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1.
Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)1023 poise (P) and 104 (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 1023 P with upper and lower limits of 1.1 × 1023 and 2.8 × 1023 P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 1023 P.  相似文献   

2.
The observed time-series of precession/nutation show residuals with respect to an empirical model based on the rigid Earth theoretical nutations and a frequency dependent transfer function with resonances to the Earth's normal modes. These residuals display energy mainly in the frequency domain around 430 and 500 days in the inertial frame. In this frequency band, the energy is possibly related to two normalmode frequencies: the free core nutation (FCN) and the free inner core nutation (FICN). In this paper, we examine the possibility of obtaining this energy from the resonance effect induced by a luni-solar (or planetary) forcing, or by an atmospheric forcing at a frequency very close to these Earth free nutations. The amplification factor due to the resonance is computed from an analytical formula expressed in the case of a simplified three-layer ellipsoidal rotating earth (with an elastic inner core, a liquid outer core and an elastic mantle), as well as the empirical formula based on the analysis of VLBI observations. For the tidal forcing, the theoretical results do not show any resonance at the level of precision we have examined but it is still possible to find one frequency near the FCN or FICN frequencies which could be excited. In contrast, for the atmospheric pressure the level of energy needed could be obtained from the diurnal pressure, depending on the noise level of the Earth's global pressure. We also show that the combination of three waves can explain the observed decrease of energy with time. While the tidal potential amplitudes are too small, a pressure noise level of 0.5 Pa would be sufficient to excite these waves.  相似文献   

3.
The fossil record of the variation of the solar day and the synodic month with geological time is examined for evidence of the steady contraction of the Earth postulated by Lyttleton to explain a discrepancy between the apparent secular accelerations of the Sun and Moon. Data for the Phanerozoic and the Precambrian agree in showing that a change in the Earth's moment of inertia as large as that suggested by Lyttleton is only consistent with the fossil record if the secular change in the gravitational constant Ġ/ G ≥+ 4 × 10–11/yr. A variation of G of this magnitude appears to be ruled out by a recent analysis of lunar occultation observations utilizing Atomic Time.  相似文献   

4.
The post-seismic response of a viscoelastic Earth to a seismic dislocation can be computed analytically within the framework of normal-modes, based on the application of propagator methods. This technique, widely documented in the literature, suffers from several shortcomings; the main drawback is related to the numerical solution of the secular equation, whose degree increases linearly with the number of viscoelastic layers so that only coarse-layered models are practically solvable. Recently, a viable alternative to the standard normal-mode approach, based on the Post–Widder Laplace inversion formula, has been proposed in the realm of postglacial rebound models. The main advantage of this method is to bypass the explicit solution of the secular equation, while retaining the analytical structure of the propagator formalism. At the same time, the numerical computation is much simplified so that additional features such as linear non-Maxwell rheologies can be simply implemented. In this work, for the first time, we apply the Post–Widder Laplace inversion formula to a post-seismic rebound model. We test the method against the standard normal-mode solution and we perform various benchmarks aimed to tune the algorithm and to optimize computation performance while ensuring the stability of the solution. As an application, we address the issue of finding the minimum number of layers with distinct elastic properties needed to accurately describe the post-seismic relaxation of a realistic Earth model. Finally, we demonstrate the potentialities of our code by modelling the post-seismic relaxation after the 2004 Sumatra–Andaman earthquake comparing results based upon Maxwell and Burgers rheologies.  相似文献   

5.
During the last glacial cycles, global sea level dropped several times by about 120 m and large ice sheets covered North America, northern Europe and Antarctica during the glacial stages. The changes in the iceocean mass balance have displaced mantle material mainly via viscous flow, and the perturbation of the equilibrium figure of the Earth by glacial isostatic adjustment is still observable today in timedependent changes of gravitational and rotational observations. Contemporary iceocean mass balance from volume changes of polar ice caps also contributes to secular variations of the Earth's gravitational field.
In the near future, several satellite gravity missions will significantly improve the accuracy of the observed timedependent gravitational field. In view of the expected improvements in the observations, we predict glacially induced perturbations of the gravitational field, induced by Late Pleistocene and contemporary ice volume changes, for a variety of radial mantle viscosity profiles. We assess the degree of uncertainty for the glacially induced contributions to gravitational and rotational parameters, both in the spectral and the spatial domain.
Predictions of power spectra for the glacially induced freeair gravity and geoid anomalies are about one order of magnitude lower than the observed values, and uncertainties arising from different plausible viscosity profiles are around 0.150.4 mGal and 0.21.5 m, respectively. Uncertainties from different ice models are of secondary importance for the predicted power spectra. Predicted secular changes in geoid anomalies in formerly glaciated areas are mainly controlled by the viscosity profile and contemporary ice volume changes. We also show that the simple threelayer viscosity profiles currently employed for the majority of postglacial rebound studies represent a limited subset for model predictions of the timedependent gravitational field.  相似文献   

6.
Monopoly     
Summary. A model for the geomagnetic secular variation field is given, consisting of a series of magnetic monopoles at the surface of the Earth's core. These are distributed according to the density of the data to allow more detailed representation in areas where the density of observations is high, without introducing spurious detail where data are sparse. A monopole model is calculated from observatory secular change data for the epoch 1957.5–1962.5 and its usefulness assessed.  相似文献   

7.
Summary. The power spectrum of the Earth's spin has important components with periods ranging from a few days to at least a few thousand years, and probably to the age of the Earth. The secular acceleration, as the term is used here, refers to the components with periods longer than three centuries. In the year 600, the secular acceleration was —19.9 ± 0.8 parts in 109 per century, while the value at the present time is less than half this size. The spin acceleration has important contributions from tidal friction and from an effect that is proportional to the square of the magnetic dipole moment. When these contributions are subtracted from the observed acceleration, we are left with a contribution that amounts to +41 parts in 109 per century. This amount probably results from an unknown combination of changes in the size of the core, in the amount of glaciation, and in the size of the gravitational constant.  相似文献   

8.
Summary. A precision magnetic survey for the investigation of current activity in the Earth's lithosphere has been carried out in the Urals and in the Carpathians. As a result of this research three types of time variation of the total field were discovered. These are:
(1) The normal field variation reflecting the general pattern of secular variation. The difference of initial and repeat observation where only this type of variation operates, is rather small and usually does not exceed 0.2–0.3 nT. The field changes in such regions can be used only to evaluate the observation errors and to provide the regional pattern of secular variation.
(2) The slow but localized'anomalous field'change from year to year corresponding, presumably, to anomalies of a tectonomagnetic nature. The normal pattern of the secular variation field here is disturbed by sources located in the upper part of the lithosphere.
(3) Irregular time changes of the field with rather large amplitudes (up to 10–20 nT). Repeated observations of such anomalies show that the field changes significantly here even during one day. Both in the Urals and Carpathians these anomalies form extended elongated structures with widths up to 10–30 km. These anomalies usually coincide with those deep faults where the strongest recent crustal movements have been determined by means of geodetic observations. The analysis of the results of precision geomagnetic surveys in the Urals and in the Carpathians shows that geomagnetic investigations can be used for the exploration of tectonically active zones.  相似文献   

9.
Absolute gravity observations yield insight into geophysical phenomena such as postglacial rebound, change in the Earth's hydrological cycle, sea level change, and changes in the Earth's cryosphere. In the article, the first gravity values at 16 Norwegian stations measured by a modern absolute gravimeter of the FG5 type are presented. The gravity observations were corrected for Earth tides, varying atmospheric pressure, polar motion, and ocean tide loading. The ocean tide loading corrections were subject to special attention. A model based on locally observed ocean tides was applied at some of the stations. The authors estimated the total uncertainties of the gravity values to range from 3 to 4 µgal (1 µgal = 10?8 m s?2). These errors are of magnitude one order less than previously presented absolute gravity values from Norway. The final gravity values are time tagged and will change due to postglacial rebound. The maximum effect is expected to be approximately ?1 µgal yr?1.  相似文献   

10.
A time-varying spherical harmonic model of the palaeomagnetic field for 0–7 ka is used to investigate large-scale global geomagnetic secular variation on centennial to millennial scales. We study dipole moment evolution over the past 7 kyr, and estimate its rate of change using the Gauss coefficients of degree 1 (dipole coefficients) from the CALS7K.2 field model and by two alternative methods that confirm the robustness of the predicted variations. All methods show substantial dipole moment variation on timescales ranging from centennial to millennial. The dipole moment from CALS7K.2 has the best resolution and is able to resolve the general decrease in dipole moment seen in historical observations since about 1830. The currently observed rate of dipole decay is underestimated by CALS7K.2, but is still not extraordinarily strong in comparison to the rates of change shown by the model over the whole 7 kyr interval. Truly continuous phases of dipole decrease or increase are decadal to centennial in length rather than longer-term features. The general large-scale secular variation shows substantial changes in power in higher spherical harmonic degrees on similar timescales to the dipole. Comparisons are made between statistical variations calculated directly from CALS7K.2 and longer-term palaeosecular variation models: CALS7K.2 has lower overall variance in the dipole and quadrupole terms, but exhibits an imbalance between dispersion in   g 12  and   h 12  , suggestive of long-term non-zonal structure in the secular variations.  相似文献   

11.
A 2-D time-dependent finite-difference numerical model is used to investigate the thermal character and evolution of a convecting layer which is cooling as it convects. Two basic cooling modes are considered: in the first, both upper and lower boundaries are cooled at the same rate, while maintaining the same temperature difference across the layer; in the second, the lower boundary temperature decreases with time while the upper boundary temperature is fixed at 0°C. The first cooling mode simulates the effects of internal heating while the second simulates planetary cooling as mantle convection extracts heat from, and thereby cools, the Earth's core. The mathematical analogue between the effects of cooling and internal heating is verified for finite-amplitude convection. It is found that after an initial transient period the central core of a steady but vigorous convection cell cools at a constant rate which is governed by the rate of cooling of the boundaries and the viscosity structure of the layer. For upper-mantle models the transient stage lasts for about 30 per cent of the age of the Earth, while for the whole mantle it lasts for longer than the age of the Earth. Consequently, in our models the bulk cooling of the mantle lags behind the cooling of the core-mantle boundary. Models with temperature-dependent viscosity are found to cool in the same manner as models with depth-dependent viscosity; the rate of cooling is controlled primarily by the horizontally averaged variation of viscosity with depth. If the Earth's mantle cools in a similar fashion, secular cooling of the planet may be insensitive to lateral variations of viscosity.  相似文献   

12.
Summary. The convergence of two methods of inferring bounds on seismic velocity in the Earth from finite sets of inexact observations of τ ( p ) and X( p ) are examined: the linear programming (LP) method of Garmany, Orcutt & Parker and the quadratic programming (QP) method of Stark & Parker. The LP method uses strict limits on the observations of τ and X as its data, while QP uses estimated means and variances of τ and X. The approaches are quite similar and involve only one inherent approximation: they use a finite-dimensional representation of seismic velocity within the Earth. Clearly, not every Earth model can be written this way. It is proved that this does not hinder the methods - they may be made as accurate as desired by increasing the number of dimensions in a specified way. It is shown how to get the highest accuracy with a given number of dimensions.  相似文献   

13.
Summary. Under project IRIS (International Radio Interferometric Surveying) geodesists are using Very Long Baseline Interferometry (VLBI) to monitor polar motion to 1-2 ms of arc and UT1 to 0.05-0.10 ms, and to develop a global geodynamic network to detect and study centimetre level displacements of reference points associated with large-scale phenomena such as tectonic plate motion and glacial rebound. Differential positioning techniques using the signals broadcast by the satellites of the Global Positioning System (GPS) are being used to study finer scale phenomena, such as localized subsidence, and economically to relate these specialized surveys to the geodynamic network. Including tide gauge stations in this system will make it possible to detect motions of specific gauges and correct or delete the measurements from those gauges when computing changes in sea-level. The National Oceanic and Atmospheric Administration (NOAA) has selected several tide gauges on the east and west coasts of the United States, and initial epoch GPS surveys to tie the gauges to VLBI observations have already begun. Other countries participating in project IRIS are planning similar activities. In addition to providing a globally based land reference datum for the tide gauge measurements, the IRIS polar motion and UT1 time series may contribute directly to monitoring and interpreting global sea level changes. Changes in the volume and distribution of ice masses result in long-term motions of the axis of rotation, and sea-level changes affect the length of day (lod). The IRIS time series will certainly have the resolution required to detect the expected polar motion and changes in lod, and a properly designed global VLBI/GPS network should allow the ice/sea-level effects to be separated from crustal dynamics effects.  相似文献   

14.
Summary The problems of reducing geomagnetic observations from ships at sea in areas influenced by the effect of the equatorial electrojet are discussed. In particular, observations within the Gulf of Aden have been corrected for daily variation and secular variation for the purposes of constructing a contoured magnetic anomaly chart.
An empirical formula is given with which the range of daily variation at different latitudes within the Gulf was estimated for the purpose of correcting the data for daily variation. The observed secular variation, which was used to correct the data, is—11 γ/yr. which differs from the secular variation of +19 γ/yr. in the Gulf of Aden given by the recently adopted International Geomagnetic Reference Field (Zmuda 1969).  相似文献   

15.
Pragmatic experimental design requires objective consideration of several classes of information including the survey goals, the range of expected Earth responses, acquisition costs, instrumental capabilities, experimental conditions and logistics. In this study we consider the ramifications of maximizing model parameter resolution through non-linear experimental design. Global optimization theory is employed to examine and rank different EM sounding survey designs in terms of model resolution as defined by linearized inverse theory. By studying both theoretically optimal and heuristic experimental survey configurations for various quantities of data, it is shown that design optimization is critical for minimizing model variance estimates, and is particularly important when the inverse problem becomes nearly underdetermined. We introduce the concept of robustness so that survey designs are relatively immune to the presence of potential bias errors in important data. Bias may arise during practical measurement, or from designing a survey using an appropriate model.  相似文献   

16.
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The results are presented from tidal gravity measurements at five sites in Europe using LaCoste and Romberg ET gravimeters. Improvements that we have made to the accuracies of these gravimeters are discussed. It is shown that the 'standard' calibration of the International Center for Earth Tides, used for worldwide tidal gravity profiles, is 1.2 per cent too high. The M2 and O1 observations are compared with model calculations of the Earth's body tide and ocean tide loading and it is shown that there is a very significant improvement in the agreement between observations and models compared to that obtained with previous tidal gravity measurements. For O1, where the ocean tide loading and attraction in central Europe is only 0.4 per cent of the body tide, our measurements verify that the Dehant-Wahr anelastic body tide model gravimetric factor is accurate to 0.2 per cent. It is also shown that the effects of lateral heterogeneities in Earth structure on tidal gravity are too small to explain the large anomalies in previously published tidal gravity amplitudes. The observations clearly show the importance of conserving tidal mass in the Schwiderski ocean tide model. For sites in central Europe, the M2 and O1 observations and the models are in agreement at the 0.1 μgal (10−9 m s−2) level and tidal corrections to this accuracy can now be made to absolute gravity measurements.  相似文献   

17.
Summary. An existing experimentally verified model for energy dissipation in a processing spherical cavity filled with liquid assumed to be in a semirigidized state except for a viscous Ekman boundary layer is applied to the Earth's liquid core to assess energy dissipation magnitudes. Application of the model to the best available Earth data occurs at the derived energy dissipation maximum for the model. Other existing research showing that the Earth's atmosphere appears to adjust to a state of maximum dissipation led to generic models for systems of maximum dissipation. The maximum dissipation mantle—core model with core motion driven by Earth precession alone, coupled to the mantle only by viscous shear stresses, and with a spherical mantle—core boundary leads to energy dissipation rates on the order of 104 times those necessary for an Earth dynamo. The maximum dissipation model also leads to excessive magnetic field drift rates and to excessive retardation of the Earth's rotation rate. Effects of the mantle—core ellipticity and of magnetic field coupling are briefly discussed and are used to help develop a less than maximum dissipation model also driven by precession alone but using the additional coupling to yield a model more consistent with observed phenomena.  相似文献   

18.
Secular polar motion has been recorded in ILS data over the past 75 years, an amount greater by a factor of ten than the 'true polar wandering' deduced from paleomagnetic data. In this work, the possibility that the secular trend is an observational artifact of the continental drift of the ILS stations is directly examined by consideration of several absolute plate velocity models earlier proposed by Minster et al. (1974), Kaula (1975), and Solomon, Sleep & Richardson (1975). The assumptions underlying those models are discussed; in general, the absolute velocity models are more likely to be valid when geologically short timescales are considered.
The corrections to the ILS data due to the stations' motion fail by an order of magnitude to explain the ILS trend; even by taking into account possible plate hyperactivity and non-rigidity, the corrections could explain no more than 30 per cent of the trend. The corrections are small because the absolute plate velocities of North America and Eurasia are small and primarily east—west. Consequently, the rotation pole is undergoing significant motion of its own relative to the surface of the Earth.
The Kimura z term found by the ILS observations provides an independent means of estimating the relative motion between Eurasia and North America. It also contains other geophysical information; the 7.5-yr periodicity discovered by Naito & Ishii (1974) may be widespread.
Lastly, tectonically induced changes in the zenith direction, such as at Mizusawa, are probably too small to be detected, contrary to earlier proposals.  相似文献   

19.
Summary. A spherical harmonic model of the second time-derivative of the geomagnetic field is determined, for the first time, directly from measures of the secular acceleration based on observatory annual mean data. The data span the interval 1964.5–1975.5, and 165 observatories are included. The model comprises the 32 coefficients of degree and order up to 6 that are significant at the 5 per cent level. Its primary purpose is to aid in the reduction of data to epoch for the 1980 series of navigational charts. The model is compared with earlier estimates of secular acceleration, derived by less direct methods.  相似文献   

20.
A new statistical approach to the alignment of time series   总被引：1，自引：0，他引：1  
Summary. Much research in the Earth Sciences is centred on the search for similarities in waveforms or amongst sets of observations. For example, in seismology and palaeomagnetism, this matching of records is used to align several series of observations against one another or to compare one set of observations against a master series. This paper gives a general mathematical and statistical formulation of the problem of transforming, linearly or otherwise, the time-scale or depth-scale of one series of data relative to another. Existing approaches to this problem, involving visual matching or the use of correlation coefficients, are shown to have several serious deficiencies, and a new statistical procedure, using least-squares cubic splines, is presented. The new method provides not only a best estimate of the 'stretching function' defining the relative alignment of the two series of observations, but also a statement, by means of confidence regions, of the precision of this transformation. The new procedure is illustrated by analyses of artificially generated data and of palaeomagnetic observations from two cores from Lake Vuokonjarvi, Finland. It may be applied in a wide variety of situations, wherever the observations satisfy the general underlying mathematical model.  相似文献   

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