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1.
Seismic sources with observable glut moments of spatial degree two   总被引：1，自引：0，他引：1  
Let ζΛ and r Λ. be the hypocentral position and time of an extended indigenous seismic source. Backus showed that the force moment tensors of the source, Γ( m +1, n )(ζΛ, r Λ), determine and are determined by the motion which the source produces. For small m + n , only the long-period motion is relevant. The glut moment tensor Λ( m,n ) (ζΛ, r Λ.) can be calculated uniquely from γ( m +1, n )(ζΛ r Λ) only if m = 0 or m = 1. The tensor G =Λ(2,0)(ζΛ) gives the spatial variance tensor WΛ of the source, and WΛ. roughly describes the size, shape and orientation of the source region. Therefore the failure of the observed F =Γ(3,0)(ζΛ) to determine G uniquely is of seismological interest. In the present paper we show that F determines G uniquely if we assume the source to be a simple straight line source (SSLS) or an ideal fault in an isotropic medium with isotropic prestress (IFIMIP). We give tests on F which determine whether it can come from a SSLS, from an IFIMIP or from a simple plane surface source (SPSS). If we assume the source to be a SPSS then knowing F and the fault plane determines G to within an unknown scalar multiple of a certain tensor tangent to the fault plane. Moreover F determines the fault plane uniquely unless F can come from a SSLS. If it can, then F determines this virtual source line uniquely, and F permits the fault plane to be any plane containing the virtual source line.  相似文献   

2.
A new model that accounts for the stress dependence of the phase velocity of elastodynamic waves propagating in a cracked solid under compression is presented. The phase velocities of longitudinal and shear waves are derived from the effective elastic properties of a cracked solid, which are evaluated within the framework of Kachanov's approach. Following Kachanov, the extra-compliance tensor of the cracked solid is related to the crack compliances, which display a marked non-linear behaviour when subjected to a compressive load. Such non-linear behaviour is shown to be derived from the elastic interaction between the contacting crack faces under compression. This work does not address the effect of mutual interaction among cracks and the generation of higher harmonics due to the medium non-linearity. Numerical examples are presented that illustrate the phase velocity changes occurring in a solid with a random distribution of parallel cracks as a function of an external compressive load. A distinctive feature of the acoustoelastic effect in solids with large parallel fractures and in solids with distributions of aligned microcracks is also illustrated.  相似文献   

3.
Shock-compressed MgO radiates thermally at temperatures between 2900 and 3700 K in the 170–200 GPa pressure range. A simple energy-transport model of the shocked-MgO-targets distinguishes between different shock-induced radiation sources in these targets and provides estimates of spectral absorption-coefficients, α ΛMgO, for shocked MgO (e.g. at 203 GPa, α ΛMgO˜ 630, 7500, 4200 and 3800 m−1, at 450, 600, 750 and 900 nm, respectively). The experimentally inferred temperatures of the shock-compressed states of MgO are consistent with temperatures calculated for MgO assuming that (1) it deforms as an elastic fluid, (2) has a Dulong-Petit value for specific heat at constant volume in its shocked state, and (3) undergoes no phase transformation below 200 GPa.  相似文献   

4.
Ultrasonic P-wave tests of frozen silt and frozen sand were conducted during uniaxial loading by using an RSM®-SY5(T) nonmetal ultrasonic test meter to study the velocity characteristics of P-waves. The experimental results indicate that the P-wave velocity is affected by soil materials, temperature, and external loads, so the P-wave velocity is different in frozen silt and frozen sand, but all decrease with an increase of temperature and increase at first and then decrease with strain during the loading process. There is an exponential relationship between uniaxial compressive strength and P-wave velocity, and the correlation between them is very good. The characteristic parameters of acoustic waves can, to some extent, reflect the development of internal cracks in frozen soils during loading.  相似文献   

5.
2012年11月—2013年4月中国第29次南极科学考察期间,针对南极夏季固定冰单轴压缩性质开展了研究。使用冰芯钻直接在平整冰层钻取力学试样,取样冰厚为149 cm,其中颗粒冰、柱状冰和片状冰分别占采样冰芯总长度的15.4%、72.5%和12.1%;单轴压缩试样只采用柱状冰部分,加工好的力学冰样尺寸为直径9 cm,长度为18 cm;共设置5个试验温度(-2、-4、-6、-8和-10℃),加载应变速率在10-6—10-2s-1。利用统计方法分析试验结果,建立了南极夏季海冰单轴压缩强度与孔隙率和应变速率的关系式,以及综合考虑应变速率和温度影响下的单轴压缩强度定量表达式;同时,基于分形理论对单轴压缩试样破碎块分布规律进行了分析,结果显示碎块长度分形维数随着温度和应变速率的降低有增大趋势。在特别低应变速率下海冰试样整体发生蠕变时,无法采用分形方法讨论海冰内部破碎程度。  相似文献   

6.
Numerical simulation of the propagation of P waves in fractured media   总被引：1，自引：0，他引：1  
We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q −1 of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q −1 of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) −1 in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials.  相似文献   

7.
Summary. Using the techniques of linear and quadratic programming, it can be shown that the isostatic response function for the continental United States, computed by Lewis & Dorman (1970), is incompatible with any local compensation model that involves only negative density contrasts beneath topographic loads. We interpret the need for positive densities as indicating that compensation is regional rather than local. The regional compensation model that we investigate treats the outer shell of the Earth as a thin elastic plate, floating on the surface of a liquid. The response of such a model can be inverted to yield the absolute density gradient in the plate, provided the flexural rigidity of the plate and the density contrast between mantle and topography are specified.
If only positive density gradients are allowed, such a regional model fits the United States response data provided the flexural rigidity of the plate lies between 1021 and 1022 N m. The fit of the model is insensitive to the mantle/ load density contrast, but certain bounds on the density structure can be established if the model is assumed correct. In particular, the maximum density increase within the plate at depths greater than 34 kin must not exceed 470 kg m−3; this can be regarded as an upper bound on the density contrast at the Mohorovicic discontinuity.
The permitted values of the flexural rigidity correspond to plate thicknesses in the range 5–10 km, yet deformations at depths greater than 20 km are indicated by other geophysical data. We conclude that the plate cannot be perfectly elastic; its effective elastic moduli must be much smaller than the seismically determined values. Estimates of the stress-differences produced in the earth by topographic loads, that use the elastic plate model, together with seismically determined elastic parameters, will be too large by a factor of four or more.  相似文献   

8.
Summary. Following the classic work of Eshelby, the slip and stress distributions due to an elliptical plane shear crack are evaluated. The relation between average (or maximum) slip on the crack and the (constant) static stress drop, for faults of different aspect ratios, is found. The slip vector is not parallel to the applied stress but makes a small angle to it, except when the stress is applied along the major or minor axis of the ellipse. The stress -distribution around the crack shows that in addition to the expected stress concentration along the crack edge, there are broad regions of stress increase off the crack plane for circular and elliptical cracks, similar to those known to exist for in-plane but not for antiplane shear cracks. Whether the stress- intensity factor at the end of one axis is greater or less than that at the end of the other axis ( ka ≶ kb ), depends on the condition: √ b/a ≶ (1 − v ) where a and b are the semi-axes of the ellipse, ka and kb are the stress-intensity factors at the end of the a- and b -axes and v is Poisson's ratio. The total stress-intensity factor varies smoothly along the edge of the ellipse from one axis to the other and it is found that this variation is rather small.  相似文献   

9.
Geoscientists have undertaken mapping of the Earth's crustal strain (or stress) fields using a great variety of field data. The output can be represented by a 3-D second-rank symmetric random strain tensor. The random principal strains-land rotations of the random tensor are frequently computed. The accuracy is calculated using a first-order approximation. The distribution aspects of the random principal strains and rotations have received almost no attention in Earth Sciences. A first-order approximation of accuracy may not be sufficient if the signal-to-noise ratio is small, as is often the case for geodetically derived random strain tensors. Therefore, the purpose of this paper is to investigate the distribution and estimation problems of the general 3-D second-rank tensor equation GΛG T= T , where T is a given 3-D second-rank symmetric random tensor, Λ a diagonal (3 × 3) random eigenvalue matrix, and G a (3 × 3) random orientation matrix, which is also orthogonal. Λ and G are to be estimated (or solved) from T . If some eigenvalues coincide, additional conditions are imposed on the eigenvectors so that they can be chosen uniquely. The joint probability density function (pdf) of the random eigenvalues and rotations will be worked out, given a joint pdf of the elements of random tensors T. Because the rotations are of special interest in Earth Sciences, we shall also derive the joint marginal pdf of random rotations. The geometry of eigenspectra will be studied. The biases of random eigenvalues and rotations will be derived, which have been neglected in the past. They can be very crucial in interpreting the pattern of a derived strain field, however, when applied to a real Earth Science problem. The variance-covariance matrices will be computed using a second-order approximation.  相似文献   

10.
Summary. The paper gives the results of a study of the anisotropy of seismic wave velocities within the Ashkhabad test field in Central Asia. The anisotropy was studied by analysing variations in the values of apparent velocities of first arrivals for epicentral distances ranging from 30 to 130 km and by analysing the delays (Δ ts1-s2 ) between the arrival times of shear waves with different polarizations.
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s-1 and the velocities of S -waves vary from 3.15 to 3.5 km s-1.
The delay times Δ tS1 - S2 depend on the direction of the propagation. The character of the variation of the propagation velocity of the longitudinal wave, the presence of two differently polarized shear waves S 1 and S 2 propagating at different velocities, and the character of the distribution of Δ tS1 - S2 on the stereogram suggest that the symmetry of the anisotropic medium is close to hexagonal with a nearly horizontal symmetry axis coinciding with the direction of maximal velocity. The azimuth of the symmetry axis of the medium is 140° and coincides with the direction of geological faults.  相似文献   

11.
Summary. A structural model of the Mid-Atlantic Ridge at 37° N is proposed on the basis of travel-time data and synthetic seismograms. At the ridge axis the crust is only 3 km thick and overlies material with an anomalously low'upper mantle'velocity of 7.2 km s−1. Crustal thickening and the formation of layer 3 and a layer with velocity 7.2–7.3 km s−1 takes place within a few kilometres of the axis, producing a 6–7 km thick crust by less than 10 km from the axis. A normal upper mantle velocity of 8.1 km s−1 exists within 10 km of the axis. Shear waves propagate across the axis, thus precluding the existence of any sizeable magma chamber at shallow depth.  相似文献   

12.
The traveltime perturbation equations for the quasi-compressional and the two quasi-shear waves propagating in a factorized anisotropic inhomogeneous (FAI) media are derived. The concept of FAI media simplifies considerably these equations. In the FAI medium, the density normalized elastic parameters a ijkl ( X i ) can be described by the relation a ijkl ( X i) = f 2( x i ) A ijkl, where A ijkl are constants, independent of coordinates x i and f 2( x i) is a continuous smooth function of x i . The types of anisotropy ( A ijkl ) and inhomogeneity [ f ( x i)] are not restricted. The traveltime perturbations of individual seismic body waves ( q P , qS 1 and qS 2) propagating in the FAI medium depend, of course, both on the structural pertubations [δ f 2( x i)] and on the anisotropy perturbations (δ A ijkl ), but both these effects are fully separated. The perturbation equations for the time delay between the two qS -waves propagating in the FAI medium are simplified even more. If the unperturbed (background) medium is isotropic, the perturbation of the time delay does not depend on the structural perturbations (δ f 2( x i) at all. This striking result, valid of course only in the framework of first-order perturbation theory, will simplify considerably the interpretation of the time delay between the two split qS -waves in inhomogeneous anisotropic media. Numerical examples are presented.  相似文献   

13.
Summary. The tidal deformation of a homogeneous viscoelastic sphere due to the gravitational attraction of an external body is calculated. The sphere is modelled as an incompressible Kelvin-Voigt solid. An equation for the displacement field is obtained assuming that strains are small and inertia is negligible. This equation has a series solution in terms of Legendre polynomials. The resulting expression for the displacement field reduces to that for an elastic solid and a viscous fluid in the appropriate limits of the material constants. The first term in the viscoelastic solution is used to calculate the moments induced by tidal deformation assuming a circular orbit. In the absence of obliquity and precession, these moments reduced to a torque about the spin axis. This torque is compared to that predicted by a phase lag analysis. These two approaches are formally equivalent if the tidal dissipation function Q −1 depends in a specific way on the difference of the spin and orbital angular velocities.  相似文献   

14.
Summary. We have implemented an algorithm which is based on Bailey's solution of the inverse problem of electromagnetic induction in the Earth. The study was motivated by recent determinations of very long period data and also benefited from recent redeterminations of high frequency data. The algorithm has been successfully tested to provide reliable estimates of conductivity down to a depth of 2000 km, using synthetic data in the period range from 4 days to 11 years. Smooth data sets, which are required for the inversion, were constructed from various sources. At a given depth, the range of inverted models is less than one order of magnitude. Due to the lack of high frequency data, the conductivity of the upper 600 km of the mantle, which is found to be of the order of 10−1Ω−1 m−1, may be overestimated. The algorithm performs well in the middle mantle, where conductivity rises steadily from 1 to 50 Ω−1 m−1. The lack of very low frequency data and limitations of the algorithm prevent one from obtaining meaningful estimates in the lower mantle. However, the study of the propagation of the late 1960s secular variation acceleration provides an estimate of the mean conductivity of the whole mantle. Thus, a complete mantle profile can be constructed. It is found that deep mantle conductivity probability does not exceed a few hundred Ω−1 m−1.  相似文献   

15.
Summary. This note presents an exact analytical formula for determining the magnitude of coseismic surface volume change (δ V ) of earthquake faults in a half-space. For a Poisson solid, the formula is remarkably simple; δ V = M zz |8μ, where M zz is one of the moment tensor elements of the source. Maximum δ V values derive from dip slip on faults plunging 45°. For these events, surface volume changes of 0.0001 and 4.3 km3 can be expected for magnitude 5 and 8 earthquakes respectively. All of the coseismic surface volume change is recovered in the interseismic period through relaxation of the Earth and rebound of the surface. A useful rule of thumb for estimating the magnitude of vertical rebound in 45° dip slip events is δ h p=Δ s /24, where Δ s is the coseismic slip on the fault.  相似文献   

16.
The inversion of high-resolution geoid anomaly maps derived from satellite altimetry should allow one to retrieve the lithospheric elastic thickness, T e , and crustal density, c . Indeed, the bending of a lithospheric plate under the load of a seamount depends on both parameters, and the associated geoid anomaly is correspondingly dependent on the two parameters. The difference between the observed and modelled geoid signatures is estimated by a cost function, J , of the two variables, T e and c . We show that this cost function forms a valley structure along which many local minima appear, the global minimum of J corresponding to the true values of the lithospheric parameters. Classical gradient methods fail to find this global minimum because they converge to the first local minimum of J encountered, so that the final parameter estimate strongly depends on the starting pair of values ( T e ,   c ). We here implement a non-linear optimization algorithm to recover these two parameters from altimetry data. We demonstrate from the inversion of synthetic data that this approach ensures robust estimates of T e and c by activating two search phases alternately: a gradient phase to find a local minimum of J , and a tunnelling phase through high values of the cost function. The accuracy of the solution can be improved by a search in an iteratively restricted parameter subspace. Applying our non-linear inversion to the Great Meteor Seamount geoid data, we further show that the inverse problem is intrinsically ill-posed. As a consequence, minute geoid (or gravity) data errors can induce large changes in any recovery of lithospheric elastic thickness and crustal density.  相似文献   

17.
Summary. The elastodynamic fields of point forces and shear dislocations of finite source duration are analysed with the aim of establishing the frequency and time-domain characteristics of the field in the near-source region. Criteria are obtained for amplitude dominance in regions where the source–sensor distance is much smaller than the wavelength.
It is shown that in the frequency domain , the Green's tensor (and hence the displacement field of a single point force) attenuates like R −1 in the near-source region and there exists no region in which the 'near-field' term becomes dominant such that the 'far-field' term can be neglected. Hence, there is no real 'near-field' term for the elastodynamic Green's tensor. The near-field terms of the displacements, velocities and accelerations excited by a shear dislocation attenuate like R −2, since the R −3 and R −4 terms tend to be eliminated due to mutual cancellation of P and S motions in the near-source region.
In the time domain , the corresponding near field of the displacement field is defined for the steady amplitude interval (away from transients) R /β < t < R /α+ T by the condition R ≤βT where β is the shear velocity and T is the source's duration. The relative strengths of all other arrivals will depend on the particular time window under consideration.
The particle motion patterns due to a single force in the near-source region are shown to be similar to rotating hyperbolas with an axis along the force direction, which are quite different from the 'smoke ring' motion patterns of the so-called 'near-field' term itself.  相似文献   

18.
Summary. A method is outlined to determine the dynamic behaviour of a phase boundary in the Earth when non-uniform time-varying pressure and temperature conditions are assumed at the Earth's surface. An integral equation describing the phase boundary motion is derived and it is solved under a linearizing assumption. The solution is obtained in the form of a double integral transform. Short and long time-expansions of the solution can be obtained from series expansion and integration of the Laplace transform along a branch cut. The method is illustrated by considering a stepwise change in surface pressure conditions.
For short times, the solution exhibits the same type of time dependence (i.e. the first-order term is in t 1/2) as the one obtained in the one-dimensional case (i.e. uniform pressure perturbation at the Earth's surface).
For long times, it is shown that the time dependence of the phase boundary motion is almost identical to the one derived for the one- dimensional case if the wavenumber k L of the surface excitation is such that κ k 2Lτ≤ 1 (where τ is the relaxation time associated with the one-dimensional phase boundary motion and κ is the thermal diffusivity). If κ k 2Lτ > 1, then the relaxation time for the phase boundary motion in two dimensions is of the order of κ−1 k −2L.
When considering parameters that would be appropriate for a basalt to eclogite phase transition at Moho depth, the latter situation is met only when the load wavelength is smaller than 35 km.  相似文献   

19.
We present velocity constraints for the upper-mantle transition zones beneath Central Siberia based on observations of the 1982 RIFT Deep Seismic Sounding (DSS) profile. The data consist of seismic recordings of a nuclear explosion in north-western Siberia along a 2600 km long seismic profile extending from the Yamal Peninsula to Lake Baikal. We invert seismic data from the mantle transition zones using a non-linear inversion scheme using a genetic algorithm for optimization and the WKBJ method to compute the synthetic seismograms. A statistical error analysis using a graph-binning technique was performed to provide uncertainty values in the velocity models.
Our best model for the upper-mantle velocity discontinuity near 410 km depth has a two-stage velocity-gradient structure, with velocities increasing from 8.70–9.25 km s−1 over a depth range of 400–415 km, a gradient of 0.0433 s−1, and from 9.25–9.60 km s−1 over a depth range of 415–435 km, a gradient of 0.0175 s−1. This derived model is consistent with other seismological observations and mineral-physics models. The model for the velocity discontinuity near 660 km depth is simple, sharp and includes velocities increasing from 10.15 km s−1 at 655 km depth to 10.70 km s−1 at 660 km depth, a gradient of 0.055 s−1.  相似文献   

20.
Summary. A variety of near-regional (300 km) data, including spectral amplitudes of Pg , surface-wave forms, and close-in (5–10 km) accelerograms have been used to build an elastic seismic source model for a 1-Mton explosion in tuff at near-regional distances. The model consists of: (1) a pressure pulse which injects 3 × 1012 cm3 of volume into the medium, (2) a vertical, upward force impulse that imparts 1018 dyn-s of momentum to the medium, each source component having a time duration of 0.6 s and a depth of 1.3 km. The force impulse appears to be required by two considerations: (a) the striking similarity, apart from sign, of explosion surface waves with those of their cavity collapses, (b) the observation of considerable SV energy leaving the source of the 1-Mton explosions JORUM and HANDLEY . Scaling curves have been constructed which fit the proposed source model. These scaling curves employ: very slow decrease, as (yield)−0.10 of the primary corner frequency; decay as (frequency)4 or (frequency)3 to high frequency. While these scaling curves are unconventional, they appear to be the only ones which can satisfy the near-regional data. The slow scaling with yield of the spectral carner frequency suggests that it is caused by something other than the equivalent elastic radius, e.g. the time duration of motion at the source. The results, at odds with similar studies at teleseismic distances, suggest that significantly different equivalent elastic sources are required at near-regional (as compared with teleseismic) distances; therefore, the effect of the upward impulse might not be seen at teleseismic distances. Consequently, these results probably do not pertain to the seismic discrimination problem at teleseismic distances.  相似文献   

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