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1.
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
2.
The existence of uncoupled shear (S) and compression (P) wave velocity variations in Earth's mantle is a characteristic that might only be explained by the presence of significant chemical and/or phase heterogeneity, with important implications for the dynamics and evolution of Earth's interior. While making a one-to-one comparison between tomographic models for P and S velocity (VP and VS) variations for a particular geographic region is ill-posed, their global statistical distributions reveal several robust characteristics indicative of the nature of uncoupled VP and VS in the deep mantle. We find that all of the VP and VS model distributions at a given depth are Gaussian-like throughout the lowermost mantle. However, a distinct low velocity feature is present in VS distributions below ≈ 2200 km depth that is not present or is relatively weak in VP models. The presence of anomalously low VS material cannot be explained as an artifact, nor can the absence of a similarly strong feature in P models be ascribed to under-resolution. We propose that this feature can be partly explained by laterally variable occurrences of post-perovskite (pPv) lenses in the D″ layer, however, the persistence of significantly slow VS regions at heights up to ≈ 700 km or more above the core–mantle boundary is likely to be incompatible with a pPv origin and might only be explained by the presence of a laterally discontinuous layer of chemically distinct material and/or some other kind of phase heterogeneity. There also exist significant discrepancies between tomographic models with respect to the width of the distributions as well as differences between the modeled peak values. We propose a scheme for comparison between different seismic models in which the widths of the dominant features in their statistical distributions is exploited. 相似文献
3.
4.
The lower mantle and outer core are subjected to tests for homogeneity and adiabaticity. An earth model is used which is based on the inversion of body waves and Q-corrected normal-mode data. Homogeneous regions are found at radii between 5125 and 4825 km, 4600 and 3850 km, and 3200 and 2200 km. The lower mantle and outer core are inhomogeneous on the whole and are only homogeneous in the above local regions.Finite-strain and atomistic equations of state are fit to the homogeneous regions. The apparent convergence of the finite-strain relations is examined to judge their applicability to a given region. In some cases the observed pressure derivatives of the elastic moduli are used as additional constraints. The effect of minor deviations from adiabaticity on the extrapolations is also considered. An ensemble of zero-pressure values of the density and seismic velocities are found for these regions. The range of extrapolated values from these several approaches provides a measure of uncertainties involved. 相似文献
5.
We model the internal structure of the Moon, initially homogeneous and later differentiated due to partial melting. The chemical
composition and the internal structure of the Moon are retrieved by the Monte-Carlo inversion of the gravity (the mass and
the moment of inertia), seismic (compressional and shear velocities), and petrological (balance equations) data. For the computation
of phase equilibrium relations and physical properties, we have used a method of minimization of the Gibbs free energy combined
with a Mie-Gr@uneisen equation of state within the CaO-FeO-MgO-Al2O3-SiO2 system. The lunar models with a different degree of constraints on the solution are considered. For all models, the geophysically
and geochemically permissible ranges of seismic velocities and concentrations in three mantle zones and the sizes of Fe-10%S
core are estimated. The lunar mantle is chemically stratified; different mantle zones, where orthopyroxene is the dominant
phase, have different concentrations of FeO, Al2O3, and CaO. The silicate portion of the Moon (crust + mantle) may contain 3.5–5.5% Al2O3 and 10.5–12.5% FeO. The chemical boundary between the middle and the lower mantle lies at a depth of 620–750 km. The lunar
models with and without a chemical boundary at a depth of 250–300 km are both possible. The main parameters of the crust,
the mantle, and the core of the Moon are estimated. At the depths of the lower mantle, the P and S velocities range from 7.88 to 8.10 km/s and from 4.40 to 4.55 km/s, respectively. The radius of a Fe-10%S core is 340 ± 30
km. 相似文献
6.
Two-dimensional crustal velocity models are derived from passive seismic observations for the Archean Karelian bedrock of north-eastern Finland. In addition, an updated Moho depth map is constructed by integrating the results of this study with previous data sets. The structural models image a typical three-layer Archean crust, with thickness varying between 40 and 52 km. P wave velocities within the 12–20 km thick upper crust range from 6.1 to 6.4 km/s. The relatively high velocities are related to layered mafic intrusive and volcanic rocks. The middle crust is a fairly homogeneous layer associated with velocities of 6.5–6.8 km/s. The boundary between middle and lower crust is located at depths between 28 and 38 km. The thickness of the lower crust increases from 5–15 km in the Archean part to 15–22 km in the Archean–Proterozoic transition zone. In the lower crust and uppermost mantle, P wave velocities vary between 6.9–7.3 km/s and 7.9–8.2 km/s. The average Vp/Vs ratio increases from 1.71 in the upper crust to 1.76 in the lower crust.The crust attains its maximum thickness in the south-east, where the Archean crust is both over- and underthrust by the Proterozoic crust. A crustal depression bulging out from that zone to the N–NE towards Kuusamo is linked to a collision between major Archean blocks. Further north, crustal thickening under the Salla and Kittilä greenstone belts is tentatively associated with a NW–SE-oriented collision zone or major shear zone. Elevated Moho beneath the Pudasjärvi block is primarily explained with rift-related extension and crustal thinning at ∼2.4–2.1 Ga.The new crustal velocity models and synthetic waveform modelling are used to outline the thickness of the seismogenic layer beneath the temporary Kuusamo seismic network. Lack of seismic activity within the mafic high-velocity body in the uppermost 8 km of crust and relative abundance of mid-crustal, i.e., 14–30 km deep earthquakes are characteristic features of the Kuusamo seismicity. The upper limit of seismicity is attributed to the excess of strong mafic material in the uppermost crust. Comparison with the rheological profiles of the lithosphere, calculated at nearby locations, indicates that the base of the seismogenic layer correlates best with the onset of brittle to ductile transition at about 30 km depth.We found no evidence on microearthquake activity in the lower crust beneath the Archean Karelian craton. However, a data set of relatively well-constrained events extracted from the regional earthquake catalogue implies a deeper cut-off depth for earthquakes in the Norrbotten tectonic province of northern Sweden. 相似文献
7.
Nikolas I. Christensen 《Earth and Planetary Science Letters》1977,36(2):297-300
Rocks ranging in composition from trondhjemite to diorite (plagiogranites) have been recovered from ocean ridges and are common constituents of ophiolites. Velocities and densities of diorite and trondhjemite from the Mid-Atlantic Ridge are shown to differ significantly from similar properties of metadolerite and gabbro. Compressional (Vp) and shear (Vs) velocities of plagiogranites are relatively low (Vp = 4.78–5.91km/s at1kbar,Vs = 2.81–3.37km/s at1kbar), as are densities (2.57–2.64 g/cm3) and Poisson's ratios (0.24–0.27). These data lend strong support to the probable existence of a low-velocity/density zone within layer 3 of the oceanic crust. Based on observations in ophiolites, it is postulated that this zone can be up to 1 km in thickness and is laterally discontinuous. 相似文献
8.
Compressional (Vp) and shear (Vs) wave velocities have been measured to 10 kb in 32 cores of basalt from 14 Pacific sites of the Deep Sea Drilling Project. Both VpandVs show wide ranges (3.70to6.38km/sec forVpand1.77to3.40km/sec forVsat0.5kb) which are linearly related to density and sea floor age, confirming earlier findings by Christensen and Salisbury of decreasing velocity with progressive submarine weathering based on studies of basalts from five sites in the Atlantic. Combined Pacific and Atlantic data give rates of decreasing velocity of ?1.89and?1.35km/sec per100my forVpandVs respectively. New analyses of oceanic seismic refraction data indicate a decrease in layer 2 velocities with age similar to that observed in the laboratory, suggesting that weathering penetrates to several hundred meters in many regions and is largely responsible for the extreme range and variability of layer 2 refraction velocities. 相似文献
9.
The presence of a phenomenological relationship between high velocity regions in the Benioff zone and sources of relatively strong earthquakes (M ≥ 6) was established for the first time from the comparison of such earthquakes with the velocity structure of central Kamchatka in the early 1970s. It was found that, in the region with P wave velocities of 8.1–8.5 km/s, the number of M ≥ 6 earthquakes over 1926–1965 was 2.5 times greater than their number in the region with velocities of 7.5–8.0 km/s. Later (in 1979), within the southern Kurile area, Sakhalin seismologists established that regions with V P = 7.3–7.7 km/s are associated with source zones of M = 7.0–7.6 earthquakes and regions with V P = 8.1–8.4 km/s are associated with M = 7.9–8.4 earthquakes. In light of these facts, we compared the positions of M = 7.0–7.4 earthquake sources in the Benioff zone of southern Kamchatka over the period 1907–1993 with the distribution of regions of high P velocities (8.0–8.5 to 8.5–9.0 km/s) derived from the interpretation of arrival time residuals at the Shipunskii station from numerous weak earthquakes in this zone (more than 2200 events of M = 2.3–4.9) over the period 1983–1995. This comparison is possible only in the case of long-term stability of the velocity field within the Benioff zone. This stability is confirmed by the relationship between velocity parameters and tectonics in the southern part of the Kurile arc, where island blocks are confined to high velocity regions in the Benioff zone and the straits between islands are confined to low velocity regions. The sources of southern Kamchatka earthquakes with M = 7.0–7.4, which are not the strongest events, are located predominantly within high velocity regions and at their boundaries with low velocity regions; i.e., the tendency previously established for the strongest earthquakes of the southern Kuriles and central Kamchatka is confirmed. However, to demonstrate more definitely their association with regions of high P wave velocities, a larger statistics of such earthquakes is required. On the basis of a direct correlation between P wave velocities and densities, the distributions of density, bulk modulus K, and shear modulus μ in the upper mantle of the Benioff zone of southern Kamchatka are obtained for the first time. Estimated densities vary from 3.6–3.9 g/cm3 in regions of high V P values to 3.0–3.2 g/cm3 for regions of low V P values. The bulk modulus K in the same velocity regions varies from (1.4–1.8) × 1012 to (0.8–1.1) × 1012 dyn/cm2, respectively, and the shear modulus μ varies from (0.8–1.0) × 1012 to (0.5–0.7) × 1012 dyn/cm2, respectively. Examination of the spatial correlation of the source areas of southern Kamchatka M = 7.0–7.4 earthquakes with the distribution of elastic moduli in the Benioff zone failed to reveal any relationship between their magnitudes and the moduli because of the insufficient statistics of the earthquakes used. 相似文献
10.
This paper presents new data on the upper mantle characteristics, and on seismicity and volcanism in Kamchatka. It is shown that the seismic activity in the Pacific focal layer decreases sharply below that narrow line on which the foci of the active volcanoes are situated. A map of longitudinal wave velocitiesV p in the mantle upper layers under Kamchatka is given. The lowest values ofV p (7.3–7.6 km/sec) are found near the volcanic belt. The graphs Θ=lg (Es/Ep) (h) for the Kamchatka earthquakes indicate that Θmin at the depths of 120–250 km may be caused by a concentration of magmatic melts. A map of bodies (magma chambers?) screening S- and P-waves at the depths of 30–100 km under Kamchatka has been compiled. These bodies are mainly located under the belt of active volcanoes. 相似文献
11.
A new model is proposed for the structure of the Kaapvaal craton lithosphere. Based on chemical thermodynamics methods, profiles of the chemical composition, temperature, density, and S wave velocities are constructed for depths of 100–300 km. A solid-state zone of lower velocities is discovered on the S velocity profile in the depth interval 150–260 km. The temperature profiles are obtained from absolute values of P and S velocities, taking into account phase transformations, anharmonicity, and anelastic effects. The examination of the sensitivity of seismic models to the chemical composition showed that relatively small variations in the composition of South African xenoliths result in lateral temperature variations of ～200°C. Inversion of some seismic profiles (including IASP91) with a fixed bulk composition of garnet peridotites (the primitive mantle material) leads to a temperature inversion at depths of 200–250 km, which is physically meaningless. It is supposed that the temperature inversion can be removed by gradual fertilization of the mantle with depth. In this case, the craton lithosphere should be stratified in chemical composition. The depleted lithosphere composed by garnet peridotites exists to depths of 175–200 km. The lithospheric material at depths of 200–250 km is enriched in basaltoid components (FeO, Al2O3, and CaO) as compared with the material of garnet peridotites but is depleted in the same components as compared with the fertile substance of the underlying primitive mantle. The material composing the craton root at a depth of ～275 km does not differ in its physical and chemical characteristics from the composition of the normal mantle, and this allows one to estimate the thickness of the lithosphere at 275 km. The results of this work are compared with data of seismology, thermal investigations, and thermobarometry. 相似文献
12.
The derivation of P and S velocities at the core-mantle boundary (CMB) from long-period diffracted waves by the use of the simple ray-theoretical formulav
CMB=r
c
/p (v
CMB=velocity at the CMB;r
c
=core radius;p=ray parameter) yields apparent velocity values which differ from the true velocities. Using a dominant period of about 20 sec for calculating theoretical seismograms, we found a linear relation between the apparent velocity and the average velocity in a transition zone at the base of the mantle with fixed velocity on top.The ray parameters determined from long-period earthquake data are found to be 4.540±0.035 and 8.427±0.072 sec/deg for Pdiff and Sdiff, respectively. These values yield apparent velocities of 13.378±0.103 for P and 7.207±0.062 km/sec for S waves. By means of the theoretical relation between apparent and average velocity and under the assumption of linear variation of velocity with depth, one can invert the apparent velocities into true CMB velocities of 13.736±0.170 and 7.320±0.124 km/sec. These results imply positive velocity gradients at the base of the mantle and hence no significant departures from adiabaticity and homogeneity.Contribution No. 211 of the Geophysical Institute, University of Karlsruhe. 相似文献
13.
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
14.
This activation volume ΔV for creep may be derived from Keyes's elastic strain energy model or from Weertman's empirical relationship between viscosity and the melting temperature. These formulations are shown to be equivalent if the anharmonic Grüneisen parameters γ of all acoustic modes are equal and if the pressure dependence of the melting temperature follows Lindemann's law, both of which assumptions are valid for the close-packed mineral structure of the lower mantle. The pressure derivative of ΔV depends only on the bulk modulus and the acoustic γ, both of which are directly available from seismic models. Using the data of Brown and Shankland, we show that ΔV decreases by almost 50% between the top and the bottom of the lower mantle, which makes it easier to maintain a constant viscosity in this region. The isoviscous temperature profile can be adiabatic in the deep lower mantle only below 1700 km depth; it is super-adiabatic in the top 1000 km of the lower mantle. 相似文献
15.
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
16.
Various xenoliths have been found in lavas of the 1763 (“La Montagnola”), 2001, and 2002–03 eruptions at Mt. Etna whose petrographic evidence and mineral chemistry exclude a mantle origin and clearly point to a cognate nature. Consequently, cognate xenoliths might represent a proxy to infer the nature of the high-velocity body (HVB) imaged beneath the volcano by seismic tomography. Petrography allows us to group the cognate xenoliths as follows: i) gabbros with amphibole and amphibole-bearing mela-gabbros, ii) olivine-bearing leuco-gabbros, iii) leuco-gabbros with amphibole, and iv) Plg-rich leuco gabbros. Geobarometry estimates the crystallization pressure of the cognate xenoliths between 1.9 and 4.1 kbar. The bulk density of the cognate xenoliths varies from 2.6 to 3.0 g/cm3. P wave velocities (V P ), calculated in relation to xenolith density, range from 4.9 to 6.1 km/s. The integration of mineralogical, compositional, geobarometric data, and density-dependent V P with recent literature data on 3D V P seismic tomography enabled us to formulate the first hypothesis about the nature of the HVB which, in the depth range of 3–13 km b.s.l., is likely made of intrusive gabbroic rocks. These are believed to have formed at the “solidification front”, a marginal zone that encompasses a deep region (>5 km b.s.l.) of Mt. Etna’s plumbing system, within which magma crystallization takes place. The intrusive rocks were afterwards fragmented and transported as cognate xenoliths by the volatile-rich and fast-ascending magmas of the 1763 “La Montagnola”, 2001 and 2002–03 eruptions. 相似文献
17.
Long-range seismic sounding carried out during the last few years on the territory of the U.S.S.R. has shown a basic inhomogeneity of the uppermost mantle, as well as evidence of regularities in the distribution of its seismic parameters. The following data were used: times and apparent velocities of P- and S-waves for investigation of mantle velocities, converted waves for seismic discontinuity model studies and wave attenuation for Q-factor estimation. Strong regularities were distinguished in the distribution of average seismic velocities for the uppermost mantle, in their dependence on the age and type of geostructure and on their position relative to the central part of the continent. Old platforms and the inner part of the continent are marked by velocities under the Mohorovi?i? discontinuity of more than 8.2–8.3 km s?1, young platforms and outer parts of the continent by 8.0–8.2 km s?1, and orogenic and rift zones by 7.8–8.0 km s?1. The difference becomes more pronounced at a depth of about 100–200 km: for the old platform mantle velocities of 8.5–8.6 km s?1 are typical; beneath the orogenic and rift areas, inversion zones with velocities less than 7.8 km s?1 are observed.The converted waves show fine inhomogeneities of the crust and uppermost mantle, the presence of many discontinuities with positive and negative changes of velocity, and anisotropy of seismic waves in some of the layers. Wave attenuation allowed the determination of the Q-factor in the mantle. It varied from one region to another but a close relation between Q and P-wave velocity is the main cause of its variation. 相似文献
18.
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
19.
The crustal structure in Myanmar can provide valuable information for the eastern margin of the ongoing Indo-Eurasian collision system. We successively performed H–k stacking of the receiver function and joint inversion of the receiver function and surface wave dispersion to invert the crustal thickness (H), shear wave velocity (VS), and the VP/VS ratio (k) beneath nine permanent seismic stations in Myanmar. H was found to increase from 26 ?km in the south and east of the study area to 51 ?km in the north and west, and the VP/VS ratio was complex and high. Striking differences in the crust were observed for different tectonic areas. In the Indo-Burma Range, the thick crust (H ?～ ?51 ?km) and lower velocities may be related to the accretionary wedge from the Indian Plate. In the Central Myanmar Basin, the thin crust (H ?= ?26.9–35.5 ?km) and complex VP/VS ratio and VS suggest extensional tectonics. In the Eastern Shan Plateau, the relatively thick crust and normal VP/VS ratio are consistent with its location along the western edge of the rigid Sunda Block. 相似文献
20.
We compare lateral variations at the base of the mantle as inferred from a global dataset of PcP-P travel time residuals, measured on broadband records, and existing P and S tomographic velocity models, as well as ScS-S travel time data in some selected regions. In many regions, the PcP-P dataset implies short scale lateral variations that are not resolved by global tomographic models, except under eastern Eurasia, where data and models describe a broad region of fast velocity anomalies across which variations appear to be of thermal origin. In other regions, such as central America and southeastern Africa, correlated short scale lateral variations (several hundred kilometers) are observed in PcP and ScS, implying large but not excessive values for the ratio R=∂ ln Vs/∂ ln Vp (∼2.5). On the other hand, in at least two instances, in the heart of the African Plume and on the edge of the Pacific Plume, variations in P and S velocities appear to be incompatible, implying strong lateral gradients across compositionally different domains, possibly also involving topography on the core-mantle boundary. One should be cautious in estimating R at the base of the mantle from global datasets, as different smoothing and sampling of P and S datasets may result in strong biases and meaningless results. 相似文献