Interaction of a compressional impulse with a slot normal to the surface of an elastic half space

Summary. An improved finite difference scheme is applied to simulate wave propagation in the vicinity of a slot normal to the surface of an elastic half space. It provides visualization of the scattered wave pattern at a sequence of time steps, and also the components of displacement as functions of time at a series of observation points.
After being hit by a normally incident plane P pulse, the slot oscillates with two main cycles and two shear-compressional pairs of diffracted waves, and also Rayleigh pulses, are scattered from it. The resulting wavefronts are parallel to the vertical surfaces of the slot and curve in semicircular arcs around the bottom of the slot.
Experimental tests of the theory were performed, using 0.5–6 MHz ultrasonic pulses on duralumin cylinders with surface-breaking slots ranging from 0.5–2 mm in width and from 2–6 mm in depth. The numerical results were confirmed by these experiments.     

Polarization and amplitude attributes of reflected plane and spherical waves

The characteristics of a reflected spherical wave at a free surface are investigated by numerical methods; in particular, the polarization angles and amplitude coefficients of a reflected spherical wave are studied. The classical case of the reflection of a plane P wave from a free surface is revisited in order to establish our terminology, and the classical results are recast in a way which is more suited for the study undertaken. The polarization angle of a plane P wave, for a given angle of incidence, is shown to be 90° minus twice the angle of reflection of the reflected S wave. For a Poisson's ratio less than 1/3, there is a non-normal incident angle for which both amplification coefficients are 2 precisely; for this incident angle the direction of the particle motion at the free surface is also the direction of the incident wave. For a wave emanating from a spherical source, the polarization angle, for all angles of incidence, is always less than, or equal to, the polarization angle of a plane P wave. The vector amplification coefficient of a spherical wave, for all angles of incidence, is always greater than the vector amplification coefficient of a plane P wave. As expected, the results for a spherical wave approach the results for a plane P wave in the far field. Furthermore, there was a good agreement between the theoretical modelling and the numerical modelling using the dynamic finite element method (DFEM).     

Diffraction of P, S and Rayleigh waves by three-dimensional topographies

The diffraction of P, S and Rayleigh waves by 3-D topographies in an elastic half-space is studied using a simplified indirect boundary element method (IBEM). This technique is based on the integral representation of the diffracted elastic fields in terms of single-layer boundary sources. It can be seen as a numerical realization of Huygens principle because diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. A Fredholm integral equation of the second kind for such sources is obtained from the stress-free boundary conditions. A simplified discretization scheme for the numerical and analytical integration of the exact Green's functions, which employs circles of various sizes to cover most of the boundary surface, is used.
The incidence of elastic waves on 3-D topographical profiles is studied. We analyse the displacement amplitudes in the frequency, space and time domains. The results show that the vertical walls of a cylindrical cavity are strong diffractors producing emission of energy in all directions. In the case of a mountain and incident P, SV and SH waves the results show a great variability of the surface ground motion. These spatial variations are due to the interference between locally generated diffracted waves. A polarization analysis of the surface displacement at different locations shows that the diffracted waves are mostly surface and creeping waves.     

Influence of the Interface Fresnel zone on the reflected P-wave amplitude modelling

The aim of the paper is to emphasize the importance of accounting for the Fresnel volume and for the Interface Fresnel zone (IFZ) for calculating the amplitude of the P wave emanating from a point source and recorded at a receiver after its specular reflection on a smooth homogeneous interface between elastic media. For this purpose, by considering the problem of interest as a problem of diffraction by the IFZ, that is, the physically relevant part of the interface which actually affects the reflected wavefield, we have developed a method which combines the Angular Spectrum Approach (ASA) with the IFZ concept to get the 3-D analytical solution. The variation in the reflected P -wave amplitude evaluated with the ASA, as a function of the incidence angle, is compared with the plane wave (PW) reflection coefficient and with the exact solution provided by the 3-D code OASES, for one solid/solid configuration and two dominant frequencies of the source. For subcritical incidence angles the geometrical spreading compensation is mostly quite sufficient to reduce the point-source amplitudes to the PW amplitudes. On the contrary, for specific regions of incidence angles for which the geometrical spreading compensation is not sufficient anymore, that is, near the critical region and in the post-critical domain, the ASA combined with the IFZ concept yields better results than the PW theory whatever the dominant frequency of the source, which suggests that the additional application of the IFZ concept is necessary to obtain the reflected P -wave amplitude. Nevertheless, as the ASA combined with the IFZ has been used only for evaluating the contribution of the reflected wavefield at the receiver, its predictions fail when the interference between the reflected wave and the head wave becomes predominant.     

Modelling of scattering of seismic waves from a corrugated rough sea surface: a comparison of three methods

We compare three numerical methods to model the sea surface interaction in a marine seismic reflection experiment (the frequencies considered are in the band 10–100 Hz): the finite-difference method (FDM), the spectral element method (SEM) and the Kirchhoff method (KM). A plane wave is incident at angles of 0° and 30° with respect to the vertical on a rough Pierson–Moskowitz surface with 2 m significant wave height and the response is synthesized at 6, 10 and 50 m below the average height of the sea surface. All three methods display an excellent agreement for the main reflected arrival. The FDM and SEM also agree very well all through the scattered coda. The KM shows some discrepancies, particularly in terms of amplitudes.     

Cross-dependence of finite-frequency compressional waveforms to shear seismic wave speeds

Seismic tomography has been one of the primary tools to image the interior of the earth and other elastic structures. To date the inversions of compressional ( P ) and shear ( S ) wave speeds have been carried out separately under the assumption that P traveltimes are affected only by the P wave speed of the elastic media and S traveltimes by the S wave speed. Using numerical and analytical solutions, we show that for finite-frequency seismic waves, S wave speed perturbations may have significant effects on P waveforms. This suggests that when waveform-derived traveltime and amplitude anomalies are used in tomographic inversions, the P -wave measurements should be related to not only P wave speed perturbations but also S wave speed perturbations.     

Numerical simulation of the propagation of P waves in fractured media

We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q ⁻¹ of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q ⁻¹ of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) ⁻¹ in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials.     

Seismic body waves in anisotropic media: propagation through a layer

Summary. The square-root energy ratios and pulse shapes are presented for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces. Off incident planes of symmetry, incident P waves generate two small amplitude SH waves (one from each interface), whose amplitudes decrease slowly with increasing period. Incident SV (or SH ) waves can generate large amplitude SH (or SV ) waves which decrease rapidly with increasing period. For incident S waves, many pulses not present in isotropic models are generated, often of large relative amplitude, with many of the transmitted S pulses showing evidence of double arrivals, either in the form of S-wave splitting, or a modification of the shape of the input waveform.     

Reflection—refraction of general P-and type-I S-waves in elastic and anelastic solids

Summary. The reflection and refraction of general (homogeneous or inhomo-geneous) plane P and type-I S ( SV ) body waves incident on plane boundaries are considered for general linear viscoelastic solids. Reflection—refraction laws, physical characteristics of the waves, and the nature of critical angles are examined in detail at welded boundaries and a free surface. General visco-elasticity with no low-loss approximations predicts that contrasts in intrinsic absorption at boundaries give rise to inhomogeneous reflected and refracted waves with elliptical particle motions, velocities and maximum attenuations that vary with frequency and angle of incidence, energy propagation at speeds and directions different from phase propagation, phase propagation that in general is parallel to the boundary for at most one angle of incidence, and reflection—transmission coefficients dependent on energy flow due to wave interaction. None of these physical characteristics are predicted for waves incident on boundaries that respond instantaneously.     

Earthquake seismograms that show Doppler effects due to crack propagation

Summary. Examples are presented of earthquake P -wave pulses seen on broadband seismograms, to show that on such recordings the pulse shapes are more clearly seen than on conventional short-period and long-period seismograms. Most of the broadband seismograms have been chosen because they show marked differences between the pulse lengths of P and those of the surface reflections. In addition some of the pulses appear to have smooth onsets and abrupt trailing edges so that the onset of the pulse is difficult to observe and the largest amplitude arrivals seen on the seismogram coincide not with the onset of motion but with the termination of motion: that is the large arrivals mark stopping phases of motion.
We assume that the differences in pulse length are due to the effects of a moving source – that is a Doppler effect – and that the pulses with smooth onsets and abrupt trailing edges can be modelled simply by a source propagating on a line with low radiation amplitude at the start of motion. A trial and error method guided by a published fault plane solution is then used to obtain a fit between observed and computed seismograms for one of the earthquakes. This process leads to an estimate of the crack speed of about 1.4 times the 5-wave speed.
The errors that may arise in estimating source depths and orientation, if stopping phases are not recognized as such, is discussed.     

P-wave seismograms from continuously varying transition zones—II. Elastic media

Summary. A class of elastic transition zones are modelled by considering a homogeneous half space overlying an inhomogeneous half space with a bounded and monotonically increasing profile for the rigidity modulus and constant Poisson's ratio and density. Reflected P waves due to a compressional point source in the upper half space are studied in the frequency and time domains by means of numerical contour integration in the complex k plane and the Fast Fourier Transform (FFT). Results from the exact fourth-order elasticity theory are compared with those from the approximate decoupled equations for P and SV waves. Agreement is observed between the two theories at high frequencies beyond the caustic range.     

Reflected-diffracted waves in fracture zone models

Summary. The paper presents the results of modelling of diffracted and reflected-diffracted waves in fracture zones. The Berryhill method was used and the calculations were made for a profile perpendicular to the diffracting edge. Several homogeneous models of the Earth's crust, characterized by different values of crustal thickness, velocity and horizontal distance between shot point and diffracting edge were considered. A dependence of the relative amplitude of diffracted waves on the location of the diffracting edge is given. The pattern of the seismic wavefield depends upon the dimensions of the fracture zone. Amplitude curves of reflected-diffracted waves are presented for a series of models of fracture zones. The possibility of applying the amplitudes of reflected-diffracted wave trains to the interpretation of the structure of fracture zones in the Earth's crust is andysed for different types of fracture zones.     

风向对半固定沙垄表面风速影响——以古尔班通古特沙漠为例

利用DETI可移动测风系统对古尔班通古特沙漠半固定沙垄表面风速进行实地观测,获取了主要风季不同风向条件下沙垄表面7个典型部位距离地表20 cm、40 cm、60 cm、100 cm和200 cm 5个高度的风速系列数据,系统研究风向对半固定沙垄表面坡面风速及风速廓线的影响。结果表明,迎风坡的气流加速和背风坡的风速降低现象在实际观测中得到证实,但受风向的影响甚大。垄顶风速放大率随入射角的增大呈指数关系递增,而背风坡风速占垄顶风速的比率则随入射角的增大呈线性关系递减。大角度入射气流速度变化主要受控于沙垄形态,小角度入射气流速度变化主要受控于地表植被状况。无论气流以何种角度入射,距沙垄表面20 cm高度气流的加速均较其他高度缓和。沙垄底部和坡中下部的风速廓线变化趋势基本一致,且呈较好的对数拟合关系;两坡中上部和垄顶部的对数拟合方程相关系数偏小;受回旋涡流的影响,风速廓线在背风坡上部有明显偏折,初步断定涡流中心在距地表40 cm左右的高度。     

Freezing and thawing effects of sand-silt mixtures on elastic waves

Freezing and thawing during the winter season change soil properties such as density. The density change in the particulate media influences soil stiffness. In addition, freezing of partially or fully saturated soils changes the soil matrix from a particulate media to a continuum. The goal of this study is to investigate the cyclic freezing and thawing effects on elastic waves. Sand-silt mixtures with 10% silt fraction in weight and 40% saturation are prepared. The sand-silt mixtures are placed in a nylon cell, onto which a pair of bender elements and a pair of piezoelectric disk elements are installed for the measurement of shear and compressional waves, respectively. The temperature of the mixtures decreases from 20°C to 10°C to freezing. The frozen sample is gradually thawed at room temperature (20°C). These freezing-thawing processes are repeated three times. The test result shows that the shear and compressional wave velocities significantly increase when the specimen is frozen. When the temperature is greater than 0°C, the elastic wave velocities are lower during thawing than during freezing due to soil structure change. This study demonstrates that soil structure change during the winter season may be effectively estimated from elastic waves.     

A Preliminary Investigation into the Relationship between Long-Period Seismic Noise and Local Fluctuations in the Atmospheric Pressure Field

Summary The displacement response of an elastic half space to a plane pressure wave is examined in order to establish the conditions under which sources of this type can contribute significantly to the long-period seismic noise field. The study is restricted to pressure waves which propagate at velocities well below the seismic wave velocities characteristic of the half space. The numerical studies indicate that pressure waves with amplitudes of 100 μbar or more can contribute significantly to the long-period vertical background noise observed at the surface, provided that the detectors are located on sections of alluvial fill or poorly to moderately indurated sandstones and shales whose thicknesses are greater than about a kilometre. These same waves can also create significant tilt noise on long-period horizontal seismographs located at or near the surface, regardless of the rock type. The seismic disturbances created by pressure waves decay rapidly away from the surface. Therefore, it appears that it may be possible to eliminate the effects of atmospherically generated noise by placing the detectors at moderate depths.     

Structural development along the Billefjorden Fault Zone in the area between Kjellströmdalen and Adventdalen/Sassendalen, central Spitsbergen

The Billefjorden Fault Zone represents a major lineament on Spitsbergen with a history of tectonic activity going back into the Devonian and possibly earlier. Recent structural, sedimcntological and stratigraphical investigations indicate that most of the stratigraphic thickness variations within the Mesozoic strata along the Billefjorden Fault Zone south of Isfjordcn are due to Tertiary compressional tectonics related to the transpressive Eocene West-Spitsbergen Orogeny. No convincing evidence of distinct Mesozoic extensional events, as suggested by previous workers, has been recognized. Tertiary compressional tectonics are characterized by a combined thin-skinned/thick-skinned structural style. Decollement zones arc recognized in the Triassic Sassendalen Group (tower Décollement Zone) and in the Jurassic/Cretaceous Janusfjellet Subgroup (Upper Décollement Zone). East-vergent folding and reverse faulting associated with these decollement' zones have resulted in the development of compressional structures, of which the major arc the Skolten and Tronfjellct Anticlines and the Advcntelva Duplex. Movements on one or more high angle east-dipping reverse faults in the pre-Mesozoic basement have resulted in the development of the Juvdalskampcn Monocline, and are responsible for out-of-sequence thrusting and thinning of the Mesozoic sequence across the Billefjorden Fault Zone. Preliminary shortening calculations indicate an eastward displacement of minimum 3-4 km, possibly as much as 10 km for the Lower Cretaceous and younger rocks across the Billefjorden Fault Zone.     

Temperature Dependence of Single-Crystal Spinel (MgAl2O4) Elastic Constants from 293 to 423°K Measured by Light-Sound Scattering in the Raman-Nath Region

Summary. The temperature dependence of single-crystal elastic constants of synthetic stoichiometric MgAl₂O₄ spinel has been measured by the light-sound scattering technique in the Raman-Nath region. The crystal is set into forced vibration by a single crystal LiNbO₃ transducer coupled to one crystal face. A He-Ne Laser beam is diffracted by the stress-induced birefringence inside the crystal. The diffraction angle is determined from the distance between two spots exposed on a photographic plate by the first order diffracted beams as measured by a microdensitometer. The sound wavelength inside the crystal is then inferred from the laser diffraction angle. Combining the sound wavelength with the measured transducer frequency, the velocity inside the crystal is determined typically to a precision of 0·05 per cent. In this method, the measurement of velocity is not dependent on either the determination of sample length or on phase shifts at sample-transducer interface. Velocities of four pure modes, L //[001], T //[001], L //[110], and T //[110]( P //[1 1 0] are measured in the temperature range between 293 and 423 °K. A linear temperature dependence is fit to the data by a least square method. Values obtained at 25 °C from this linear fit are
The temperature dependence of the adiabatic elastic constants and bulk and shear (VRH average) moduli is computed using the density and literature value of thermal expansion coefficient. Values obtained are:
A comparison with previous measurements by pulse superposition and ultrasonic interferometry methods is made. Disagreement, when present, is discussed in terms of the separate measuring techniques. Finally, the present method, with its possibility for further improvement, is evaluated as a new method to measure temperature and pressure dependence of elastic constants.     

Numerical simulation of roadbed slope under seismic action in permafrost regions

The deformation and strength characteristics of roadbed slope under seismic loading in permafrost regions are simulated numerically. The seismic response of roadbed at different positions and inclinati...     

Measuring anisotropy in rocks using laser-generated ultrasound

Summary. Measurements using standard contacting piezoelectric transducers and non-contacting laser sources and detectors, have been investigated for the study of ultrasonic anisotropy in rocks. An ultrasonic polariscope has been constructed in order to obtain reproducible travel-time and amplitude measurements. Three case studies are described to demonstrate the apparatus, namely isotropic halite, anisotropic calcite and transversely anisotropic mudstone. A novel technique has been developed in order to construct pseudo-particle motion diagrams, to highlight shear-wave birefringence in rock samples using 2.25 MHz transducers. A pulsed laser has been used to generate compressional and shear waves for comparison with piezoelectric transducer results. The pulses generated by laser irradiation have many advantages for the study of velocity and attenuation anisotropy because of their known characteristics, broad bandwidth and high level of reproducibility. The use of a non-contacting laser source and detector eliminates the need for elaborate coupling agents, stress bonding or immersion techniques. Point-source and line-focusing of the laser beam provides an indirect method of studying shear-wave polarization phenomena. Results from rotation of the line-focused laser beam and rotation of piezoelectric shear-wave transducers with respect to anisotropy, are compared for both velocity and amplitude phenomena in an anisotropic rock sample.