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1.
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   

2.
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   

3.
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   

4.
Summary. Asymptotic expressions for components of the electromagnetic field of a grounded electric dipole are considered for the model consisting of a thin surface-layer overlapping a stratified medium with a highly resistive screen on the roof. It is shown that the method of spatial derivatives makes it possible to obtain proper estimates of the impedance at distances of r ≥|λ0| from the nearest edge of the surface anomaly (|λ0| being the effective depth of the field penetration in the underlying section). the magnetotelluric methods allow one to obtain the true values of impedance, provided r ≥ max {|λ0|, |/( S −1+ Z −0|1/2} where S is the integrated conductivity of the surface layer, is the transverse resistance of the screen, and Z −0 is the Tikhonov—Cagniard impedance for the medium underlying the surface layer.  相似文献   

5.
Summary. Palaeomagnetic results are presented from the c . 160 km2 Caledonian synorogenic layered Fongen-Hyllingen gabbro complex (of probable late Silurian age) located about 75 km SE of Trondheim, Norway, in the allochthonous Seve-Kdli Nappe Complex. A total of 80 oriented samples from eight sites in the northern part of the gabbro were investigated. After detailed af demagnetization two stable high coercivity components emerge: one with a well defined NW direction with D =325°, I =−21° (α95=8°, N =8), and another, less well defined, probably younger, SW direction with D = 237°, I = 6° (α95= 9°, N = 8). Correction for dip of these two directions gives D = 329°, I =−7° (α95= 10°) and D = 238°, I =−11° (α95= 12°), respectively. The corresponding pole positions are P 1 : 19° N, 225° E and P 2: 19° S, 308° E, respectively. The reversed pole -P 2 of the SW direction lies close to other NW European palaeomagnetic poles of Caledonian, Upper Silurian-Lower Devonian age. However, the dominant pole PI is far away from these, and could be due to a late Caledonian geomagnetic excursion of considerable duration; or it could record a c . 90° rotation around a vertical axis of a crustal block within the Scandinavian Caledonides. Block rotation could have been related to nappe translation, although geological observations do not at present appear to support the occurrence of such an event.  相似文献   

6.
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   

7.
Summary. Fifty-six orientated samples were collected from 13 sites on five dolerite dykes (between lat.14°23°N, long.77°43'E and lat.14°08'N, long. 77°49'E), which adjoin the south-western margin of the Cuddapah basin in Anantapur district, Andhra Pradesh. After af demagnetization, two dykes (five sites) striking ENE possess similar magnetic directions, (1) D = 57°, 1=-69° (K = 52, α95= 7°) and (2) D = 71°, I = -72° ( K = 260, α95= 5°). Again dykes (3) (three sites), and (4) (two sites) have similar strike (NE) and magnetic directions, D = 64°. I=-7 α( K = 142, α95 = 8°) and D = 53°, I =-8° (K = 142, α95= 6°) and dyke (5) (two sites) striking NW shows D = 320°, I = -34° ( K = 68, α95= 13°). Remanent directions estimated from total field magnetic anomaly data agree well with these results. Synthesis of these data with 10 other published palaeomagnetic studies of Precambrian dolerite dykes on the Indian peninsula, suggest that these three systems of dykes adjoining the Cuddapah basin had been emplaced prior to the basin formation perhaps representing the initial thermal event responsible for the basin development and also that there have been at least three separate periods of dyke emplacement on this shield. The radiometric data, however, are very sparse and these periods cannot be dated with confidence.  相似文献   

8.
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   

9.
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   

10.
Oxygen consumption by rotifers Macrotrachela musculosa and Trichotria truncata from Spitsbergen tundra (77°N) was measured using the method of Cartesian divers. The metabolic rate of M. musculosa was: 0.205 10−3mm3 02 per g 10−6 per hour at 2°C, 0.201 10−6mm3 at 6°C and 0.616 10−3mm3 02 per g 10−6 per hour at 10°C. The metabolic rate of Trichotria truncata at 6° was 0.103 10−3mm3 per g 10−6 per hour. The relation between body weight and oxygen consumption by M. musculosa at 2°C is expressed with the equation R = 0.18W0.67, with R – oxygen consumption in mm310−3 per individual per hour and W – wet weight of an animal in g 10−6.  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.
Magnetic susceptibility ( χ ) variations and the behaviour of the ratio of susceptibility to saturation magnetization ( χ/J s ) along the loess/palaeosol section at Koriten (NE Bulgaria) are used to deduce climatic changes during the Pleistocene in southeastern Europe. A good correlation of susceptibility variations with the astronomically tuned oxygen isotope record from ODP site 677 enables us to propose a more precise dating of the upper part of the Bulgarian loess complex. Close correspondence between susceptibility and δ 1 8 O records demonstrates the global significance of the palaeoclimatic signal recorded, although differences in relative amplitudes of χ and χ/J s and δ 1 8 O create difficulties in making quantitative estimates of the climatic humidity in the past. The role of local factors affecting the palaeoclimatic mineral magnetic record deduced from the profile studied in Bulgaria is discussed.  相似文献   

13.
Measurement of samples from 154 sites in the continental sector of the Cameroon Volcanic Line yielded six palaeomagnetic poles, at 243.6°E, 84.6°N, α 95 = 6.8°; 224.3°E, 81.2°N, α 95 = 8.4°; 176.1°E, 82.0°N, α 95 = 8.5°; 164.3°E, 86.4°N, α 95 = 3.4°; 169.4°E, 82.6°N, α 95 = 4.6° and 174.7°E, 72.8°N, α 95 = 9.5°, belonging to rocks which have been dated by the K–Ar method at 0.4–0.9  Ma, 2.6  Ma, 6.5–11  Ma, 12–17  Ma, 20–24  Ma and 28–31  Ma, respectively. The results are in general agreement with other palaeomagnetic poles from Oligocene to Recent formations in Africa.
  The first three poles for rocks formed between 0.4 and 11  Ma are not significantly different from the present geographical pole. Together with other African poles for the same period, this suggests that the African continent has moved very little relative to the pole since 11  Ma. The other three poles for rocks dated between 12 and 31  Ma are significantly different from the present geographical pole, showing a 5° polar deviation from the present pole in the Miocene and 13° in the Middle Oligocene.  相似文献   

14.
Summary. The Cordova gabbro of southern Ontario intrudes 1300 Myr old volcanic rocks of the Hastings Lowlands in the Grenville Structural Province. Three distinct vector magnetizations (A, B and C) have been isolated, using a combination of stable endpoints, subtracted vectors from orthogonal vector plots and converging remagnetization circles. The A magnetization, with mean direction D = 294° I =– 55.5° ( k = 42, α95= 5.5°, N = 18 sites), is a high coercivity, high blocking temperature remanence recorded by 49 samples. The B magnetization was isolated in 33 samples and has a mean direction D = 305.5° I =– 1.5° ( k = 24, α95, N = 11 sites). B has lower coercivities and blocking temperatures than A where the two are superimposed. The A and B palaeopoles, 151°E, 10.5°S ( dp = 6°, dm = 8°) and 165.5°E, 24°N ( dp = 5°, dm = 9.5°), fall on the Grenville Track around 900 and 820 Ma respectively. The A and B magnetizations thus date from uplift and cooling following the Grenvillian orogeny. The third magnetization, the C component, has been isolated in 23 samples. Its mean direction is D = 180° I = 27.5° ( k = 18, α95= 10.5°, N = 12 sites). The C is a low coercivity, low blocking temperature overprint of A and B. Its palaeopole, 102°E, 31°N ( dp = 6.5°, dm = 12°), is unlike post-1300 Precambrian poles for cratonic North America but matches Silurian and late Ordovician poles. 40Ar/39Ar plateau ages of 446 and 447 Ma determined by Lopez-Martinez and York for plagioclases from one of the Cordova samples confirm this age assignment. The C magnetization therefore records a previously unrecognized mild thermal or hydrothermal event that occurred in Palaeozoic time, long after the Grenvillian orogeny.  相似文献   

15.
207Pb/206Pb single-grain zircon, 40Ar/39Ar single-grain hornblende and biotite, and 40Ar/39Ar bulk-sample muscovite and biotite ages from the Nelshoogte trondhjemite pluton located in eastern Transvaal, South Africa, show that this granitoid had a protracted thermal history spanning 3213±4  Ma to about 3000  Ma. Whole-rock 40Ar/39Ar ages from cross-cutting dolerite dykes indicate that these were intruded at about 1900  Ma. There is no evidence of this or other, later events significantly affecting the argon systematics of the minerals from the pluton dated by the 40Ar/39Ar method.
  The pluton has a well-defined palaeomagnetic pole which is dated at 3179±18 (2 σ ) Ma by 40Ar/39Ar dating of hornblende. This pole (18°N, 310°E, A 95=9°) yields a palaeolatitude of 0°, significantly different from other Archaean poles from the Kaapvaal Craton. The palaeolatitude difference implies that there was significant apparent polar wander during the Archaean. A second, overprinting magnetization seen in the pluton is also seen in the lower-Proterozoic dolerite dykes, and is consistent with other lower-Proterozoic (2150–1950  Ma) poles for southern Africa.  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. Attenuation of earthquake intensities with epicentral distance was studied by analysing the intensity data for 39 earthquakes in the United States. Attenuation of MM intensity ( I ) with distance (Δ km) follows a simple relation of the type log I = log I 0 - m Δ, where I 0 is the intensity at the epicentre and m is a constant. Slope m is found to be inversely proportional to the square of the focal depth. Intensity attenuation pattern in the United States in general can be represented by a unified relation I/I 0= exp [-(0.8999/ h 2+ 0.0014)Δ] where 16km ≤ h ≤ 60km. Intensities were calculated with the help of this equation and a good agreement with the observed intensities were found. A comparative study has also been made between the attenuation relations applicable to India and the United States.  相似文献   

18.
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   

19.
10 m and 2.3 m ice cores were obtained on Austre Brøggerbreen, Spitsbergen in Svalbard (78°53 ' N, 11°56 ' E, 450 m a.s.l.) in September 1994 and in March 1995, respectively. Stratigraphy, bulk density, pH, electrical conductivity, and major ions were obtained from the core samples.
The chemical effect of meltwater percolation through snow/ice is examined. Good correlation between Cl− and Na+ was obtained. The ratio of Cl− to Na+ was 1.14 which was nearly the same value as in bulk sea water. However, the variation of Cl−/Na+ shows that higher ratio occured in the bubble-free ice. Furthermore the Cl− ions remain in higher concentration than SO 4 2− or Na+ ions.  相似文献   

20.
Summary. After thermal and alternating field (AF) cleaning, the characteristic high blocking temperature A component of natural remanent magnetization (NRM) of the Tudor gabbro of southern Ontario has a mean direction D = 326°, I =–46° ( k = 132, α95= 4.8°, N = 8 sites). The corresponding palaeopole, 133°E, 12°N ( dp = 4°, dm = 6°), confirms the palaeopole 137°E, 17°N (α95= 8.4°) reported earlier by Palmer & Carmichael, based on AF cleaning only. The A NRM has unblocking temperatures > 515–525°C which exceed the estimated 500°C peak temperature reached locally during ∼ 1050 Ma Grenvillian regional metamorphism. The A NRM therefore predates metamorphism and is probably a primary thermoremanence (TRM). The age of the Tudor NRM has previously been taken to be about 675 Ma, but recent 40Ar/39Ar dating by Baksi has shown that this is the time of post-metamorphic cooling to 200–250°C. Hornblendes record initial cooling of the intrusion to 590±20°C at 1110 Ma and this is the best estimate of the age of the A remanence. Successful Thellier-type palaeointensity determinations on 11 Tudor samples confirm that the A NRM is a TRM and indicate a palaeofield at this time of 18–27 μT, about 50–70 per cent of the present field intensity at 27° magnetic latitude. The anomalous Tudor A palaeopole, which lies well to the west of both 1000–800 Ma Grenvillian palaeopoles and 1100–1050 Ma poles from Interior Laurentia, is interpreted as recording divergence between Grenvillia and Interior Laurentia just before the Grenvillian orogeny, rather than a post-metamorphic extension of the apparent polar wander path as previously assumed.  相似文献   

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