震台网记录到的Pb震相为基础,采用折合走时分析,将其结果作为参考数据;另一方面重点分析海南省地震台网记录到的地震事件,并使用PTD方法(朱元清等,1990)重新定位地震事件的震源深度,以Pb震相理论到时结合实际波形,标注Pb震相,进而拟合标注的震相速度(林建民等,2008)。 此外,综合前人的研究成果(李志雄等,2008刘赛君等,2011黄海波等,2012Kumar et al,2016 )来分析Pb震相的物理特性,最后确定Pb震相。通过识别Pb震相,探查海南地区康拉德面的深度变化,对该地区一维速度模型的建立、地震定位精度的提高以及地震活动、地震定位深度等研究均具有重要意义。

    本文研究区域为海南地区(106°E—114°E,17°N—23°N),选取2009年1月1日至2016年8月25日期间发生在研究区域内的地震,并按照以下标准严格筛选地震事件:① 至少被10个台站记录到;② 地震震级ML≥2.0;③ 地震事件含有Pn震相。最终统计筛选得到Pg震相1 549个,Pn震相588个,无Pb震相。由于研究区域的数据中不包含Pb震相,故以2009年至2016年云南省、广东省地震台网的数据为参考资料,按照上述标准,最终云南地区的震相筛选结果为:Pg震相49 521个,Pb震相3 406个,Pn震相10 781个;广东地区的震相筛选结果为:Pg震相5 038个,Pb震相23个,Pn震相2 240个。

    由于近震波的传播路程短,受地球曲率影响小,因此在研究近震问题时,通常将地球表面及各层界面看作水平界面(刘瑞丰等,2014)。Pb震相是在康拉德面上的纵波性首波,其传播路径如图1所示。由该图所示的Pb震相走时路径,依据斯奈尔(Snell)定理和地震波走时方程,可求得Pb的理论走时为

    图  1  P波传播路径图
    Figure  1.  P wave propagation paths

    ${t_{{\rm{Pb}}}} {\text{=}} \frac{\varDelta }{{{v_2}}} {\text{+}} \left( {2{H_1} - h} \right)\frac{{\cos i}}{{{v_1}}},$

    (1)

    式中,tPb为Pb震相走时,Δ为震中距,H1为康拉德面深度,h为震源深度,v1为一维速度模型中第一层的Pg波平均速度,v2为第二层的Pb波速度,i为Pb波入射角。

    折合走时与介质厚度(康拉德界面或者莫霍面深度)、震源深度和波速相关(王莉婵等,2016),在同一震源深度的情况下,理论折合走时应为常数值b,震相走时可理解为横向走时和折合走时,因此将式(1)变换为

    ${t_{\rm redu}} {\text{=}} t - \frac{\varDelta }{v},$

    (2)

    式中tredu为折合走时,t为理论震相或观测震相走时,v为波速。

    PTD定位方法是采用初至波为Pg直达波的台站到时和初至波为Pn首波的台站到时,经转换后的到时差来确定地震的震源深度(朱元清等,1990)。测定震源深度的分辨率为深度每改变5 km,到时差改变0.7 s,换句话说,初动到时测量误差每增加0.1 s,深度误差则增加0.7 km (朱元清等,1997)。

    本文可辨别出Pb震相的地震共计52次,由于原震源深度定位偏浅,8 km左右的深度占大部分,因此重新测定震源深度,便于下一步震相理论到时的计算。图2给出了使用PTD定位前后的震源深度比较,可见使用PTD方法测定深度可减小初动到时测量误差引起的深度误差,在深度测定方面有较大的优势。

    图  2  使用PTD方法定位前、后震源深度沿纬度(上)和经度(下)方向的变化比较图
    Figure  2.  Comparison of focal depths of the seismic events along latitude (upper) and longitude (lower) directions before and after location by PTD method

    数据处理涉及理论值计算,速度模型是必不可少的部分,虽然目前大多采用IASP91模型,但由于本文涉及云南省(2015模型)、广东省(华南模型)和海南省(2015模型)的数据(朱元清等,2017),考虑到一维速度模型与到时数据之间的一致性(Wang,2014),本文采用各省的一维速度模型作为各自省份参与计算的理论到时,各省的速度模型列于表1

    表  1  云南、广东和海南各省份的地壳速度模型表
    Table  1.  The crustal velocity model of Yunnan,Guangdong and Hainan Provinces
    省份 v1/(km·s−1 v2/(km·s−1 v3/(km·s−1 H1/km H/km
    云南 6.01 6.60 7.89 20 41
    广东 6.00 6.87 7.96 22 33
    海南 6.00 6.84 7.97 21 30
    注:v1v2分别表示第一、二层的平均速度,v3表示莫霍面的平均速度,H1表示第一层的平均厚度,H表示莫霍面的平均厚度。
    下载: 导出CSV 
    | 显示表格

    采用折合走时分析云南、广东两省份的数据,结果显示:云南省的Pb震相数据基本处于理论震相范围内,标注的Pb震相接近该地区的康拉德面;广东省的Pb震相数据几乎全在理论震相范围内,标注的Pb震相在康拉德面上。这表明结果良好,与预期结果相符,故可用此方法分析海南的Pb震相数据。

    震相识别的步骤为:① 对资料进行预处理,筛选出含有Pn震相的地震事件,共计281次;② 对281次地震事件使用PTD法重新定位其震源深度;③ 计算震相理论到时,结合人工分析识别出Pb震相;④ 对识别出的Pb震相进行速度拟合;⑤ 分析和佐证识别的Pb震相结果。

    以近几年海南地区发生的影响较大的两次地震为例:事件1为2012年11月5日19时51分海南万宁ML4.1地震,那大台记录的波形见图3左;事件2为2014年7月28日10时10分海南儋州ML3.3地震,万宁台记录的波形见图3右。

    那大台的震中距为169 km,PTD重新定位深度为10 km,计算其Pg,Pb,Pn的理论走时分别为28.21,27.26,26.06 s,在实际波形识别的相应结果分别为28.54,27.33,26.33 s。依据波形特性、振幅、周期等因素,Pb震相处于Pn震相与Pg震相之间,其振幅稍大于Pn,但小于Pg振幅,符合绕射波的动力学特征。实际人工识别Pb震相走时t2与理论走时t1相差无几,人工识别的Pb震相标注见图3

    以同样的方法,对万宁台记录到的事件2进行PTD定位计算,结果显示重定位深度为13 km,Pg,Pb,Pn震相的理论走时分别为21.60,21.18,20.71 s,实际波形识别的相应结果分别为21.61,21.22,21.04 s。

    依据上述震相识别步骤,在281次地震事件中,从52次地震事件能识别出Pb震相57个,含有Pb震相的地震分布如图4所示。通过分析识别结果可知,能记录到Pb震相的台站共计16个,占全部台站个数(24)的67%,且分布均匀,统计台站记录到Pb震相的震中距处于66.75—234 km范围内,这与海南岛西南海域地壳剖面海陆联合探测研究中追踪到的Pb震相的震中距结果(刘赛君等,2011)基本相近。

    采用速度线性拟合(图5)和折合走时(图6)两种方式分析Pb震相的速度,以佐证识别的震相是否与其物理意义相符,图6中折合走时理论值是基于海南模型计算而得。从图5可知,Pb速度为6.47 km/s,在对数据进行折合走时分析的过程中,扰动第二层的速度为6.65 km/s时,能达到图6的效果,这说明实际震相处于理论值范围内。海南地区在区域构造的伸展作用下,其地壳厚度相对正常大陆型地壳较薄,具有西南厚、东北薄的特点(黄海波等,2012),康拉德面作为上下地壳的分界面,穿过界面的波速由6.0 km/s激增至6.4 km/s (刘赛君等,2011)。

    图  3  Pb震相识别
    Figure  3.  Pb phase identification
    图  4  本文所用含有Pb震相的地震分布图
    Figure  4.  Seismic events distribution with Pb phase used in this paper
    图  5  Pb震相线性拟合图
    Figure  5.  Linear fitting of Pb phase
    图  6  海南地区Pb震相折合走时图
    Figure  6.  The reduced travel time diagram of Pb data in Hainan area

    使用折合走时分析全部Pb震相,结果表明,实际震相基本处于理论震相范围内,尽管有些震相的实际走时与理论走时有偏差,这可能与一维模型单一、不能有效地反映局部地壳内部结构的复杂性和不均匀性有关。综合上述速度拟合分析,识别的Pb震相符合海南地区地震波在康拉德面滑行的物理意义。

    康拉德面是地球内部的次级不连续面,其深度介于10—40 km之间,在陆壳内的平均深度约为20 km (殷伟伟等,2017)。考虑到海南地区的地壳较薄,选取10—30 km作为反演海南地区的康拉德面深度Hi。当Hi以一定步长从10 km依次增加至30 km时,将记录到Pb震相的台站震中距、地震震源深度代入式(1),可得到理论走时t1t1与实测走时t2之差的绝对值的最小值,即Pb震相的走时残差,为Y=min|t1t2|,则57次地震的平均走时残差Si

    ${S_i} = \frac{1}{{57}}\sum\limits_{i = 1}^{57} {{Y_i}} .$

    (3)

    为了较好地反映康拉德面的深度和速度情况,通过计算康拉德面的速度和深度变化,可得到平均走时残差Si随深度和速度变化的分布。取Pb波速度为6.40—6.84 km/s,以0.1 km/s的步长计算所有走时残差;深度范围取10—30 km,以1 km的步长计算。计算结果表明速度为6.60—6.80 km/s、深度为19—22 km时残差最小。基于该结果,按上述方法重复,进一步细算速度和深度变化,速度以0.02 km/s为步长,深度以0.5 km为步长,计算结果如图7所示。结果表明,海南地区的Pb波速度为6.60—6.72 km/s、深度为19—21.5 km较为合理。

    图  7  康拉德面深度及速度变化
    Figure  7.  Variation of Conrad depth and Pb wave velocity

    本文利用海南省记录到的地震事件,识别了Pb震相并反演得到海南地区的康拉德面深度。结果显示,海南地区的Pb波速度介于6.60—6.72 km/s之间、康拉德面在19—21.5 km左右较合理。海南地区Pb波速度与前人的研究结果(范玉兰等,1990刘赛君等,2011)基本吻合,首次在海南地区得出康拉德面的合理范围。由于初至Pb震相难识别,缺乏实际震相支持,今后会持续关注这方面的震相数据。

    本文结果能对地震分析识别Pb震相起到辅助作用,可为建立海南地区的地壳速度模型提供参考资料。但是,由于本文研究的大部分震源位于上地壳,研究结果具有一定的局限性,震源位于下地壳时震相的识别有待进一步研究。

    上海市地震局的朱元清研究员和海南省地震局的李志雄研究员、张慧高工对本研究给予了指导,江苏省地震局廖发军高工分别为本文提供了PTD软件,审稿专家提出了修改意见,作者在此一并表示衷心的感谢!

  • 图  11   脉冲波入射下盆地-四面梯形凹陷耦合地形的地表位移峰值PGD放大系数分布

    Figure  11.   Distribution of surface PGD amplification coefficient for basin models coupled with four-sided trapezoidal depression topography under pulse waves incidence

    图  1   多次透射边界原理示意图

    图中方块为各单元内配置的节点,圆点为透射公式计算点,Δt为时间步长

    Figure  1.   Schematic diagram of multiple transmission boundary principle

    The squares and dots denote the allocated SEM nodes and the referential points used by MTF,respectively. ∆t represents the time step

    图  2   本文模拟结果与 Mossessian和Dravinski (1990)结果的对比

    Figure  2.   Comparison between the results of this paper and those of Mossessian and Dravinski (1990

    图  3   计算模型示意图

    Figure  3.   Schematic diagram of calculation model

    图  4   输入脉冲波(左)、宁河波(中)和Kobe波(右)的位移时程曲线(a)及其傅里叶谱(b)

    Figure  4.   Time histories (a) and Fourier spectrum (b) of inputted pulse wave (left),Ninghe wave (middle),and Kobe wave (right)

    图  5   不同无量纲宽度κ下三种入射波对应的地表峰值位移PGD分布

    (a) 脉冲波入射;(b) 宁河波入射;(c) Kobe波入射。黑色圆代表盆地的范围,中心处的方形线框表示凹陷范围

    Figure  5.   Peak ground displacement (PGD) distribution under different dimensionless widths κ under three incident waves

    (a) Pulse wave incidence;(b) Ninghe wave incidence;(c) Kobe wave incidence. The black circle and box represent the boundaries of the basin and canyon,respectively

    图  6   不同无量纲宽度κ下脉冲波(左)、宁河波(中)和Kobe波(右)入射对应的地表x分量的峰值位移PGD放大系数分布

    Figure  6.   Distribution of peak ground displacement amplification coefficient in x component for pulse wave (left),Ninghe wave (middle),and Kobe wave (right) incidence under different dimensionless widths κ

    图  7   脉冲波入射下不同无量纲宽度κ对应的x=0 (左)和y=0 (右)剖面的位移时程及峰值位移PGD分布

    Figure  7.   Displacement time histories and PGD distributions along x=0 (left) and y=0 (right) profiles for pulse wave input under different dimensionless widths κ

    (a) κ=0.1;(b) κ=0.2;(c) κ=0.3;(d) κ=0.4

    图  8   含凹陷盆地不同无量纲宽度κy=0 (a)和x=0 (b)剖面对应的峰值位移PGD放大系数分布

    Figure  8.   Distribution of PGD amplification coefficient along y=0 (a) and x=0 (b) profiles under different dimensionless widths ratio κ in the basin containing canyon

    图  9   耦合四面梯形凹陷地形的半球形盆地模型

    Figure  9.   Hemispherical basin model coupled with four-sided trapezoidal depression topography

    图  10   脉冲波入射下盆地-四面梯形凹陷耦合地形的地表峰值位移PGD分布

    Figure  10.   Distribution of surface PGD for basin models coupled with four-sided trapezoidal depression topography under pulse waves incidence

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  • 收稿日期:  2024-01-21
  • 修回日期:  2024-04-15
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  • 刊出日期:  2025-05-14

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