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1.
-- I present a new algorithm for calculating seismic wave propagation through a three-dimensional heterogeneous medium using the framework of mode coupling theory originally developed to perform very low frequency (f < ~0.01т.05 Hz) seismic wavefield computation. It is a Greens function approach for multiple scattering within a defined volume and employs a truncated traveling wave basis set using the locked mode approximation. Interactions between incident and scattered wavefields are prescribed by mode coupling theory and account for the coupling among surface waves, body waves, and evanescent waves. The described algorithm is, in principle, applicable to global and regional wave propagation problems, but I focus on higher frequency (typically f S ~0.25 Hz) applications at regional and local distances where the locked mode approximation is best utilized and which involve wavefields strongly shaped by propagation through a highly heterogeneous crust. Synthetic examples are shown for P-SV-wave propagation through a semi-ellipsoidal basin and SH-wave propagation through a fault zone.  相似文献   

2.
In this paper, we have considered the reflection and refraction of a plane wave at an interface between two half-spaces. The lower half-spaces is composed of highly anisotropic triclinic crystalline material and the upper half-space is homogeneous and isotropic. It has been assumed that due to incidence of a plane quasi-P (qP) wave, three types of waves, namely, quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH), will be generated in the lower half space whereas P and S waves will be generated in the upper half space. The phase velocities of all the quasi waves have been calculated. It has been assumed that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Some specific relations have been established between directions of motion and propagation, respectively. The expressions for reflection coefficients of qP, qSV, qSH and refracted coefficients of P and SV waves are obtained. Results of reflection and refraction coefficients are presented.  相似文献   

3.
Summary The effects of a uniform external magnetic field on the propagation of waves in a homogeneous, infinitely conducting flat plate with free boundaries have been studied. It has been found that in general all the three types of waves —P, SV andSH waves—are coupled and the influence may be more pronounced in coupling the symmetric and antisymmetric types of motions in every mode.When the magnetic field is parallel to the plane faces and transverse to the direction of wave propagation, the shear wave polarized parallel to the field is purely elastic whereas the coupledP andS V waves are magnetoelastic and exhibit dispersion strikingly similar to the non-magnetic case, provided the electro-magnetic radiation into the surrounding free space is neglected.The results reported in an earlier communication [1]2) are also confirmed.  相似文献   

4.
This paper presents a relationship between the focal depth in terms of Rayleigh-wave wavelength and the dominant frequency of Rayleigh waves generated in a homogeneous half-space. Rayleigh waves were simulated using a (2, 4) staggered grid P-SV wave finite difference algorithm with VGR-stress imaging technique as a free surface boundary condition. VGR is an acronym for vertical grid-size reduction. The simulated seismic responses using P-wave and SV-wave sources at different focal depths revealed Rayleigh-wave generation up to certain focal depth only for the considered frequency bandwidth. A shift of normalized spectral shape of Rayleigh wave towards lower frequency with increasing focal depth was inferred. Largest spectral amplitude was obtained in the wavelength for which the ratio of focal depth to the wavelength of Rayleigh wave was around 0.17 in the case of P-wave source and 0.9 in the case of SV-wave source. An exponential decrease of spectral amplitude of Rayleigh wave with the departure of the ratio of focal depth to Rayleigh wave wavelength from the above mentioned values was obtained.  相似文献   

5.
The attenuation of amplitude is seen in seismic waves which pass through the central region of the Aso caldera, in Kyushu, Japan. It is also recognized from spectral analysis of seismic waves that the higher frequencies of the P-wave are reduced in the waves which pass through the central region of the caldera. It is shown that the relative attenuation increases remarkably for the frequency range of 5 to 10 Hz. The specific attenuation factor Q of the P-wave train is about 100. From the surface projection of the ray paths with low Q values through the Aso caldera to each station, the attenuating region is located beneath the center of the caldera, extending to the north of the central cones. In conjunction with the low Q value of the P-wave and the decreases of S-wave amplitudes, the relative P-wave residual times have comparatively large values for seismic waves passing through the central region beneath the caldera. In order to attempt to provide additional information on the depth configuration of the attenuating material, the ray paths of P-wave's first arrivals are located in three-dimensional space. It indicates that the low-velocity material is located beneath the center of the caldera at depths of about 6 to 9 km. However, lowvelocity anomalies above the depth of 6 km and below the depth of 15 km were not able to be detected, because most of the available seismic ray paths had crossed the caldera at depths of about 6 to 15 km. Furthermore, the relative residual times have numerous errors resulting from incorrect hypocenter locations, origin times, inhomogeneities in the structure and uncertainty of the velocity structure. At shallow depths in the Aso caldera, refraction or reflection studies are required for an accurate estimate of the structure and more detailed properties of the attenuating material.  相似文献   

6.
A layeredP- andS-wave velocity model is obtained for the Friuli seismic area using the arrival time data ofP- andS-waves from local earthquakes. A damped least-squares method is applied in the inversion.The data used are 994P-wave arrival times for 177 events which have epicenters in the region covered by the Friuli seismic network operated by Osservatorio Geofisico sperimentale (OGS) di Trieste, which are jointly inverted for the earthquake hypocenters andP-wave velocity model. TheS-wave velocity model is estimated on the basis of 978S-wave arrival times and the hypocenters obtained from theP-wave arrival time inversion. We also applied an approach thatP- andS-wave arrival time data are jointly used in the inversion (Roecker, 1982). The results show thatS-wave velocity structures obtained from the two methods are quite consistent, butP-wave velocity structures have obvious differences. This is apparent becauseP-waves are more sensitive to the hypocentral location thanS-waves, and the reading errors ofS-wave arrival times, which are much larger than those ofP-waves, bring large location errors in the joint inversion ofP- andS-wave arrival time. The synthetic data tests indicated that when the reading errors ofS-wave arrivals are larger than four times that ofP-wave arrivals, the method proposed in this paper seems more valid thanP- andS-wave data joint inversion. Most of the relocated events occurred in the depth range between 7 and 11 km, just above the biggest jump in velocity. This jump might be related to the detachment line hypothesized byCarulli et al. (1982). From the invertedP- andS-wave velocities, we obtain an average value 1.82 forV p /V s in the first 16 km depth.  相似文献   

7.
This paper reviews applications of the finite-difference and finite-element methods to the study of seismic wave scattering in both simple and complex velocity models. These numerical simulations have improved our understanding of seismic scattering in portions of the earth where there is significant lateral heterogeneity, such as the crust. The methods propagate complete seismic wavefields through highly complex media and include multiply scattered waves and converted phases (e.g.,P toSV, SV toP, body wave to surface wave). The numerical methods have been especially useful in cases of moderate and strong scattering in complex media where multiple scattering becomes important. Progress has been made with numerical methods in understanding how near-surface, low-velocity basin structures scatter surface waves and vertically-incident body waves. The numerical methods have proven useful in evaluating scattering of surface waves and body waves from topography of both the free surface and interfaces buried at depth. Numerical studies have demonstrated the importance of conversions from body waves to surface waves (andvice versa) when lateral heterogeneities and topographic relief are present in the uppermost crust. Recently, several investigations have applied numerical methods to study seismic wave propagation in velocity models which vary randomly in space. This stochastic approach seeks to understand the effects of small-scale complexity in the earth which cannot be resolved deterministically. These experiments have quantified the relationships between the statistical properties of the random heterogeneity and the measurable properties of high-frequency (1 Hz) seismograms. These simulations have been applied to the study of many features observed in actual high-frequency seismic waves, including: the amplitude and time decay of seismic coda, the apparent attenuation from scattering, the dispersion of waveforms, and the travel time and waveform variations across arrays of receivers.  相似文献   

8.
Scaling relations for seismic events induced by mining   总被引：1，自引：0，他引：1  
The values of seismic moment andS-wave corner frequency from 1575 seismic events induced in South African, Canadian, Polish, and German underground mines were collected to study their scaling relations. The values ofP-wave corner frequency from 649 events were also available. Seismic moments of these events range from 5*103 to 2*1015 N·m (moment magnitude is from –3.6 to 4.1), theS-wave corner frequency ranges from 0.7 to 4438 Hz, and theP-wave corner frequency is between 5 and 4010 Hz. The slope of a regression line between the logarithm ofS- andP-wave corner frequencies is equal to one, and the corner frequencies ofP waves are higher than those ofS waves on the average by about 25 percent. In studies of large and moderate earthquakes it has been found that stress drop is approximately independent of the seismic moment, which means that seismic moment is inversely proportional to the third power of corner frequency. Such a behavior was confirmed for most of the data considered here. A breakdown in the similarity betwen large and small events seems to occur for the events with moment magnitude below –2.5. The average values of seismic moment referred to the same range of corner frequency, however, are vastly different in various mining areas.  相似文献   

9.
We show that the multiple scattering by small fractures of seismic waves with wavelengths long compared to the fracture size and fracture spacing is indistinguishable from multiple-scattering effects produced by regular porosity, except for an orientation factor due to fracture alignment. The fractures reduce theP-wave andS-wave velocities and produce an effective attenuation of the coherent component of the seismic waves. The attenuation corresponds to 1000/Q of about unity for a Gaussian spectrum of fractures, and it varies with frequencyf asf 3. For a Kolmogorov spectrum of fractures of spectral index the attenuation is an order of magnitude or so larger and varies with frequency asf 3-v The precise degree of attenuation depends upon the matrix properties, the fracture porosity, the degree of fracture anisotropy, the type of fluid filling the fractures, and the incidence angle of the wave.For fracture porosities less than about 15% theP-wave andS-wave velocities are decreased by the order of 5–10% with a lesser dependence on the type of fluid filling the fractures (gas, oil, or brine) and with a dependence on both the degree of anisotropy and the incident angle made by the wave. The tendency of fractures to occur perpendicularly to bedding suggests that the best way to measure seismically fractured rock behavior in situ is by using the travel-time delay and reflection amplitude. As both the offset and the azimuth of receivers vary from a shot, the travel-time delay and reflection amplitude should both show an elliptical pattern of behavior—the travel-time delay in response to the varying seismic speed, and the reflection amplitude in response to angular variations in the multiple scattering. Observations of attenuation at several frequencies should permit (a) determination of the spectrum of fractures (Gaussian versus Kolmogorovian) and (b) determination of the contribution of viscous damping to the effective attenuation.  相似文献   

10.
Summary First motions ofP waves and amplitude spectra ofG 2 andG 3 waves have been used to determine the source mechanism and rupture propagation. The amplitudes ofG 3 waves have been corrected for the attenuation using aQ-model obtained from the amplitude spectra ofG 2 andG 3 waves. Observed directivities for the strike-direction agreed with a model of a bilateral fault propagated primarily from east to west.  相似文献   

11.
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 (VS), compressional (P)-wave velocity (VP), and Rayleigh wave phase velocities, it is feasible to solve for P-wave quality factor QP and S-wave quality factor QS in a layered earth model by inverting Rayleigh wave attenuation coefficients. Model results demonstrate the plausibility of inverting QS from Rayleigh wave attenuation coefficients. Contributions to the Rayleigh wave attenuation coefficients from QP cannot be ignored when Vs/VP reaches 0.45, which is not uncommon in near-surface settings. It is possible to invert QP 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 QP than to QS. 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.  相似文献   

12.
From August 2016 to July 2017, a passive seismic survey was conducted in South Western Iran as a part of a pilot project aimed to improve the imaging in geologically complex areas. Passive seismic methods have shown to be a useful tool to infer the physical properties of the underground geological structures where traditional hydrocarbon exploration methods are challenging. For this purpose, a dense passive seismic network consisting of 119 three-component borehole seismic stations was deployed over an area of 400 km2 around the city of Dehdasht. This paper focuses on the details of the network design, which was devoted to high-resolution seismological applications, including local earthquake tomography and seismic attenuation imaging. In this regard, we describe the instrument types and the station installation procedures used to obtain high-quality data that were used to retrieve three-dimensional models of P- and S-wave velocity and P-wave attenuation in the area using tomographic inversion techniques. We also assess the network performance in terms of the seismic ambient noise levels recorded at each station site, and we revise the horizontal orientation of the sensors using surface waves from teleseismic earthquakes.  相似文献   

13.
The propagation of seismic P and SV waves within inhomogeneous alluvial valleys has been investigated using the indirect boundary element method (IBEM). An improvement on the formulae published early, for the 2D Green's functions in an inhomogeneous medium is presented in this work. A modification has been done over these functions in view of its connection to the ray theory. An accuracy analysis validates these modified Green's functions computing the relative error in frequency domain for the SH case, and with a quantitative analysis obtaining envelope and phase misfits of the solution in time domain, for the P–SV case.  相似文献   

14.
In this research four earthquakes, which are considered to compose two earthquake doublets, recorded prior to and after a magnitudeM s =5.0 and a magnitudeM s =4.8 event in W. Greece are used to derive temporal variations ofP-wave attenuation in the region.Spectral ratios at four stations are computed and the results indicated a variation (increase) ofQ of the order of 15–20%. To confirm that this variation is not an artifact due to changes of the source parameters, a smaller event which occurred at the same hypocentre was used as a Green function and the deconvolution proved that the earthquakes of one of the doublet possessed the same source parameters.The outcome of this research verifies the possible role of the migration of fluids in the crust in the focal region and their effect on the attenuation of seismic waves.  相似文献   

15.
T phases of three earthquakes from the Indian Ocean region, recorded by a short-period vertical-component seismic station network located in the vicinity of Kanyakumari on the southernmost tip of India, are studied. Two of these earthquakes are located west of 90°E ridge and one in the Nicobar Island region. However, seven other earthquakes which occurred 150–200 km south of Kanyakumari in the ocean did not produceT phases. An analysis ofT-waves (tertiary waves) travel time reveals the zone ofP-wave toT-wave conversion (i.e.,PT phase) region to coincide with the western continental slope of Srilanka. Further, it is observed that the disposition of the bathymetry between Srilanka and southern India strongly favours the downslope propagation mechanism ofT-wave travel to the southern coast of India through SOFAR channel. These observations are reported for the first time from India.  相似文献   

16.
In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. It has been shown that an incidentSH orSV type of wave gives rise to reflectedSH, P andSV waves, the main components beingSH andP, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity , where measures the deviation of the medium from homogeneity. An incidentP-type wave produces mainly aP component and also a weakSH component to the order of 2. The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.  相似文献   

17.
We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena.We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ –1 peaks aroundka1, the phase velocity is almost independent ofk in the rangeka<1 and it increases monotonically withk in the rangeka>1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ –1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ –1 is proportional tok –1 independently of model parameters and the wave modes. If the seismological observation thatQ –1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.  相似文献   

18.
To study the effects of strong scattering on elastic waves, spatial fluctuation and scattering attenuation ofP waves were examined by laboratory experiments for 2-D models of random media approximately characterized by a triangular correlation function in the range of 2<ka<33, wherek is the wave number anda is the correlation distance of the heterogeneities, i.e., the heterogeneity size. The results obtained are as follows: (1) Forka>10, both the intensity and the correlation distance of the amplitude fluctuation are approximate for any phase of theP-wave train. The correlation distance nearly agrees with the heterogeneity size. These fluctuation properties are quite consistent with the theoretical prediction by the forward-scattering approximation. (2) For 3<ka<6, the fluctuation intensity becomes stronger in later phases of theP-wave train. This shows that scattering is approximately isotropic, and therefore, the scattered energy increases with time within theP-wave train. The correlation distance of the amplitude fluctuation disagrees with the heterogeneity size, and it shows a frequency-dependent property decreasing from 7a to 4a with the increase ofka from 3 to 6. These properties for 3<ka<6 have not yet been predicted theoretically. (3) Forka<3, though the fluctuation is considerably smaller compared with that ofka>10 and 3<ka<6, the fluctuation property is considered similar to that of 3<ka<6. (4) The observed scattering attenuation,Q –1, increases withka forka<3, has a peak aroundka=35, and then decreases withka. (5) When min = 15° and = 0.075, the theoreticalQ –1 curve, predicted by the approximate theory of Wu, roughly matches the observedQ –1 values, where min is the minimum scattering angle measured from the propagation direction of theP waves and is the rms of fractional velocity fluctuation. This suggests that the energy scattered in the range of >15° is lost from theP waves, while the energy scattered in the range of <15° is retained; and that the approximate theory overestimates by about three times the value of the model media used owing to the neglect of multiple scattering. (6) When the size of velocity heterogeneities responsible for forward scattering at 3<ka<6 is estimated from the min value of 15° on the basis of Wu's theory, it nearly agrees with the correlation distance for the initial phase of theP-wave train.  相似文献   

19.
The analysis and interpretation of coda waves have received increasing attention since the early seventies. In the past few years interest in this subject has spread worldwide, and the study of high-frequency seismic coda waves has become a very important seismological topic. As a conclusion of the studies accomplished in this time, coda waves are considered the result of scattering processes caused by heterogeneities acting on seismic waves.P andS waves play a particularly important role in this interaction. The process introduces an attenuation which, added to the intrinsic absorption, gives the observed apparent attenuation. Therefore, coda waves constitute a thumbprint left by the heterogeneities on the seismograms. Coda waves offer decisive information about the mechanism of how scattering and attenuation take place. This review describes coda waves in detail, and summarizes the work done in this subject to 1986. The relation between coda waves and attenuation in the context of research on seismic scattering problems is stressed. Particular attention has been given to the application of coda waves to estimate source and medium parameters. The state-of-the-art of the temporal variations of coda wave shape, and the possible use of these variations as an earthquake precursor also are presented. Care has been taken to introduce the statistical models used to deal with the heterogeneities responsible for scattering.  相似文献   

20.
—?Plans for a hydroacoustic network intended to monitor compliance with the CTBT call for the inclusion of five T-phase stations situated at optimal locations for the detection of seismic phases converted from ocean-borne T phases. We examine factors affecting the sensitivity of land-based stations to the seismic T phase. The acoustic to seismic coupling phenomenon is described by upslope propagation of an acoustic ray impinging at a sloping elastic wedge. We examine acoustic to seismic coupling characteristics for two cases; the first in which the shear velocity of the bottom is greater than the compressional velocity of the fluid (i.e., v p > v s > v w ), the second is a weakly elastic solid in which v s << v w < v p . The former is representative of velocities in solid rock, which might be encountered at volcanic islands; the latter is representative of marine sediments. For the case where v s > v w , we show that acoustic energy couples primarily to shear wave energy, except at very high slope angles. We show that the weakly elastic solid (i.e., v s << v w ) behaves nearly like a fluid bottom, with acoustic energy coupling to both P and S waves even at low slope angles.¶We examine converted T-wave arrivals at northern California seismic stations for two event clusters; one a series of earthquakes near the Hawaiian Islands, the other a series of nuclear tests conducted near the Tuamoto archipelago. Each cluster yielded characteristic arrivals at each station which were consistent from event to event within a cluster, but differed between clusters. The seismic T-phases consisted of both P- and S-wave arrivals, consistent with the conversion of acoustic to seismic energy at a gently sloping sediment-covered seafloor. In general, the amplitudes of the seismic T phases were highest for stations nearest the continental slope, where seafloor slopes are greatest, however noise levels decrease rapidly with increasing distance from the coastline, so that T-wave arrivals were observable at distances reaching several hundred kilometers from the coast. Signal-to-noise levels at the seismic stations are lower over the entire frequency spectrum than at the Pt. Sur hydrophone nearby, and decrease more rapidly with increasing frequency, particularly for stations furthest from the continental slope.  相似文献   

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