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1.
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   

2.
We report on calculations of the on-shore run-up of waves that might be generated by the impact of subkilometre asteroids into the deep ocean. The calculations were done with the COULWAVE code, which models the propagation and shore-interaction of non-linear moderate- to long-wavelength waves  ( kh < π)  using the extended Boussinesq approximation. We carried out run-up calculations for several different situations: (1) laboratory-scale monochromatic wave trains onto simple slopes; (2) 10–100 m monochromatic wave trains onto simple slopes; (3) 10–100 m monochromatic wave trains onto a compound slope representing a typical bathymetric profile of the Pacific coast of North America; (4) time-variable scaled trains generated by the collapse of an impact cavity in deep water onto simple slopes and (5) full-amplitude trains onto the Pacific coast profile. For the last case, we also investigated the effects of bottom friction on the run-up. For all cases, we compare our results with the so-called 'Irribaren scaling': The relative run-up   R / H 0=ξ= s ( H 0/ L 0)−1/2  , where the run-up is   R , H 0  is the deep-water waveheight, L 0 is the deep-water wavelength, s is the slope and ξ is a dimensionless quantity known as the Irribaren number. Our results suggest that Irribaren scaling breaks down for shallow slopes   s ≤ 0.01  when  ξ < 0.1 − 0.2  , below which   R / H 0  is approximately constant. This regime corresponds to steep waves and very shallow slopes, which are the most relevant for impact tsunami, but also the most difficult to access experimentally.  相似文献   

3.
Summary. The inverse gravity potential problem consists in the determination of the form and the density of the body by its exterior gravity potential. We describe two similar classes of bodies for which this problem has a unique constructive solution.
(1) The first class contains the cylindrical bodies with finite length, arbitrary form of section and ρ( R , ø, z) =ρ1( z )ρ2( R , ø) density distribution, where z is the cylindrical coordinate; R , ø are the polar coordinates in a section plane. This class is important for prospecting geophysics in that it allows us to determine in a unique and constructive way, the function ρ1( R , ø), the length, form and orientation of the cylinder if we know the function ρ1( z ) and the exterior potential. The classical moment problem of functions is the basis for the solution of this problem.
(2) The analogous problem for the class of the spherical cylinders, or bodies bounded by arbitrary similar sections of two different concentric spheres and the radial lateral surface, appears when bodies of planetary size are studied. (An example of these bodies would be the Moon mascons.) The density distribution of these cylinders is ρ(τ, θ, ø) =ρ1(τ)ρ2(θ, ø) where τ, θ, ø are the spherical coordinates. The function ρ1(θ, ø), length and form of spherical sections can be uniquely determined by exterior potential if we know the function ρ1(τ). We propose a new constructive method for harmonic continuation of the gravity potential into the region containing the perturbing masses for the solution of the problem.  相似文献   

4.
In order to approximate the free-surface motion of an Earth-sized planet subjected to a giant impact, we have described the excitation of body and surface waves in a spherical compressible fluid planet without gravity or intrinsic material attenuation for a buried explosion source. Using the mode summation method, we obtained an analytical solution for the surface motion of the fluid planet in terms of an infinite series involving the products of spherical Bessel functions and Legendre polynomials. We established a closed form expression for the mode summation excitation coefficient for a spherical buried explosion source, and then calculated the surface motion for different spherical explosion source radii a (for cases of   a / R = 0.001  to 0.035, R is the radius of the Earth) We also studied the effect of placing the explosion source at different radii r 0 (for cases of   r 0/ R = 0.90  to 0.96) from the centre of the planet. The amplitude of the quasi-surface waves depends substantially on a / R , and slightly on   r 0/ R   . For example, in our base-line case,   a / R = 0.03, r 0/ R = 0.96  , the free-surface velocity above the source is 0.26 c , whereas antipodal to the source, the peak free surface velocity is 0.19 c . Here c is the acoustic velocity of the fluid planet. These results can then be applied to studies of atmosphere erosion via blow-off caused by asteroid impacts.  相似文献   

5.
Some comments on the descriptions of the polarization states of waves   总被引：4，自引：0，他引：4  
Summary. Procedures are developed for specifying the polarization characteristics of n -dimensional waves, and in particular three-dimensional waves of geophysical interest. We show that when a wave is in a pure state or is totally polarized, all the polarization information can be represented by a single vector u in an n -dimensional unitary space. Simple measures of the degree of polarization of the wave are constructed from the characteristic equation of the spectral matrix S . These measures are functions only of the scalar invariants of S and consequently S need not be diagonalized. If S represents a purely polarized wave, the unitary vector which contains the polarization information about the wave can be obtained directly from S using any 2 n – 1 equations of n 2 possible equations. By multiplying by a phase-factor this unitary vector can be written in the form u = r 1+ i r 2 where r 1 and r 2 are orthogonal vectors in a real space. For an elliptically polarized wave, r 1 and r 2 locate the major and minor axes of the ellipse, and the ellipticity is given by the ratio of their magnitudes. The polarization parameters of ULF magnetic waves at the Earth's surface are computed from one set of five equations ( n = 3) and compared with parameters calculated using established techniques.  相似文献   

6.
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7.
We evaluate the stress field in and around the southern Korean Peninsula with focal mechanism solutions, using the data collected from 71 earthquakes ( ML = 1.9–5.2) between 1999 and 2004. For this, the hypocentres were relocated and well-constrained fault plane solutions were obtained from the data set of 1270 clear P -wave polarities and 46 SH / P amplitude ratios. The focal mechanism solutions indicate that the prevailing faulting types in South Korea are strike-slip-dominant-oblique-slip faultings with minor reverse-slip component. The maximum principal stresses (σ1) estimated from fault-slip inversion analysis of the focal mechanism solutions show a similar orientation with E–W trend (269°–275°) and low-angle plunge (10°–25°) for all tectonic provinces in South Korea, consistent with the E–W trending maximum horizontal stress (σHmax) of the Amurian microplate reported from in situ stress measurements and earthquake focal mechanisms. The directions of the intermediate (σ2) and minimum (σ3) principal stresses of the Gyeongsang Basin are, however, about 90 deg off from those of the other tectonic provinces on a common σ2–σ3 plane, suggesting a permutation of σ2 and σ3. Our results incorporated with those from the kinematic studies of the Quaternary faults imply that NNW- to NE-striking faults (dextral strike-slip or oblique-slip with a reverse-slip component) are highly likely to generate earthquakes in South Korea.  相似文献   

8.
3-D images of P velocity and P - to S -velocity ratio have been produced for the upper crust of the Friuli area (northeastern Italy) using local earthquake tomography. The data consist of 2565 P and 930 S arrival times of high quality. The best-fitting V P and V P / V S 1-D models were computed before the 3-D inversion. V P was measured on two rock samples representative of the investigated upper layers of the Friuli crust. The tomographic V P model was used for modelling the gravity anomalies, by converting the velocity values into densities along three vertical cross-sections. The computed gravity anomalies were optimized with respect to the observed gravity anomalies. The crust investigated is characterized by sharp lateral and deep V P and V P / V S anomalies that are associated with the complex geological structure. High V P / V S values are associated with highly fractured zones related to the main faulting pattern. The relocated seismicity is generally associated with sharp variations in the V P / V S anomalies. The V P images show a high-velocity body below 6 km depth in the central part of the Friuli area, marked also by strong V P / V S heterogeneities, and this is interpreted as a tectonic wedge. Comparison with the distribution of earthquakes supports the hypothesis that the tectonic wedge controls most of the seismicity and can be considered to be the main seismogenic zone in the Friuli area.  相似文献   

9.
Summary. The statistical capability of the m b: M s discriminant for the discrimination of earthquake and explosion populations is examined by application of discriminant functions to a group of 83 explosions and 72 earthquakes in Eurasia. Equations are derived for the probability that an event is an earthquake or an explosion. The positive sign of DIS in the decision index equation, DIS i = 34.3383 – 11.9569 mb t + 7.1161 M si , indicates that the event i is an earthquake. Its negative sign indicates that event i is an explosion. The probability of correct classification for an event, P i , is related to its DIS i value, by P i = [1-exp (DIS i )]−1, where a large, positive DIS indicates a high probability that an event is an earthquake and a large, negative DIS indicates a high probability that an event is an explosion. The discrimination line M s = 1.680 m b– 4.825, or m b= 0.595 M s+ 2.872 very successfully separates the explosion population from the earthquake population. The points on this line have an equal chance of being an earthquake or an explosion; moreover, for any event, the distance parallel to the M s-axis from the point representing that event in the m b: M s plane to this line is a measure of the probability for the correct classification of that event.  相似文献   

10.
Summary. In cases where directional data, such as palaeomagnetic directions, lie nearly along a great circle, a good approximation to the maximum likelihood estimate of the intermediate concentration parameter k 2 in the Bingham probability distribution is given by: 2( t 2/ N ) – 1 = I 1(1/2 k 2)/ I 0(1/2 k 2), where t 2 is the intermediate eigenvalue, N is the number of samples, and the Ii are the appropriate modified Bessel functions of the first kind. This estimate, the asymptotic limit as the smallest eigenvalue t 1→ 0, corresponds to restricting all points to lie on a great circle. The limit is also useful as an endpoint for interpolation, especially since numerical calculation in this region is difficult.  相似文献   

11.
The tidal dynamics of the Irish and Celtic Seas   总被引：1，自引：0，他引：1  
Summary. Current meter data collected over periods of more than 14 day from the Irish and Celtic Seas are harmonically analysed and presented in maps of tidal stream information. Making use of the analysed current data, and by constructing time series of frictional and inertial stresses which are also harmonically analysed, harmonic constituents of the surface tidal slopes at current meter stations are obtained. Using these with data collected from offshore tide gauges, and in conjunction with coastal tide data, cotidal maps are drawn with some confidence for M 2, S 2, O 1 and K 1, the M 2 chart resolving the discrepancy which exists between the different charts of the Celtic Sea already produced. Cotidal maps for M 3 and M 4 are also presented.
The mean over a tidal cycle of the energy flux for M 2, S 2 and O 1 is also presented in the form of the total energy flux in these constituents which crosses different sectional lines. A flux of 44 × 106 kW is observed to enter the Celtic Sea from the Atlantic and this is compared with previous estimates. An energy budget is also performed for M 2, including all the effects of astronomical forcing and Earth tides to enable comparison to be made between the true energy inflow and the estimated frictional dissipation. Finally, comparison is made between the mean of the instantaneous energy flux and the sum of the energy fluxes associated with the major harmonics.  相似文献   

12.
Summary. Using nine IDA records for the Indonesian earthquake of 1977 August 19, we have formed an optimal linear combination of the records and have measured the frequency and Q of 0 S 0 and 1 S 0. The frequency was measured using the moment ratio method. The attenuation was measured by the minimum width method and by the time-lapse method. The frequency and attenuation were measured simultaneously by varying them to obtain a best fit to the data. A 2000-hr stack, the sum of nine individual records, for 0 S 0 gave a frequency of 0.814664 mHz±4 ppm. The values for the Q of 0 S 0 for the three different methods of measurement were 5600,5833 and 5700, respectively. The error in the estimates of Q -1 is about 5 per cent for the minimum power method. For 1 S 0 a 300-hr stack yielded a frequency of 1.63151 mHz±30 ppm. The values of Q for this mode were 1960, 1800 and 1850, respectively, with an error in Q -1 of about 12 per cent for the minimum power method.  相似文献   

13.
We have studied the response of normal modes to perturbations in inner-core shear velocity and attenuation, using fully coupled mode synthetics. Our results indicate that (i) mode pairs   n S l – n ±1 S l   are strongly coupled by anelasticity, (ii) this coupling causes shear velocity perturbations to strongly affect the Q values of modes through exchange of inner-core characteristics, (iii) there is no evidence for a weakly attenuating inner core in shear, and (iv) the discrepancy between attenuation models returned from normal modes and body waves is small. These results suggest that inversions for inner-core attenuation and shear velocity should be performed simultaneously and should take account of the strong cross-coupling due to attenuation.  相似文献   

14.
Summary. Differences between estimated average heat flow values for the Mesozoic and Cenozoic formations ( Q 1) and estimated average heat flow values for the Palaeozoic formations below the erosional unconformity ( Q 2) are calculated for the Alberta part of the western Canadian sedimentary basin. Significant heat flow differences exist for these two intervals and the map of Δ Q = Q 1– Q 2 shows that Q 2 is generally greater than Q 1 in the western and south-western part of Alberta, while in the northern part of the province Q 2 is generally less than Q 1. The regional variations of Δ Q are large, with standard deviation of 26 mW m−2 and average value –13.5 mW m−2. A regional trend of Δ Q correlates with topographic relief and the hydraulic head variations in the basin. It is shown that there is a heat flow increase with depth in water recharge areas and a decrease in heat flow with depth in the low topographic elevation water discharge areas when comparing the average heat flow in Mesozoic + Cenozoic and Palaeozoic formations.  相似文献   

15.
Summary. The geopotential is usually expressed as an infinite series of spherical harmonics, and the odd zonal harmonics are the terms independent of longitude and antisymmetric about the equator: they define the 'pear-shape' effect. The coefficients J 3, J 5, J 7, … of these harmonics have been evaluated by analysing the variations in eccentricity of 28 satellite orbits from near-equatorial to polar. Most of the orbits from our previous determination in 1974 are used again, but three new orbits are added, including two at inclinations between 62° and 63°, which have been specially observed for more than five years by the Hewitt cameras. With the help of the new orbits and revised theory, we have obtained sets of J -coefficients with standard deviations about 40 per cent lower than before. A 9-coefficient set is chosen as representative, and is as follows (all × 109): J 3=– 2530 ± 4, J 5=–245 ± 5, J 7=–336 ± 6, J 9=–90 ± 7, J 11= 159 ± 9, J 13=–158 ± 15, J 15=– 20 ± 15, J 17=– 236 ± 14, J 19=– 27 ± 19. With this set of values, the pear-shape asymmetry of the geoid (north polar minus south polar radius) amounts to 45.1 m instead of the previous 44.7 m. The accuracy of the longitude-averaged geoid profile is estimated as 50 cm, except at latitudes above 86°. The geoid profile and predicted amplitude of the oscillation in eccentricity are compared with those from other sources.  相似文献   

16.
Summary. A simple normal approximation is given for the joint probability density function of the polar coordinates (θ, φ) of a random vector following the Fisher distribution with arbitrary mean direction (θ0, φ0). Two important applications of this approximation are discussed, and conditions for the validity of the approximation are investigated and summarized.  相似文献   

17.
Summary. A method that enables the objective resolution of almost parallel multi-component magnetizations is described and demonstrated. A feature distinguishing this method from others is its simultaneous analysis of demagnetization data from a group of specimens, rather than the analysis of data from one specimen at a time. The only prerequisite is that the specimens are derived from a homogeneous source. Thus for a formation carrying a simple single component magnetization, all specimens from the formation may be simultaneously reduced. For a more complicated two component magnetization it is shown that only specimens from a particular site can be considered homogeneous, and for a complex three component system each sample often requires undivided attention. Thus the workload is proportionally increased to achieve analyses of comparable reliability from data of variable quality.
New pole positions from Mesozoic intrusions of the Sydney Basin, NSW are: from the Marsden Park Breccia pipe 48°S, 127°E ( A 95= 6°); the St Marys Breccia pipe 46°S, 150°E ( A 95= 8°); the Prospect Dolerite 60°S, 142°E ( A 95= 13°) and 53°S, 180°E ( A 95= 6°); and from the Dundas Breccia pipe 58°S, 162°E ( A 95= 36°) and 31°S, 195°E ( A 95= 16°). The last two formations possess multi-component magnetizations. These pole positions are consistent with previous results from south-eastern Australia.  相似文献   

18.
Further evidence for oceanic excitation of polar motion   总被引：3，自引：0，他引：3  
While the role of the atmosphere in driving variations in polar motion is well established, the importance of the oceans has been recognized only recently. Further evidence for the role of the oceans in the excitation of polar motion is presented. To estimate the equatorial excitation functions, χ 1 and χ 2 , for the ocean, we use velocity and mass fields from a constant-density ocean model, driven by observed surface wind stresses and atmospheric pressure, for the period 1993–1995; comparison with similar functions derived from a more complex density-stratified ocean model indicates the effectiveness of the simple constant-density modelling approach. Corresponding atmospheric excitation functions are computed from NCEP/NCAR re-analyses. Results indicate significant improvements in the agreement with the observed polar motion excitation when the simulated oceanic effects are added to atmospheric excitation. Correlations between the polar motion and the geophysical signals at periods of 15–150 days increase from 0.53 to 0.80 and from 0.75 to 0.88 for χ 1 and χ 2 , respectively. The oceanic signals are particularly important for seasonal variations in χ 1 (correlation increases from 0.28 to 0.85 when oceanic excitation is included). A positive impact of the oceans on more rapid polar motion is also observed, up to periods as short as 5 days. The sensitivity of the results to different forcing fields and different amounts of friction in the oceans is also discussed.  相似文献   

19.
This paper presents a method to invert underside-reflection ( P d P or S d S arrivals) data for lateral depth variations of upper-mantle discontinuities, combining traveltime and amplitude data. The method greatly improves the resolution of small-scale undulations obtained by existing imaging methods and does not suffer from the long-wavelength biases that are likely to be present in currently available models. Existing inversion methods account for the large size of the Fresnel zone of underside reflections, but not for its complexity, arising from the mini-max traveltime nature of PP- and SS -related waves. This neglect results in long-wavelength artefacts from small-scale undulations of the discontinuities, obscuring true long-wavelength depth variations. The inversion method presented in this paper uses a complex-valued sensitivity kernel, derived from the representation of underside reflections through a Kirchhoff integral formulation. The sensitivity kernel accounts for the varying sensitivity of the waveforms to discontinuity structure over the Fresnel zone. The method is applied to a large, synthetic data set. The data set consists of P d P amplitudes and traveltimes. The results show that the new inversion method resolves depth variations on a lateral scale that is smaller than the size of the Fresnel zone of individual underside reflections (but larger than the dominant wavelength), retaining the resolution of large-scale variations. The results presented here suggest that the discontinuity depth variations induced by slab penetration of the 670 discontinuity could be resolved by current broad-band P 670 P data sets.  相似文献   

20.
Summary. The response of many dynamical systems to an impulse is a linear combination of decaying cosines. The frequencies of the cosines have generally been estimated in geophysics by periodogram analysis and little formal indication of uncertainty has been provided. This work presents an estimation procedure by the methods of complex demodulation and nonlinear regression that specifically incorporates in the basic model the decaying aspect of the cosines (periodogram analysis does not). The use of plots of the instantaneous phase as a function of time is shown to greatly enhance resolution. Expressions for the variances of eigenfrequencies, amplitudes, phases and damping constants Q are derived by non-linear least-squares. The results are illustrated, for the problem of the free oscillations of the Earth, by computations with the record made at Trieste of the Chilean earthquake of 1960 May 22. Sample values are periods and standard errors of 737.79 ± 0.13 s, 506.25 ± 0.13 s and 429.60 ± 0.14 s for 0 T 8, 0 T 13 and 0 T 16 with Q values and standard errors of 200 ± 14, 230 ± 28 and 215 ± 30, respectively.  相似文献   

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