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1.
S. M. Molodenskii M. S. Molodenskii M. S. Molodenskaya 《Izvestiya Physics of the Solid Earth》2014,50(5):603-610
We discuss the problem of the ambiguity of gravity inversion, i.e., finding the depth distribution of density and the depth and frequency dependences of the Q-factor from the entire set of the present-day seismic and astrometric data on the travel times of seismic waves, the periods and attenuation factors of the free oscillations of the Earth, as well as the amplitudes and phases of the forced nutations. In the first part of the paper, we present the new and more accurate determinations of the periods and Q-factors for the fundamental tones and overtones of the spheroidal and toroidal oscillations of the Earth, which have periods longer than 3 min. These determinations are based on analyzing the signals from the Sumatra, Tohoku, and Okhotsk earthquakes of magnitude 9, which were recorded by the stations of the Global Seismographic Network (GSN) in Obninsk and Kazakhstan. It is shown that, although the Okhotsk earthquake had a lower magnitude than the other quakes analyzed (since its seismic source was extremely deep (about 600 km)), the amplitudes of the overtones excited by this event are significantly higher than the amplitudes of the overtones caused by the Sumatra and Tohoku events of magnitude 9. Moreover, the amplitudes of the overtones from the Okhotsk earthquake exceed the amplitudes of the overtones of the free oscillations caused by the other seismic events of magnitude 9 that occurred in the second half of the 20th century. Due to this, the data on the Okhotsk Sea earthquake are of utmost importance for the solution of the inverse problems of reconstructing the vertical profiles of Q-factor in the ultra-low frequency (ULF) range and for reconstructing the vertical distribution of density. Based on the new empirical data, we obtained new and more accurate estimates for the periods and attenuation factors of the free oscillations of the Earth. 相似文献
2.
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
3.
S. M. Molodenskii 《Izvestiya Physics of the Solid Earth》2011,47(4):263-275
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
4.
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
5.
S. M. Molodensky 《Izvestiya Physics of the Solid Earth》2011,47(7):559-574
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.
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
7.
Free oscillation and body wave data are used to construct average Q models for the earth. The data set includes fundamental and overtone observations of the radial, spheroidal and toroidal modes, ScS observations and amplitudes of body waves as a function of distance. The preferred model includes a low-Q zone at both the top and the bottom of the mantle. In these regions the seismic velocities are likely to be frequency dependent in the “seismic” band. Absorption in the mantle is predominantly due to losses in shear. Compressional absorption may be important in the inner core.A grain-boundary relaxation model is proposed that explains the dominance of shear over compressional dissipation, the roughly frequency independent average values for Q and the variation of Q with depth. In the high-Q regions, the lithosphere and the midmantle (200–2000 km), Q is predicted to be frequency dependent. However, the low-Q regions of the earth, where Q is roughly frequency independent, dominate the observations of attenuation. 相似文献
8.
G. Roult 《Physics of the Earth and Planetary Interiors》1975,10(2):159-166
The quality factor of the free oscillations of the earth is calculated from the observed time rate of decay of the energy. Records of the I.P.G.P. long-period data acquisition system are used, after a process enhancing a chosen mode, so that the scatter in the Q results is reduced. Determination of attenuation is made for the spheroidal and torsional fundamental modes and two torsional higher modes.The attenuation of seismic waves is determined from the decay of energy of standing-wave patterns with time, and from the damping of travelling waves with distance, using the surface mantle waves recorded at a single I.P.G.P. long-period seismic station after each great circle path (Gaulon, 1971). 相似文献
9.
地震方位各向异性广泛存在于地球上地幔中,目前利用地震体波或面波分析研究上地幔各向异性的地球物理方法有很多种,但是由于各自的局限性均难以分析上地幔过渡区中的各向异性特征.方位各向异性可导致球形简正模和环形简正模之间发生耦合.地球长周期自由振荡的简正模可深入到上地幔过渡区.本文利用各向异性地球模型计算各向异性简正模耦合深度敏感核,表明长周期(250~400 s)简正模各向异性耦合(如0S20-0T21 和0S25-0T25)的敏感度峰值在400~600 km之间.在不受地球自转影响的台站,如位于南极极点的QSPA站,仍然可以观测到强烈的简正模耦合现象.本文的研究表明:只有在地震观测台站靠近长周期球形振荡的节点时,才能在其观测数据中观测到各向异性耦合现象,许多各向异性耦合在震后18~24 h期间最强,并可导致垂直方向的环形简正模的振幅大于球形耦合简正模的振幅.这些特征是在地震观测数据中寻找各向异性耦合的重要线索.长周期简正模的方位各向异性耦合为我们提供了一个新的认识上地幔过渡区各向异性的窗口. 相似文献
10.
在构建现代地球模型时,地球内部分层结构主要是根据地震波资料确定的;而地球内部密度及弹性参数,特别是地幔以下大尺度结构的密度分布,则主要是根据地球自由振荡的弹性简正模观测资料确定的.本文概述了地球自由振荡简正模本征值的求解理论和方法,介绍了球型和环型模态位移场表达式,讨论了地球自由振荡模态的衰减、分裂与耦合效应;总结了多线态分裂谱线探测和分裂参数估计的方法,综述了利用弹性简正模开展地震矩张量、地球三维非均匀性结构和内核超速旋转约束与反演研究的主要进展和存在的问题.最后作为展望,本文还讨论了地球自由振荡简正模的未来研究趋势. 相似文献
11.
S. M. Molodensky 《Izvestiya Physics of the Solid Earth》2006,42(7):546-550
As was shown in [Molodensky, 2004a, 2004b], modern very long base interferometer (VLBI) data on the amplitudes and phases of the Earth’s forced nutation can provide significantly more rigid constraints on possible values of the quality factor of the lower mantle Q μ and on the dynamic flattening of the liquid core e lc as compared with seismic evidence and data on damping of the free oscillations of the Earth. On the other hand, the accuracy of modern tidal gravity data (obtained from twenty-year series of observations with a cryogenic gravimeter) is also very high and these data must be taken into account while estimating the parameters Q μ and e lc . The paper presents comparative estimates of the determination accuracy of the parameters Q μ and the dynamic flattening of the liquid core from VLBI and the aforementioned tidal gravity data. 相似文献
12.
Preliminary reference Earth model 总被引：29，自引：0，他引：29
A large data set consisting of about 1000 normal mode periods, 500 summary travel time observations, 100 normal mode Q values, mass and moment of inertia have been inverted to obtain the radial distribution of elastic properties, Q values and density in the Earth's interior. The data set was supplemented with a special study of 12 years of ISC phase data which yielded an additional 1.75 × 106 travel time observations for P and S waves. In order to obtain satisfactory agreement with the entire data set we were required to take into account anelastic dispersion. The introduction of transverse isotropy into the outer 220 km of the mantle was required in order to satisfy the shorter period fundamental toroidal and spheroidal modes. This anisotropy also improved the fit of the larger data set. The horizontal and vertical velocities in the upper mantle differ by 2–4%, both for P and S waves. The mantle below 220 km is not required to be anisotropic. Mantle Rayleigh waves are surprisingly sensitive to compressional velocity in the upper mantle. High Sn velocities, low Pn velocities and a pronounced low-velocity zone are features of most global inversion models that are suppressed when anisotropy is allowed for in the inversion.The Preliminary Reference Earth Model, PREM, and auxiliary tables showing fits to the data are presented. 相似文献
13.
We study a set of very high-quality records of first-order overtone Rayleigh waves from the deep-focus earthquake of September 29, 1973, in the Japan Sea. Standard surface wave techniques are used with these overtones, treated as individual seismic phases, to retrieve radiation pattern, Q, moment and phase velocity. A figure of M0 = (6.7 ± 1.4) × 1027dyn-cm is obtained, in total agreement with published values computed from either P waves, or fundamental Rayleigh waves. We also demonstrate the feasibility of using overtones as individual seismic phases in order to investigate their dispersion and attenuation properties. 相似文献
14.
Paolo Lanzano 《Journal of Geodynamics》1984,1(2)
We establish a general theory that describes the rotational motion of a layered, oblate, elastic Earth under the influence of tidal forces when account is taken of the liquid outer core. We obtain a linearized version of the Navier-Stokes equation; within it not only have we retained the Coriolis and centrifugal acceleration terms, but also have included the nutational terms. We also make use of the Euler equation for angular momentum to analytically relate the nutational motion of the rotational axis with the oscillations of the liquid core and obtain a constraint for the nutational amplitude. Consideration of the Poisson equation for density variation completes our analytical model.We primarily discuss the equations of motion for the liquid core and present the solution as the sum of two terms: one being a component of the spheroidal displacement field, the other of the toroidal field. We also formulate the equations valid for the solid mantle when rotational effects are included, and establish the boundary conditions that must hold at the various interfaces in order that a complete integration of the differential system of equations be accomplished.We assume that the outer core consists of an inviscid fluid and ignore the existence of any boundary layer. We do not impose, however, any restriction on the stratification of the fluid. The dynamical coupling between liquid core and solid mantle is represented by a torque which is generated by the forced oscillations within the liquid core; these oscillations are in turn triggered by the diurnal tides.The expected influence of the liquid core/solid mantle boundary on the nutational motion is discussed in view of Poincare's results concerning a liquid core surrounded by a rigid shell. Comparison is finally made of our model with Molodenskii's 1961 theory for a neutral core and the 1976 Shen-Mansinha nutational theory for an unrestricted core. 相似文献
15.
综合分析了中国数字地震台网（CDSN）改造后的5个长周期地震仪台站观测的3天的VHZ、VHE和VHN波形资料，利用功率谱密度估计方法，在没有对资料进行去固体潮处理的情况下，准确获得了2004年12月26日印度洋地震激发的0S3~0S78的基频球型振荡和部分谐频球型振荡和0T3~0T67的基频环型振荡，并与地球初步参考模型（PREM）的理论自由振荡周期进行了对比，发现实测振荡周期与PREM预测的振荡周期符合的很好.频率与PREM模型略微不一致的球型或环型振荡可以解释为地球介质的横向不均匀性和各向异性所致.因此地球自由振荡信息可用于揭示地球的三维不均匀结构信息或各向异性信息，并可能对区分地幔对流模式有所帮助. 相似文献
16.
S. M. Molodenskii 《Izvestiya Physics of the Solid Earth》2017,53(2):173-180
The question of ambiguity in the solution of the inverse problem for determining the Brünt-Väisäla frequency in the Earth’s mantle from the entire set of the up-to-date data on seismicity, free oscillations, and forced nutations of the Earth, as well as the data on the Earth’s total mass and total moment of inertia, is considered. Based on the results of a series of numerical experiments, the band of admissible distributions of the Brünt-Väisäla frequency and mantle density with depth is calculated. This estimate is used for investigating the convective and gravitational stability of the different regions of the mantle against relatively small adiabatic and nonadiabatic perturbations. The generalization of the known Rayleigh criterion of convective stability of homogeneous and a nonself-gravitating incompressible viscous fluid for the case of a compressible self-gravitating fluid is given. A system of the ordinary eight-order differential equations with complex coefficients and homogeneous boundary conditions, whose eigenvalues determine the transition from the stable state to instability, is obtained. Examples of the numerical determination of these eignevalues are presented. For interpreting the data about the band of the admissible distributions of the Brünt-Väisäla frequency with depth, the notion of the effective bulk modulus of the medium at different depths is introduced. This quantity governs the depth changes in temperature in a convecting mantle and allows us to make a conclusion about the role of heat conduction and the radial heterogeneity of the mantle composition without imposing any constraints on the convection mechanism. It is shown that within the present-day observation errors in the frequencies of the Earth’s free oscillations, the simplest reasonable model is that in which the ratio of the effective bulk modulus to its adiabatic value in the lower and middle mantle is 1.043 ± 0.05. The closeness of this value to unity indicates that convection in the lower and middle mantle is fairly close to adiabatic. At the same time, when the analysis only relies on seismic data and on the information about the periods of the free oscillations of the Earth, there is a significant uncertainty in the models of the effective bulk modulus distribution in the upper mantle and crust. This uncertainty precludes us from making purely empirically derived conclusions that reliably and unambiguously describe the role of the effects of heat conduction and radially heterogeneous material composition in the convection in the upper mantle. 相似文献
17.
The nutations of the planets Mars andEarth are investigated and compared. Alarge number of interior structureparameters are involved in the nutationcomputations. The comparison between the observations and the computationsprovides several constraints on these parmeters andtherefore allows a better understanding of the physics of the interior of theplanet. For the Earth, the high precision of the observations of the nutationshas led to a very good determination of interior properties of the planet. ForMars, observations of nutations are not yet available, and we review how theamplitude of the Martian nutations depends on the hypotheses consideredfor its interior. Although Mars is very similar to the Earth, its interior is not well known;for example, we don't knowif its core is liquid or solid. Only if the core is liquid,the Free Core Nutation (FCN) normal mode exists and can alter the nutationswhich are close to the resonance. From the observed geoids, it is known thatboth planets are not in hydrostatic equilibrium. The departure is larger forMars than for the Earth, and consequently, the implication of considering a convective mantle instead of a mantle in hydrostatic equilibrium described byClairaut's equation for the initial equilibrium state of the planet is largeron the Martian nutations than on the Earth nutations. The consequences of theuncertainty in the core dimensions are also examined and shown to be of a veryhigh influence for Mars if the core is liquid, due to the potential changes inthe FCN resonance. The influence of the presence of an inner core, which isknown to exist for the Earth, could be more important for Mars than for theEarth if the inner core is large. Due to the presence of Tharsis on Mars, thetriaxiality of this planet has, additionally, larger effects than on Earth. 相似文献
18.
S. M. Molodensky 《Izvestiya Physics of the Solid Earth》2006,42(5):357-361
The amplitudes and phases of forced nutation and diurnal earth tides depend significantly on the moment of forces between the liquid core and mantle of the Earth, resulting from the differential rotation of the core. The solution to the dynamic problem of rotation of an imperfectly elastic mantle with an imperfectly liquid core and an ocean indicates that the predominant role is played by the so-called core-mantle inertial coupling (related to the effect of hydrodynamic pressure in the liquid core on the ellipsoidal core-mantle boundary). The magnitude of this coupling depends significantly not only on the dynamic flattening of the liquid core but also on the elastic and inelastic properties of the mantle, as well as on the amplitudes and phases of oceanic tides. In this paper, the effects of oceanic tides on the magnitude of inertial coupling between the liquid core and the mantle and on the period and damping decrement of free nearly diurnal nutation are estimated. 相似文献
19.
Based on the long period surface wave data recorded by the China Digital Seismograph Network (CDSN), theQ R of fundamental mode Rayleigh wave with periods from 10 s to 146 s is determined for the eastern Sino-Korean paraplatform in this paper. TheQ β models of the crust and upper mantle are respectively obtained for the 4 paths, with the aid of stochastic inverse method. It shows that in the eastern Sino-Korean paraplatform, the average crustalQ β is about 200, and that there exists a weak attenuation layer in the middle crust (about 10–20 km deep) which is possibly related to earthquake-prone layer. A strong attenuation layer (lowQ) of 70 km thick extensively exists in the uppermost mantle, with the buried depth about 80 km. The averageQ R of fundamental mode Rayleigh wave is between the value of stable tectonic region and that of active tectonic region, and much close to the latter. 相似文献
20.
甚长周期VP型垂直摆倾斜仪对某些地球物理信号有特殊的敏感性,除了在观测小地震、慢地震等方面有优势之外,还可有效应用于低频地球自由振荡信号的探测.利用安置在武汉大学珞珈山的我国自行研制的VP型垂直摆倾斜仪在2011日本Mw9.0级大地震之后不同长度的观测数据,联合EEMD方法、自回归估计(AR)方法和bootstrap法,本文不仅检测到该地震激发的频率小于4.7 mHz的零阶球型振荡(0S2至0S38)和环型振荡(0T4至0T35)几乎所有振型以及15个谐频振型,还检测到5个其频率低于1mHz的低阶球型多线态(0S2、2S1、0S3、0S4和1S2)的部分或全部谱峰分裂现象,并给出了所有检测结果的精度评估.此外,本文分析了某些球型和环型振荡之间的耦合效应,结果表明耦合效应将显著影响地球自由振荡信号的相关参数. 相似文献