Diffraction of seismic waves in an elastic, cracked halfplane using a boundary integral formulation

The presence of subsurface cracks in a halfspace excited by elastic waves may give rise to scattered body and surface waves. For many engineering applications, such as non-destructive testing or oil exploration, the scattered field may yield valuable information to detect cracks and other scatterers. We use the Indirect Boundary Element Method (IBEM) to study the diffraction of P, SV waves with various incidence angles and Rayleigh surface waves. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. Our approach is usually called indirect BEM as the sources' strengths should be obtained as an intermediate step. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' Principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with previous results in the literature. Various crack configurations, including multiple cracks, are investigated. Results in frequency and time domains are displayed. Under certain conditions the amplitude spectra of those waves clearly show conspicuous resonance peaks.     

Rapidly installed temporary gauging for hurricane waves and surge,and application to Hurricane Gustav

Hurricanes can produce extreme nearshore waves and surge, but permanent gauging stations are often much sparser than is desired. This paper describes the rationale behind and outline for rapidly installed temporary coastal gauges, and presents results during Hurricane Gustav (2008). Within 48 h prior to landfall, twenty self-recording pressure gauges were deployed in depths of 1.4–23 m over more than 700 km of coastline, using helicopters to cover the large distances. Results showed a complex picture that was strongly dependent on location. East of the Mississippi Delta, open coast waves were large, and surge reached 3.8 m NAVD88 in marshes. West of the delta but near landfall, waves and surge were generally smaller as the river levees blocked flow from East to West. West of landfall, both waves and surge were very small and the most prominent feature was a water level drawdown that reached 1.5 m. Wave spectra varied strongly depending both on location and time from landfall.     

Pc3–4 ULF waves at polar latitudes

A search for Pc3–4 wave activity was performed using data from a trans-Antarctic profile of search-coil magnetometers extending from the auroral zone through cusp latitudes and deep into the polar cap. Pc3–4 pulsations were found to be a ubiquitous element of ULF wave activity in all these regions. The diurnal variations of Pc3 and Pc4 pulsations at different latitudes have been statistically examined using discrimination between wave packets (pulsations) and noise. Daily variations of the Pc3–4 wave power differ for the stations at the polar cap, cusp, and auroral latitudes, which suggests the occurrence of several channels of propagation of upstream wave energy to the ground: via the equatorial magnetosphere, cusp, and lobe/mantle. An additional maximum of Pc3 pulsations during early-morning hours in the polar cap has been detected. This maximum, possibly, is due to the proximity of the geomagnetic field lines at these hours to the exterior cusp. The statistical relation between the occurrence of Pc3–4 pulsations and interplanetary parameters has been examined by analyzing normalized distributions of wave occurrence probability. The dependences of the occurrence probability of Pc3–4 pulsations on the IMF and solar wind parameters are nearly the same at all latitudes, but remarkably different for the Pc3 and Pc4 bands. We conclude that the mechanisms of high-latitude Pc3 and Pc4 pulsations are different: Pc3 waves are generated in the foreshock upstream of the quasi-parallel bow shock, whereas the source of the Pc4 activity is related to magnetospheric activity. Hourly Pc3 power has been found to be strongly dependent on the season: the power ratio between the polar summer and winter seasons is 8. The effect of substantial suppression of the Pc3 amplitudes during the polar night is reasonably well explained by the features of Alfven wave transmission through the ionosphere. Spectral analysis of the daily energy of Pc3 and Pc4 pulsations in the polar cap revealed the occurrence of several periodicities. Periodic modulations with periods 26, 13 and 8–9 days are caused by similar periodicities in the solar wind and IMF parameters, whereas the 18-day periodicity, observed during the polar winter only, is caused, probably, by modulation of the ionospheric conductance by atmospheric planetary waves. The occurrence of the narrow-band Pc3 waves in the polar cap is a challenge to modelers, because so far no band-pass filtering mechanism on open field lines has been identified.     

Scattering of plane SV waves by cylindrical canyons in saturated porous medium

On the basis of Biot dynamic theory, an analytic solution of two-dimensional scattering and diffraction of plane SV waves by circular cylindrical canyons in a half space of saturated porous media is presented in this paper for the first time. The solution is obtained by employing the Fourier–Bessel series expansion technique. Parametric studies had been carried out, which includes: the angle of incidence, the frequency of the incident SV wave, the porosity of saturated porous medium and the stiffness and Poisson's ratio of the solid-skeleton. All the outcomes are useful for the seismic analysis of the surface topography conditions.     

热源激发重力波特征以及波流作用的数值模拟研究

本文在二维等温可压大气中引入了一个随时间和空间变化的热源扰动,分别以静止风和中纬1月份月平均向东的纬向风急流为背景,对不同背景下热源激发的重力波的传播详细过程及其特性进行了数值模拟研究.热源激发出来的重力波在初始阶段有很宽的频谱范围,随后由于重力波的传播效应,水平波长和垂直波长分布范围随时间都有所减小.顺风传播的重力波的小尺度和低频部分会容易被急流吸收,从而加强了对流层急流,而逆风传播的重力波更容易上传,会导致中间层区域向西的背景风增强.这体现了低层大气急流对中间层大气风场结构的影响.热源的尺度直接决定激发波的尺度;激发波的垂直尺度和时间尺度对热源的变化比其水平尺度更敏感.     

Momentum transfer at the ocean–atmosphere interface: the wave basis for the inertial coupling approach

 The inertial coupling approach for the momentum transfer at the ocean–atmosphere interface, which is based on the assumption of a similarity hypothesis in which the ratio between the water and air reference velocities is equal to the square root of the ratio between the air and water densities, is reviewed using a wave model. In this model, the air and water reference velocities are identified, respectively, with the spectrally weighted phase velocity of the gravity waves and the Stokes velocity at the water roughness length, which are evaluated in terms of the dimensionless frequency limits in Toba's equilibrium spectrum. It is shown that the similarity hypothesis is approximately satisfied by the wave model over the range of wave ages encountered in typical sea states, and that the predicted values of the dimensionless surface drift velocity, the dimensionless water reference velocity, and the Charnock constant are in reasonable agreement with observational evidence. The application of the bulk relationship for the surface shear stress, derived from the inertial coupling hypothesis in general circulation modeling, is also discussed. Received: 6 January 2001 / Accepted: 28 June 2001     

Propagation of partially coherent non-stationary random waves in a viscoelastic layered half-space

This paper presents a highly accurate method based on the precise integration method (PIM) and on the pseudo excitation method (PEM). The method computes the propagation behaviour of partially coherent non-stationary random waves in a viscoelastic, transversely isotropic solid, which consists of a multi-layered soil resting on a homogeneous semi-infinite space. The excitation source is a local rupture between two layers, which causes a partially coherent non-stationary random field. The analysis of non-stationary random wave propagation is transformed into that for deterministic waves by using PEM. The resulting governing equations in the frequency-wavenumber domain are linear ordinary differential equations, which are solved very precisely by using PIM. The evolutionary power spectral densities of the ground level responses are investigated and some typical earthquake phenomena are explained.     

具有饱和土沉积层的充水河谷对平面瑞雷波的散射

针对具有饱和土沉积层的充水河谷对平面瑞雷波的散射问题,把半空间场地用单相弹性介质模拟,河谷中的饱和土沉积层用Biot饱和多孔介质动力理论模拟,河谷中的水假定为无黏性流体（理想流体）,利用波函数展开法在频域内给出了具有饱和土沉积层的圆弧形充水河谷对平面瑞雷波散射问题的解析解答.文中给出了算例,计算了不同输入频率和高宽比时河谷谷底的位移幅值.算例表明由于具有饱和土沉积层的充水河谷存在,使得河谷谷底的位移幅值放大4倍多,并且它的幅值随着河谷谷底位置的不同而产生较大的变化.     

The effect of Newtonian cooling on vertically propagating magneto-acoustic waves in a thermally conducting isothermal atmosphere (II)

In this article, we examine reflection, dissipation and attenuation of vertically propagating waves in an isothermal atmosphere under the combined effect of Newtonian cooling, thermal conduction and viscosity with a weak horizontal magnetic field. We consider the case in which the combined effect of viscosity and magnetic field is dominated by that of the thermal conduction and for small values of the Newtonian parameter. As a result, the atmosphere can be divided into three distinct regions that are connected by two transition regions. The lower and middle regions are connected by a semi-transparent barrier and the middle and upper regions are connected by an absorbing and reflecting barrier. In the connecting barriers the reflection and transmission of the waves takes place. The presence of Newtonian cooling effects on the adiabatic region, produces attenuation in the amplitudes of the waves and reduces the energy absorption in the transition regions. The reflection coefficient is determined in the lower and middle regions and the results are discussed in the context of the heating of the solar atmosphere.     

Effect of coastal waves on sea level in Óbidos Lagoon,Portugal

This study reports the role of waves, tide, wind and freshwater discharges over the sea level in Óbidos Lagoon, a coastal system connected to the sea through a narrow and shallow mobile inlet. To address the hydrodynamic features of this coastal system, the relative importance of different physical forcings were evaluated. For this purpose, observations together with realistic and idealized numerical modeling were used. Both model and measurements show that the lagoon sea level remains above offshore sea level during storm wave periods. Hence, a simplified inlet-lagoon idealized model was described through mathematical expressions, to understand and highlight the physical processes responsible for sea-level elevation.     

Simulation of irregular waves in an offshore wind farm with a spectral wave model

A numerical study of irregular waves in the Norwegian continental shelf wind farm (HAVSUL-II) was conducted using 3rd generation spectral wave models. The study was composed of two parts: the study of the effect of a single windmill monopile in the local incoming wave field using an empirical JONSWAP spectrum, and a wave hindcast study in the wind farm area using realistic incoming wave spectra obtained from large scale simulations for the 1991-1992 winter period. In the single windmill monopile study the SWAN wave model was used, while the hindcast study was conducted by successively nesting from a coarse grid using the WAM model up to a high-resolution (56 m) grid covering 26.2 km² of the HAVSUL-II windmill farm using the SWAN model. The effect of a single monopile on incident waves with realistic spectra was also studied. In the single windmill study the monopile was represented as a closed circular obstacle and in the hindcast study it was represented as a dry grid point. The results showed that the single windmill monopile creates a shadow zone in the down wave region with lower significant wave height (H_s) values and a slight increase of H_s in the up wave region. The effects of the windmill monopile on the wave field were found to be dependent on the directional distribution of the incoming wave spectrum and also on the wave diffraction and reflection. The hindcast study showed that the group of windmill monopiles may contribute to the reduction of the wave energy inside the offshore wind farm and that once the waves enter into the offshore wind farm they experience modifications due to the presence of the windmill monopiles, which cause a blocking of the wave energy propagation resulting in an altered distribution of the H_s field.     

极坐标系有限差分中起伏地表边界条件处理

有限差分算法是地震学中重要的算法,在直角坐标系下同位网格有限差分中使用牵引力镜像方法,可以高效准确地处理起伏地表边界条件.当研究区域-全球尺度问题时需要考虑地球曲率影响,此时选择极坐标系更加直观方便,但已有方法无法在极坐标系下准确计算起伏地表影响.本文在极坐标系有限差分中引入贴体网格和牵引力镜像方法处理起伏地表边界条件,并在多个算例中验证算法正确性和适用范围,证明牵引力镜像法在极坐标系有限差分中有效.

     

超声反射法套管-地层环空间介质波阻抗反演方法与成像实例

针对套管井反射式超声波水泥固井质量检测问题,本文利用超声反射波频谱中套管共振透射窗内的复合反射系数,提出了定量反演套管-地层环空间内介质的波阻抗的方法. 利用复合反射系数中多个频率点的相移反正切函数主值,给出了波阻抗的计算公式,并把套管-地层环空间介质中波的相移的整、实特性作为波阻抗反演收敛的判据. 针对井下实际测井环境中超声换能器性能受温度和压力等的影响而发生变化,导致的声源波形（子波）和复合反射系数不确定的困难,提出了用井下原地（in situ）实测波形定量估计声源波形和复合反射系数的方法. 通过对合成数据的处理,分别考察了已知介质的声学和几何参数存在的偏差对套管-地层环空间内介质的波阻抗反演结果的影响. 本文对多组模型井检验数据进行了目的层介质的波阻抗反演与成像,成像结果与真实情况吻合,验证了反演方法的有效性. 最后对现场实测资料进行了套管-地层环空间内介质的波阻抗定量反演与成像.     

Antiplane response of isosceles triangular hill to incident SH waves

In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill‘s peak on ground motion are discussed.     

A theoretical inquiry into aspects of the structure and the management of ecological–economic systems

 We use the theory of continuous-time Markov chains (CTMCs) to analyze hitherto unstudied questions about jointly determined ecological–economic systems. Two specific questions are examined. First, on the methodological front, we show how the theory of CTMCs can be used to effectively model dynamic and stochastic ecological–economic systems. Then, given recent concern about the sustainability of desirable states and lock-in into undesirable states, we partition the state space of our stylized ecological–economic system into good and bad states, and demonstrate the formal relationship between these two sets of states. Second, we discuss a way of looking at the task of managing ecological–economic systems that captures this formal link between the good and the bad states, and has other desirable properties.     

SH波入射时柔性基础上等腰三角形坝体结构的出平面反应

本文利用复变函数和坐标移动方法研究了SH波入射对柔性基础上等腰三角形坝体结构的影响。首先建立问题的数学模型并根据分区和辅助函数法将模型分割为2部分,其1为等腰三角形和半圆形组成的区域Ⅰ,其余为区域Ⅱ;其2在区域Ⅰ内构造1个满足等腰三角形两边应力自由的驻波解,在区域Ⅱ内构造满足水平边界应力自由的散射波;通过移动坐标在区域Ⅰ、Ⅱ的公共边界实现位移和应力的连续,建立起求解该问题的无穷代数方程组;最后,本文给出了例题和数值结果并对其进行了讨论,并通过算例强调了与文献[9]的本质区别。     

Antiplane response of isoceles triangular hill to incident SH waves

In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill's peak on ground motion are discussed.     

The rotated Cartesian coordinate method to remove the axial singularity of cylindrical coordinates in finite‐difference schemes for elastic and viscoelastic waves

When modelling the propagation of 3D non‐axisymmetric elastic and viscoelastic waves in cylindrical coordinates using the finite‐difference time‐domain method, a mathematical singularity occurs due to the presence of terms in the elastic and viscoelastic wave equations. For many years, this issue has been impeding the accurate numerical solution near the axis. In this work, we propose a simple but effective method for the treatment of this numerical singularity problem. By rotating the Cartesian coordinate system around the z‐axis in cylindrical coordinates, the numerical singularity problems in both 2D and 3D cylindrical coordinates can be removed. This algorithm has three advantages over the conventional treatment techniques: (i) the excitation source can be directly loaded at , (ii) the central difference scheme with second‐order accuracy is maintained, and (iii) the stability condition at the axis is consistent with the finite‐difference time‐domain in Cartesian coordinates. This method is verified by several 3D numerical examples. Results show that the rotating the Cartesian coordinate method is accurate and stable at the singularity axis. The improved finite‐difference time‐domain algorithm is also applied to sonic logging simulations in non‐axisymmetric formations and sources.     

Statistical analyses and characteristics of volcanic tremor on Stromboli Volcano (Italy)

 A study of volcanic tremor on Stromboli is carried out on the basis of data recorded daily between 1993 and 1995 by a permanent seismic station (STR) located 1.8 km away from the active craters. We also consider the signal of a second station (TF1), which operated for a shorter time span. Changes in the spectral tremor characteristics can be related to modifications in volcanic activity, particularly to lava effusions and explosive sequences. Statistical analyses were carried out on a set of spectra calculated daily from seismic signals where explosion quakes were present or excluded. Principal component analysis and cluster analysis were applied to identify different classes of spectra. Three clusters of spectra are associated with two different states of volcanic activity. One cluster corresponds to a state of low to moderate activity, whereas the two other clusters are present during phases with a high magma column as inferred from the occurrence of lava fountains or effusions. We therefore conclude that variations in volcanic activity at Stromboli are usually linked to changes in the spectral characteristics of volcanic tremor. Site effects are evident when comparing the spectra calculated from signals synchronously recorded at STR and TF1. However, some major spectral peaks at both stations may reflect source properties. Statistical considerations and polarization analysis are in favor of a prevailing presence of P-waves in the tremor signal along with a position of the source northwest of the craters and at shallow depth. Received: 15 December 1996 / Accepted: 31 March 1998