瑞雷波

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瑞雷波在地基测试中的应用

设瑞雷波的传播速度为Vr ，频率为fr ，则瑞雷波的波长λ r 为
λ
r＝Vr/fr
当速度不变时，频率越低，
测试深度就越大。
瑞雷波法是利用瑞雷波的上述运动学特征和动力学特征来进行工程地质测试的物探方法。
瑞雷波有三个与被测地层有关的主要特征：
在分层介质中，瑞雷波具有频散特性；瑞雷波的波长不同，穿透深度也不同；瑞雷波的传播速度与介质的物理力学性质密切相关。
1 、瑞雷波法作为工程勘察的一种物理勘探技术，可服务于天然地基、人工地基的各个阶段，通过一定量的钻探对比，可以较准确地揭示地质体分布情况。 2 、瑞雷波法作为一种现代原位测试技术，可以服务于地基处理检测的各个阶段，通过一定量的静载对比，可以较准确地提供地基的物理力学参数，并可揭示其处理的深度情况。
2、地基处理效果的检测，包括强夯地基、强夯置换块石墩、碎石桩、搅拌桩检验等，评价其承载力、模量、加固深度、判别砂土液化等。 3、边坡挡墙的检测，包括挡墙的厚度、砂浆的饱满度、填土的密实度、地基承载力的检验等，配合其它方法对挡墙进行验算。

3.1.1道路勘察
（1）由于道路勘察中通常详勘钻孔间距

深圳某填海工程瑞雷波频散曲线之一
深圳某填海工程瑞雷波频散曲线之二
该工程围堰瑞雷波探测断面图
深圳某海堤施工现场
该海堤滑塌的现场
对该堤进行瑞雷波检测的实况
检测的成果之一
桂庙路南堤0+700断面
路堤高程 5.7
10.6(3.6) 11.7(2.5) 9.8(4.4) 9.1(5.1) 8.5(5.7)
用瑞雷波法测试挡墙的工作照
该工程的瑞雷波曲线
测试成果：

瑞雷波法地基检测原理与工程实例

有足够的相位差：
,
保证
2
3
2
随着勘探深度的增大，λR增大， f 越低，△x的距离也相应的增大
一次击发出各种频率成分，同时检波器也接收到富含各种频率成分的信号剩下的工作，即稳态法中靠仪器硬件逐个频点的变更及相应的运算工作，在瞬态法中，主要靠软件来完成。
优点：仪器轻便，施工快速目前主要问题是如何激发出频率较低的信号
2 瑞雷波勘探原理
面波频谱分析方法（SASW）
分析面波的频散曲线建立近地表的面波速度剖面（面波相速度的测量）瑞雷波频散特性:瑞雷波在非均匀介质中的相速度VR 随频率ｆ变化而变化
N
VR 2fi Nx / i i 1
λR=VR/ f Ｈ＝β·λ
求取相速度深度曲线VR－Ｈ
震源
有一定能量、有效波能量强、频带较宽、同点击发重复性好
稳态激振法
两道信号的互相关来求取时间差并计算平均速度勘探深度越大，扫描频率越低；精度要求越高，频点间隔越密。
优点：可以降至2～3Hz的较低频率，从而达到较大的勘探深度并且可以从各频点资料的过程中，总结出一套地层地质解释的经验；缺点：仪器大，施工慢，效率低
瞬态激振法
傅里叶变换及一系列的谱分析，求取相位差得到平均速度值
次生波。这类地震波与界面有关，且主要沿着介质的分界面传播，其能量随着与界面距离的增加迅速衰减，因而被称为面波。在岩土工程中，分界面常指岩土介质各层之间的界面，地表面是一层较为特殊的分界面，其上的介质为空气（密度很小的流体），有时又把它称为自由表面，把自由表面上形成的面波称作表面波
地震波
从各类波在介质中传播的速度来看，在离震源较远的观测点处应该接收到一地震波列，其到达的先后次序是P波，S波，拉夫面波和瑞雷面波

面波

第五章瑞雷面波探测
面波，一般是指在自由界面(地表面）与地下弹性分界面附近传播的波;一般有瑞雷面波（Rayleigh Wave）、勒夫波（Love Wave）、斯通利波。
面波探测主要为瑞雷面波探测，本章主要介绍瑞雷面波的形成与传播原理以及探测方法与探测技术。
一、瑞雷波（也习惯称作地滚波－ ground roll）的探测原理
aZ bZ
i ( K R x t )
故此有： 2ab i ( K R x t ) aZ bZ R u x iAK（e 2 K 2 K 2 e ) e R S 2ab i ( K R x t ) bZ u AK （ ae aZ e )e z R 2 2 2K R K S
对u x、uz 取实部：
2ab aZ bZ R u x AK （e 2 K 2 K 2 e ) sin(t K R x ) R S 2ab bZ u AK （ a e aZ e ) cos(t K R x ) R 2 2 z KR 2K R K S — —（） 13 分析：
1、一般介绍：
瑞雷波是地震勘探中常见的一种面波，常把它作为一种干扰波，在工程地震探测中是非常重要的一种探测方法——面波探测。而在天然地震中该波对建筑物危害极大，是十分有害的波。
瑞雷面波是在近地表传播的波，其能量是几乎全部集中在一个波长内，其传播形式是：波前为一个高度为Z=R的圆柱体，如图所示，在震源作用△t时间内，面波仅作用在厚度为 △r＝VR △t的圆柱层内，圆柱层外层为波前，内层为波尾，体积为： W＝22r △r，r—— 半径。R面波振幅随 r1/2衰减，较体波球面扩散快得多，R面波为面极化振动，且具有频散现象。

1.7瑞雷波法

7.3.3.2 层速度与厚度解释 1．解释步骤 1）频散曲线的绘制
在以土体为勘探对象的工作中，以实测VR 为横坐标，以H = 0.8λR 为纵坐标绘制VR - 0.8λR曲线，这样绘制的频散曲线，纵坐标可近似代表勘探深度
2）定性解释
分析频散曲线的形态和变化规律，初步确定可能的层数以及各层厚度和速度可能的范围
7
瑞雷波法
瑞雷波法勘探实质上是根据瑞雷面波传播的频散特性，利用人工震源激发产生多种频率成分的瑞雷面波，寻找出波速随频率的变化关系，从而最终确定出地表岩土的瑞雷波速度随场点坐标的变化关系，以解决浅层工程地质和地基岩土的地震工程等问题。
均匀半空间瑞利面波的传播特征
1. 瑞利面波的速度
与泊松比有关，约为横波速度的0.91-0.95倍；
7.1 勘探原理瑞雷波沿地面表层传播，表层的厚度约为一个波长，因此，同一波长的瑞雷波的传播特性反映了地质条件在水平方向的变化情况，不同波长的瑞雷波的传播特性反映着不同深度的地质情况。
V Ri x / t i V Ri
2f i x / i
（1.7.1）
已知在图中0.8~1.2m 间有一宽度为1cm 的裂隙，其中充填了砂土。在裂隙处形成“U”字形
7.4.4 地下空洞和掩埋物探测
图1.7.15 是旧煤矿矿井的探测实例，图中（a）是工作布置图，（b）是实测的6个间距的频散曲线
利用70Hz 和23Hz 的速度值分别确定管道的上下边界，利用50Hz 曲线确定管道的水平位置。两处解释推断的管道位置如图1.7.16 所示，已知该处管道埋深0.9m，直径约1m，底坐厚度不详，解释的管道顶部埋深为0.8m，与实际情况误差0.1m。
（ V R f 曲线 → （ λ =VR/f ） → VR R 曲线 → (H= β × λ R) → VR—H 曲线）

瑞雷波法

在这种地层分层结构情况下，时距窗口的设臵和基阶模态数据的提取都比较容易，并可以得到稳定的结果。速度逐层增加的三层大地上的基阶模态面波理论频散曲线如图所示。
（2）底层横波速度最高，中间某层为低速层当大地中某一中间层为低速层时，面波的能量分布不再集中于基阶模态，能量分布于各阶模态中，并随频率变化。在这样的地层结构上，时间空间域各道面波波形随距离增大出现明显的高阶模态面波（高视速度）干涉现象。而频率波数谱中会出现两个或多个很强的高阶模态面波能量峰。离震源的距离增大，长波长（反映更大深度）面波的能量比重增大，时间空间域中高阶面波和基阶面波逐渐分离。
二、稳态面波法
稳态面波法的特点稳态面波法资料处理简单直观，观测结果准确，受其他类型地震波的干扰较小。但对震源的要求较高，需要能产生稳定的、可调控频率的、激发时仅发射单一频率的机械震源。
三、瞬态面波法
瞬态面波法勘探利用瞬态冲击力作震源激发面波，地表在脉冲荷载作用下，产生波动。在离震源稍远处，用传感器记录面波的垂直分量。对记录的面波信号作频谱分析和处理，计算并绘制频散曲线，根据频散曲线特征分析解决地质问题。瞬态面波法的数据采集方式与反射波或折射波法相似，以SWS 型多功能瞬态面波仪为例，数据采集系统如图所示。
分辨基阶或高阶面波。
3）同相轴的斜率改变。引起面波的同相轴的斜率变化的原因有多种，最主要的原因有两种：
a）高阶面波存在。高阶面波在地震记录上的形态，在远距离道上可以明显的分开，而在实际工作中，无法采用很远的偏移距。
一般存在的高阶面波如图所示，面波记录偏移距25米，道间距1米。面波群在34米附近分成两支，同相轴斜率明显不同，其中箭头所指的面波为基阶面波。这表明在时间域中无法利用窗口完全分离高阶面波。这种记录的面波窗口设计应尽量取面波的基阶部分，不可分离的高阶干扰将在频率波数域中进一步处理。

矿井物探-8(瑞雷波地震勘探)

第8章瑞雷波地震勘探
§8.1 瑞雷波的性质
8.1.2 瑞雷波的特征
沿自由界面传播的这种瑞雷面波具有以下特征： 1）它具有一个沿表面传播的与频率无关的速度，这一速度比介质体波
中的横波速度略小。
2）表面上质点的运动轨迹不是线性的而是椭圆形的(它是由纵波P和横波S波沿自由界面传播相互叠加而形成)。
3）这种波的振幅随距界面深度的加大而呈指数下降。
以上是指在均匀、各向同性介质表面的情况。在实际观测中，各种岩石都是成层的非均匀介质。在这样的介质表面，所观测到的瑞雷面波将是频散的；也就是说，瑞雷波的速度将与频率有关，是频率的函数。这样，在成层的非均匀介质的自由表面，所观测到的瑞雷波应是频散的，质点运动呈椭圆形的，其振幅随界面深度加大而呈指数下降的一种面波。
第8章瑞雷波地震勘探
瑞雷波勘探方法是一种以瑞雷面波作为有效波，在几十米深
度范围内探查地质体的一种物探方法。作为地震勘探中的一个分
支，瑞雷波勘探是自20世纪80年代发展起来的一种新的浅层勘探手段。它是基于不同振动频率的瑞雷波沿深度方向衰减的差异，
通过测量不同频率成分(反映不同深度)瑞雷波的传播速度，来探
§8.3 瑞雷波勘探的应用
8.3.1 地层界面异常特征
实测“之”字型
VR H
曲线
实测“之”字型VR—H 曲线
第8章瑞雷波地震勘探
§8.3 瑞雷波勘探的应用
8.3.2 洞穴界面的异常特征
洞穴曲线的中断
第8章瑞雷波地震勘探
§8.3 瑞雷波勘探的应用
8.3.2 洞穴界面的异常特征
洞穴曲线的错断
第8章瑞雷波地震勘探
§8.2 瑞雷波勘探的基本原理
瑞雷波勘探方法的实质：根据不同振动频率的瑞雷波沿深度方向衰减的差异，通过测量不同频率成分(反映不同深度)瑞

瑞雷波勘探实验报告(3篇)

第1篇一、实验目的本次实验旨在通过瑞雷波勘探技术，对地下介质进行探测，了解其结构和性质。

瑞雷波勘探技术具有探测深度大、分辨率高、成本低等优点，广泛应用于地质勘探、岩土工程等领域。

通过本次实验，掌握瑞雷波勘探的基本原理、操作方法以及数据处理技术，为实际工程应用提供理论依据。

二、实验原理瑞雷波（Rayleigh wave）是一种沿介质表面传播的剪切波，其波速较低，衰减较慢，能够有效地穿透较深的地层。

瑞雷波勘探技术基于瑞雷波在地下介质中传播的特性，通过测量瑞雷波的速度、振幅等参数，分析地下介质的结构和性质。

三、实验设备1. 地震勘探仪：用于采集地震波数据。

2. 地震检波器：用于接收瑞雷波信号。

3. 数据采集系统：用于记录地震波数据。

4. 地震数据处理软件：用于处理和分析地震波数据。

四、实验步骤1. 实验场地选择：选择适合进行瑞雷波勘探的场地，确保场地平整、开阔，无大型障碍物。

2. 检波器布设：按照设计要求，将地震检波器按照一定的间距布设在勘探区域。

3. 数据采集：启动地震勘探仪，进行地震波数据采集。

采集过程中，注意调整仪器参数，确保数据质量。

4. 数据处理：将采集到的地震波数据导入地震数据处理软件，进行预处理、滤波、提取瑞雷波等处理步骤。

5. 结果分析：对处理后的瑞雷波数据进行时距曲线分析、层析成像等，分析地下介质的结构和性质。

五、实验结果与分析1. 时距曲线分析：通过对瑞雷波数据进行时距曲线分析，可以确定瑞雷波在地下介质中的传播速度。

实验结果显示，瑞雷波在勘探区域内的传播速度为X km/s。

2. 层析成像：通过对瑞雷波数据进行层析成像，可以分析地下介质的结构。

实验结果显示，勘探区域内的地下介质可以分为多个层，各层的厚度和速度如下：- 第1层：厚度为Y m，速度为Z km/s；- 第2层：厚度为W m，速度为V km/s；- 第3层：厚度为U m，速度为T km/s。

3. 地下介质性质分析：根据瑞雷波勘探结果，可以分析地下介质的性质。

瑞雷波基本原理范文

瑞雷波基本原理范文瑞雷波（Rayleigh wave）是一种地震波，它主要以滚动波形式传播在地球表面上。

它得名于英国物理学家约翰·威廉·斯特劳德·雷莱（John William Strutt Rayleigh），他于1885年首次描述了这种波动现象。

瑞雷波是地震波中最慢的一种，但也是最具破坏性的一种。

瑞雷波的形成是由地震事件引发的，当地震发生时，震源产生的能量会以压缩波和剪切波的形式向外传播。

压缩波和剪切波沿着地球内部传播，但当它们在地表遇到边界时，产生了瑞雷波。

瑞雷波的基本原理可以通过波动方程来解释。

波动方程描述了波动传播的行为，它可以写成以下形式：∇²u-1/v²∂²u/∂t²=0其中，∇²u表示波动的传播方向，u表示波动的位移，v表示波速，∂²u/∂t²表示波动的加速度。

这个方程表明波动的位移和加速度与波速有关。

对于瑞雷波，它是一种沿地表表面传播的表面波。

它的波速较慢，大约在地震波的S波和面波之间，这使得瑞雷波的振幅比较大，具有较高的破坏性。

瑞雷波的波动方向与波动传播方向相同，呈现滚动的形态，这也是它被称为滚动波的原因。

当瑞雷波传播时，它会产生地球表面上的垂直和水平位移，导致地表上的振动和地质变形。

这些振动和变形可能对建筑物、桥梁和其他基础设施造成损坏。

此外，瑞雷波的振动还可以导致土壤液化现象的发生，这进一步增加了地震灾害的严重程度。

瑞雷波的传播速度取决于地表的密度和刚度。

当瑞雷波遇到地层变化的边界时，例如岩石和土壤之间的过渡区域，它会发生折射和反射。

这些折射和反射现象可以用来研究地球的内部结构和地质特征。

总之，瑞雷波是一种重要的地震波，它以滚动的形态沿地表传播。

瑞雷波的形成是由地震事件引发的，其传播速度取决于地表的密度和刚度。

瑞雷波的振动和变形对建筑物和基础设施具有较高的破坏性，对地球内部结构和地质特征的研究也起到了重要的作用。

第三章第二节瑞雷面波法

三.关于瑞雷面波勘探的历史
之后，时福荣提出用互相关法计算稳态瑞利波的传播速度，以克服最初采用的同相痊时间法抗干扰能力差的不足。朱裕林将GR810全自动地下勘探机用于建筑地基勘察、软土地基加固效果评功价和人工洞穴及岩溶探测也取得了一定的效果。 1990年，陈云敏、吴世明等用瞬态法测量机场跑道地基的剪切波速，并提出用相干函数法判别信号有效性，用互谱法求取频散曲线。这是我国瞬态瑞利面波勘探的开端。
（3）资料处理其主要步骤为：时－空域面波提取面波信号的二维富氏变换绘制频率－波数域振幅谱等值线图提取面波频散曲线数据绘制半波长频散曲线
时－空域面波提取
通常，面波记录有以下几种情况： a. 同相轴清晰，相位少(图3-58) b. 同相轴清晰，相位多(图3-59 ) c. 同相轴的斜率改变（下页）
图3-67基阶面波频散曲线图3-68高阶面波频散曲线
§2－3面波频散曲线的反演解释
2.3.1几种典型的频散曲线 1、地层结构类型及其频散曲线特征（1）横波速度逐层增高（2）底层横波速度最高，中间某层为低速层
图3-59 同相轴图3-58 提取面清晰、相位多波窗口（虚线框）的面波记录
c. 同相轴的斜率改变
引起面波同相轴改变的原因主要有两种：
（1）有高阶面波存在（图3-60）（2）地层中有局部地质体或岩性突变面存在（3-61）
图3-60 高阶和基阶面波共存的情况图3-61直立界面存在时的面波记录
（8）瑞雷波对自由表面的垂直裂缝非常敏感，因此目前还没有比它更好的混凝土表面裂缝和爆破松动层厚度检测方法。
二. 瑞雷波勘探主要解决的浅层地质问题
工程勘察：用于划分第四系地层，确定地层的持力层，划分地层中的软弱夹层；

第七讲(瑞雷波)

面波主要有两种类型：瑞雷面波和拉夫面波。瑞雷面波沿界面传播时，在垂直于界面的入射面内各介质质点在其平衡位置附近的运动即有平行于波传播方向的分量，也有垂直于界面的分量，因而质点合成运动的轨迹呈逆椭圆；拉夫面波传播时，介质质点的运动方向垂直于波的传播方向且平行于界面。目前在岩土工程测试中以应用瑞雷面波勘探为主。
一、瑞雷波与瑞雷波勘探
研究层状地层面波的频散特征，可以求得地层不同深度范围内的弹性参数，这也就是面波测深方法依据的基本原理。
利用人工激发的瑞雷波可以解决如下几方面的具体浅层地质问题。
(1) 地层划分：通过对瑞雷波频散曲线进行定性及定量解释，得到各地层的厚度及弹性波的传播速度。
(2) 地基加固处理效果评价：通过实测地基加固前后的波速差异得到处理后的地基较处理前的物理力学性质的改善程度。
二、瑞雷波勘探的基本原理
VR—f曲线或VR-λR曲线的变化规律与地下介质条件存在着内在联系，通过对频散曲线进行反演解释，可得到地下某一深度范围内的地质构造情况和不同深度的瑞雷波传播速度 VR值，另一方面，VR值的大小与介质的物理特性有关，据此可以对岩土的物理性质作出评价。
瑞雷波法根据其激发的震源的不同，可分为稳态法和瞬态法两种。
(3) 岩土的物理力学参数原位测试：通过对实测资料的反演解释，可以得到岩、土层的S波速度、P波速度及密度等参数。
一、瑞雷波与瑞雷波勘探
(4) 公路、机场跑道质量无损检测：利用人工激发的高频瑞雷波，可以确定路面的抗折、抗压强度及路基的载荷能力，以及各结构层厚度。该方法用于机场跑道及高等公路的另一项意义是实现质量随年代变化的连续监控。
三、瑞雷波勘探的资料采集
3.2 瞬态激振法
四、瑞雷波勘探资料的处理与解释

瑞雷波Rayleigh Wave

Chapter 3Rayleigh Waves3.1OverviewWaves that propagate in a medium can be roughly divided into two main categories: body waves and surface waves. Surface waves are generated only in presence of a free boundary and they can be essentially of two types: Love waves and Rayleigh waves. Love waves can exist only in presence of a soft superficial layer over a stiffer halfspace and they are produced by energy trapping in the softer layer for multiple reflections. Rayleigh waves are always generated when a free surface exists in a continuous body.John Strutt Lord of Rayleigh firstly introduced them as solution of the free vibration problem for an elastic halfspace in 1885 (“On waves propagated along the plane surface of an elastic solid”). In the last sentences of the above paper, he anticipated the importance that such kind of wave could have in earthquake tremor transmission. Indeed the introduction of surface waves was preceded by some seismic observations that couldn’t be explained using only body wave theory, which was well known at that time. First of all the nature of the major tremor was not clear, because the first arrivals were a couple of minor tremors corresponding to P and S waves respectively. The greater amount of energy associated to this late tremor if compared to that of body wave was a strong evidence of less attenuation passing through the same medium and this could be explained only assuming that this further kind of wave was essentially confined to the surface (Graff 1975).Another main contribution regarding the forced vibrations was successively28Multistation methods for geotechnical characterization using surface waves S.Foti given by Horace Lamb (“On the propagation of tremors over the surface of an elastic solid”, 1904), who solved the problem of a point harmonic force acting on the ground surface. He also proposed the solution for the case of a general pulse,by using the Fourier synthesis concept.Usefulness of surface waves for characterization problems has been soon clear due to some important features and especially to the possibility of detecting them from the surface of a solid, with strong implications on non-invasive techniques development (Viktorov 1967).In this chapter an overview will be given about specific properties of Rayleigh waves, with special aim at soil characterization purposes, leaving more comprehensive treatment to specific references.Also some numerical simulations and some experimental data will be presented in the view of clarifying some important aspects related to Rayleigh waves propagation and to its modelling.3.2 Homogeneous halfspace3.2.1 Linear elastic mediumIf the free boundary condition is imposed on the general equations for wave propagation in a linear elastic homogeneous medium, the solution for surface Rayleigh wave can be deduced from the P-SV components of the wave. It is important to note that a SH wave propagating on a free boundary can exist only under restrictive layering condition (and in that case it is usually called Love wave)and hence it cannot exist for the homogeneous halfspace.The Navier’s equations for dynamical equilibrium in vector formulation can be expressed as:u f u u !!44((*'+5+&55+2)((3.1)where u is the particle displacement vector, 4 the medium density, * and ( the Lamè’s constants and f the body forces. Neglecting the latter contribution, the free vibration problem is addressed.The solution can be searched using Helmholtz decomposition and assuming an exponential form (Richart et Al. 1970). The motivation for assuming the exponential form is that by definition a surface wave must decay quickly with depth.Chapter 3Rayleigh Waves 29Imposing the boundary conditions of null stress at the free surface:0ó'(3.2)the surface wave solution can be found. In particular for the case of plane strain,discarding the solutions that give infinite amplitude at infinite depth, a solution (Rayleigh wave) can be found only if the following characteristic equation is satisfied by the velocity of propagation of the surface wave:0)1(16)1624(822246'-&+&-+-##K K K (3.3)where K and G are the following ratios between velocities of longitudinal (P),distortional (S) and Rayleigh (R) waves:S RV V K '(3.4)P SV V '#(3.5)This equation is a cubic on 2K and its roots are a function of Poisson Ratio ,since, as shown in Paragraph 2.3.1, )1(2212,,#--'. It can be shown (Viktorov 1967) that for real media (5.00P P :) only one real and acceptable (i.e. in the range 0 to 1) solution exists. The relationship between velocities of propagation of the different waves as a function of Poisson Ratio is reported in Figure 3.1.An approximate solution of the characteristic equation (3.3) has been suggest by Viktorov (1967):::++'112.187.0K (3.6)From Figure 3.1, it is evident that the difference between shear wave velocity and Rayleigh wave velocity is very limited, being the latter slightly smaller than the former. In particular the exact range of variation is given by:96.087.0P P S R V V (3.7)Note that there is no dependence of Rayleigh wave velocity on frequency, i.e.a homogenous linear elastic medium is characterised by a unique value of Rayleigh wave velocity.30Multistation methods for geotechnical characterization using surface waves S.FotiFigure 3.1 Relation between Poisson’s ratio and velocity of propagation of compression (P), shear (S) and Rayleigh (R) waves in a linear elastic homogeneous halfspace (from Richart 1962)It is important to remark that since the solution has been obtained using Helmholtz decomposition, the surface wave can be seen as the superposition of two separate components: one longitudinal and the other transverse. They propagate along the surface with the same velocity but they have different exponential laws of attenuation with depth. Obviously the wave fields are such that the superposition of the two gives a null total stress on the boundary of the halfspace.Figure 3.2 Particle motion on the surface during the passage of a Rayleigh waves in an elastic homogeneous halfspaceChapter 3Rayleigh Waves31 As far as the displacement fields are concerned, they can be computed introducing the solution of the characteristic equation into the respective formulations. The resulting horizontal and vertical components of motion are out of phase of exactly 90° one with the other, with the vertical component bigger in amplitude than the horizontal one, hence the resulting particle motion is an ellipse. On the ground surface the ellipse is retrograde (e.g. counter-clockwise if the motion is propagating from left to right as shown in Figure 3.2), but going into depth the ellipse is reversed at a depth equal to about 1/2@ of the wavelength.Another important remark is that being the decrease with depth exponential, the particle motion amplitude becomes rapidly negligible with depth. For this reason it can be assessed that the wave propagation affects a confined superficial zone (see Figure 3.3), hence it is not influenced by mechanical characteristics of layers deeper than about a wavelength.Figure 3.3 Amplitude ratio vs. dimensionless depth for Rayleigh wave in a homogenous halfspace (from Richart et Al. 1970)32Multistation methods for geotechnical characterization using surface waves S.FotiThe solution for a line or point source acting on the ground surface can be found in the Lamb’s paper that has been cited above. In this regard it is important to remark that, due to the axial-symmetry of the problem, the disturbance spreads away in the form of an annular wave field. The reduced geometrical attenuation of surface waves can be directly associated to this property.Also Lord Rayleigh, although he didn’t solve the case of a point source, had a similar intuition about surface waves: "Diverging in two dimensions only, they must acquire at a great distance from the source a continually increasing preponderance" (concluding remarks of the above cited paper).The geometric spreading factor, i.e. the factor according to which the waves attenuate as they go away from the source, can be estimate with the following physical considerations about the wave fronts.Considering a buried point source in an infinite medium, the released energy spreads over a spherical surface and hence its attenuation is proportional to the square of distance from the source. Since the energy is proportional to the square of displacements, the latter ones attenuate proportionally to distance. Analogously since Rayleigh waves, that are generated by a point source acting on the ground surface, propagate with a cylindrical wave-front, their energy attenuation must be proportional to distance and displacement attenuation to the square root of distance.Concerning the geometrical attenuation of longitudinal and shear waves along the free surface, it is not possible an analogy to previous cases, but it can be shown that because of leaking of energy into the free space the displacement attenuation goes with the square of distance (Richart et al. 1970). In summary for a linear elastic halfspace a simple power law of the following type can express the radiation damping consequences on waves amplitude:Q Q R Q Q S T 'waves Rayleigh for 21solid the into waves body for 1surface the on waves shear and al longitudin for 2with 1n r n(3.8)where r is the distance from the point source.Back to Lamb’s work, the displacements at great distance r from a vertical harmonic point force t i z e F 3& can be expressed as:Chapter 3Rayleigh Waves 33A B C D E F --&&'4@3kr t i z z z e r b F u (3.9)A B C D E F +-&&'4@3kr t i r z r e r b F u (3.10)where z u and r u are the vertical and radial displacements, z b and r b are functions of the mechanical parameters of the medium and k is the wavenumber that is defined by the following relation:R V k 3'(3.11)The two displacements are out of phase of 90° and hence the particles describe an elliptical path, as it was predicted by the solution of the homogeneous problem related to free vibration.Figure 3.4 Complete wavefield predicted by Lamb (1904) for a surface point source on an elastic halfspace (a) horizontal radial motion; (b) vertical motion; (c) particle path of Rayleigh waves.34Multistation methods for geotechnical characterization using surface waves S.FotiFigure 3.5 Harmonic vertical point source acting on the surface of a homogenous,isotropic, linear elastic halfspace: (a) Complete displacements wave field; (b) Partition of energy between different types of waves (from Woods 1968).The position of a given characteristic point of the wave (such for example a peak or a trough) is described by constant values of the phase:/0const kr t '-3(3.12)thus with some manipulation and recalling Equation (3.11) it is clear the reason why R V is often denoted as Rayleigh wave phase velocity.Considering a circular footing vibrating harmonically at low frequency over a homogeneous isotropic linear elastic halfspace, Miller and Pursey (1955) showed that 2/3 of the total input energy goes into Rayleigh waves and the left fraction isChapter 3Rayleigh Waves 35divided between body waves (see Figure 3.5b). Adding this information to the above considerations about geometrical attenuation, the conclusion is that at a certain distance from the source the wavefield is essentially dominated by the Rayleigh waves. This is essentially the same conclusion reached by Lamb (1904),who divided the wave contributions in two minor tremors (P and S) and a major tremor (R) (Figure 3.4).All the important features of the complete wave-field generated by a low frequency harmonic point source are summarised in Figure 3.5.3.2.2 Linear viscoelastic mediumAs seen in Chapter 2, also at very low strain levels soil behaviour can’t be considered elastic, indeed cycles of loading and unloading show energy dissipation.Recalling the actual nature of soil, it is intuitive that dissipation is essentially due to the friction between particles and the motion of the pore fluid, and hence it occurs also for very small strains, when the soil is far from the plasticity conditions.To account for dissipation, an equivalent linear viscoelastic model can be assumed at small strains. In this regard the correspondence principle can be used to extend the result obtained in the case of a linear elastic medium. According to it,the velocity of propagation of seismic waves can be substituted by a complex valued velocity that accounts for the attenuation of such waves. Adopting this principle Viktorov (1967) showed that the attenuation of surface waves in a homogeneous linear viscoelastic medium is governed primarily by the shear wave attenuation factor. In particular he found that the Rayleigh wave attenuation R G could be expressed as a linear combination of the longitudinal wave attenuation P G and the shear wave attenuation S G , according to the expression:/0S P R A A G G G &-+&'1(3.13)where is A a quantity depending only on the Poisson Ratio. Since A is always smaller than 5.0, the shear wave attenuation is prevalent in determining the Rayleigh wave attenuation. Moreover for Poisson Ratio values higher than 0.2, A is less than 2.0 (see Figure 3.6).The wave field generated by a vertical harmonic point source acting on the ground surface can be obtained applying the correspondence principle to the Lamb’s solution. For example substituting a complex wavenumber in (3.9) it is possible to evaluate the vertical displacements as:36Multistation methods for geotechnical characterization using surface waves S.FotiA B C D E F --&&'4**@3r k t i zz z e r b F u (3.14)where obviously also the quantity *zb is changed since it is dependent on the mechanical parameters, that now are those of the viscoelastic medium.The complex wavenumber is defined as:/03G 33G i V i k k R -'-')(*(3.15)where /03G is the material attenuation of surface waves and R V is now frequency dependent because of material dispersion. With some manipulations of Equation (3.14) the phase and the amplitude of the displacements can be separated as follows:A B C D E F ---&&&'4*@3G kr t i r zz z e e r b F u (3.16)and in this formulation the exponential effects due to the material attenuation is evident. Note also that the quantity re rG - represents the combined effect of material and geometrical attenuation as the wave spreads out from the source.Figure 3.6 Body waves attenuation participation factors vs. Poisson ratio (Viktorov 1967)Chapter 3Rayleigh Waves 373.3 Vertically heterogeneous media3.3.1 Linear elastic mediumFor heterogeneous and anisotropic media the mathematical formulation of Rayleigh waves becomes very complex and there can be cases of anisotropic media where they do not exist at all. However in the case of transverse isotropic medium with the free surface parallel to the isotropy plane (common situation for soil systems) Rayleigh waves exist and the analogous of the Lamb solution can be found (Butchwald 1961).As far as heterogeneity is concerned, when the mechanical properties of the medium are assumed to be dependent only on depth z , the formal expression of the Navier’s equations, neglecting body force, is:u u u e .u e u .u !!4(*((*'A B C D EF >>&+757+5+5+55+z dz d dz d z z 2)(2(3.17)where z e is the base vector for the direction perpendicular to the free surface.Lai (1998) has showed that introducing in (3.17) the condition of plane strain (that causes no loss of generality) and assuming the classical exponential form for the solution, the final solution is given by a linear differential eigenvalue problem.Assuming the usual boundary condition of null stress at the surface, the eigenvalues )(3k can be found as the values that makes equal to zero the equivalent of the Rayleigh characteristic equation, that in this case can only be written in implicit form (Lai 1998):/0/0/0890,,,,R '34(*j k z z z F (3.18)It is noteworthy to remark some important features of this equation. First of all the dependence on the frequency means that also the relative solution will be frequency dependant and hence the resulting wave field is dispersive, meaning that its phase velocity will be a function of frequency. This dispersion is related to the geometrical variations of Lamé’s parameters and density with depth and hence it is often called geometric dispersion. The equation (3.18) itself is often named dispersion equation.For a given frequency the solutions of the dispersion equation are several while in the case of the homogeneous halfspace there was only one admissible solution of the characteristic equation. This means that many modes of propagation of the Rayleigh wave exist and the solution of the forced vibration case must account for them with a process of mode superposition.38Multistation methods for geotechnical characterization using surface waves S.Foti Substituting each one of the eigenvalues (wavenumbers) in the eigenproblem formulation, four eigenfunctions can be retrieved. They correspond to the two displacements and the two stresses associated to that particular wave propagation mode.The existence of several mode of propagation can be explained physically through the concept of constructive interference (Lai 1998).3.3.1.1Mathematical formulations for layered mediaIn the formulation of the dispersion equation (3.18) there was no explicit reference to any law of variation of the mechanical properties with depth. The problem can be solved once a law of variation is specified. In general it is not possible to solve the problem analytically and a numerical solution is needed.In this respect one classical assumption is that of a stratified medium with homogeneous linear elastic layers. This modelling procedure, that has been established for seismological purposes, assume a stack of layers, each one characterised by its thickness, elastic parameters and density (Figure 3.7). Obviously a price is paid in terms of generality but the eigenvalue problem can be established using a matrix formulation for a single layer and then building the global matrix, which governs the problem.Figure 3.7 Stack of homogeneous isotropic elastic layers Many version of this general procedure, also known as propagator-matrix methods (Kennett 1983), have been formulated, differing in the principles on which the single layer matrix formulation is based and consequently in the assembling process.Chapter 3Rayleigh Waves 39The oldest and probably the most famous method is the Transfer-Matrix method, originally proposed by Thomson (1950) and successively modified by Haskell (1953).The Stiffness-Matrix method proposed by Kausel and Roesset (1981) is essentially a reformulation of the Transfer-Matrix method, having the advantage of a simplified procedure for the assembly of the global matrix, according to the classical scheme of structural analysis.The third possibility is given by the construction of reflection and transmission matrices, which account for the partition of energy as the wave is propagating. The wave field is then given by the constructive interference of waves travelling from a layer to another (Kennett 1974, 1979; Kerry 1981).Once the dispersion equation has been constructed using one of the above methods, the successive and very computationally intensive step is the use of a root searching technique to obtain the eigenvalues of the problem. Great attention must be paid in this process because of the behaviour of the dispersion function. Indeed some solution searching techniques can easily fail due to the strong oscillations of the dispersion function especially at high frequencies (Hisada 1994, 1995). In this respect since these methods are borrowed from seismology, the frequencies involved in the soil characterization methods have to be considered high.Recalling the starting point of the above considerations (Equation (3.17)) the eigenvalues, and hence the correspondent eigenfunctions, that have been computed are the solution of the homogeneous problem, i.e. in absence of an external source.The obtained modes constitute the solution of the free Rayleigh oscillations of the considered medium.If a source exists, the correspondent inhomogeneous problem must be solved.In this case a term that represents the external force is included in Equation (3.17).The solution comes from a mode superposition process. Sometimes this problem is addressed as the three dimensional solution because waves spread out from the source following a 3D axial-symmetric path, whereas the free modes represent plane waves and hence are addressed as the solution of the 2D problem.For our purposes it is relevant the case of a point source acting on the ground surface. Lai (1998) has given an interesting solution for the case of a harmonic point load t i z e F 3&. According to its formulation, if body wave components are neglected (i.e. in far field conditions) the displacements induced by the load are given by:89),,(),,(),,(3U 3V V V 33z r t i z e z r F z r u -&&&'G (3.19)where V stands for the generic component either vertical or radial, ),,(3V z r G is40Multistation methods for geotechnical characterization using surface waves S.Foti the Rayleigh geometrical spreading function, that models the geometric attenuation in layered medium, and ),,(3U V z r is a composite phase function.An interesting comparison can be made between Equation (3.19) and its equivalent for a homogeneous halfspace (Eq. (3.9) and (3.10)), in which case the mode of propagation was only one. First of all the geometric attenuation for the homogeneous halfspace is much simpler. On the other side phase velocity is coincident with that of the only one mode of propagation, while in the case of the layered medium also the phase velocity comes from mode superposition and for this reason is often indicated as effective or apparent phase velocity.In analogy to Equation (3.12), the position of a given characteristic point of the harmonic wave (such for example a peak or a trough) is described by constant values of the phase:/0constz r t '-),,(3U 3V (3.20)hence differentiating with respect to time, under the hypothesis that the function ),,(3U V z r be smooth enough, it is possible to obtain the effective phase velocity RV ˆ(Lai 1998):r z r z r V R >>'),,(),,(ˆ3U 33V (3.21)It is very important to note that since the effective Rayleigh velocity is a function not only of frequency but also of the distance from the source, it is a local quantity (see Lai 1998 for a comprehensive discussion on this topic).3.3.1.2 Physical remarksSome physical aspects are implicitly included in the mathematical formulations of vertically heterogeneous media described above. It can be useful trying to describe them in a more phenomenological way.First of all the geometrical dispersion, i.e. the dependence of Rayleigh phase velocity on frequency can be easily explained recalling the characteristics of shallowness of this waves. As exposed in Paragraph 3.2.1 for a homogeneous linear elastic halfspace the exponential decay of particle motion with depth is such that the portion of the medium that is affected by the wave propagation is equal to about one wavelength. Since the wavelength R * is related to the frequency f by the following relation:Chapter 3Rayleigh Waves 41f V RR '*(3.22)it is clear that low frequency waves will penetrate more into the ground surface.Hence in the case of a vertically heterogeneous medium, surface waves at different frequency will involve in their propagation different layers and consequently the phase velocity will be related to a combination of their mechanical properties.Consequently the surface waves velocity will be a function of frequency. The above concept is summarised in Figure 3.8, where the vertical displacements wave field in depth at two different frequencies is presented for a layered medium.Figure 3.8 Geometrical dispersion in layered media (from Rix 1988)It is important to remark that the shape of the dispersion curve (Rayleigh phase velocity vs. frequency or wavelength) is strongly related to the variation of stiffness with depth. Usually a distinction is made between a layered system for which the stiffness is monotonically increasing with depth and another one in which there is the presence of stiffer layers over softer ones. The first case is indicated as normally dispersive profile, the latter one as inversely dispersive profile. An example is presented in Figure 3.9, where the shape of the dispersion curve is presented in the phase velocity-wavelength plane. This representation is often used since for the aforementioned reasons it gives a clear picture of the variation of stiffness with depth.Obviously in real media the alternation of stiff and soft layers can be much42Multistation methods for geotechnical characterization using surface waves S.Foti more complex if compared to the above cases, still Figure 3.8 gives an idea of the relation existing between the stiffness profile and the dispersion curve.Figure 3.9 Examples of non dispersive (homogeneous halfspace), normally dispersive and inversely dispersive profiles (from Rix 1988)Chapter 3Rayleigh Waves43 Another important feature of surface waves propagation in layered media is the existence of several modes of propagation. This can be explained physically by the presence of constructive interference between curved ray-paths for continuously varying heterogeneous media and between transmitted and reflected waves for layered media (Achenbach 1984). The presence of several modes of propagation makes the forced case very complex since the active energy that the source introduces into the medium is propagating away with a superposition of the different modes. It is not possible to say a priori which mode dominates and in general there is the transition from the predominance of a mode to that of another one for different frequencies (Gukunski e Woods 1992). For these reasons the case of an impulsive source is particularly complex. Nevertheless usually, for normally dispersive profiles and in absence of strong stiffness jumps, the fundamental mode of propagation dominates the wavefield. In such cases the effective phase velocity practically coincides with the phase velocity of the fundamental mode. Hence resolving only the eigenvalue problem, with no need to account for mode superposition is sufficient for the construction of a good approximation of the effective dispersion curve.Moreover also geometrical attenuation becomes very complex in the case of layered media and a geometric spreading function need to be introduced (see Equation (3.19)). Regarding this aspect (that is very important when also displacements amplitudes are of interest), if the above conditions for the predominance of the first mode of propagation are satisfied, further complications1for can be avoided by taking the usual factor of homogeneous halfspace r geometrical attenuation.Another important note can be made about the path described by particle motion on the ground surface. For the homogeneous halfspace vertical and horizontal components are 90° out of phase in such a way that as the wave is propagating the particle motion describes a retrograde ellipse. In the case of a layered medium the path is always elliptical but not necessarily retrograde. Moreover in presence of dissipative phenomena (that are likely to occur in soils) the phase difference between vertical and horizontal displacements can be different from 90° and the axes of the ellipse are not necessarily vertical and horizontal respectively (Haskell 1953).An important consequence of surface wave dispersive behaviour in layered media is the existence of a group velocity. Up to now, when talking about velocity of propagation of surface waves, we used the term phase velocity, that is the velocity of a wave front (locus of constant phase points), such as a peak or a trough. For a dispersive medium, this is not the same as the velocity of a pulse of energy, indeed the latter can be seen (Fourier analysis) as composed of several。

物探方法-瞬态瑞雷波法

平均波速为
v Ri 2f i N x / ij
j 1 N
(6.3.8)
在同一测点对一系列频率fi求取相应的vRi 值，就可以得到一条vR-f典线，即频散曲线。
• 根据 (6.3.6)式，可将vR-f曲线转换为vR-R曲线，vR-R曲线反映出该测点介质深上的变化规律。沿测线不同点的vR-R曲线则反映了介质沿剖面方向上的变化特征
瞬态面波法的震源可以采用锤击、落重、爆炸等方式。激振力较小时脉冲面波的主频率较高。检波器安臵在地面作为拾取介质振动的传感器。面波勘探所用检波器频率范围很宽，可以从数赫兹到数千赫兹。。
• 目前国内外生产的检波器类型较多，面波测试时，可从固有频率为4.5、8、 10、15、28等检波器中选择使用，瞬态面波一般使用固有频率较低的检波器
(三)在工程、环境检测与监测中的应用深圳市中兴花园的场地为山沟填土整平形成，测试区填埋土深大约15m。为检测夯实效果，深圳市地质局先后做了瑞雷波法、钻探标贯试验和33m2 大压板静载试验。
瑞雷波测试采用道间距2m，偏移距4m,32kg 重锤，1.5m高自由下落激发，记录波形经计算机处理后获得如图 6.3-4所示频散曲线。
* 1
(6.3.10)
其中的F1*(f)和F2*(f)为F1(f)和 F2(f)的复共扼谱。f1(t)和f2(t)的互功率谱为
S 21 ( f ) F2 ( f ) F ( f ) F1 ( f ) F2 F1 ( f ) F2 ( f ) e
* i ( f ) * 1
(6.3.11)
n层的平均速度及相应的界面深度为vR,n 和Hn, 并且平均速度是随深度递增的，则n-1层至n层之间的面波层速度vRi,n 的计算公式为

透射波与瑞雷波勘查

03
透射波与瑞雷波的勘查方法
透射波勘查方法
地震波激发
通过人工或天然方式激发地震波，使其在地下介质中传播。
接收地震波
在地表或井中设置接收器，接收地震波在地下的传播信号。
数据处理与分析
对采集的地震波数据进行处理与分析，提取有关地下介质的信息。
瑞雷波勘查方法
地震波激发
通过人工或天然方式激发地震波，使其在地下介质中传播。
抗干扰能力
透射波勘查具有较强的抗干扰能力，适用于复杂地质条件下的勘探。
适用范围
透射波勘查广泛应用于石油、天然气、矿产等资源勘探领域，而瑞雷波勘查在工程地质勘察、地质灾害调查等领域应用较多。
04
透射波与瑞雷波的勘查实例
透射波勘查实例
实例一
某高层建筑地下车库的透射波勘查
实例二
某桥梁基础的透射波勘查
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透射波与瑞雷波的应用前景展望
资源勘探
透射波与瑞雷波在石油、天然气、矿产等资源勘探领域具有广阔的应用前景，能够提供更准确的地质构造和资源分布信息。
工程检测
在土木工程、交通、水利等领域，透射波与瑞雷波可用于结构健康监测、地质灾害预警等方面，保障工程安全。
环境监测
透射波与瑞雷波在环境监测领域的应用将逐渐增多，如土壤污染、地下水污染等方面的监测，为环境保护提供技术支持。
透射波与瑞雷波勘查
目录
• 透射波与瑞雷波概述 • 透射波与瑞雷波的勘查原理 • 透射波与瑞雷波的勘查方法 • 透射波与瑞雷波的勘查实例 • 透射波与瑞雷波的未来发展
01
透射波与瑞雷波概述
定义与特性
定义
透射波和瑞雷波是地球物理勘探中常用的两种波型，它们在地球介质中传播时表现出不同的特性。透射波是指波在地下介质中传播时，通过不同介质分界面发生折射或反射而形成的波；瑞雷波则是在地下介质中传播时，由于介质的剪切振动而产生的波动。

第七讲(瑞雷波)

4.1 稳态法
四、瑞雷波勘探资料的处理与解释
4.1 稳态法
四、瑞雷波勘探资料的处理与解释
4.1 稳态法
四、瑞雷波勘探资料的处理与解释
4.1 稳态法
四、瑞雷波勘探资料的处理与解释
4.1 稳态法
四、瑞雷波勘探资料的处理与解释
4.1 稳态法
四、瑞雷波勘探资料的处理与解释
4.2 瞬态法
前期处理由于瞬态法勘探中波场的复杂性，即除了有效的不
瑞雷波勘探的基本原理及其在工程与环境物探中的应用
中国矿业大学
瑞雷波勘探是近年发展起来的浅层地震勘探新方法。传统的地震勘探方法以激发、测量纵波为主，面波则属于干扰波。事实上，面波传播的运动学、动力学特征同样包含着地下介质特性的丰富信息。
在地层介质中，震源处的振动（扰动）以地震波的形式传播并引起介质质点在其平衡位置附近运动。按照介质质点运动的特点和波的传播规律，地震波可分为两类：即体波和面波。纵波（P波，压缩波）和横波（S波，剪切波）统称为体波，它们在地球介质内独立传播，遇到界面时会发生反射和透射。
同频率成分的瑞雷波外，还包含规则干扰(如直达波、折射波和浅层反射波等)和不规则干扰。因此，前期波场分离(滤波处理)是非常必要的。它将直接影响到解释的精度。常采用的方法主要有初至波切除、一维和二维滤波等。此外为计算速度VR—f关系曲线，还需对记录进行频谱分析或相关谱分析等处理。常见处理流程见图。
二、瑞雷波勘探的基本原理
瑞雷波沿地面表层传播，表层的厚度约为一个波长，因此，同一波长的瑞雷波的传播特性反映了地质条件在水平方向的变化情况，不同波长的瑞雷波的传播特性反映着不同深度的地质情况。在地面上沿波的传播方向，以一定的道间距△x设置N+1个检波器，就可以检测到瑞雷波在N △x长度范围内的波场，设瑞雷波的频率为fi，相邻检波器记录的瑞雷波的时间差为△ t或相位差为△Φ，则相邻道△x长度内瑞雷波的传播速度为：

1.7瑞雷波法

7 瑞雷波法瑞雷波法勘探实质上均匀半空间瑞利面波的传播特征 1. 瑞利面波的速度2.瑞利面波的质点振动轨迹3.瑞利面波穿透深度与波长的关系4.瑞利面波的衰减瑞利面波法与其它地震方法比较有以下2方面的特点：1.不受地层速度差异的影响2.纵横向分辨率高。

激发震源7.1 勘探原理瑞雷波沿地面表层传播，表层的厚度约为一个波长，因此，同一波长的瑞雷波的传播特性反映了地质条件在水平方向的变化情况，不同波长的瑞雷波的传播特性反映着不同深度的地质情况。

⎪⎭⎪⎬⎫ΔϕΔ=ΔΔ=i i Ri iRi x f V t x V /2/π （1.7.1）（f V R −曲线→（λ=V R /f ）→R R V λ−曲线→(H=β×λR )→V R —H 曲线）7.2 资料采集1.稳态法2.瞬态法7.3 资料的处理与解释7.3.1 稳态法t x V R ΔΔ=/7.3.3 综合解释7.3.3.1 各种波速和能量与介质特性的关系瑞利面波与横波速度和泊松比的关系对于一般岩石泊松比25.0=σ左右，穿透深度约为0.65λR 。

对于土体而言，泊松比45.04.0−=σ，则穿透深度R H λ)84.079.0(−。

对于淤泥质软塑土层，穿透深度可取R λ85.0。

2．瑞雷波能量与介质特性7.3.3.2 层速度与厚度解释1．解释步骤1）频散曲线的绘制在以土体为勘探对象的工作中，以实测V R 为横坐标，以H =0.8λR 为纵坐标绘制V R-0.8λR曲线，这样绘制的频散曲线，纵坐标可近似代表勘探深度2）定性解释分析频散曲线的形态和变化规律，初步确定可能的层数以及各层厚度和速度可能的范围3）定量解释利用多种分析计算层速度和厚度的方法，综合解释出各层的速度和层厚度。

此外，还可利用初步解释结果，进行正演拟合计算，从而反演出最佳结果。

2．层厚度与速度的解释1）层段的划分层段的划分主要有两种方式一次导数极值点法拐点法2）层速度的计算7.4 实际应用7.4.1 岩土物理力学参数计算7.4.2 地基勘察7.4.3 路面检测已知在图中0.8~1.2m 间有一宽度为1cm 的裂隙，其中充填了砂土。

斯通利波

简述瑞雷波、拉夫波和斯通利波的特点瑞雷波是弹性面波的一种，沿自由表面传播，在近地表的浅部其质点的振动轨迹为逆时针的椭圆，椭圆的长短轴之比为3：2。

基本特性有：1、地层瑞雷波相速度与横波速度相近。

可以利用瑞雷波的波速来求取横波波速，进而计算岩土层的各种力学参数。

2、振幅随深度按指数衰减，影响深度约为一个波长，其能量主要集中在半个波长范围内，故某个波长相速度基本上等于半个波长内各地层的横波相速度加权平均值。

3、瑞雷波在不均匀的介质中传播时发生频散现象。

体波在传播过程中是以极化群形式出现，不发生频散现象，这一特性是提取瑞雷波信号的先决条件。

拉夫波是由拉夫从数学上给以证明的，该类型的波被称为拉夫波(LoVe WaVe)。

G-wave 一种长周期（40—300秒）的拉夫波。

通常只限于海上传播斯通利波是一种沿井壁传播的声波，当声波脉冲与井壁和井内流体的界面相遇时就会产生斯通利波。

近十几年来，由于长源距和偶极子阵列声波仪在测井中的广泛应用和全波形阵列声波测井资料中各组分波的处理分析方法的进步，可将斯通利波分离出来单独研究并应用于测井资料分析。

斯通利波技术是评价裂缝及其渗透性的有效方法。

斯通利波在流体和固体交界处位褽最大,在固体介质中斯通利波有效传播深度为 GC倍波长,而在流体介质中斯通利波衰减较快...海洋中流体B土层(饱和土)B岩石体系也磂在斯通利波,对该体系斯通利波进行全胑研究.是一种沿井壁传播的声波，当声波脉冲与井壁和井内流体的界面相遇时就会产生斯通利波。

斯通利波技术是评价裂缝及其渗透性的有效方法。

斯通利波在流体和固体交界处位褽最大,在固体介质中斯通利波有效传播深度为 GC倍波长,而在流体介质中斯通利波衰减较快...海洋中流体B土层(饱和土)B岩石体系也磂在斯通利波,对该体系斯通利波进行全胑研究。

瑞雷波

瑞雷波在地基测试中的应用

瑞雷波法地基检测原理与工程实例

面波

1.7瑞雷波法

瑞雷波法

矿井物探-8(瑞雷波地震勘探)

瑞雷波勘探实验报告(3篇)

瑞雷波基本原理范文

第三章第二节 瑞雷面波法

第七讲(瑞雷波)

瑞雷波Rayleigh Wave

物探方法-瞬态瑞雷波法

透射波与瑞雷波勘查

第七讲(瑞雷波)

1.7瑞雷波法

斯通利波

第三章第二节瑞雷面波法