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1.
The boundary value problems most frequently encountered in studies of elastic wave propagation in stratified media can be formulated in terms of a finite number of linear, first order and ordinary differential equations with variable coefficients. Volterra (1887) has shown that solutions to such a system of equations are conveniently represented by the product integral, or propagator, of the matrix of coefficients. In this paper we summarize some of the better known properties of propagators plus numerica methods for their computation. When the dispersion relation is somem th order minor of the integral matrix it is possible to deal withm th minor propagators so that the dispersion relation is a single element of them th minor integral matrix. In this way one of the major sources of loss of numerical accuracy in computing the dispersion relation is avoided. Propagator equations forSH and forP-SV waves are given for both isotropic and transversely isotropic media. In addition, the second minor propagator equations forP-SV waves are given. Matrix polynomial approximations to the propagators, obtained from the method of mean coefficients by the Cayley-Hamilton theorem and the Lagrange-Sylvester, interpolation formula, are derived.  相似文献   

2.
Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio (i.e., ellipticity), and receiver function data to better resolve 1D crustal shear wave velocity (v S) structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensitivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast (e.g., due to the existence of crustal interfaces) and v P/v S ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the v S model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute v S model and then incorporate receiver function data in the joint inversion to obtain a finer v S model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal v S structures and with little initial model dependency.  相似文献   

3.
The relationship between the characteristics of seismic waves in the Western Caucasus and the geological-tectonic structure of the region is studied for identifying the specificity of seismic propagation in the mountainous regions with a complicated geological structure and forecasting the characteristics of the propagation from the geological and tectonic data. The interpretation is presented for the estimates of the Q-factor of the medium (Q(f) ~ 55f0.9 in the region of Sochi and Q(f) ~ 90f0.7 in the region of Anapa), seismic wave enhancement in the upper crustal layers (A(f) ~ 1), and peak ground acceleration residuals, which were previously determined from the records of the local earthquakes and show the distributions of local variations in the parameters of seismic wave radiation and propagation. The obtained characteristics are interpreted in the context of the up-to-date information about the tectonic, geological, and deep structure of the epicentral zones in the Western Caucasus and neighboring territory of the Black Sea. The discrepancies revealed in the low-frequency behavior of the Q-factor in the vicinities of Sochi and Anapa is accounted for by the spatial scale and character of tectonic dislocations of the rocks in these regions. The local variations in the parameters of seismic radiation and propagation are probably related to the geological features of the region such as the fault structures, including the thrusts, shatter zones, oblique seismic boundaries, variations in the thickness and consolidation of the sedimentary cover, as well as the peculiarities in the structure and material composition of the basement.  相似文献   

4.
A method for determining medium quality factor is developed on the basis of analyzing the attenuation dispersion of the arrived first period P wave. In order to enhance signal to noise ratio, improve the resolution in measurement and reduce systematic error we applied the data resampling technique. The group velocity delay of P wave was derived by using an improved multi-filtering method. Based on a linear viscoelastic relaxation model we deduced the medium quality factor Q m, and associated error with 95% confidence level. Applying the method to the seismic record of the Xiuyan M=5.4 earthquake sequences we obtained the following result: (1) High Q m started to appear from Nov. 9, 1999. The events giving the deduced high Q m value clustered in a region with their epicenter distances being between 32 and 46 km to the Yingkou station. This Q m versus distance observation obviously deviates from the normal trend of Q m linearly increasing with distance. (2) The average Q m before the 29 Dec. 1999 M=5.4 earthquake is 460, while the average Q m between the M=5.4 event and the 12 Jan. 2000 M=5.1 earthquake is 391, and the average Q m after the M=5.1 event is 204.  相似文献   

5.
The evaluation and design of stone column improvement ground for liquefaction mitigation is a challenging issue for the state of practice. In this paper, a shear wave velocity-based approach is proposed based on the well-defined correlations of liquefaction resistance (CRR)-shear wave velocity (V s)-void ratio (e) of sandy soils, and the values of parameters in this approach are recommended for preliminary design purpose when site specific values are not available. The detailed procedures of pre- and post-improvement liquefaction evaluations and stone column design are given. According to this approach, the required level of ground improvement will be met once the target V s of soil is raised high enough (i.e., no less than the critical velocity) to resist the given earthquake loading according to the CRR-V s relationship, and then this requirement is transferred to the control of target void ratio (i.e., the critical e) according to the V s-e relationship. As this approach relies on the densification of the surrounding soil instead of the whole improved ground and is conservative by nature, specific considerations of the densification mechanism and effect are given, and the effects of drainage and reinforcement of stone columns are also discussed. A case study of a thermal power plant in Indonesia is introduced, where the effectiveness of stone column improved ground was evaluated by the proposed V s-based method and compared with the SPT-based evaluation. This improved ground performed well and experienced no liquefaction during subsequent strong earthquakes.  相似文献   

6.
An original model of atmospheric wave propagation from ground sources to the ionosphere in the atmosphere with a realistic high-altitude temperature profile is analyzed. Shaping of a narrow domain with elevated pressure in the resonance region where the horizontal phase wave velocity is equal to the sound velocity is examined theoretically within the framework of linearized Eq.s. Numerical simulations for the model profiles of atmospheric temperature and viscosity confirm analytical result for the special feature of wave fields. The formation of the narrow domain with plasma irregularities in the D and low E ionospheric layers caused by the acoustic gravity wave singularity is discussed.  相似文献   

7.
Solutions of P-SV equations of motion in a homogeneous transversely isotropic elastic layer contain a factor exp(±ν j z), where z is the vertical coordinate and j?=?1, 2. For computing Rayleigh wave dispersion in a multi-layered half space, ν j is computed at each layer. For a given phase velocity (c), ν j becomes complex depending on the transversely isotropic parameters. When ν j is complex, classical Rayleigh waves do not exist and generalised Rayleigh waves propagate along a path inclined to the interface. We use transversely isotropic parameters as α H , β V , ξ, ? and η and find their limits beyond which ν j becomes complex. It is seen that ν j depends on ? and η, but does not depend on ξ. The complex ν j occurs when ? is small and η is large. For a given c/β V , the region of complex ν j in a ? -η plane increases with the increase of α H /β V . Further, for a given α H /β V , the complex region of ν j increases significantly with the decrease of c/β V . This study is useful to compute dispersion parameters of Rayleigh waves in a layered medium.  相似文献   

8.
The observation of extreme waves at FINO 1 during storm Britta on the 1st November 2006 has initiated a series of research studies regarding the mechanisms behind. The roles of stability and the presence of the open cell structures have been previously investigated but not conclusive. To improve our understanding of these processes, which are essential for a good forecast of similarly important events offshore, this study revisits the development of storm Britta using an atmospheric and wave coupled modeling system, wind and wave measurements from ten stations across the North Sea, cloud images and Synthetic Aperture Radar (SAR) data. It is found here that a standard state-of-the-art model is capable of capturing the important characteristics of a major storm like Britta, including the storm path, storm peak wind speed, the open cells, and peak significant wave height (H s ) for open sea. It was also demonstrated that the impact of the open cells has negligible contribution to the development of extreme H s observed at FINO 1. At the same time, stability alone is not sufficient in explaining the development of extreme H s . The controlling conditions for the development of Britta extreme H s observed at FINO 1 are the persistent strong winds and a long and undisturbed fetch over a long period.  相似文献   

9.
The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor (Q) and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.  相似文献   

10.
Simultaneous observations of high-latitude long-period irregular pulsations at frequencies of 2.0–6.0 mHz (ipcl) and magnetic field disturbances in the solar wind plasma at low geomagnetic activity (Kp ~ 0) have been studied. The 1-s data on the magnetic field registration at Godhavn (GDH) high-latitude observatory and the 1-min data on the solar wind plasma and IMF parameters for 2011–2013 were used in an analysis. Ipcl (irregular pulsations continuous, long), which were observed against a background of the IMF Bz reorientation from northward to southward, have been analyzed. In this case other solar wind plasma and IMF parameters, such as velocity V, density n, solar wind dynamic pressure P = ρV2 (ρ is plasma density), and strength magnitude B, were relatively stable. The effect of the IMF Bz variation rate on the ipcl spectral composition and intensity has been studied. It was established that the ipcl spectral density reaches its maximum (~10–20 min) after IMF Bz sign reversal in a predominant number of cases. It was detected that the ipcl average frequency (f) is linearly related to the IMF Bz variation rate (ΔBz/Δt). It was shown that the dependence of f on ΔBz/Δt is controlled by the α = arctan(By/Bx) angle value responsible for the MHD discontinuity type at the front boundary of magnetosphere. The results made it possible to assume that the formation of the observed ipcl spectrum, which is related to the IMF Bz reorientation, is caused by solar wind plasma turbulence, which promotes the development of current sheet instability and surface wave amplification at the magnetopause.  相似文献   

11.
On the basis of the model of the three-dimensional (3D) generalized Kadomtsev-Petviashvili equation for magnetic field h = B ~/B the formation, stability, and dynamics of 3D soliton-like structures, such as the beams of fast magnetosonic (FMS) waves generated in ionospheric and magnetospheric plasma at a low-frequency branch of oscillations when β = 4πnT/B 2 ? 1 and β > 1, are studied. The study takes into account the highest dispersion correction determined by values of the plasma parameters and the angle θ = (B, k), which plays a key role in the FMS beam propagation at those angles to the magnetic field that are close to π/2. The stability of multidimensional solutions is studied by an investigation of the Hamiltonian boundness under its deformations on the basis of solving of the corresponding variational problem. The evolution and dynamics of the 3D FMS wave beam are studied by the numerical integration of equations with the use of specially developed methods. The results can be interpreted in terms of the self-focusing phenomenon, as the formation of a stationary beam and the scattering and self-focusing of the solitary beam of FMS waves. These cases were studied with a detailed investigation of all evolutionary stages of the 3D FMS wave beams in the ionospheric and magnetospheric plasma.  相似文献   

12.
In this work, the results of comparative analysis of morphological regularities of right-polarized (R type) and left-polarized (L type) isolated bursts of ipcl pulsations (irregular pulsations continuous long period) with an anomalously large amplitude in the region of the daytime polar cusp, as well as conditions of their excitation, are presented. It has been found that R and L bursts are similar in the maximum amplitude level, wave packet duration, spectral composition, magnitude of ellipticity, diurnal variation shape, and other characteristics. At the same time, bursts of the R and L type are excited at different degrees of plasma turbulence in the generation region, at different IMF orientations in the plane of ecliptic, as well as in the plane perpendicular to it, and at different dynamics of the parameter β (characterizing the ratio of the thermal pressure to the magnetic pressure) and Alfvén Mach number Ma. It is supposed that the generation of isolated bursts of the R and L types can be related to the amplification of the plasma turbulence level due to the development of wind instability at the front boundary of the magnetosphere, and features of their polarization can be interpreted in the scope of the model of nonlinear propagation of Alfvén waves.  相似文献   

13.
We consider a transversely isotropic medium with vertical axis of symmetry (VTI). Rayleigh wave displacement components in a homogeneous VTI medium contain exp(±krjz), where z is the vertical coordinate, k is the wave number, and j?=?1, 2; rj may be considered as depth-decay factor. In a VTI medium, rj can be a real or imaginary as in an isotropic medium, or it can be a complex depending on the elastic parameters of the VTI medium; if complex, r1 and r2 are complex conjugates. In a homogeneous VTI half space, Rayleigh wave displacement is significantly modified with a phase shift when rj changes from real to complex with variation of VTI parameters; at the transition, the displacement becomes zero when r1?=?r2. In a liquid layer over a VTI half space, Rayleigh waves are dispersive. Here, also Rayleigh wave displacement significantly modified with a phase shift when rj changes from real to complex with a decrease of period. At very low period, phase velocity of Rayleigh waves becomes less than P-wave velocity in the liquid layer giving rise to Scholte waves (interface waves). The amplitudes of Scholte waves with a VTI half space are found to be significantly larger than those with an isotropic half space.  相似文献   

14.
A search for trends k(foE) in the critical frequency of the ionospheric E layer at Juliusruh and Slough stations is performed by the method often used by the authors to analyze trends in the F2-layer parameters. It is found that k(foE) could differ in both magnitude and even sign within different time intervals. However, the k(foE) trends have been stably negative over the last two decades for both stations and all months of the year. The k(foE) values averaged over a year are ?0.012 and ?0.005 MHz per year for Juliusruh and Slough stations, respectively. The method used in the recent paper by La?tovi?ka et al. (2016) to determine foE trends is analyzed, and it is shown that the difference in linear approximation of the dependence of the observed foE values on F10.7 within different time intervals could be interpreted not as the presence of a different foE dependence on the F10.7 index within these intervals but as the presence within them of foE trends that change the slope of the linear approximation.  相似文献   

15.
The level of wave geomagnetic activity in the morning and daytime sectors of auroral latitudes during strong magnetic storms with Dst min varying from ?100 to ?150 nT in 1995–2002 have been studied using a new ULF index of wave activity proposed in [Kozyreva et al., 2007]. It has been detected that daytime Pc5 pulsations (2–6 mHz) are most intense during the main phase of a magnetic storm rather than during the recovery phase as was considered previously. It has been indicated that morning geomagnetic pulsations during the substorm recovery phase mainly contribute to daytime wave activity. The appearance of individual intervals with the southward IMF B z component during the magnetic storm recovery phase results in increases in the ULF index values.  相似文献   

16.
An alternative model for the nonlinear interaction term Snl in spectral wave models, the so called generalized kinetic equation (Janssen J Phys Oceanogr 33(4):863–884, 2003; Annenkov and Shrira J Fluid Mech 561:181–207, 2006b; Gramstad and Stiassnie J Fluid Mech 718:280–303, 2013), is discussed and implemented in the third generation wave model WAVEWATCH-III. The generalized kinetic equation includes the effects of near-resonant nonlinear interactions, and is therefore able, in theory, to describe faster nonlinear evolution than the existing forms of Snl which are based on the standard Hasselmann kinetic equation (Hasselmann J Fluid Mech 12:481–500, 1962). Numerical simulations with WAVEWATCH have been carried out to thoroughly test the performance of the new form of Snl, and to compare it to the existing models for Snl in WAVEWATCH; the DIA and WRT. Some differences between the different models for Snl are observed. As expected, the DIA is shown to perform less well compared to the exact terms in certain situations, in particular for narrow wave spectra. Also for the case of turning wind significant differences between the different models are observed. Nevertheless, different from the case of unidirectional waves where the generalized kinetic equation represents a obvious improvement to the standard forms of Snl (Gramstad and Stiassnie 2013), the differences seems to be less pronounced for the more realistic cases considered in this paper.  相似文献   

17.
The regularities of the variations in the IMF B z component have been studied based on the data on the solar wind streams and their solar sources. Isolated solar wind streams such as magnetic clouds and shock layers before them, undisturbed heliospheric current sheets (HCSs), leading edges and bodies of high-speed streams from coronal holes (HSSs from CHs) have been considered. It has been revealed that each type of isolated streams in the interplanetary medium has it own features in the variations in the value and direction of the B z component related to the stream immanent properties and conditions of propagation in the interplanetary plasma. The appearance of the southward B z component is obligatory for all these streams which are, therefore, geoeffective.  相似文献   

18.
The dynamics of wave disturbances in the ionospheric E region in the band of periods of thermal tidal waves and waves of planetary scales (T = 48, 72, and 192 h) has been studied based on the variations in the horizontal component of the geomagnetic field, observed at Paratunka and Barrow observatories in September–October 1999. It has been found that, at midlatitudes during high geomagnetic activity, the intensity of oscillations in the power spectra with T = 24 and 12 h varies with a periodicity of 16 days different from the periodicity of changes in the ΣKp index. The maximal deviations of these periods from the values under quiet conditions coincide with the maximal changes in the ΣKp index. The variations in the 48–192 h band of periods (especially with T ～192 h) intensify simultaneously with increasing geomagnetic activity. The intensity of this harmonic is several times as high as that of the harmonic with T ～ 24 h. The periodicity of changes in the harmonics intensity within the 48–192 h band coincides with the periodicity of changes in the ΣKp index. In the polar ionosphere, the effect of high geomagnetic activity is observed as an increase in the variations with a quasi-period of T ～ 24 h and as an appearance of variations in the 48–192 h band with the periodicity coinciding with the maximums in the ΣKp index variations.  相似文献   

19.
This study uses macroseismic data and wave equations to solve the problem of ultra long propagation of felt ground motion (over 9000 km from the epicenter) due to the Sea-of-Okhotsk earthquake. We show that the principal mechanism of this phenomenon could be excitation of a previously unknown standing radial wave as a mode of the Earth’s free oscillations, 0S0, due to the superposition of an incident and a reflected spherical P wave in the epicentral area of the Sea-of-Okhotsk earthquake. The standing wave generates slowly attenuating P waves that travel over the earth’s surface that act as carrying waves; when superposed on these, direct body waves acquire the ability to travel over great distances. We show previously unknown parameters of the radial mode 0S0 for the initial phase of earth deformation due to the large deep-focus earthquake. We used data on the Sea-of-Okhotsk and Bolivian earthquakes to show that large deep-focus earthquakes can excite free oscillations of the Earth that are not only recorded by instrumental means, but are also felt by people, with the amplification of the macroseismic effect being directly related to the phenomenon of resonance for multistory buildings.  相似文献   

20.
Seismic observations exhibit the presence of abnormal b-values prior to numerous earthquakes. The time interval from the appearance of abnormal b-values to the occurrence of mainshock is called the precursor time. There are two kinds of precursor times in use: the first one denoted by T is the time interval from the moment when the b-value starts to increase from the normal one to the abnormal one to the occurrence time of the forthcoming mainshock, and the second one denoted by T p is the time interval from the moment when the abnormal b-value reaches the peak one to the occurrence time of the forthcoming mainshock. Let T* be the waiting time from the moment when the abnormal b-value returned to the normal one to the occurrence time of the forthcoming mainshock. The precursor time, T (usually in days), has been found to be related to the magnitude, M, of the mainshock expected in a linear form as log(T)?=?q?+?rM where q and r are the coefficient and slope, respectively. In this study, the values of T, T p , and T* of 45 earthquakes with 3?≤?M?≤?9 occurred in various tectonic regions are compiled from or measured from the temporal variations in b-values given in numerous source materials. The relationships of T and T p , respectively, versus M are inferred from compiled data. The difference between the values of T and T p decreases with increasing M. In addition, the plots of T*/T versus M, T* versus T, and T* versus T-T* will be made and related equations between two quantities will be inferred from given data.  相似文献   

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