Dynamic response of a group of flexible foundations to incident seismic waves

The dynamic response of a finite number of flexible surface foundations subjected to harmonic incident Rayleigh or SH waves is presented. The foundations are assumed to be resting on an elastic half-space. The results show that the foundation stiffness has a marked effect on the vertical response, while there is only a minor effect on the horizontal displacements. In general, the dynamic response decreases with increasing foundation stiffness. In cases of Rayleigh wave incidence, the existence of an adjacent foundation generates a certain amount of horizontal response in the direction perpendicular to the incident wave and subsequently causes the system to undergo a torsional motion; while in cases of horizontally incident SH waves, a vertical response has been observed and its magnitude is comparable to the response in the direction of the incident wave.     

Horizontal rotation signals detected by “G-Pisa” ring laser for the M w = 9.0, March 2011, Japan earthquake

We report the observation of the ground rotation induced by the M _w = 9.0, 11th of March 2011, Japan earthquake. The rotation measurements have been conducted with a ring laser gyroscope operating in a vertical plane, thus detecting rotations around the horizontal axis. Comparison of ground rotations with vertical accelerations from a co-located force balance accelerometer shows excellent ring laser coupling at periods longer than 100?s. Under the plane wave assumption, we derive a theoretical relationship between horizontal rotation and vertical acceleration for Rayleigh waves. Due to the oblique mounting of the gyroscope with respect to the wave direction of arrival, apparent velocities derived from the acceleration/rotation rate ratio are expected to be always larger than or equal to the true wave propagation velocity. This hypothesis is confirmed through comparison with fundamental mode, Rayleigh-wave phase velocities predicted for a standard Earth model.     

Effects of Impedance Contrast and Soil Thickness on Basin-Transduced Rayleigh Waves and Associated Differential Ground Motion

This paper presents the effects of impedance contrast (IC) across the basin edge, velocity contrast between the basin and underlying bedrock, Poisson’s ratio and soil thickness on the characteristics of basin-transduced Rayleigh (BTR) waves and associated differential ground motion (DGM). Analysis of simulated results for a two-dimensional (2D) basin revealed complex mode transformation of Rayleigh waves after entering the basin. Excellent correlation of frequencies corresponding to different spectral ratio peaks in ellipticity curves of BTR waves and spectral amplification peaks was obtained. However, such correlation was not observed between values of peaks in ellipticity curves and spectral amplification at the corresponding frequencies. An increase of spectral amplification with IC was obtained. The largest spectral amplification was more than twice the IC in the horizontal component and more than the IC in the vertical component in the case of large and same impedance contrast for P- and S-waves. It was concluded that the frequency corresponding to the largest spectral amplification was greater than the fundamental frequency of soil by around 14% and 44% in the vertical and horizontal components, respectively. Spectral amplification of the vertical component was negligible when soil thickness was less than around 15–20 times the S-wave wavelength in the basin. The largest values of peak ground displacement (PGD) and peak differential ground motion (PDGM) were obtained very near the basin edge, and their values with offset from the edge were strongly dependent on the IC across the basin edge, Poisson’s ratio, velocity contrast between the basin and underlying bedrock (dispersion), damping and soil thickness. The obtained value of PDGM for a span of 50 m in the horizontal and vertical components due to the BTR wave was of the order of 0.75 × 10^?3 and 1.32 × 10^?3 for unit amplitude (1.0 cm) in the horizontal component of the Rayleigh wave at rock very near the basin edge.     

Effect of topography and subsurface inhomogeneity on seismic rayleigh waves

The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves. In the previous paper, the same effect was investigated in the case of SV waves. Several types of topography, such as cliffs both with and without a soft layer at the foot of the slope, are considered. Computations are made using a new hybrid method combining a particle model with a finite element method. In cases of harmonic Rayleigh waves, surface motions with amplitudes as large as 1.5 to 5 times the horizontal surface displacement of the incident Rayleigh waves are produced near the slope and the sloping interface. When a Rayleigh wave propagating through a hard single-layered ground encounters a sloping interface where hard ground and soft ground make contact with each other, Rayleigh waves having two different, phase velocities are produced and they correspond to the fundamental mode, and the first mode determined by Haskell's method. In addition, the transient response when Rayleigh waves propagate through the cliff is also simulated. Assuming the vertical component of the Tokachi-oki Earthquake (1968) measured on the surface to be a Rayleigh wave, the incident Rayleigh wave can be obtained by a Fourier synthesis of eigenfunctions of Rayleigh waves.     

Determining Q of near-surface materials from Rayleigh waves

High-frequency (≥2 Hz) Rayleigh wave phase velocities can be inverted to shear (S)-wave velocities for a layered earth model up to 30 m below the ground surface in many settings. Given S-wave velocity (V_S), compressional (P)-wave velocity (V_P), and Rayleigh wave phase velocities, it is feasible to solve for P-wave quality factor Q_P and S-wave quality factor Q_S in a layered earth model by inverting Rayleigh wave attenuation coefficients. Model results demonstrate the plausibility of inverting Q_S from Rayleigh wave attenuation coefficients. Contributions to the Rayleigh wave attenuation coefficients from Q_P cannot be ignored when Vs/V_P reaches 0.45, which is not uncommon in near-surface settings. It is possible to invert Q_P from Rayleigh wave attenuation coefficients in some geological setting, a concept that differs from the common perception that Rayleigh wave attenuation coefficients are always far less sensitive to Q_P than to Q_S. Sixty-channel surface wave data were acquired in an Arizona desert. For a 10-layer model with a thickness of over 20 m, the data were first inverted to obtain S-wave velocities by the multichannel analysis of surface waves (MASW) method and then quality factors were determined by inverting attenuation coefficients.     

两种不同势函数下半空间饱和多孔介质中Rayleigh波求解比较

分别对"考虑两种压缩波和幅值比例系数"和"考虑一种压缩波(P1或P2波)但不考虑幅值比例系数"两种不同势函数下的半空间饱和多孔介质中Rayleigh波求解进行详细推导,理论分析表明"考虑两种压缩波和幅值比例系数"下Rayleigh波求解推导更为严密,与饱和多孔介质中存在两种压缩波的事实相一致。在研究半空间饱和多孔介质中Rayleigh波时应采用"考虑两种压缩波和幅值比例系数"的势函数。     

煤巷小构造Rayleigh型槽波超前探测数值模拟

对煤巷小构造地震波场进行了数值模拟研究,分析了层状煤层中地震波的传播特征.研究表明:(1)在煤巷迎头前方煤层内以纵波震源激发的Rayleigh型槽波相对于体波能量较强,波列较长,波速较低.(2)沿煤层传播的Rayleigh型槽波在小构造面上产生Rayleigh型槽波反射波,反射Rayleigh型槽波垂直分量相对于水平分量能量较强.沿煤层反向传播的反射Rayleigh型槽波在煤巷迎头面上转换为沿煤巷底板传播的Rayleigh面波.沿煤巷底板可以接收到能量较强的反射Rayleigh型槽波产生的Rayleigh面波,其可以作为超前探测小构造面的特征波.在地震记录上反射Rayleigh型槽波产生的Rayleigh面波波至最迟,在时间域与其他波列时间间隔较大,其垂直分量能量相对于水平分量较强,在地震记录上容易识别.(3)在相同的地质条件下应用反射地震超前探测方法,标志煤巷迎头前方存在小构造面的反射地震波能量较弱,受煤巷顶、底板界面和采煤迎头面的强反射波干扰,在地震记录中难以识别.     

On coda waves of earthquakes

Summary Coda waves viz. the tail portion of an earthquake record have been observed and analysed byCarder, Macelwane and others. They showed that the periods of such waves increase with the increase of epicentral distances.Carder observed that these waves have very little transverse component so that these may be considered as of the type of Rayleigh waves. RecentlyOmote showed that the Coda waves contain three periodsT ₁,T ₂,T ₃ of whichT ₁ increases with epi-central distances as observed by previous observers. ButT ₂,T ₃ remain constant for all earthquakes from different epicentral distances.Omote tried to explain this phenomenon by considering that the surface of the earth consists of several layers andT ₂,T ₃ are free oscillation periods of the surface layers.T ₁ period has been explained bySezawa and also byJeffreys which has been shown byGutenberg. The author has attempted to explain the periodsT ₂,T ₃ by considering passage of cracks at the focal region. The Rayleigh wave character of Coda waves and low velocity of such waves have been explained.     

Finite amplitude holmboe waves

Abstract

We investigate the evolution of a parallel shear flow which has embedded within it a thin, symmetrically positioned layer of stable density stratification. The primary instability of this flow may deliver either Kelvin-Helmholtz waves or Holmboe waves, depending on the strength of the stratification. In this paper we describe a sequence of numerical simulations which reveal for the first time the behavior of the Holmboe wave at finite amplitude and clarify its structural relationship to the Kelvin-Helmholtz wave.

The flows investigated have initial profiles of horizontal velocity and Brunt-Vaisala frequency given in nondimensional form by U = tanhζ and N ²=J sech² RCζ, respectively, in which ζ is a nondimensional vertical coordinate, J is the value of the gradient Richardson number N ²/(dU/dζ)² at ζ=0, and R = 3. Linear stability theory predicts that the flow will develop Holmboe instability when J exceeds some critical value J_c' and Kelvin-Helmholtz instability when J is less than J_c; J_c being approximately equal to 0.25 when R=3. We simulate the evolution of flows with J=0.9, J=0.45, and J = 0.22, and find that the first two simulations yield Holmboe waves while the third yields a Kelvin-Helmholtz wave, as predicted.

The Holmboe wave is a superposition of two oppositely propagating disturbances, a right-going mode whose energy is concentrated in the region above the centre of the shear layer, and a left-going mode whose energy is concentrated below the centre of the shear layer. The horizontal speed of the modes varies periodically, and the variations are most pronounced at low values of J. If J ζ J_c' the minimum horizontal speed of the modes vanishes and the modes become phase-locked, whereupon they roll up to form a Kelvin-Helmholtz wave as predicted by Holmboe (1962). When J is moderately greater than J_c' the Holmboe wave ejects long, thin plumes of fluid into the regions above and below the shear layer, as has often been observed in laboratory experiments, and we examine in detail the mechanism by which this occurs.     

Statistics of gravity waves in the lower stratosphere over Beijing based on high vertical resolution radiosonde

Atmospheric gravity waves, with small to medium scales, prevail in the atmosphere and have global ef- fects. Many researches show that gravity waves are the main source that causes the variation of wind and temperature field in the stratosphere, and that the break-up of upward propagating gravity waves is the dominant sources of small scale turbulent and mixing processes in the middle atmosphere. Theories and ob- servations indicate that the redistribution of momen- tum, caused by the generati…     

Site effects in Mexico City: Constraints from surface wave inversion of shallow refraction data

In order to understand and simulate site effects on strong ground motion records of recent earthquakes in Mexico City, it is fundamental to determine the in situ elastic and anelastic properties of the shallow stratigraphy of the basin. The main properties of interest are the shear wave velocities and Q-quality factors and their correlation with similar parameters in zones of the city. Despite population density and paved surfaces, it is feasible to gather shallow refraction data to obtain laterally homogeneous subsoil structures at some locations. We focused our analysis in the Texcoco Lake region of the northeastern Mexico City basin. This area consists of unconsolidated clay sediments, similar to those of the lake bed zone in Mexico City, where ground motion amplification and long duration disturbances are commonly observed. We recorded Rayleigh and Love waves using explosive and sledgehammer sources and 4.5 Hz vertical and horizontal geophones, respectively. Additionally, for the explosive source, we recorded three-component seismograms using 1 Hz seismometers. We obtained phase velocity dispersion curves from ray parameter-frequency domain analyses and inverted them for vertical distribution of S wave velocity. The initial model was obtained from a standard first-break refraction analysis. We also obtained an estimation of the Q_S shear wave quality factor for the uppermost stratigraphy. Results compare well with tilt and cone penetrometer resistance measurements at the same test site, emphasizing the importance of these studies for engineering purposes.     

Wave propagation in marine sediments and water saturated soils

Summary A unification of the theories of Biot and Weiskopf has been made to form the suitable equations of motion for porous water saturated soils and marine sediments. It has been shown that the velocities of the body waves depend on the direction of propagation. In the vertical direction there are three, one distortional and two dilatational waves. In the horizontal direction there are two dilatational and two distortional waves. Finally, propagation of Love waves and Rayleigh waves have been discussed. Suitable potential functions have been derived to find the frequency equation for Rayleigh waves.     

Estimation of rocking and torsion associated with surface waves extracted from recorded motions

By exploiting the capability of identifying and extracting surface waves existing in a seismic signal, we can proceed to estimate the angular displacement (rotation about the horizontal axis normal to the direction of propagation of the wave; rocking) associated with Rayleigh waves as well as the angular displacement (rotation about the vertical axis; torsion) associated with Love waves.For a harmonic Rayleigh (Love) wave, rocking (torsion) would be proportional to the harmonic vertical (transverse horizontal) velocity component and inversely proportional to the phase velocity corresponding to the particular frequency of the harmonic wave (a fact that was originally exploited by Newmark (1969) [15] to estimate torsional excitation). Evidently, a reliable estimate of the phase velocity (as a function of frequency) is necessary. As pointed out by Stockwell (2007) [17], because of its absolutely referenced phase information, the S-Transform can be employed in a cross-spectrum analysis in a local manner. Following this suggestion a very reliable estimate of the phase velocity may be obtained from the recordings at two nearby stations, after the dispersed waves have been identified and extracted. Synthesis of the abovementioned harmonic components can provide a reliable estimate of the rocking (torsional) motion induced by an (extracted) Rayleigh (Love) wave.We apply the proposed angular displacement estimation procedure for two well recorded data sets: (1) the strong motion data generated by an aftershock of the 1999 Chi-Chi, Taiwan earthquake and recorded over the Western Coastal Plain (WCP) of Taiwan, and (2) the strong motion data generated by the 2010 Darfield, New Zealand earthquake and recorded over the Canterbury basin. The former data set is dominated by basin-induced Rayleigh waves while the latter contains primarily Love waves.     

Quasi-Rayleigh Waves in Transversely Isotropic Half-Space with Inclined Axis of Symmetry

A method for determination of characteristics of quasi-Rayleigh (qR) wave in a transversely isotropic homogeneous half-space with inclined axis of symmetry is outlined. The solution is obtained as a superposition of qP, qSV and qSH waves, and surface wave velocity is determined from the boundary conditions at the free surface and at infinity, as in case of Rayleigh wave in an isotropic half-space. Though the theory is simple enough, a numerical procedure for calculation of surface wave velocity presents some difficulties. The difficulty is caused by necessity to calculate complex roots of a non-linear equation, which in turn contains functions determined as roots of non-linear equations with complex coefficients. Numerical analysis shows that roots of the equation corresponding to the boundary conditions do not exist in the whole domain of azimuths and inclinations of the symmetry axis. The domain of existence of qR wave depends on the ratio of the elastic parameters: for some strongly anisotropic models the wave cannot exist at all. For some angles of inclination qR-wave velocities deviate from those calculated on the basis of the perturbation method valid for weak anisotropy, though they have the same tendency of variation with azimuth. The phase of qR wave varies with depth unlike Rayleigh wave in an isotropic half-space. Unlike Rayleigh wave in an isotropic half-space, qR wave has three components - vertical, radial and transverse. Particle motion in horizontal plane is elliptic. Direction of the major axis of the ellipsis coincides with the direction of propagation only in azimuths 0° (180°) and 90° (270°).     

Characterization of dipping fractures in a transverselyisotropic background

Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.     

Non-linear marginal convection in a rotating magnetic system

Abstract

An inviscid, electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by two vertical walls. The fluid is permeated by a strong uniform horizontal magnetic field aligned with the side wall boundaries and the entire system rotates rapidly about a vertical axis. The ratio of the magnitudes of the Lorentz and Coriolis forces is characterized by the Elsasser number, A, and the ratio of the thermal and magnetic diffusivities, q. By heating the fluid from below and cooling from above the system becomes unstable to small perturbations when the adverse density gradient as measured by the Rayleigh number, R, is sufficiently large.

With the viscosity ignored the geostrophic velocity, U, which is aligned with the applied magnetic field, is independent of the coordinate parallel to the rotation axis but is an arbitrary function of the horizontal cross-stream coordinate. At the onset of instability the value of U taken ensures that Taylor's condition is met. Specifically the Lorentz force, which results from marginal convection must not cause any acceleration of the geostrophic flow. It is found that the critical Rayleigh number characterising the onset of instability is generally close to the corresponding value for the usual linear problem, in which Taylor's condition is ignored and U is chosen to vanish. Significant differences can occur when q is small owing to a complicated flow structure. There is a central interior region in which the local magnetic Reynolds number, R_m , based on U is small of order q and on exterior region in which R_m is of order unity.     

On the interaction of rayleigh surface waves with structures

A two-dimensional soil-structure interaction analysis is carried out for transient Rayleigh surface waves that are incident on a structure. The structure is modelled by a three-degree of freedom rigid basemat to which is attached a flexible superstructure, modelled by a single mass-spring system. The structural responses to a given Rayleigh wave train are compared with those that would have been obtained if the free-field acceleration-time history had been applied as a normally incident body wave. The results clearly exhibit the [frequency filtering] effects of the rigid basemat on the incident Rayleigh waves. It is shown that, if seismic excitation of a structure is, in fact, due to Rayleigh surface waves, then an analysis assuming normally incident body waves can considerably over-estimate structural response, both at basemat level for horizontal and vertical motions and for vertical oscillations of the superstructure. However, in the examples considered here, relatively large rocking effects were induced by the Rayleigh waves, thus giving maximum horizontal accelerations in the superstructure that were of comparable magnitude for Rayleigh and normally incident body waves.     

PROCESSING OF PS-REFLECTION DATA APPLYING A COMMON CONVERSION-POINT STACKING TECHNIQUE1

Converted waves require special data processing as the wave paths are asymmetrical. The CMP concept is not applicable for converted PS waves, instead a sorting algorithm for a common conversion point (CCP) has to be applied. The coordinates of the conversion points in a single homogeneous layer can be calculated as a function of the offset, the reflector depth and the velocity ratio v_P/ v_s. For multilayered media, an approximation for the coordinates of the conversion points can be made. Numerical tests show that the traveltime of PS reflections can be approximated with sufficient accuracy for a certain offset range by a two-term series truncation. Therefore NMO corrections can be calculated by standard routines which use the hyperbolic approximation of the reflection traveltime curves. The CCP-stacking technique has been applied to field data which have been generated by three vertical vibrators. The in-line horizontal components have been recorded. The static corrections have been estimated from additional P- and SH-wave measurements for the source and geophone locations, respectively. The data quality has been improved by processes such as spectral balancing. A comparison with the stacked results of the corresponding P- and SH-wavefield surveys shows a good coherency of structural features in P-, SH- and PS-time sections.