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1.
The Free Core Nutation (FCN) is an important eigenmode which affects both Earth rotation and body tide. The FCN parameters, the resonance period and the quality factor are important for understanding the dynamics of the Earth at nearly diurnal periods. Those parameters are usually estimated either from the Very Long Baseline Interferometry (VLBI) observations of nutation, or from the tidal gravity measurements. In this paper we investigate the determination of the FCN parameters from gravity records covering a period of more than three years, collected with the use of a LaCoste&Romberg Earth Tide no. 26 gravimeter, located at Józefos?aw observatory near Warsaw. From the resonant enhancements of gravimetric factors and phases of diurnal tidal gravity waves, we could infer the FCN period to be equal to 430 sidereal days. This result is in very good agreement with previous gravimetric and VLBI nutation results, confirming the discrepancy in the dynamic flattening of the outer liquid core from its theoretical value based on the hydrostatic equilibrium assumption. The estimated FCN quality factor (Q ≈ 1300) is considerably smaller than the VLBI nutation result, which confirms that the local gravity measurements are more sensitive than VLBI global analyses to site-dependent phenomena (such as atmospheric and indirect ocean tidal effects). We also investigated the importance of gravimetric corrections in the FCN analysis, including numerical tests and simulations. This allowed us to estimate the uncertainty of FCN parameters due to improper or incomplete set of environmental corrections. We took also into account the impact of gravimetric factor errors and tidal wave selection on estimated FCN parameters. We demonstrated that despite relatively noisy measurements due to unfavorable gravimeter location, we were able to obtain very good results in case when proper correction and tidal wave selection were applied.  相似文献   

2.
旋转椭球型地球的固体地幔与液态地核间相互作用而产生的逆向本征模通常称之为地球自由核章动,自由核章动的品质因子（Q值）能有效反映核幔边界层能量耗散特征,与核幔边界的黏滞度密切相关.本文首次利用全球地球动力学计划网络23个台站27组高密度采样的高精度超导重力仪器观测数据,采用迭积技术,确定了自由核章动参数Q值,进而计算了核幔边界的黏滞系数.数值结果说明获得的核幔边界动力学黏滞系数达到103 Pa·s量级,与加拿大科学家Smylie等利用VLBI观测资料获得的最新结果一致,这说明重力技术是有效应用于研究地球深内部结构的重要手段之一.  相似文献   

3.
《Journal of Geodynamics》2010,49(3-5):331-339
The Free Core Nutation (FCN) is investigated with the help of its resonance effect on the tidal amplitudes in Superconducting Gravimeter (SG) records of the GGP network. The FCN resonance parameters are combined in a resonance equation involving the Earth's interior parameters. The sensitivity of the FCN parameters to the diurnal tidal waves demonstrates that the quality factor of the FCN is strongly dependent on the accuracy of the imaginary part estimates of the gravimetric factors close to the resonance. The weak amplitude of Ψ1 tidal wave on the Earth, which is the closest in frequency to the FCN, in addition to errors in ocean loading correction, explains the poor determination of the quality factor Q from surface gravimetric data. The inversion of tidal gravimetric factors leads to estimates of the period, Q and resonance strength of the FCN. We show that, by inverting log(Q) instead of Q, the results using the least-squares method optimized using the Levenberg–Marquardt algorithm are in agreement with the Bayesian probabilistic results and agree with the results obtained from VLBI nutation data. Finally, a combined inversion of 7 GGP European SG data is performed giving T = 428 ± 3 days and 7762 < Q < 31,989 (90% C.I.). An experimental estimate of the internal pressure Love number is also proposed.  相似文献   

4.
Ambiguity in the inverse problem of retrieval of the mechanical parameters of the Earth’s shell and core from the set of data on the velocities V p and V S , of longitudinal and transverse seismic body waves, the frequencies f i and quality factors Q i , of free oscillations, and the amplitudes and phases of forced nutation is considered. The numerical experiments show that the inverse problem of simultaneous retrieval of the density profile ρ in the mantle-liquid core system and the mechanical quality factor Q μ of the mantle (if the total mass M and the total mean moment of inertia I of the Earth, and V p and V S are constant at all depths) has most unstable solutions. An example of depth distributions of ρ and Q μ which are alternative to the well-known PREM model is given. In these distributions, the values of M and I and the velocities V p and V S at all depths for the period of oscillations T = 1 s exactly coincide with their counterparts yielded by PREM model (T = 1 s); however, the maximum deviations of the ρ and Q μ profiles from those in the PREM model are about 3% and 40%, respectively; the mass and the moment of inertia of the liquid core are smaller than those for the PREM model by 0.75% and 0.63%, respectively. In this model, the root mean square (rms) deviations of all the measured values of f i and Q i from their values predicted by theory are half to third the corresponding values in the PREM model; the values of Δ for natural frequencies of the fundamental tone and overtones of radial oscillations, the fundamental tones of torsional oscillations, and the fundamental tones of spheroidal oscillations, which are measured with the highest relative accuracy, are smaller by a factor of 30, 6.6, and 2 than those in the PREM model, respectively. Such a large ambiguity in the solution of the inverse problem indicates that the current models of the depth distribution of density have relatively low accuracy, and the models of the depth distribution of the mechanical Q in the mantle are extremely unreliable. It is shown that the ambiguity in the models of depth distribution of density considerably decreases after the new data on the amplitudes and phases of the forced nutation of the Earth are taken into account. Using the same data, one may also refine by several times the recent estimates of the creep function for the lower mantle within a wide interval of periods ranging from a second to a day.  相似文献   

5.
In the first part of the paper [Molodenskii, 2011], we considered the problem of ambiguity in the solution of the inverse problem of retrieval of density distribution in the Earth’s core and mantle and determination of the Q factors in the mantle from the entire set of modern data on seismic velocities (V p and V S ), the frequencies f i and quality factors Q i of free oscillations of the Earth, and the amplitudes and phases of its forced nutations. We have constructed the model distributions of these parameters, in which the root-meansquared (rms) deviations of all observed values from the predicted ones are much smaller than in the PREM model. Below, we compare the observed amplitudes of the forced nutation with the values predicted by our model. In order to understand how rigid are the constraints imposed by the amplitudes of forced nutation, we not only calculate the deviations of the observed amplitudes of nutation from the predictions by our model but also estimate the changes in these deviations caused by small variations in several parameters of the model. To the parameters to be varied we refer those which have no or barely any effect on the periods and damping constants of free oscillations but have a pronounced effect on the amplitudes of forced nutation. These parameters include (1) the rheological properties of the mantle in the interval of periods from an hour to a day; (2) the dynamical flattening of the liquid core; (3) the dynamic flattening of the solid inner core; (4) the viscosity of the liquid core; and (5) the moment of inertia of the solid inner core. In addition, we estimate the effects of variations in the moment of inertia of the liquid core to be small (±0.2%) and not to affect, within the observation error, the periods of free oscillations. We show that the uncertainty in the model depth distributions of density considerably decreases when the new data on the amplitudes and phases of the forced nutation of the Earth are taken into account. With these data, it is possible to estimate the creep function for the lower mantle in a wide range of periods from a second to a day.  相似文献   

6.
New, unique information on the inertial and dissipative coupling of the liquid core and the mantle has been retrieved from modern high-precision (radiointerferometer and GPS) data on tidal variations in the rotation velocity and nutation of the Earth. Comparison of theoretical and observed data provided new estimates for the dynamic flattening of the outer liquid and the inner solid cores, mantle quality factor, viscosity of the liquid core, and electromagnetic coupling of the liquid core and the mantle [Molodensky, 2004, 2006]. As was shown in the first part of the paper [Molodensky, 2008] (further referred to as [I]), generation of eddy flows in Proudman-Taylor columns, whose orientation is controlled by the topography of the liquid core-mantle boundary, should be taken into account for correct estimation of the inertial coupling (see formulas (8) and (34) in [I]). The range of periods within which this effect plays a significant role is determined by the decay time of these flows. This time is estimated in the paper for the case where dissipation is related to viscous friction at the core-mantle boundary or with the electromagnetic coupling of the liquid core and the mantle. Because of significant uncertainties in modern data on the viscosity of the liquid core, the magnetic field intensity at the core-mantle boundary, and the electrical conductivity of the lower mantle, the dissipative coupling of the liquid core and the mantle cannot be calculated as yet. However, as shown in the paper, the decay time of eddy flows is connected with the attenuation time of subdiurnal free nutation and with the liquid core viscosity. This enables the estimation of the frequency dependence of the dissipative coupling in a fairly wide range. It is shown that the range of periods for which relations (8) and (34) in [I] are valid encompasses the best-studied length-of-day variations and, therefore, these relations are applicable to analysis of the majority of modern data.  相似文献   

7.
We analyze the present-day data on the periods of free oscillations and amplitudes of the forced nutations of the Earth for evaluating the admissible range of the mass and moment of inertia for the liquid core. The initial model for this study is taken in the form of the model distribution of density and mechanical Q parameters of the mantle suggested in (Molodenskii, 2010; 2011a; 2011b). This model was constructed by the steepest descent method in the space of 64 parameters, which determine the distribution of density and parameters of mechanical Q in the mantle, liquid outer core, and solid inner core of the Earth. We assumed the Q parameter of the mantle and inner solid core to be constant and sought for the density variations for the simplest two-parameter model of the piecewise-linear functions with the jumps on the boundary between the liquid core and the mantle and at the olivine-spinel phase transition at a depth of 670 km in the mantle. After this, the computations were repeated for the other distributions of Q (which were also assumed to be unchanged) that correspond to their limiting admissible values. Using this approach, we managed to find the most probable values of the mass and moment of inertia of the liquid core and determine the admissible range of their values. According to our estimates, the ratios of the mass and moments of inertia of the liquid core to the mass and moment of inertia of the whole Earth fall in the intervals 0.317996 ± 0.00065 and 0.110319 ± 0.00022, respectively. These values are lower than the corresponding values for the PREM model (0.322757 and 0.112297) by (1.48 ± 0.30)% and (1.76 ± 0.35)%, respectively. The interpretation of these results requires the revision and thorough analysis of the data on the admissible temperature range of the liquid core and (or) its chemical composition.  相似文献   

8.
Variability of the Earth’s structure makes a first-order impact on attenuation measurements which often does not receive adequate attention. Geometrical spreading (GS) can be used as a simple measure of the effects of such structure. The traditional simplified GS compensation is insufficiently accurate for attenuation measurements, and the residual GS appears as biases in both Q 0 and η parameters in the frequency-dependent attenuation law Q(f) = Q 0 f η . A new interpretation approach bypassing Q(f) and using the attenuation coefficient χ(f) = γ + πf/Q e(f) resolves this problem by directly measuring the residual GS, denoted γ, and effective attenuation, Q e. The approach is illustrated by re-interpreting several published datasets, including nuclear-explosion and local-earthquake codas, Pn, and synthetic 50–300-s surface waves. Some of these examples were key to establishing the Q(f) concept. In all examples considered, χ(f) shows a linear dependence on the frequency, γ ≠ 0, and Q e can be considered frequency-independent. Short-period crustal body waves are characterized by positive γ SP values of (0.6–2.0) × 10?2 s?1 interpreted as related to the downward upper-crustal reflectivity. Long-period surface waves show negative γ LP ≈ ?1.9 × 10?5 s?1, which could be caused by insufficient modeling accuracy at long periods. The above γ values also provide a simple explanation for the absorption band observed within the Earth. The band is interpreted as apparent and formed by levels of Q e ≈ 1,100 within the crust decreasing to Q e ≈ 120 within the uppermost mantle, with frequencies of its flanks corresponding to γ LP and γ SP. Therefore, the observed absorption band could be purely geometrical in nature, and relaxation or scattering models may not be necessary for explaining the observed apparent Q(f). Linearity of the attenuation coefficient suggests that at all periods, the attenuation of both Rayleigh and Love waves should be principally accumulated at the sub-crustal depths (~38–100 km).  相似文献   

9.
The Earth＇s free core nutation （FCN） is a retrograde eigenrnode which is attributed to the interaction between the solid mantle and the liquid core of the rotational elliptical Earth. This mode appears as an eigenmode of nearly diurnal free wobble （NDFW） in a terrestrial reference frame with a period of about one day （XU et al, 2001）. Therefore, the NDFW will lead to an obvious resonance enhancement in the diurnal tidal gravity observations, especially those of the tidal waves with frequencies closed to its eigenfrequency such as P1, K1, ψ1 and Ф1. The FCN resonance parameters can be retrieved accurately by high-precision tidal gravity observations, especially those recorded with the superconducting gravimeters （SG）. The Global Geodynamics Project （GGP） organized by IUGG took it as an important content for determining the FCN resonance parameters by using gravity data. However, the results are affected by many factors such as station location, background noise, the selection of the tide-generating potential tables, ocean tide models, data processing techniques and so on. In our study, the FCN parameters will be retrieved by using the SG observations at Wuhan, and the effects of the choices of various tide-generating potential tables, oceanic models and weight functions on the estimation of the FCN parameters will be discussed in detail,  相似文献   

10.
We employ a niching genetic algorithm to invert ∼30,000 differential ScS/S attenuation values for a new spherically symmetric radial model of shear quality factor (Qμ) with high sensitivity to the lower mantle. The new radial Qμ model, QLM9, possesses greater sensitivity to Qμ at large mantle depths than previous studies. On average, lower mantle Qμ increases with depth, which supports models of increasing viscosity with depth [B.M. Steinberger, A.R. Calderwood. Mineral physics constraints on viscous flow models of mantle flow, J. Conf. Abs., 6, 2001., 2001.]. There are two higher-Qμ regions at ∼1000 and ∼2500 km depth, which roughly correspond to high-viscosity regions observed by Forte and Mitrovica [A.M. Forte and J.X. Mitrovica, Deep-mantle high-viscosity flow and thermochemical structure inferred from seismic and geodynamic data, Nature 410, 1049–1056, 2001.]. There is a lower-Qμ layer at the core–mantle boundary and a relatively low-Qμ region in the mid-lower mantle. With several caveats, we infer a divergence of the solidus and geotherm in the lower mantle and a convergence within Dʺ by relating Qμ to homologous temperature.  相似文献   

11.
The results of processing and analyzing the instrumental observations of the Earth’s magnetic field at the Geophysical Observatory Mikhnevo of the Institute of Geosphere Dynamics of the Russian Academy of Sciences (IGD RAS) for 2010–2015 are presented. Quasi-harmonic components with the periods close to the lunar–solar tidal waves are revealed in the spectra of geomagnetic variations over a period of 0.4 to 30 days. The elliptical S1 tidal wave which is detected in the geomagnetic variations has modulations with periods of 1/3, 1/2, and 1 year. The spectra of the geomagnetic variations contain peaks corresponding to the free oscillations of the Earth. The analysis of the time series of the magnetic field for the period of the strong earthquakes in the absence of geomagnetic disturbances revealed the fine structure of the Earth’s fundamental spheroidal mode 0S2, which splits into five singlets. The established features of the spectrum of geomagnetic variations are helping the development of the new method for studying the deep structure of the Earth and the properties of the inner geospheres for estimating the viscosity of the Earth’s outer core and dynamics of the current systems in the outer (liquid) core, as well as for exploring, with the use of empirical data, the general regularities governing the regimes of energy exchange processes in the geospheres.  相似文献   

12.
Short-period seismograms are synthesized for PKP phases in anelastic Earth models. The synthetics were constructed using a synthetic technique valid at grazing incidence, a source-time function appropriate for deep-focus earthquakes, and an instrument response for either a short-period WWSSN or SRO seismograph. The agreement between predicted and observed amplitudes and spectral ratios requires neither a low-Qα zone at 0.2–2 Hz nor a low or negative P-velocity gradient at the bottom of the outer core. Thin low-Qα zones beneath the inner core boundary fit spectral ratio data that sample the upper 200 km of the inner core but fail to fit data that sample the lower inner core. Only a model having Qα?1?[0.003, 0.004] at 0.2–2 Hz, nearly constant with depth in the inner core, satisfies all of the spectral ratio and amplitude data. The assumption of a bulk viscosity of 10-103 Pa s for the liquid phase of a partially molten inner core combined with the observation of low shear attenuation in the inner core at frequencies less than 0.005 Hz limit the physical parameters associated with two possible attenuation mechanisms: (1) fluid flow and viscous relaxation due to ellipsoidally shaped inclusions of melt, and (2) the solid-liquid phase transformation induced by the stress change during the passage of a seismic wave. Both mechanisms require an order of 0.1% partial melt to reproduce the observed Qα?1. In the outer core, the time constant of the mechanism of phase transformation is predicted to be 104–106 s. Confirmation of small shear attenuation in the inner core in the frequency band of seismic body waves would favor the mechanism of phase transformation.  相似文献   

13.
We have estimated the parameters of fluid core resonance (FCR) due to the nearly diurnal free wobble of the Earth's core based on the superconducting gravimeter (SG) data obtained at the following four observation sites; Esashi and Matsushiro in Japan, Canberra in Australia and Membach in Belgium. By fitting the tidal admittances normalized with the O1 wave at each site to a model of the damped harmonic oscillator, we obtained values of 429.66 ± 1.43 sidereal days, 9350–10,835, −4.828E−4 ± 3.4E−6, −3.0E−5 ± 4.5E−6 for the eigenperiod, the Q-value and the real and imaginary parts of the resonance strength, respectively. Our values obtained from only using the gravity data are very consistent with those inferred from the VLBI nutation data. Our study strongly indicates that the systematic difference between two estimations from the gravity and the nutation in particular for the Q-value, which has been shown in previous works, is mainly caused by the inaccurate correction for the ocean tide effects. The error in the ocean tide correction is discussed based on the comparison among four global ocean tide models; Schwiderski model (1980), NAO.99b (Matsumoto et al., 2000), CSR4.0 (Eanes and Bettadpur, 1994) and GOT99.2b (Ray, 1999).  相似文献   

14.
The models of the mechanical Q factor of the inner solid core of the Earth are reconstructed from the amplitudes and phases of forced nutation and the periods and damping constants of the high-order overtones of free radial modes. The admissible range of the Q-factor in the solid core is estimated and the stability of the obtained distributions is analyzed. The real accuracy of the obtained model distributions is estimated on the basis of the previous conclusions concerning the uncertainty in the solution of the inverse problem of reconstructing the internal structure of the Earth in the low-frequency range.  相似文献   

15.
The spectrum of high frequency Earth rotation variations contains strong harmonic signal components mainly excited by ocean tides along with much weaker non-harmonic fluctuations driven by irregular processes like the diurnal thermal tides in the atmosphere and oceans. In order to properly investigate non-harmonic phenomena a representation in time domain is inevitable. We present a method, operating in time domain, which is easily applicable within Earth rotation estimation from Very Long Baseline Interferometry (VLBI). It enables the determination of diurnal and subdiurnal variations, and is still effective with merely diurnal parameter sampling. The features of complex demodulation are used in an extended parameterization of polar motion and universal time which was implemented into a dedicated version of the Vienna VLBI Software VieVS. The functionality of the approach was evaluated by comparing amplitudes and phases of harmonic variations at tidal periods (diurnal/semidiurnal), derived from demodulated Earth rotation parameters (ERP), estimated from hourly resolved VLBI ERP time series and taken from a recently published VLBI ERP model to the terms of the conventional model for ocean tidal effects in Earth rotation recommended by the International Earth Rotation and Reference System Service (IERS). The three sets of tidal terms derived from VLBI observations extensively agree among each other within the three-sigma level of the demodulation approach, which is below 6 μas for polar motion and universal time. They also coincide in terms of differences to the IERS model, where significant deviations primarily for several major tidal terms are apparent. An additional spectral analysis of the as well estimated demodulated ERP series of the ter- and quarterdiurnal frequency bands did not reveal any significant signal structure. The complex demodulation applied in VLBI parameter estimation could be demonstrated a suitable procedure for the reliable reproduction of high frequency Earth rotation components and thus represents a qualified tool for future studies of irregular geophysical signals in ERP measured by space geodetic techniques.  相似文献   

16.
In this paper, we investigate the perturbations induced by the nearly-diurnal luni-solar tidal potential on the surface gravity changes and on the spatial nutations. The effects of the magnetic friction at the inner core boundary (ICB) and on the inner core viscosity at this time scale are studied. We show that very precise very long baseline interferometry (VLBI) observations of the in-phase and out-of-phase components of some nutations can give information on the Earth’s deep interior, especially on the effective viscosity of the inner core and on the amplitude of the radial component of the magnetic field at the ICB.  相似文献   

17.
Earth orientation parameters (EOP) are essential for the interconnection of different reference systems involved in Chang’E-1 (CE-1) lunar exploration, such as the Earth fixed reference system, celestial reference system and dynamical reference system. To improve the accuracy of predicted EOP values and to reduce their influence on the accuracy of CE-1 orbital parameters, a relativistic mathematical model of differential VLBI (ΔVLBI) time delay observations for the CE-1 transfer orbit is derived in this paper, which is generated by differencing CE-1 time delay observations with a simulated radio source's time delay observations. The CE-1 orbital parameters and EOP are simultaneously estimated with least squares adjustment using the measured time delay observations of the CE-1 transfer orbit. The results show that the accuracy of the CE-1 orbit and EOP estimates is improved by the CE-1 ΔVLBI observations with optimal orbital arc length and the win-win approach is able to improve the accuracy of both the CE-1 orbital parameters and EOP estimates. The estimated CE-1 orbital accuracy can achieve a few hundred meters and the estimated EOP accuracies are better than their predicted values.  相似文献   

18.
GOCE, Satellite Gravimetry and Antarctic Mass Transports   总被引：1，自引：0，他引：1  
In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) was launched. Its objectives are the precise and detailed determination of the Earth’s gravity field and geoid. Its core instrument, a three axis gravitational gradiometer, measures the gravity gradient components V xx , V yy , V zz and V xz (second-order derivatives of the gravity potential V) with high precision and V xy , V yz with low precision, all in the instrument reference frame. The long wavelength gravity field is recovered from the orbit, measured by GPS (Global Positioning System). Characteristic elements of the mission are precise star tracking, a Sun-synchronous and very low (260 km) orbit, angular control by magnetic torquing and an extremely stiff and thermally stable instrument environment. GOCE is complementary to GRACE (Gravity Recovery and Climate Experiment), another satellite gravity mission, launched in 2002. While GRACE is designed to measure temporal gravity variations, albeit with limited spatial resolution, GOCE is aiming at maximum spatial resolution, at the expense of accuracy at large spatial scales. Thus, GOCE will not provide temporal variations but is tailored to the recovery of the fine scales of the stationary field. GRACE is very successful in delivering time series of large-scale mass changes of the Antarctic ice sheet, among other things. Currently, emphasis of respective GRACE analyses is on regional refinement and on changes of temporal trends. One of the challenges is the separation of ice mass changes from glacial isostatic adjustment. Already from a few months of GOCE data, detailed gravity gradients can be recovered. They are presented here for the area of Antarctica. As one application, GOCE gravity gradients are an important addition to the sparse gravity data of Antarctica. They will help studies of the crustal and lithospheric field. A second area of application is ocean circulation. The geoid surface from the gravity field model GOCO01S allows us now to generate rather detailed maps of the mean dynamic ocean topography and of geostrophic flow velocities in the region of the Antarctic Circumpolar Current.  相似文献   

19.
In the first part of the paper, we obtained the refined estimates for the periods and Q-factors of the fundamental modes and overtones of spherical and toroidal oscillations with periods longer than 3 min from the data on the free oscillations of the Earth, which were excited by the earthquakes with magnitude 9 that occurred in Sumatra, Japan, and the Sea of Okhotsk. In (Molodenskii et al., 2013), we analyzed the limits of the admissible density distributions in the mantle and liquid core of the Earth, using the data on the amplitudes and phases of the forced nutations, as well as the periods and attenuation factors of the fundamental modes of the free spheroidal and toroidal oscillations of the Earth. These studies were conducted with the fixed values of the total mass and total moment of inertia of the Earth and the fixed distributions of the body seismic waves in the mantle and in the core. The solution was obtained by orthogonalizing the kernels of the integral equations that link the residuals of the observed frequencies and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, with the sought densities and Q-factors of the mantle and liquid core. Below, we present the solution of the same problem with allowance for the results obtained in the first part of this paper, namely, the new data on the periods and attenuation factors of the fundamental modes of free oscillations of the Earth and on the periods of the first four overtones of the free spheroidal and toroidal oscillations. Despite the involvement of the new data on the overtones, which have not been considered in our calculations, the weighted root mean square deviations of the theoretical predictions from the observed periods and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, have significantly decreased. This is due to (1) the noticeable reduction of the real errors in estimating the parameters of the free oscillations described in the first part of the paper and (2) the inclusion of the quantities determining the depth- and frequency dependences of the Q-factor in the mantle in the set of the independently varied parameters.  相似文献   

20.
The results of solving the inverse problem of forced nutations and free oscillations of the Earth by decomposing the Q-factor and small depth variations in density in a system of orthogonal functions are considered. These functions are determined by orthogonalization of the functional derivatives of the observed parameters with respect to the depth distributions of the sought parameters (assuming there are no distributions of the velocities of body seismic waves V p and V S with depth and unchanged total mass M and inertia moments I of the Earth). The examples are presented to illustrate the numerical solution of the inverse problem on finding the density distributions in the mantle and core of the Earth using orthogonalization of the integral constraints for the probable depth distributions of density describing the conditions of unchanged M and I, as well as the constraints posed by the data on the periods of the free low-order oscillations of the Earth.  相似文献   

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