PREM Model Research Articles

Shear‐wave velocities under the Transantarctic Mountains and terror rift from surface wave inversion

Rayleigh wave data between 20 and 120s period recorded in the western Ross Sea region of Antarctica are inverted using the waveform inversion technique described in Passier and Snieder [1995]. From the data we extract estimates of local S velocity structure beneath the Transantarctic Mountains and the Terror Rift. The shear wave velocities found are up to 6% slower than the PREM model at between 40 and 160 km depth, depending on the propagation path, providing evidence of an anomalously warm upper mantle beneath the Terror Rift and, to a lesser extent, beneath the front of the Transantarctic Mountains.

On the dynamical effects of an inhomogeneous liquid core in the theory of nutation

As shown in previous work, dynamical effects of a realistic model of a heterogeneous, compressible, stably stratified liquid core may be obtained by means of a simple analysis of the generalized two-dimensional Laplace tidal equation which describes tidal flows of an incompressible and non-gravitating fluid in a thin spherical layer with mobile boundaries. The solution was presented in the form of expansions in powers of a small parameter κ being the ratio of nutational motion frequency in space to the frequency of the Earth's diurnal rotation. Whereas in an earlier paper only first-order terms were taken into account, our present approach includes not only main second-order terms in the spherical harmonic expansions of the solutions, but also the terms of higher orders. These effects are calculated numerically for realistic models of the Earth's outer liquid core, solid inner core and anelastic mantle (PREM model). All tables are found in electronic version at http://www.tu-darmstadt.de/fb/vw/ipg/Welcome2.html

Elasticity, composition and temperature of the Earth’s lower mantle: a reappraisal

The interpretation of seismological models for the Earth’s lower mantle in terms of chemical composition and temperature is sensitive both to the details of the methodology employed and also to uncertainties in key thermoelastic parameters, especially for the dominant (Mg, Fe)SiO3 perovskite phase. Here the alternative approaches—adiabatic decompression of the lower mantle for comparison at zero pressure with laboratory data, and the projection of laboratory data to lower-mantle P–T conditions for direct comparison with seismological observations—are assessed, along with the equations of state on which they are based. It is argued that adiabatic decompression of the lower mantle is best effected by a strategy in which consistent third-order finite-strain expressions are required simultaneously to fit the strain dependence of both the seismic parameter and the density. This procedure accords due weight to the most robust seismological observations, namely the wave speeds, and reduces to an acceptable level the otherwise very strong covariance among the fitted coefficients. It is demonstrated that this approach can readily be adapted to include the effects of relaxation, from the Hill average to the Reuss lower bound, of the aggregate bulk modulus which governs the radial variation of density. For the projection of laboratory thermoelastic data to lower-mantle P–T conditions, the preferred equation of state is of the Mie–Gruneisen type, involving the addition at constant volume of the pressure along a finite-strain principal (300 K) isotherm and the thermal pressure calculated from the Debye approximation to the lattice vibrational energy. A high degree of consistency is demonstrated between these alternative equations of state. Possible departures of the lower mantle from conditions of adiabaticity and large-scale homogeneity are assessed; these are negligible for the PREM model (Bullen parameter ηB = 0.99 ± 0.01) but significant for ak135 (ηB ∼ 0.94 ± 0.02), reviving the possibility of a substantially superadiabatic temperature gradient. Experimentally determined thermoelastic properties of the major (Mg, Fe)SiO3 perovskite and (Mg, Fe)O magnesiowustite phases are used to constrain the equation-of-state parameters employed in the analysis of seismological information, although the scarcity of information concerning the pressure and temperature dependence of the elastic moduli for the perovskite phase remains a serious impediment. Nevertheless, it is demonstrated that the combination of a pyrolite composition simplified to the three-component system (SiO2–MgO–FeO) with molar XPv = 0.67 and XMg = 0.89, and a lower-mantle adiabat with a potential temperature of 1600 K—consistent with the preferred geotherm for the upper mantle and transition zone—is compatible with the PREM seismological model, within the residual uncertainties of the thermoelastic parameters for the perovskite phase. In particular, such consistency requires values for the perovskite phase of KS′ = (∂KS /∂P)T and q = (∂ ln γ/∂ ln V )T of approximately 3.8 and 2, and ∂G/∂T near −0.022 GPa K−1 for the lower-mantle assemblage. More silicic models, which have sometimes been advocated, can also be reconciled with the seismological data, but require lower-mantle temperatures which are much higher—by about 700 K for pyroxene stoichiometry. However, the absence of seismological and rheological evidence for the pair of thermal boundary layers separating convection above and below, which is implied by such models, remains a formidable difficulty. Under these circumstances, the simplest possible model, that of grossly uniform chemical composition throughout the mantle, is preferred.

Thermal parameters of the Earth's lower mantle

Laboratory and seismological measurements of bulk and shear moduli ( K S and μ S) have been combined to derive the specific temperature and frequency dependencies of pressure, K S and μ S as a function of depth in the lower mantle of the Earth. The results depend on the mineralogical model and temperature profiles chosen, as well as on the bulk Fe content in the lower mantle. If the Fe/Mg+Fe content in the lower mantle does not exceed 0.15, two important conclusions remain after a large variety of models have been investigated. (1) High-frequency (MHz or GHz) laboratory measurements of μ S of mantle phases should be corrected by 3–20% before comparison with seismological data can be done. Dispersion laws such as those provided by the PREM model underestimate this correction. (2) The lower mantle material, described as a Debye solid, cannot be silicon rich (e.g., pure perovskite) and the values of K 0′ are constrained between 3.5 and 3.7.

P-V-T equation of state of MgSiO 3 perovskite

A pressure-volume-temperature data set has been obtained for MgSiO 3 perovskite, using synchrotron X-ray diffraction with a laser-heated diamond-anvil cell. The unit cell parameters of the silicate perovskite were measured by angle dispersive X-ray diffraction using imaging plates up to pressures of 57 GPa and temperature in excess of 2500 K. These measurements are in good agreement with the previously reported data of Funamori et al. [Funamori, N., Yagi, T., Utsumi, W., Kondo, T., Uchida, T., Funamori, M., 1996. J. Geophys. Res. 101 (B4), 8257–8269] at lower pressure and yield ( ∂K ∂T ) P = −0.027 GPa K −1 for a fixed value K′ 0 of 4 and a zero-pressure thermal expansion parameter α = 1.55 × 10 −5 K −1 at 300 K. Assuming that the thermoelastic parameters of MgSiO 3 perovskite are applicable to perovskites with moderate iron content, the comparison of the density and K T profiles calculated for a mixture of perovskite and magnesiowüstite and for PREM model indicates that a pure perovskite lower mantle is very unlikely. On the other hand, we obtain a very good match with PREM density and K T profiles for a mixture of 83 vol % (Mg 0.93Fe 0.07)SiO 3 perovskite and 17 vol % (Mg 0.79Fe 0.21)O magnesiowüstite, compatible with a pyrolytic lower mantle.

A study of the secular deceleration of the earth's rotation using a hamiltonian formalism

In this article, the secular rotational varitation of the Earth whose elastic mantle is deformed by gravitational attraction of the Moon and the Sun is studied by means of a Hamiltonian method. The expression of the tidal potential with phase lag is given. The value of the secular deceleration of the Earth's rotation is obtained for the Earth model PREM. it theoretically is −5.7 × 10 −22 rad/s 2, which agrees perfectly with the latest observational results. The results also show that the principle contribution to this deceleration is the sectorial tide corresponding to the term m = 2, and that the deformation produced by the Moon is much more important than that due to the Sun.

Effects of a mushy transition zone at the inner core boundary on the Slichter modes

This article investigates the effects of a mushy inner core boundary on the eigenperiods of the Slichter modes for a simple, but realistic, earth model (rotating, spherical configuration, elastic inner core and mantle, neutrally stratified, inviscid, compressible liquid core). It is found that the influence of the mushy boundary layer is substantial compared with some other effects, such as those from elasticity of the mantle, non-neutral stratification of the liquid outer core and ellipticity of the Earth and centrifugal potential. The results obtained here may set a lower bound on the eigenperiods of the Slichter modes for a realistic earth model. For example, for a PREM model, the lower bound of the central period of the Slichter modes should be about 5.3 hr.

Reply to comment by L. Cathles and W. Fjeldskaar on ‘The inference of mantle viscosity from an inversion of the Fennoscandian relaxation spectrum’

The analysis of Mitrovica & Peltier (1993; henceforth ‘MP’) involved inferences of mantle viscosity based on Bayesian inversions of the Fennoscandian relaxation spectrum (henceforth ‘FRS’). The inversions yielded constraints on the average viscosity within a set of radial regions resolved by the data, and quantified various trade-offs associated with the inference. The MP study also used forward calculations to predict the relaxation spectrum for a set of nine viscosity models. The inversion-derived constraints were then used to determine the cause of any misfit between these predictions and the observational constraints on the FRS. One of the models chosen in this exercise, labelled LVZ, was characterized by the elastic structure of the seismic model PREM (Dziewonski & Anderson 1981), an elastic lithosphere of thickness 70 km, and a 90 km thick sublithospheric region of low (2 x 1019 Pa s) viscosity overlying an isoviscous, 10” Pas, mantle. The x2 misfit between the observed FRS and the spectrum computed using the LVZ model (- 295) was significantly in excess of the 99 per cent confidence limit (- 74). The comment by Cathles & Fjeldskaar ( 1996; henceforth ‘CF) is directed toward results associated with the LVZ model only. In particular, CF argue that: (1) the LVZ model is a ‘miscalculation’ of their preferred model for the region, which they label ‘FC‘; and (2) their own calculation of the relaxation spectrum using the LVZ model differs from the MP prediction-they are able to reproduce the MP results only by altering the thickness of the low-viscosity zone to 55 km. We consider both of these points in turn.

Discussion of the Features of Synthetic Amplitude-Distance Curves of Teleseismic P Waves for Global Earth Models

The reason why the synthetic amplitude distance curves of P-waves for models IASP91 and PREM, observed for shallow sources up to epicentral distance of 28°, oscillate is illustrated by means of synthetic seismograms. Furthermore the position of the beginning of the diffraction of the P-wave at the CMB, depending on the prevailing signal period, is discussed in connection with the extension of Fresnel volumes.

A new test of Earth tide models in central Europe

New improved ocean tide models allow a corresponding improvement in ocean tide loading computations. During recent years various groups have made more accurate tidal gravity observations in central Europe, using gravimeters carefully calibrated on various calibration lines. This progress with tidal gravity measurements and ocean loading corrections now allows a more comprehensive test of body tide models than was possible previously. It is shown that the O1 and M2 gravimetric factors, corrected using the latest ocean tide models, are very consistent between the sites, despite the different instruments and gravity calibration lines that have been used. These observations allow constraints to be put on the anelasticity of the Earth at tidal frequencies. The corrected gravimetric factors are consistent with recent model results for both the elastic PREM model and with α ≤ 0.09 for an anelastic PREM model with the Q for dissipation in shear varying as frequency to the power α.

Compressible rotational deformation

In recent years a number of studies have investigated the influence of compressibility on geophysical observables such as postglacial rebound deformation rates and the geoid. Some of these studies indicate that long-term signatures such as the geoid might be sensitive to compressibility. As both load relaxation and tidal-effective relaxation of the equatorial bulge are operative in a dependent way, polar wander can potentially be more sensitive to compressible rheologies if the interference between the two relaxation mechanisms is constructive. This has motivated us to study the influence of compressibility on true polar wander by means of spherical, laterally homogeneous, self-gravitating analytical earth models. As we wish to study both short-term rotational changes and polar wander on geological time-scales, we employ a Maxwell viscoelastic model instead of a Newtonian viscous model. The latter is commonly used in geoid modelling. The purpose of this paper is to concentrate on the basic physical aspects of the differences between compressible and incompressible rotational deformation, rather than applying the procedures to fine-graded multi-layered PREM models with realistic forcing functions. An important issue of our method concerns the analytical instead of numerical way of solving the differential equations by the propagator matrix method. Compressible viscoelastic relaxation has usually been treated numerically until now. The results show that homogeneous earth models do not have significant differences on long time-scales between compressible and the corresponding incompressible cases. Compressibility introduces a denumerably infinite set of short-time relaxation modes. The relaxation times of these dilatation modes can be approximated analytically. Two-layer core-mantle models show relatively large differences between incompressible and compressible Maxwell rheologies. Simplified models of true polar wander triggered by Heaviside loads show that differences of several tens of per cent between incompressible and compressible Maxwell rheologies are possible. True polar wander is decreased in the compressible case on both short and long time-scales, which means that smaller viscosities are required to explain polar-wander measurements than in the incompressible case.

Analytical visco‐elastic relaxation models

In the past, relaxation processes employing PREM or 1066B‐stratified earth models have been solved numerically, either directly in the time domain (initial value models) or in the Laplace‐transformed domain (normal mode models). Solving N‐layer stratified models analytically has only been performed for small values of N. We present a brief outline of the analytical method of general radially stratified N‐layer, self‐gravitating, Maxwell rheological models. The analytical models allow for the relaxation times of the myriad of relaxation modes to be determined with very high accuracies, as the secular determinant from which they derive is an analytical function. We show by explicitly comparing results on a 5 and 30‐layer incompressible Maxwell model with a convex mantle viscosity profile, that the differences in the results between the two models are small when the 5‐layer model has the volume‐averaged structural and rheological properties of the 30‐layer model. The fact that in both models the fluid values of the Love numbers reach the same expected limits leaves no room for hypothetical so‐called non‐modal contributions. The application to compressible linear rheologies of this generalized analytical normal mode method is more involved, but straightforward.

Pure silicate perovskite and the PREM lower mantle model: a thermodynamic analysis

A recently published thermodynamic theory enables one to calculate α, the volume thermal expansivity; ΔV V 0 , the thermal expansion; and ϱ, the density in V, T space or P, T space, based on the values of seven thermoelastic parameters evaluated at P = 0. These parameters are themselves based on high-pressure and high-temperature measurements of V. Especially useful are calculated isobars of ΔV V 0 versus T or isentropes of ϱ versus P, because with these, seismic models of the earth can be compared with the perovskite compositional model. There is general agreement on the thermoelastic parameters of V 0, K T 0 and K′ 0 for perovskite, but not on the value of δ T 0 , the dimensionless Anderson-Grüneisen parameter, or of γ 0, the Grüneisen ratio. In comparing the calculated isentrope of ϱ( P) with the geotherm of ϱ( P) from the PREM seismic model, we find the most sensitive parameter is γ 0. We also find a number of reasons to select γ 0 = 1.5 ± 0.2 for perovskite. This range of γ 0 values leads to the conclusion that perovskite satisfies the PREM model of density in the lower mantle without the addition of heavy elements, like iron or silicon. The value range γ 0 > 1.9 for perovskite would require a significant amount of iron or silicon to satisfy PREM, but we cannot justify a value of γ 0 that high.

Free particle modelling of hypervelocity asteroid collisions with the Earth

This paper presents a time-dependent two-dimensional numerical model of the impact phenomena. The model deals with formation and evolution of a crater, formation of an impact jet, and with global deformation and dynamical parameters of the impacted body. The model is applied to study the problem of deformation of the Earth when impacted by an asteroid. A hydrodynamical code of the free particle numerical method (HEFP) is applied to a silicate asteroid (impactor) and to the multilayered spherical Earth (target) described by the PREM model. The asteroids radii are within a range between 5 and 800 km. The velocity range is 20–30 km s −1. Calculations cover the time intervals up to 2000 s. Each of the material points of the bodies under consideration (the Earth and an asteroid) is described by its time-dependent position, velocity, specific internal energy, pressure and density. The global results, among others, are as follows: (i) deformation of the Earth's surface; (ii) position of the shock wave within the Earth; (iii) deformation of consecutive layers within the Earth's interior, and (iv) morphology of the crater including behavior of the impact jet and deformation of the impactor.

Amplitudes of core waves near the PKP caustic, from nuclear explosions in the South Pacific recorded at the “laboratoire de détection et géophysique” network, in France

The purpose of this paper is 2-fold. It is first a continuation of the study of Massot and Rocard (1982) on the amplitude variations of the core waves near the PKP caustic, for French nuclear explosions in the South Pacific recorded on the LDG network in France. Taking advantage of a larger available data set, and using current methods to compute synthetic seismograms, such as the WKBJ method, we reinvestigate the core waves amplitude versus distance variation pattern derived by Massot and Rocard (1982). The second purpose is to give precise constraints on the PKP caustic phenomenon, using waveform and amplitude comparisons between data and synthetics. WKBJ synthetics are computed for several global spherical Earth models. Recent models with a D″ discontinuity, or a low velocity gradient at the top and the bottom of the liquid core are also tested. Our computations do not support the highly variable amplitude versus distance profile of Massot and Rocard, which displays a major peak at 145.6° and many secondary interference fringes. Between 142° and 147°, the theoretical amplitude variations we have calculated are dominated by the large PKP caustic peak, and only modulated by the simultaneous arrival of the PKIKP wave near 145°. Using a data set of 17 nuclear explosions, we have measured relative amplitudes as a function of distance, in the 142° to 147° distance range, and analyzed the waveform variations. Our observations (amplitudes and waveforms) are well modeled by the 1066B model of Gilbert and Dziewonski (1975). The agreement on amplitude variations is still good for models PREM (Dziewonski and Anderson, 1981) and IASP91 (Kennett and Engdahl, 1991). Accurate quantitative constraints are derived on the PKP caustic, among which the position of the B caustic point (144.5° ± 0.5°) for the mean 296° Mururoa-LDG network azimuth. This location depends, as a whole, on the depth of the core-mantle boundary, and on the velocity gradients in the mantle and in outermost core. Although the depth of the core-mantle boundary, and the existence of a discontinuity at the top of D″ can slightly affect the position of the B caustic point, the focusing effect at the PKP caustic is rather a global derivation of the models.

Laterally varying reflector at the top ofD″beneath northern Siberia

SUMMARY We analyse P-wave data from the French 'Laboratoire de DCtection et GCophysique' (L.D.G) network of digital short-period seismic stations. Whereas our previous paper (Houard & Nataf 1992) showed a few promising Kurd events and depicted the methods we proposed to apply, an extensive analysis of 32 earthquakes from the KuriVKamchatka region has now been carried out. By using the deconvolution technique previously described (Houard & Nataf 1992), clear and quantitative evidence of intermediate arrivals between the P and PcP waves is shown, in the 75-82 distance range. Our approach is complementary to previous studies in the same region, which used broad-band data recorded at a dense narrow-aperture array (Weber & Davis 1990; Weber 1993) or long-period data recorded at the WWSSN stations (Gaherty & Lay 1992). For each station, record sections of deconvolved signals from different earthquakes are built, and lead us to eliminate crustal reverberations beneath L.D.G stations as a major explanation for these secondary arrivals. A compilation of the most conclusive signals has been made. It is perhaps one of the most complete PdP-wave record sections, since the move out with distance can be followed clearly with a good sampling over more than 5. The move out with distance of this extra 'PdP' arrival, its residual slowness value, eliminates source complexities, diffraction, or multipathing through the Kuril subduction slab as possible explanations. The extra arrivals indicate the existence of a lower mantle reflector. The structure of the 'Lay discontinuity' is investigated, using TpdP-Tp residual traveltimes. Two different residual time versus distance tendencies are found, which correlate to different geographical bounce point regions, indicating the existence of lateral variations of the structure. The D region is also sampled further south at distances well beyond the theoretical triplication cross-over by analysing events from the Honshu/Ryukyu Islands region, but only one P-wave branch is observed. The hodochrones and p-A curves of the first P arrival are used as a complementary analysis. The global PREM model (Dziewonski & Anderson 1981), predicts correct P wave slownesses, though its smooth lower mantle structure does not account for PdP observations. This may be an indication that the 'Lay discontinuity' is a global feature. However, the hodochrones of the first P arrival do not allow us to test the existence of the discontinuity in the 82-85' cross-over distance range.

Low P‐wave velocity at the base of the mantle

A tool for investigating P‐wave (VP) structure at the base of the mantle is presented. SKS waves at distances around 107° are incident upon the core‐mantle boundary (CMB) with a slowness that allows for coupling with diffracted P‐waves (Pd) at the base of the mantle. The P‐wave diffraction occurs at both the SKS entrance and exit locations of the outer core. The resulting phase, SPdKS, arrives slightly later in time than SKS, having a wave path through the mantle and core very close to SKS. The difference time between SKS and SPdKS most strongly depends on VP at the base of the mantle near SKS core entrance and exit points. Digitized long‐period (5‐15s) observations from deep focus Tonga events recorded by North American WWSSN and Canadian Seismographic Network stations, and South American events recorded by European and Eurasian WWSSN stations exhibit anomalously large SPdKS‐SKS difference times. SKS and the later arriving SPdKS are separated by several seconds more than predictions made by the global average PREM model. Models having a pronounced low‐velocity zone in VP at the base of the mantle best predict the observations. These models are perturbations of the PREM model, whereby the lowermost 50–100 km of the D″ layer has a negative VP gradient, with the mantle‐side CMB VP reduced from PREM by 5% (to 13.0 km/s) at the base of the mantle.

Rapid source mechanism determination of large (Mw≥5) earthquakes in the western United States

Inversion of complete long‐period ground motions is used for rapid determination of source mechanisms of Mw ≥ 5 earthquakes in the western United States. The first few minutes of ground motions on local and regional distance waveforms are inverted for point‐source centroid moment tensors. Waveforms recorded at regional distances (300–1500 km) can be adequately modeled at periods longer than 50 s using the laterally homogeneous PREM model [Dziewonski and Anderson, 1981]; at closer distances (<300 km) waves with periods as short as 35 s can be analyzed using PREM. Best double‐couple focal mechanisms for 18 recent large western U.S. earthquakes compare very well with those obtained by other methods. Our procedure, interfaced with automated data retrieval and source location methods, is a viable tool for reliable determination of seismic moment and fault mechanism within 30 minutes after an earthquake.

The equilibrium pole tide of the anelastic Earth and its effect on the Chandler wobble

According to the perturbation principle of the Love numbers and load Love numbers, the perturbation of mantle anelasticity to the equilibrium pole tide of the elastic Earth and its effect on the period and Q value of the Chandler wobble are discussed by using the elastic Earth model PREM and Zschau's mantle theological model. The results obtained show that the effect of the anelastic perturbation of the equilibrium pole tide on the Chandler wobble is much larger than that of the non-equilibrium part of the pole tide, but it is still in the range of error of the present astronomically observed values.

Spectral amplitude-distance curves for P-waves: effects of velocity and Q-distribution

Earthquake magnitude calibrating functions are based on amplitude-distance curves. The curves can be obtained either empirically or theoretically, in the latter case from standard velocity and Q-models of the Earth. Theoretical amplitude variation curves for P-waves are presented for the PREM and IASP91 velocity models. A comparison with the empirical HMS-curve, available for a particular period (8 s), shows better agreement with the IASP91 model. A further improvement is achieved by adjusting the Q-model, as well as the ratio of radiation intensity of S- to P-waves at the source. Broadband observations of seismic waves require the amplitude-distance curves to be computed in the period range of up to 10 octaves. A strong dependence of the curves on the Q-model is found at periods shorter than about 4 s. It is concluded that the standard Q-model for the magnitude calibrating functions can be ultimately selected only on the basis of amplitude measurements at possibly short periods and from the comparison of the resulting amplitude variation curves with theoretical ones.