Studies on seismic waves

The development of seismic wave study in China in the past four years is reviewed. The discussion is divided into several aspects, including seismic wave propagation in laterally homogeneous media, laterally heterogeneous me-dia, anisotropie and porous media, surface wave and seismic wave inversion, and seismic wave study in prospect-ing and logging problems. Important projects in the current studies on seismic wave is suggested as the develop-ment of high efficient numerical methods, and applying them to the studies of excitation and propagation of seis-mic waves in complex media and strong ground motion, which will form a foundation for refined earthquake haz-ard analysis and prediction.     

Studies on seismic source

During the period of 1999~2002, the Chinese seismologists made a serious of developments in the study on seismic sources including observations, experiments and theory. In the field of observation, the methods of the accuracy location of earthquake sources, the inversion of seismic moment tensor and the mechanism of earthquake source are improved and developed. A lot of important earthquake events are studied by using these methods. The rupture processes of these events are inverted and investigated combined with the local stress fields and the tectonic moment by using the measurements of surface deformation. In the fields of experiments and theory, many developments are obtained in cause of seismic formation, condition of stress and tectonics, dynamics of earthquake rupture, rock fracture and nucleation of strong earthquakes.     

Studies on seismic source

During the period of 1999-2002, the Chinese seismologists made a serious of developments in the study on seis-mic sources including observations, experiments and theory. In the field of observation, the methods of the accu-racy location of earthquake sources, the inversion of seismic moment tensor and the mechanism of earthquake source are improved and developed. A lot of important earthquake events are studied by using these methods. The rupture processes of these events are inverted and investigated combined with the local stress fields and the tec-tonic moment by using the measurements of surface deformation. In the fields of experiments and theory, many developments are obtained in cause of seismic formation, condition of stress and tectonics, dynamics of earthquake rupture, rock fracture and nucleation of strong earthquakes.     

Amplitudes of explosion-generated seismic waves

Summary Records of underwater explosions in Iceland in 1959 and 1960, mainly performed for crustal studies, have been investigated with regard to amplitudes. The amplitudes ofP2 in the 1959 explosions and of the first arrivingP waves in the 1960 explosions were found to be proportional to the first power of the charge weight, whereas amplitudes ofP1 andS1 in the 1959 explosions were proportional to the 3/4-power of the charge up to 200 kg, but increased much slower for larger charges. The influence of water depth of shot point on the charge weights, required to obtain a certain amplitude, has been determined and it was found that the logarithm of the charge weight has a linear relation to water depth down to about 8 meters. The amplitudes of first arrivingP waves decrease as the inverse 2.2-power of the distance up to about 30 km. For greater distances an exponential decrease of the form (const./) exp (–) is valid. ForP2 waves with a frequency of 10 cps we found =0.027±0.003 km^–1 for a profile across central Iceland and =0.009±0.004 km^–1 for a profile in the western part of Iceland.

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Zusammenfassung In den Jahren 1959 und 1960 wurden auf Island Unterwasser-Explosionen ausgelöst, deren Hauptziel Untersuchung der Erdkruste waren. Die Aufzeichnungen der Explosionen werden hier in Hinsicht auf die Amplituden der Wellen untersucht. DieP2-Amplituden in den Explosionen von 1959 und die Amplituden der zuerst ankommendenP-Wellen in den Explosionen von 1960 waren proportional der ersten Potenz des Ladungsgewichtes, während diePl-undSl-Amplituden in den Explosionen von 1959 proportional der 3/4-Potenz des Ladungsgewichtes bis 200 kg waren. Für höhere Ladungsgewichte wuchsen die Amplituden langsamer an. Es wurde der Einfluss der Tiefe des Schusspunktes unterhalb des Wasserspiegels auf das für eine gewisse Amplitude benötigte Ladungsgewicht bestimmt. Es ergab sich dabei, dass der Logarithmus des Ladungsgewichtes in einer linearen Beziehung zur Tiefe, bis etwa 8 m, steht. Die Amplituden der zuerst ankommendenP-Wellen sind umgekehrt proportional der 2.2-Potenz der Entfernung, bis etwa 30 km. Für grössere Entfernungen ist die Abnahme der Amplituden exponential und kann durch (Konst./) exp (–) dargestellt werden. FürP2 mit einer Frequenz von 10 cps haben wir =0.027±0.003 km^–1 für ein Profil in Zentral-Island und =0.009 ± 0.004 km^–1 für ein Profil in West-Island gefunden.

     

论可能存在的地幔柱地震导波

假想的地幔热地幔柱预期地震波速低,因而可支持类似于断层带地震导波、光纤波和海洋声音固定和测距通道声波的弹性导波传播。地幔柱导波在波导中对几何复杂性并不敏感,其频散会使其在地震记录中与众不同并提供可以补充地震层析成像波导结构的有关信息。检测这类波将成为地幔柱存在新一类强有力的证据。嵌于无限介质中的圆柱形通道支持两类轴对称弹性波振型,即扭转振型和纵向—径向振型。扭转振型有与柱体表面横切的直线质点运动。纵向—径向振型在含有圆柱体轴的平面上有椭圆形质点运动,在轴附近有反向运动。椭圆形质点运动的方向随距离与轴反向:基本振型为一倍,第一谐波为两倍,依此类推。每种振型只有在超过其截止频率时才存在,相速度和群速度在无限介质中等于剪切波速。在高频率时两种速度在通道中接近剪切波速。所有振型在它们的群速度中均有最小值,在地震记录上产生艾里相位。对于剪切波速有百分之几的反差尽管对于地球的热地幔柱而言是现实的,但最大的信号是反向频散的,并有约0.1～1Hz和15～30s持续时间的优势频率。可观测到的地幔柱波至少有两个可能的来源:(1)深地幔中地幔柱与高振幅核震相焦散线的相交;(2)向下传播的导波在核幔边界ScS状的反射。最近广泛部署的宽带地震仪使搜索这些波成为可能。     

On surface seismic waves formation

Summary The interpretation of surface seismic waves records is rather complicated as they include a superposition of oscillations of the fundamental mode and higher modes. Besides recorded oscillations depend on spectral characteristics of motions in earthquakes sources. The consideration of these problems is based on results of surface waves two-dimensional modelling [1]³. Some physical ideas about their formation deals with the change of the nature of the oscillation propagating with dispersion. This report represents a condensate of several independent works. , , . , . , . () . .Scientific communication presented to the IASPEI Assembly, Madrid, 1969.     

Effects of causal absorption on seismic body waves

Summary The effects of the causal absorption on seismic wave fields are discussed. Several computer programs for the evaluation of seismic wave fields have been modified to include the causal absorption. The programs are based mostly on matrix and ray methods. The main attention is paid to ray methods. A simple plane wave algorithm is described, which can be used along the ray to compute elementary seismograms in dissipative media. For a certain class of signals, commonly used in seismology, its application does not require any convolution or frequency-domain computations, and is only slightly slower than the evaluation of elementary seismograms in non-dissipative media. The derived algorithm even describes the velocity dispersion related to absorption and the decrease of the prevailing frequency of the signal well. Numerical examples are presented, both exact and approximate.     

Soil amplification of plane seismic waves

Amplitudes of surface particle velocities are calculated when time-harmonic seismic waves of uniform amplitude are incident upon an arbitrary stratified elastic soil layer from the underlying bedrock. Whereas previous workers have mainly treated normally incident S waves, we allow the waves to be of SV, P, or SH types and to have arbitrary angles of incidence. Following standard practice the problem is set up as a matrix differential system, but in such a way that incident SV and P waves may be treated together (the system for SH decoupling). Though complicated, the 4 × 4 SVP system has considerable structure which is elucidated in Appendices 1 and 2. These results, though not altogether new, are of independent interest, and are gathered together in concise form for reference. The theory for low- and for high-frequency approximations is given. The main results of the work are illustrated by two numerical examples: Model 1 where the soil layer is homogeneous; and Model 2 where the soil layer has a linear velocity profile.     

Continental dispersion of seismic surface waves

Summary Continental dispersion curves for Love and Rayleigh waves have been determined by means of the Uppsala seismograph records for three earthquakes near the south coast of Turkey in April, 1957. To the authors' knowledge this is the first time dispersion curves have been determined for a relatively homogenous path across the whole of continental Europe and covering a good range of periods, namely from 3 to 86 sec for Love waves and from 5 to 61 sec for Rayleigh waves. The dispersion curves obtained are relevant to determinations of the average structure along the path traversed in particular, and to determinations of crustal structure of the European continent in general.

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Zusammenfassung Kontinentale Dispersionskurven für Love-und Rayleigh-Wellen wurden vermittels Registrierungen an der Station Uppsala von drei Erdbeben in der Nähe der Südküste der Türkei im April 1957 bestimmt. Soweit es den Autoren bekannt ist, wurden damit erstmalig Dispersionskurven für einen relativ homogenen Weg über das gesamte kontinentale Europa mit einem beträchtlichen Periodenbereich, der 3 bis 86 Sek für Love-Wellen und 5 bis 61 Sek für Rayleigh-Wellen umfasst, ausgearbeitet. Die erhaltenen Dispersionskurven haben ihre Bedeutung in der Festlegung der mittleren Krustenstruktur entlang dem durchlaufenen Wellenweg und überhaupt in der Festlegung der Krustenstruktur im Bereich des europäischen Kontinents.

     

Sensitivity of seismic waves to structure

We study how the perturbations of a generally heterogeneous isotropic or anisotropic structure manifest themselves in the wavefield, and which perturbations can be detected within a limited aperture and a limited frequency band. A short-duration broad-band incident wavefield with a smooth frequency spectrum is considered. In-finitesimally small perturbations of elastic moduli and density are decomposed into Gabor functions. The wavefield scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves are estimated using the first-order Born approximation with the paraxial ray approximation. For each incident wave, each Gabor function generates at most 5 scattered waves, propagating in specific directions and having specific polarisations. A Gabor function corresponding to a low wavenumber may generate a single broad-band unconverted wave scattered in forward or narrow-angle directions. A Gabor function corresponding to a high wavenumber usually generates 0 to 5 narrow-band Gaussian packets scattered in wide angles, but may also occasionally generate a narrow-band P to S or S to P converted Gaussian packet scattered in a forward direction, or a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in wide angles. In this paper, we concentrate on the Gaussian packets caused by narrow-band scattering. For a particular source, each Gaussian packet scattered by a Gabor function at a given spatial location is sensitive to just a single linear combination of 22 values of the elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered wave does not fall into the aperture covered by the receivers and into the legible frequency band.     

Propagation of seismic waves through liquefied soils

To predict the earthquake response of saturated porous media it is essential to correctly simulate the generation, redistribution, and dissipation of excess pore water pressure during and after earthquake shaking. To this end, a reliable numerical tool requires a dynamic, fully coupled formulation for solid–fluid interaction and a versatile constitutive model. Presented in this paper is a 3D finite element framework that has been developed and utilized for this purpose. The framework employs fully coupled dynamic field equations with a u–p–U formulation for simulation of pore fluid and solid skeleton interaction and a SANISAND constitutive model for response of solid skeleton. After a detailed verification and validation of the formulation and implementation of the developed numerical tool, it is employed in the seismic response of saturated porous media. The study includes examination of the mechanism of propagation of the earthquake-induced shear waves and liquefaction phenomenon in uniform and layered profiles of saturated sand deposits.     

Spectra of seismic waves of Matsushiro micro-earthquakes

Summary The spectra of Matsushiro micro-earthquakes were studied using a spectrum analyser and discussed in relation to their magnitude and the epicentral distance. It was found that the spectra of seismic waves by Matsushiro micro-earthquakes did not depend upon the epicentral distance since the sonagrams showed a peak around 5 cps at Matsushiro as well as Suzaka. The spectrum also failed to show any distinct peak for micro-earthquakes of magnitude lower than 1.0 due to the decrease of signal to noise ratio.     

On rigid foundations subjected to seismic waves

In the analysis of structural foundations for seismic loads, it is customary to distinguish two types of soil-structure interaction effect: kinematic interaction (or wave passage), and inertial interaction. The former refers to the phenomenon of wave scattering, which occurs because the foundation is much stiffer than the surrounding soil and cannot accommodate to its distortions. Inertial interaction, on the other hand, is caused by feedback of kinetic energy of the structure into the soil. This paper is concerned only with the first phenomenon. The rigorous analysis of rigid, embedded foundations subjected to seismic disturbances requires, in general, substantial computational effort. Indeed, a typical analysis would normally require models with finite elements and/or boundary elements. Although such methods may be used to find an accurate solution to the problem of kinematic interaction, their use is not always warranted, given the many uncertainties involved and the multitude of assumptions that must be considered. Hence, approximate solutions are attractive for this problem. One such approximate method is the remarkably simple algorithm proposed by Iguchi.³ This paper presents first an appraisal of this method by way of a comparison with accurate numerical solutions for cylindrical foundations; next the algorithm is applied to rectangular (prismatic) foundations. It is found that Iguchi's method gives results that are adequate for engineering purposes, even if not entirely accurate.     

高铁地震数据干涉成像技术初探

高铁运行会引起铁轨的震动,从而产生地震波向地下介质中传播,通过研究该地震波可对高铁沿线的地质情况进行持续监测.与常规地震勘探中的震源相比,高铁地震中的震源较为复杂,为移动震源,而地震干涉技术可以通过地震记录间的相互干涉,消除震源的影响,因此可利用地震干涉技术对高铁地震信号进行处理并成像.本文通过分析研究,总结出地震干涉方法在处理高铁地震数据时的关键技术问题：不同于常规地震干涉中先干涉后叠加的干涉成像方式,高铁地震移动源的特点使得干涉顺序变为先叠加后干涉,由此带入了大量震源串扰噪声;初步提出两种解决高铁地震干涉成像的思路：通过对高铁地震信号的处理,使高铁变相"提速"或"降速",给出了"提速"或"降速"后各自的成像思路,并给出了数据处理的技术设想.     

Effect of topography and subsurface inhomogeneities on seismic SV waves

The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of incident SV waves. Several types of topography, such as a cliff, a cliff with a soft layer and filled land, are considered. Computations are made using a new method combining a particle model with a finite element method. The accuracy of this method is discussed through comparisons with Wong's solutions, which are in good agreement. It is found that the surface displacement is very much influenced by surface irregularities when the incident wavelengths are comparable to the size of the topographic features. Rayleigh waves are strongly produced in the neighbourhoods of the slopes of a cliff and a cliff with a soft layer, the latter being a cliff adjacent to and covered at its foot by a soft layer. Thus, a zone of large amplification takes place near a slope, combining incident SV waves and Rayleigh waves. A large displacement also occurs at the upper corner of the slope. In filled land, vertical and horizontal displacements are produced, which are 3 times larger than those at a distance. The present results are considered to be significant from the viewpoint of engineering seismology.     

近地表低降速带地震波传播规律初探

通过对沙漠区近地表地层大量微测井资料的对比分析发现,速度梯度带的存在可能是导致低降速带地震波衰减的一个重要原因.本文在沙漠地区低降速带速度结构分析的基础上,研究地震波在线性过渡体地层的传播规律,并同实际观测记录进行对比,从理论和实际上验证上述推论的正确性.     

地震槽波的数学-物理模拟初探

针对地震槽波在低速层的传播特性,开展了煤层内地震槽波勘探的数值模拟和物理模拟研究的初探工作.在数值模拟研究方面,采用交错网格有限差分法对煤层中的地震槽波进行三分量全波场模拟.基于波场快照和人工合成地震记录研究了不同模型中的波场特征和各种波型的传播规律.在物理模拟方面,通过选用不同配比的环氧树脂和硅橡胶类材料构建地震槽波物理模型,利用透射法和反射法观测系统获得了清晰的地震槽波记录以研究槽波的地震学特征.研究表明,在煤层内槽波的地震波场中,Love型槽波的能量小于Rayleigh型槽波的SV分量,大于Rayleigh型槽波的SH分量.相对于Love型槽波和Rayleigh型槽波的SH分量,Rayleigh型槽波的SV分量在围岩中的泄露能量较强.在煤层界面附近的围岩中,地震波仍以槽波形式传播,随着距离的增加能量逐渐衰减.随着煤层变薄,煤层槽波主频向高频方向移动,频散现象增强,传播速度增大.

     

Dependence of amplitudes of seismic body waves on the distance

Резюме Нзменение амплитуд объемных волн с расстоянием было изучено на основании б аемлетрясений, регистрированных 30 сейсмическими станциями в эпицентральных расстояниях<30°. Из рисунков видно, что амплитуды продолных и поперечных волн меняются в изучаемых расстояниях подобным образом, но минимум и максимум кривой (A ^*, Δ) для волнSH подвинуты к ббльшим эпицентральным расстояниям чем в случае воумPH.

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Address: Boční II, Praha 13-Spořilov.     

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.