A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms

The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well.     

Boundary element simulation of scattering of elastic waves by 3-D cracks

Numerical modelling techniques are now becoming common for understanding the complicated nature of seismic wave propagation in fractured rock. Here the Indirect Boundary Element Method (IBEM) is applied to study scattering of elastic waves by cracks. The problem addressed in this paper is the diffraction of P and S waves by open 3-D cracks of arbitrary shape embedded in a homogeneous isotropic medium. The IBEM yields the value of the jump of displacements between opposite surfaces of the crack, often called Crack Opening Displacement (COD). This is used to evaluate the solution away from the crack. We use a multi-regional approach which consists of splitting a surface S into two identical surfaces S⁺ and S⁻ chosen such that the crack lies at the interface. The resulting integral equations are not hyper-singular and wave propagation within media that contain open cracks can be rigorously solved. In order to validate the method, we compare results of displacements of a penny-shaped crack for a vertical incident P-wave with the classic results by Mal (1970) obtaining excellent agreement. This comparison gives us confidence to study cases where no analytic solutions exist. Some examples of incidence of P or S waves upon cracks with various shapes are depicted and the salient aspects of the method are also discussed. Both frequency and time-domain results are included.     

Scattering of SH waves from a partially debonded rigid elliptic cylinder

Scattering of SH waves by an embedded rigid elliptic cylinder of finite length, which is partially debonded from elastic soil is studied. The debonding regions are modeled as multiple elliptic arc-shaped interface cracks with non-contacting faces. The scattered wave field is expressed as a Mathieu function expansion with unknown coefficients. The mixed boundary conditions of the problem lead to a set of singular integral equations of the first type in terms of the dislocation density functions of the cracks. A quadrature method is used to solve these integral equations numerically. The results for dynamic stress intensity factors, far-field pattern of the displacement and scattering cross sections are presented. We particularly discuss the effects of the ratio of the short radius to long radius of the cylinder.     

Disturbances of the ionosphere of blast and acoustic waves generated at ionospheric heights by rockets

In this paper we present a model, which describes the propagation of acoustic impulses produced by flight of rockets through a model terrestrial atmosphere, and effect of these impulses onto the ionosphere above a rocket. We show, that experimentally observed ionospheric disturbances with duration about 300 s cannot be explained by effect of acoustic impulses onto the ionosphere. We have calculated parameters of a blast wave produced by launch vehicle on the ionospheric heights. It was shown that the blast wave is intense and this wave can generate great disturbance of electron density. The disturbance of electron density can exceed the ambient electron density in 2.6 times. We supposed that the observed ionospheric disturbances might be produced by propagation of delayed magnetoacoustic wave, which, in turn, was produced by the blast wave.     

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.     

Antiplane response of a dike with flexible soil-structure interface to incident SH waves

Studies of the effects of differential ground motions on structural response generally do not consider the effects of the soil-structure interaction. On the other end, studies of soil-structure interaction commonly assume that the foundation of the structure (surface or embedded) is rigid. The former ignore the scattering of waves from the foundation and radiation of energy from the structure back to the soil, while the latter ignore quasi-static forces in the foundations and lower part of the structure deforming due to the wave passage. This paper studies a simple model of a dike but considers both the soil-structure interaction and the flexibility of the foundation. The structure is represented by a wedge resting on a half-space and excited by incident plane SH-waves. The structural ‘foundation’ is a flexible surface that can deform during the passage of seismic waves. The wave function expansion method is used to solve for the motions in the half-pace and in the structure. The displacements and stresses in the structure are compared with those for a fixed-base model shaken by the free-field motion. The results show large displacements near the base of the structure due to the differential motion of the base caused by the wave passage.     

Interaction of waves,currents and tides,and wave-energy impact on the beach area of Sylt Island

Erosion due to waves is an important and actual problem for most coastal areas of the North Sea. The objective of this study was to estimate the impact of wave action on the coastline of Sylt Island. From a 2-year time series (November 1999 to October 2001) of hydrological and wave parameters generated with a coupled wave–current modelling system, a period comprising storm ‘Anatol’ (3–4 December 1999) is used to investigate the effects of waves on currents and water levels and the input of wave energy into the coastline. The wave-induced stress causes an increase of the current velocity of 1 m/s over sand and an additional drift along the coast of about 20 cm/s. This produces a water level increase of more than 20 cm in parts of the tidal basin. The model system also calculates the wave energy input into the coastline. Scenario runs for December 1999 with a water level increase of 50 cm and wind velocity increased by 10% show that the input of the wave energy into the west coast of Sylt Island increases by 30% compared to present conditions. With regard to the forecasted near-future (Woth et al., Ocean Dyn 56:3–15, 2006) increase of strong storm surges, the scenario results indicate an increased risk of coastal erosion in the surf zone of Sylt Island.     

Seismic waves generated by oscillating buildings: analysis of a release test

A three-stories, base-isolated building located in Rapolla (Potenza, Italy) was tested with a snap-back experiment. Free-field measures were performed using 3D seismometers, located at 10 and 50 m from the buildings in direction of motion and at 10 m from the building in direction transverse to the motion. At each measurement point it was possible to separate the soil amplification effects from two source terms, due to the base-isolated building and to the reaction block. The ground motion was noticeable: at 10 m in the longitudinal direction it was comparable with a small size, near-field earthquake.     

Spatiotemporal spectrum and momentum flux of the stratospheric gravity waves generated by a typhoon

The simulation results of Typhoon Matsa (2005) by using the Weather Research and Forecasting (WRF) model show that pronounced stratospheric gravity waves (GWs) are generated in the vicinity of the typhoon. Using the model output, we investigate the spatial structures and the temporal variations of the GWs through a three dimensional (3-d) spectral analysis, i.e. the spectrum with respect to two horizontal wavenumbers and frequency. We further derive the momentum flux carried by the GWs. Spectral investigation results show that the power spectral density (PSD) of the GWs exhibits a single-peaked spectrum, which consists primarily of a distinct spectrum at horizontal wavelength of ~1000km, time period of 12-18h, and vertical wavelength of 7-9km. This spectrum is different from the spectra of GWs generated by deep convections disclosed by the previous researches. Both the PSD and momentum flux spectrum are prominent in positive k h portion, which is consistent with the fact that the GWs propagate in the upstream of mean flow. Large momentum flux is found to be associated with the GWs, and the net zonal momentum flux is 0.7845×10 3 Pa at 20km height, which can account for ~26% of the momentum flux that is required in driving the QBO phenomenon.     

Berm formation and dynamics on a gently sloping beach; the effect of water level and swash overtopping

Berm formation and morphological development of the beach face have been observed during a neap–neap tidal cycle on the gently sloping and accreting beach at Vejers, Denmark. During the field campaign, an intertidal bar migrated onshore and stabilized as a berm on the foreshore. A new intertidal bar occurred on the lower beach face, migrated onshore on the rising tide and finally merged with the pre‐existing berm. As the tide continued to rise, the new berm translated further onshore as an intertidal bar to the uppermost part of the foreshore. The sediment transport during the berm transition was onshore directed in the upper swash and offshore directed in the lower swash. This berm development can be described through both the neap‐berm, ridge‐and‐runnel and berm‐ridge development concepts proposed by Hine (Sedimentology 1979; 26: 333–351), and all three stages were observed during only three tidal cycles. The main factors controlling this fast transformation were the gentle slope of the cross‐shore profile, rapid water level translation rates, substantial swash overtopping of the berm, and low infiltration rates. Despite the onshore migration of intertidal bars and berm formation, no net foreshore accretion took place during the field campaign. This was largely due to the formation of rip channels with strong rip currents cutting through the intertidal bars and the berm, which acted as a sediment drain in the profile. Copyright © 2009 John Wiley & Sons, Ltd.     

Spatial dispersion of surface waves at the free surface of a general anisotropic elastic medium

A new technique relates the wave velocity of the surface waves in anisotropic elastic medium to its elastic constants. Anisotropic propagation of surface waves is studied in a half-space occupied by a general anisotropic elastic solid. The phase velocity expressions of quasi-waves, in three-dimensional space, are used to derive the secular equation of surface waves. The complex secular equation is resolved, analytically, into real and imaginary parts and is then solved, numerically, for phase velocity along a given phase direction on the surface. The complete procedure is thus analogous to the one used for conventional Rayleigh waves in isotropic medium. A non-linear equation relates the ray direction of the surface waves to its phase direction on the (plane) surface of the medium. The analytical differentiation of secular equation yields the directional derivative of phase velocity. This derivative is used to calculate the wave velocity of surface waves. Spatial variations of phase velocity, wave velocity and ray direction over the free plane surface are plotted for the numerical models of crustal rocks with orthorhombic, monoclinic and triclinic anisotropies.     

Two-phase SPH modelling of waves caused by dam break over a movable bed

This paper describes the application of the Smoothed Particle Hydrodynamics（SPH） method for modeling two dimensional waves caused by dam break over a movable bed in two dimensions.The two phase SPH method is developed to solve the Navier-Stokes equations.Both fluid and sediment phases are described by particles as weakly compressible fluids and the incompressibility is achieved by the equation of state.The sediment phase is modeled as a non-Newtonian fluid using three alternative approaches of artificial viscosity and Bingham Model.In this paper,the new formulations for two-phase flows are proposed.The numerical results obtained from the developed SPH model show acceptable accuracy with comparison to experimental data.     

Observations of acoustic-gravity waves in the ionosphere generated by severe tropospheric weather

Atmospheric waves influence the dynamics and energetic budget of the upper atmosphere. Using the continuous HF Doppler sounder, we study the wave activity in the ionosphere during tropospheric convective storms in western and central part of the Czech Republic. The study is focused on acoustic-gravity waves in the period range 2–30 minutes. We discuss possible methods of distinguishing the waves emitted by meteorological sources from waves of different origin, particularly waves of geomagnetic origin. In two cases out of twenty-five analysed, we found waves in the infrasonic period range which might be generated by exceptionally intense meteorological activity in the troposphere. The results differ considerably from those previously obtained in North America. In the central part of the United States, infrasonic waves were frequently observed during convective storms. As a possible reason, we discuss different intensity and dynamics of weather systems in both regions.     

Simulation of the stratospheric gravity waves generated by the Typhoon Matsa in 2005

The generation of stratospheric gravity waves(GWs) due to typhoon is simulated by using a meso-scale model(WRF) with a typhoon case,the Matsa in 2005.An 8-day model run that covers the major stages of the Matsa’s development reproduces the key features of the typhoon.For example,good agreements in the typhoon’s track,the intensity,and the spiral clouds,as well as mean state of stratosphere,are seen between the simulation results and the observation.Simulation results clearly show that with typhoon propagates northwestward,pronounced stratospheric GWs are generated continuously in the vicinity of Matsa.The GWs exhibit the typical curve-like wave fronts away from the Typhoon Matsa,and propagate preferentially in the upstream of the background winds.These characteristics reflect that the stratospheric GWs are closely associated with the typhoon,and thus the GWs are referred to as Tropical Cyclone related Gravity Waves(TC-GWs).The results also show that these waves should have a rather large horizontal scale so that the outmost wave fronts can be seen at the distance of ～1000 km to the typhoon center in the horizontal plane of 20 km.This is consistent with the phenomenon of stratospheric TC-GWs with ～1000 km horizontal scale disclosed by the previous observational analysis results.     

四阶龙格-库塔方法的一种改进算法及地震波场模拟

提出了求解波动方程的四阶龙格-库塔方法的一种改进算法.首先将原四阶龙格-库塔方法合并为两级格式, 然后在第一级中引入加权参数以获得加权算法. 针对这种改进方法,研究了它的稳定性条件; 对一维问题导出了频散关系, 给出了数值频散结果,并与四阶的 Lax-Wendroff (LWC) 方法和位移-应力交错网格方法进行了对比; 对二维问题, 使用我们的改进方法、四阶LWC和交错网格三种方法进行了声波波场模拟, 并进行了计算效率分析和不同方法计算结果的比较; 最后选取两个层状介质模型进行了声波和弹性波波场模拟. 数值结果表明,本文的改进方法具有非常弱的数值频散和高的计算效率, 是一种在地震勘探领域具有巨大应用潜力的数值方法.     

Transformation and absorption of magnetosonic waves generated by solar wind in the magnetosphere

Resonant transformation of fast magnetosonic (FMS) wave flux into Alfven and slow magnetosonic (SMS) oscillations is investigated in the one-dimensionally inhomogeneous magnetosphere. Spatial distribution of energy absorption rate of FMS oscillations penetrating into the magnetosphere from the solar wind is studied. The FMS wave energy absorption rate caused by magnetosonic resonance excitation is shown to be several orders of magnitude greater than that caused by Alfven resonance excitation at the same surface. It is connected with the spectrum of incident FMS waves. The Kolmogorov spectrum is used in numerical calculations. Magnitude of the Fourier harmonics exciting resonant Alfven oscillations is much smaller than that of the harmonics driving lower-frequency magnetosonic resonance. It is shown that resonant transformation of FMS waves into SMS oscillations can be an effective mechanism of energy transfer from the solar wind to the magnetosphere.     

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fic...     

平面SV波在饱和半空间中沉积谷地周围的散射

采用一种特殊的间接边界积分方程法,求解了平面SV波在饱和半空间中任意形状沉积谷地周围的二维散射问题。结合饱和半空间中膨胀波源和剪切波源格林函数,由分布在沉积和半空间交界面附近两虚拟波源面上的波源分别构造沉积内外的散射波场,由交界面连续条件建立方程并求解确定虚拟波源密度,总波场反应即可由自由波场和散射波场叠加而得。然后通过边界条件验算、退化解答与现有结果的比较以及稳定性检验,验证了方法的计算精度。通过一组典型算例,研究了平面SV波在饱和半空间中沉积谷地周围散射的基本规律,详细给出了不同参数情况沉积谷地附近地表位移幅值和孔隙水压,着重分析了入射SV波频率和角度、边界渗透条件、沉积孔隙率等因素对场地反应的影响,得出了一些有益的结论。     

求解二次方程的二维VTI介质qSV波和qSH波走时快速扫描算法

地震波走时计算在观测系统设计、偏移成像、速度模型走时反演和地震定位等方面起到重要作用.各向异性广泛存在于地球介质中,影响地震波传播的振幅和走时,忽略各向异性的影响将对成像、反演以及地震定位等造成一定的误差.因此对于高分辨率成像和反演,走时计算中考虑各向异性十分重要.快速扫描法不需要存储和追踪波前面信息,在各向异性初至波走时计算方面应用广泛.传统的方法通过将慢度四次方程转换为走时四次方程并结合快速扫描法求解走时.该方法没有对程函方程做近似,适用于强各向异性介质,但存在计算效率低的问题.对于求解qSV波走时,本文发展了一种在局部解中将慢度四次方程简化为二次方程解析地快速求解走时的方法,极大地提高了计算效率.对于qSH波,慢度方程是二次的,可以直接解析求解.最后,本文用各向异性均匀模型和BP复杂模型进行测试,计算结果表明走时计算准确,验证了该方法的有效性.