Body Wave Propagation Research Articles

Effects of seismic wave propagation on a long and narrow building: Body wave and surface wave propagation

In the case of the dynamic analysis of the structures using the recorded earthquake ground motions, it is usually assumed that the ground motion consists of body waves propagating vertically. However, the response of a long and narrow structure may be influenced by the oblique propagation of body waves and the dispersion of surface waves. In this paper, the effects of the seismic wave propagation on the response of this kind of structure are investigated. The characteristics of the wave propagation were verified using the recorded motions and soil information at the building site. The ground motion at every input point of the building was evaluated using the difference of arrival time of seismic waves calculated by assuming the velocity and the direction of the wave propagation. Using these ground motions, response analyses of the lumped mass model for the structure were performed. By considering the characteristics of the seismic wave propagation, the average response decreased but the local response increased around the end of the roof. Further studies of the structure were also performed in order to restrain the response around the end of the roof.

The seismic coda, site effects, and scattering in alluvial basins studied using aftershocks of the 1986 North Palm Springs, California, earthquake as source arrays

Abstract We use single-station recordings of widely distributed earthquake sources to identify heterogeneities in the Earth9s crust that scatter energy into the early part of the observed S -wave codas. We assume that ray theory accurately describes the propagation of body waves from the earthquake sources to the scatterers, but we assume no propagation mechanism between the scatterers and the seismic station. A grid of hypothetical scatterers is assumed to cover the Earth9s surface, and the strength of each scatterer is determined by an iterative inversion method. Our data are recordings of aftershocks of the 1986 North Palm Springs earthquake recorded at a seismic station in the Coachella Valley, SMP, and at a station in the Morongo Valley, SMC. The technique is applied separately to each horizontal component of motion at each station. We identify a particular spot at the northwest edge of the Quaternary alluvium in the Coachella Valley that scatters waves into the S coda observed at SMP 8 km distant in the valley. The geologic structure that causes the strong scattering seems to be the basin-edge structure rather than the mountainous terrain 3 km farther west. The early coda at SMC is dominated by scattering within a few kilometers of SMC, either in the basin itself or in the Morongo Valley fault zone. This study shows that laterally propagating waves are sometimes observable in the early coda, casting doubt on the use of 1-D techniques for estimating site responses. The northwest edge of the Coachella Valley seems to be an especially strong scatterer of incident waves. If other basins have similar loci of strong scattering, perhaps these places can be identified using microearthquake seismograms and used to predict strong ground motions in the basins.

On the relations governing rayleigh wave propagation in bodies with initial stresses

On the relations governing rayleigh wave propagation in bodies with initial stresses

Wavefield extrapolation of body waves for 3-D imaging of earthquake sources

Reverse-time imaging of earthquake source parameters is extended from two to three spatial dimensions and from two- to three-component recordings. Provided that the recording aperture is sufficiently large, and the data are not spatially aliased, source radiation patterns, in both time and space, can be reconstructed by elastic reverse-time propagation of body waves; such reconstructions are necessarily partial as only the energy that was recorded is available for reconstruction. For a point source, the origin time and the (3-D) spatial location of an event can be reconstructed by extracting the time and position, of the best focused energy from the backward propagating wavefield. For a spatially and temporally extended source, biased estimates of fault position and rupture/slip time history can be estimated if the recording aperture is sufficient; for smaller recording apertures, the time history can still be estimated if the fault location and geometry are known a priori. The latter is viable for a reasonable number (<200) of three-component recordings, and so is potentially applicable to real data. All these processes assume that a smoothed representation of the 3-D velocity distribution in the volume containing the source and receivers is available.

Wave propagation in elastic bodies with restricted shear

This paper examines the propagation of waves in unbounded elastic bodies within which shear is restricted in a specific, preferred plane. It is shown that three waves propagate normal to this plane but only two propagate in any other direction. The singularities arising on the associated slowness surface are elucidated by considering materials for which the modulus of shear is high in a preferred plane. We show that the innermost sheet of the slowness surface is then a thin pencil shape normal to the preferred plane. This paper concludes with an investigation of energy propagation.

Wave propagation in exceptional directions in multi-constrained elastic solids

When three or more internal constraints are imposed on an elastic body wave propagation is found to be possible only in certain exceptional directions. These directions are fully classified in the case of three arbitrary constraints. The nature of the phenomenon of wave propagation in these exceptional directions is elucidated by relaxing the constraints slightly and then approaching the exact constraint as a certain limit. The slowness surface is examined in some detail for two specific problems: (1) an incompressible material reinforced by two sets of perpendicular inextensible fibres, and (2) a material reinforced by three mutually orthogonal sets of fibres.

Analytic waveforms for a line source in a transversely isotropic medium

In order to clarify anisotropy effects on body wave propagation, exact transient solutions radiated from horizontal line sources of stress discontinuities in a transversely isotropic medium with a vertical axis of symmetry are formulated by a modified Cagniard method which gives the inverse Laplace transform in an ingenious manner. The advantage of the exact transient solutions is the clear onset of elastic displacements at the time of body wave arrivals that are defined by corresponding group velocities. The exact transient solutions display three principal effects of anisotropy: (1) noncircular propagation of wave fronts; (2) deviation of polarizations of particle motions of qP, qSV, and qSH waves from those in an isotropic medium; and (3) separation of group velocity from phase velocity, depending on the relative orientation of anisotropy and wave propagation directions.

Die Beziehung zwischen Fusspunktkurve und Kr�mmungsmittelpunktkurve

In view of applications to elastic wave propagation in anisotropic bodies, it is noted that the evolute (locus of centers of curvature) of the podaria (locus of intersections of normals through the origin to the tangents to a curve with these tangents) of a given plane curve is the given curve contracted to halfsize.

Propagation of nonlinear body waves in a magnetic tube

The propagation of slow symmetrical small-amplitude body waves in a cylindrical magnetic tube is investigated on the basis of the nonlinear equation obtained in [3, 4]. The breaking of periodic disturbances of a certain type in a finite time is numerically demonstrated. It is noted that the equation in question does not have solutions in the form of solitary waves.

Dynamics of Saturated Rocks. II: Body Waves

The propagation of plane harmonic body waves in an unbounded, fully saturated, elastic rock medium characterized by two degrees of porosity—one due to the pores and the other due to the fissures—is studied analytically‐numerically. The analysis reveals the existence of four kinds of body waves, one shear and three compressional, which are characterized by dispersion and attenuation. A parametric numerical study leads to the conclusion that, for certain ranges of frequency, velocity and attenuation of the two‐porosity model exhibit considerable differences from their values for the single‐porosity model.

Singularities of the interaction of a vibrating stamp with an inhomogeneous heavy base

A method is developed for studying the fundamental characteristics of the wave process on the surface of an initally isotropic prestressed elastic half-space caused by an oscillating rigid stamp. The following is taken as the model of the inhomogeneous medium: an elastic layer 0 ⩽ x 3 ⩽ h, x 1, x 2, < ∞ whose mechanical characteristics as well as the initial stresses are arbitrary, fairly smooth functions of the coordinate x 3 in the general case, lies on the surface of a homogeneous half-space x 3, ⩾ h, x 1, x 2, < ∞ ( x 1, x 2, x 3, are a rectangular Cartesian coordinate system). The linearized boundary value problem of the dynamic theory of elasticity of vibrations with frequency ω for a rigid stamp on the surface of an inhomogeneous medium reduces to an integral equation or to a system of integral equations of the first kind whose integral operator kernel is constructed numerically. Approximation of the kernel of the integral operator by a special kind of function enables an approximate solution of the integral equation to be constructed by the factorization method /1, 2/. On the basis of the latter, an effective investigation of the influence of the parameters characterising the inhomogeneity of the medium and the initial state of stress on the wave process both under (stress wave) and outside the stamp is possible. The construction of a general linearized theory and the regularities of elastic wave propagation in bodies with homogeneous initial stresses are considered in /3/, where a fairly complete survey is also given of the literature on this question. A systematic exposition of the theory of wave propagation in elastic media with an inhomogeneous initial state was first given in /4/. The contact problem of the vibrations of an inhomogeneous half-space subjected to a rigid stamp oscillating on its surface was examined in /5, 6/ without taking the initial stresses into account. A method of investigating the regularities of electric-wave excitation in semibounded bodies (layers and cylinders) with varying properties and magnitude of the initial stresses was proposed in /7/ on the basis of the solution of the contact problem. A method of investigating the singularities of elàstic wave propagation in an inhomogeneous initially strained half-space caused by an oscillating load distributed in a certain domain on the surface of the medium has been developed (∗Kalinchuk V.V., Lysenko I.V. and Polyakova I.B., Singularities of elastic wave excitation and propagation in an inhomogeneous heavy half-space. Deposited Manuscript, December 10, 1986, 8877-B86, VINITI, Rostov, 1986).

AN INVESTIGATION INTO EARTHQUAKE GROUND MOTION CHARACTERISTICS IN EASTERN NORTH AMERICA

Abstract A random-vibration model of the Hanks-McGuire type is used to predict peak ground motions at rock sites in eastern North America. The assumed geometric decay and distance-dependent duration approximate the propagation of direct body waves (at short distances) and Lg waves (at regional distances). The model predicts peak acceleration and velocities, as well as response spectra and magnitude for a given seismic moment and corner frequency. To predict ground motions for a given Lg magnitude ( m Lg ), the model is first used to calculate the seismic moment corresponding to that magnitude, assuming a source scaling law. Then, knowing the moment and corner frequency, the model is used to calculate peak ground motions. Available data from strong motion recordings and from the ECTN and LRSM networks, modified to estimate horizontal ground motions on rock where appropriate, are used to verify the model9s assumption and predictions. Modified Mercalli intensity data are also used. Ground motions predicted by the model with a stress drop of 50 to 200 bars agree with the ground motion data, but the m Lg values computed by the model for given seismic moments do not agree with Nuttli9s (1983) moment versus m Lg data for large earthquakes. Resolution of the latter disagreement awaits the collection of instrumental data from large events in eastern North America.

Theory of body-wave propagation in inhomogeneous anisotropic media : Petrashen, G I; Kashtan, B M Geophys J R Astr SocV76, N1, Jan 1984, P29–39 (Paper to the Proceedings of the 1st International Workshop on Seismic Anisotropy, Suzdal, 11–19 May 1982)

Theory of body-wave propagation in inhomogeneous anisotropic media : Petrashen, G I; Kashtan, B M Geophys J R Astr SocV76, N1, Jan 1984, P29–39 (Paper to the Proceedings of the 1st International Workshop on Seismic Anisotropy, Suzdal, 11–19 May 1982)

TheMLscale in central California

AbstractNine hundred fifty-seven maximum zero-to-peak Wood-Anderson amplitudes A (synthesized or recorded) from 40 horizontal-component seismographs (20 sites) with 0 ≲ Δ ≲ 400 km for 106 earthquakes with 18 ≦ log M0 ≦ 22.3 in central California have been fit in a least-squares sense using the parametric form log A ij = − n log R ij − K R ij − ∑ l = 1 40 S l δ ij + ∑ k = 1 106 C k δ ik where Aij = A (mm) for earthquake i on seismograph component j, δik = Kronecker delta, R = hypocentral distance, and n, K, Sl, and Ck are variables determined by regression analysis. The Ck are a magnitude measure, and the Sl are station corrections constrained to have zero average. We find n = 1.018 ± 0.107 and K = 0.00291 ± 0.00070 km−1. Setting n = 1, appropriate for body-wave propagation in homogeneous media, yields K = 0.00301 ± 0.00036 km−1. Following Richter's definition of an ML = 3 earthquake as one for which A = 1 mm at Δ = 100 km and S1 = 0, we express the local magnitude ML as ML = log A − log A0, where -log A0 = n log (R/100) + K (R − 100) + 3. For 30 ≲ Δ ≲ 475 km, the -log A0 values using n = 1 and K = 0.00301 km−1 are within 0.15 of Richter's values for southern California. For Δ ≲ 30 km, Richter's values are significantly smaller than those obtained here, a result consistent with recent studies of −log A0 for southern California. Our results suggest that the ML scale as commonly used underestimates the sizes of small shocks that are predominantly recorded at Δ ≲ 30 km.

Theory of body-wave propagation in inhomogeneous anisotropic media

Summary. The paper reviews recent work of a Leningrad group of geophysicists on the development of the ray method for arbitrary anisotropic elastic media. The methods and algorithms can be applied for descriptions of both the body and head waves.

Attenuation and anisotropy of channel waves in coal seams

In recent years channel‐wave seismology has shown itself to be a useful aid to coal mining. Small geologic faults which interrupt a coal seam can seriously disrupt mining by modern longwall methods. Such features have been accurately predicted at distances of several hundred meters by underground seismic surveys. The useful range of the method in a particular seam depends critically on the rate at which channel waves in the frequency range of interest (50 to 500 Hz) are attenuated during passage through the coal; when no faulting is located by a given survey, it is always important to know at what range a fault would have been detected had it been present. To this end, the attenuation characteristics must be studied. Frequently, coal seams are highly anisotropic wave‐guides. Perpendicular to the bedding plane one or two “cleat” or cleavage planes exist, along which the coal is extensively cracked and jointed. Recent work by Crampin (1978, 1981) and by Hudson (1981) has shown that such systems of parallel cracks in crustal rocks lead to anisotropic propagation of body waves, with both velocity and attenuation varying considerably as a function of angle of travel through the cracked medium. The polarization of seismic energy propagating through such media can no longer be defined as simple shear or compression. It is reasonable to expect that guided channel waves in coal seams will exhibit similar properties. A number of transmission surveys have been carried out to investigate both attenuation and anisotropy. The principal requirement for such surveys is that in‐seam shot and geophone arrays be designed to provide a large range of both source‐detector distance and angle of travel through the coal. Given this condition, anisotropy of group velocity can be detected by adapting Dziewonski’s multiple filter analysis of single traces to transmission stacking over selected raypath angles (Dziewonski et al, 1969); attenuation similarly can be investigated by a least‐squares regression of the logarithm of the amplitude spectrum of a particular mode onto the path length. The methods and results of these investigations are reported here, the significance of anisotropy for the collection and processing of in‐seam data is discussed, and consideration is given to the type and size of errors introduced into the position of fault predictions made on the basis of an isotropic model. The equivalence of Fermat’s principle and Snell’s law for anisotropic raypaths results in a computationally efficient modification to enable our previously reported dynamic trace gathering (DTG) stacking procedure to be used for such data.

Nonlinear waves in elastic media

We ask about the possible existence of solitary waves in infinite, homogeneous, isotropic, elastic media. Namely, can a nonlinear localized wave packet propagate without altering its shape in such materials? We consider one- dimensional propagation both of body and surface waves. In the first case we show, under rather general assumptions, that if a wave packet propagates without altering its shape it must, of necessity, be a solution of a linear wave equation and in this sense, (body) solitary waves do not exist. Surface solitary waves may however exist: a model equation is derived in which nonlinear and dispersive effects balance each other to allow for waves-both periodic and solitary-of constant shape. It is conceivable they are of some relevance in seismology.

Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid-saturated porous solid

abstractA systematic theory of the propagation of seismic waves in liquid-saturated porous solids was first developed by Biot in 1956. Since then, some theoretical investigations have been carried out on the propagation of body and surface waves in such media. Further studies in this area may be useful in giving greater insight into the propagation of seismic waves in underground layers of porous solids saturated with oil or groundwater. In this connection, the transmission of normally incident seismic waves across the boundary of a liquid-saturated porous solid has been considered earlier. Keeping in view the fact that oblique incidence is more likely than normal incidence for such seismic waves, the authors have investigated the reflection and refraction of P and SV waves, which become obliquely incident at the boundary of a liquid-saturated porous solid, after propagating through an elastic solid. It is found that, corresponding to both P and SV waves obliquely incident at the boundary, there will be two refracted dilatational waves traveling with different velocities, which may be called the Pf and Ps waves, and one refracted SV wave, in the liquid-saturated porous solid, together with reflected P and SV waves in the elastic solid. The amplitude and energy ratios for the different reflected and refracted waves have been calculated theoretically. Numerical values of the amplitude and energy ratios have been computed for different angles of incidence for P and SV waves which propagate through granite, and then become incident at the boundary between the granite and oil-saturated sandstone, using results of laboratory experiments on the elastic behavior of oil-saturated sandstone. It is found that the amplitudes of the reflected and refracted waves depend significantly on the angle of incidence. It is also found that the amplitude of the second refracted P wave is usually much smaller than that of the other reflected and refracted P and SV waves, so that this slower refracted P wave will be difficult to detect. Similar amplitudes and energy ratios are also calculated for P and SV waves incident at the boundary between granite and dry sandstone. Comparison between the cases of dry sandstone and oil-saturated sandstone shows that the presence of oil usually has a significant effect on the amplitudes of the reflected and refracted P and SV waves.It is noted that such theoretical investigations may be useful in utilizing the amplitudes and other characteristics of reflected and refracted seismic waves in the detection and study of underground layers of porous solids saturated with oil or groundwater.

A comparison of the upper mantle structure beneath North America and Europe

The techniques of modeling upper mantle structure by matching long‐period waveforms with synthetic seismograms have been applied to observations from the tectonically stable part of North America and from Europe. The consistent differences, which can be resolved by the long‐period data between Europe and North America, can be interpreted in terms of variations in the crust, lid, and low‐velocity zone. At epicentral ranges less than 15° the effects of shallow lateral variations are strong and body wave propagation is regionally dependent. Between ranges of 15° and 20°, regional effects are still observed, but they can be explained in terms of variations above 250 km. Beyond 20°, wave propagation appears to be stable and independent of region. Most of the observed long‐period P waves from 20° to 30° are consistent with a single model. This indicates that the relative depths and sizes of the major discontinuities do not vary substantially. A comparison of the upper mantle models of this study with those of other studies indicates that the shape of the P velocity profile is fairly uniform through the transition region (300–700km) though there may be differences in the absolute depth to the discontinuities. These differences could, however, be the result of systematic errors in travel time data.

A local magnitude scale for New Zealand earthquakes

abstract New procedures have been used since 1977 for assigning local earthquake magnitudes in New Zealand, based on a slightly modified form of Richter9s definition and derived from amplitude-distance relations determined from New Zealand earthquakes. The magnitudes for all crustal earthquakes, and for subcrustal earthquakes in or north of the Main Seismic Region, are determined using a formula for geometric spreading which is appropriate to head-wave propagation; for subcrustal earthquakes south of the Main Seismic Region, they are determined assuming body-wave propagation. Inelastic attenuation needs to be taken into account for subcrustal earthquakes south of the Main Seismic Region, and when paths from crustal earthquakes pass through a region which includes the zone of recent volcanism in the center of the North Island.