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1.
The single-crystal elastic moduli of the olivine and spinel phases of Mg 2GeO 4 have been measured using Brillouin scattering spectra. The moduli for the olivine phase are: C 11 = 3.12, C 22 = 1.87, C 33 = 2.17, C 66 = 0.71, C 23 = 0.66, C 31 = 0.65 and C 12 = 0.60. The moduli for the spinel phase are: C 11 = 3.00, C 44 = 1.26 and C 12 = 1.18.These data are analyzed to define the best type of elastic analogue for magnesium orthosilicates. The character of the many-bodied, non-central force associated with the divalent cation is found to significantly influence the relative magnitudes of the elastic moduli. Since the nature of the many-bodied, non-central force is quite different for alkaline earth cations than for transition metal cations, we conclude that materials which contain one of these cation types is not a good analogue for materials with the other type. Magnesium orthogermanate, however, is a good analogue of magnesium orthosilicate. On the other hand, the high elastic anisotropy of the spinel phase of the germanate suggests that the germanium tetrahedron is less rigid under shear than the corresponding silicon tetrahedron. The success of the magnesium orthogermanate to model the magnesium orthosilicate is probably a result of the mechanical isolation of the tetrahedra, thus requiring the conclusions of this study to be further tested before applying them to other silicate systems. 相似文献
2.
Pressure-induced phase transformations in each of the rutile-structured difluorides (NiF 2, MgF 2, CoF 2, ZnF 2, FeF 2 and MnF 2) exhibit unique behavior; however, a general trend is found in the major structural changes: rutile phase → “distorted fluorite” phase → post-“distorted fluorite” phase with volume changes of about 5–10%. For a given phase transformation sequence found commonly in two or more difluorides, the phase transformation pressure is related inversely to the unit cell volume and thus inversely to the mean cation-anion bond length. The relationship in oxides (SnO 2, TiO 2 and GeO 2) is much less systematic. It is therefore not possible to predict without uncertainty the post-stishovite phases in the lower mantle.Velocity-density systematics in the difluorides and oxides are governed, to a large extent, by cationic radius. The pressure dependence of shear elastic constant CS = ( C11 ? C12)/2 is negative in all of the nine difluorides and oxides. However, the CS mode does not vanish at the initial phase transformation pressure; rather, the ratios of are 0.10 and 0.04 to 0.10 for transitions of rutile → orthorhombic and of rutile → “distorted fluorite”, respectively, and are in agreement with the approach of Demarest et al. 相似文献
3.
The elastic constants of sixteen garnet specimens of wide variety in chemical composition are accurately determined by means of the rectangular parallelpiped resonance method. The dependence of the elastic properties on chemical composition is analyzed using the present data and those for seven garnets investigated by other authors. The property Xi of a garnet solid solution i is given by a linear addition law in terms of the mole fraction nij of component j; Xi = ΣnijXj where the Xj's are the properties of the end-members j ( j = pyrope, almandine, spessartine, grossular and andradite). The Xj's are determined for density ρ, bulk modulus K, and shear moduli Cs = ( C11 ? C12)/2 and C44. No systematic deviation is observed from the linear addition law for the elastic moduli nor for other quantities such as the elastic wave velocities. The extrapolated elastic moduli (Mbar) of the end-members are: | Almandine | Pyrope | Spessartine | Grossular | Andradite | | 1.779 ± 0.008 | 1.730 ± 0.009 | 1.742 ± 0.009 | 1.691 ± 0.008 | 1.379 ± 0.017 | | 0.981 ± 0.004 | 0.925 ± 0.004 | 0.964 ± 0.004 | 1.106 ± 0.004 | 0.979 ± 0.007 | | 0.958 ± 0.005 | 0.919 ± 0.005 | 0.937 ± 0.005 | 1.017 ± 0.006 | 0.827 ± 0.010 | 相似文献
4.
Ultrasonic data for the velocities of the ilmenite and perovskite polymorphs of CdTiO 3 have been determined as a function of pressure to 7.5 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 25 kbar. This transition is characterized by the following velocity (ν)-density (?) relationships: (1) the changes in compressional (ν p) and bulk sound (ν ?) velocities are comparable in percentage magnitude to the density jump, while the shear (ν s) velocity jump is three times greater than that for ?; (2) (ν p/ν s) decreases across the transition from the low- to high-pressure phase; and (3) low slopes (linear or logarithmic) on ν-? diagrams. The (ν p/ν s) behaviour for the ilmenite-perovskite transformation is unusual for the transitions studied in our laboratory. The observed relationships (1) and (2) are typical of the elasticity behaviour across phase transformations which involve increases in cation-anion co-ordination and in nearest-neighbour interatomic distances, such as those exhibited by CdTiO 3 in transforming from the ilmenite to the perovskite phase. Elasticity systematics for isostructural sequences are used to estimate the bulk moduli of the perovskite polymorphs of CaSiO 3 (2.7 Mbar) and MgSiO 3 (2.8 Mbar). 相似文献
5.
Existing data supporting or disputing the validity of the Hashin-Shtrikman bounds on the elastic properties of multiphase aggregates often do not consider porosity, elastic anisotropy, or experimental errors. In this experiment, two-phase aggregates of KCl + (NH 4Br, TlBr, CsCl, NaCl, Cu, and LiF) at every 20% volume fraction were vacuum hot-pressed and the compressional and shear velocities were measured with a computer-controlled ultrasonic interferometer to ±0.2%. The ratio of the shear moduli, μ, (phase 2/KCl) varied from about 1 to 5, producing a range of separations between the theoretical two-phase Hashin-Shtrikman bounds for the composites. Samples were generally 99% or better of the theoretical density, with less than 1% velocity anisotropy. Porosity corrections were applied assuming spherical pores, based on the observed velocity-pressure behaviour. Velocities agreed with the HS bounds calculated from the end-member single-crystal stiffnesses when anisotropy was taken into account.The velocity data were also used to estimate the bulk modulus, K, and shear modulus of the second phase by means of the matrix method — taking the K and μ of KCl as known and calculating the moduli of the other phase assuming that the measured velocities were the two-phase Hashin-Shtrikman bounds or the Voigt-Reuss-Hill average. A narrow range of moduli estimates results only if the μ's of both phases are fairly closely matched. For μ's mismatched by a factor of 5, the theoretical uncertainty in the estimates can be 10 times larger than the experimental uncertainty. Estimates using the VRH average can lie outside the HS-based results. 相似文献
6.
Using acoustic measurement interfaced with a large volume multi-anvil apparatus in conjunction with in situ X-radiation techniques, we are able to measure the density and elastic wave velocities ( VP and VS) for both ortho- and high-pressure clino-MgSiO 3 polymorphs in the same experimental run. The elastic bulk and shear moduli of the unquenchable high-pressure clinoenstatite phase were measured within its stability field for the first time. The measured density contrast associated with the phase transition OEN → HP-CEN is 2.6-2.9% in the pressure of 7-9 GPa, and the corresponding velocity jumps are 3-4% for P waves and 5-6% for S waves. The elastic moduli of the HP-CEN phase are KS=156.7(8) GPa, G = 98.5(4) GPa and their pressure derivatives are KS′=5.5(3) and G′ = 1.5(1) at a pressure of 6.5 GPa, room temperature. In addition, we observed anomalous elastic behavior in orthoenstatite at pressure above 9 GPa at room temperature. Both elastic wave velocities exhibited softening between 9 and 13-14 GPa, which we suggest is associated with a transition to a metastable phase intermediate between OEN and HP-CEN. 相似文献
7.
Mudrocks, defined to be fine‐grained siliclastic sedimentary rocks such as siltstones, claystones, mudstones and shales, are often anisotropic due to lamination and microscopic alignments of clay platelets. The resulting elastic anisotropy is often non‐negligible for many applications in the earth sciences such as wellbore stability, well stimulation and seismic imaging. Anisotropic elastic properties reported in the open literature have been compiled and statistically analysed. Correlations between elastic parameters are observed, which will be useful in the typical case that limited information on a rock's elastic properties is known. For example, it is observed that the highest degree of correlation is between the horizontal elastic stiffnesses C11 and C66. The results of statistical analysis are generally consistent with prior observations. In particular, it is observed that Thomsen's ? and γ parameters are almost always positive, Thomsen's ? and γ parameters are well correlated, Thomsen's δ is most frequently small and Thomsen's ? is generally larger than Thomsen's δ. These observations suggest that the typical range for the elastic properties of mudrocks span a sub‐space less than the five elastic constants required to fully define a Vertical Transversel Isotropic medium. Principal component analysis confirms this and that four principal components can be used to span the space of observed elastic parameters. 相似文献
8.
MgSiO 3, ZnSiO 3, MgGeO 3, MnGeO 3, and ZnGeO 3 are the only silicates and germanates known to crystallize in the ilmenite-like structure at high pressures and high temperatures. With the exception of the zinc compounds, the above-mentioned ilmenites have all been found to transform to the orthorhombic modification of the perovskite structure at higher pressures. The ilmenite phase of ZnSiO 3, on the other hand, transforms to its component oxide mixture with the rocksalt and rutile structures, whereas ZnGeO 3 (ilmenite) transforms first to an as yet undetermined orthorhombic phase and then to its component oxide mixture. The direct transformation from the ilmenite to perovskite structures observed in the metasilicates and metagermanates is consistent with all other reported high-pressure post-ilmenite phases (CdTiO 3, CdSnO 3, MnVO 3, and (Fe,Mg)TiO 3). The observation of the ilmenite-perovskite transformation in MgSiO 3 and its solid solutions towards Al 2O 3 suggests that MgO (rocksalt) + SiO 2 (rutile) + Al 2O 3 (corundum) is not a stable mineral assemblage for the earth's lower mantle. 相似文献
9.
Single-crystal elasticity of stishovite was examined using a new experimental technique and an empirical macroscopic model. Employing high-frequency resonant ultrasound spectroscopy, single-crystal elastic constants of stishovite were determined: C11 = 443(3), C33 = 781(4), C12 = 193(2), C23 = 199(2), C44 = 256(2), and C33 = 316(2) GPa. The frequency range of the resonant ultrasound spectroscopy techniques was 6–20 MHz, which is much lower than the ～10 GHz range of the Brillouin scattering technique. Of the elastic constants, the shear elastic constants C44 and C66 are consistent with the average value of the previously mentioned Brillouin scattering. Conversely, the four elastic constants, C11, C33, C12, and C23, slightly deviate outside the range of previous Brillouin scattering results. The present results, except those for C12, are consistent with recent lattice dynamic analysis of inelastic X-ray scattering data. The adiabatic bulk modulus was calculated as 298 GPa, which is smaller and more consistent with the result of compression experiments than any other Brillouin scattering results (301–312 GPa). The present result shows greater P-wave velocity anisotropy (24.7%) than any preceding work. To understand the unique elastic properties of stishovite, the Gingham check model was proposed and examined. The result shows that the octahedron of 6-coordinated Si in stishovite crystal has stiffness comparable to that of diamond. 相似文献
10.
Electron microprobe and reflected light microscopic examinations confirm the presence of composite grains of ferrian ilmenite with Xilm = 0.53 and titanomagnetite with Xusp = 0.13 in a dacite with self-reversed TRM. A parallel TRM component associated with titanomagnetite and a reversed component associated with self-reversing ferrian ilmenite are the principal NRM components. A subordinate, parallel component is associated with ferrian ilmenite which is not magnetically coupled to an “χ-phase”. The natural self-reversing properties are mainly a consequence of the dacite's high quenching temperature, calculated at 862–864°C using the Fe—Ti oxide geothermometer, and are most consistent with the self-reversal mechanism proposed by Lawson et al. [9].The conduction of thermal demagnetization and TRM induction tests in air had a much greater effect on the Fe—Ti oxides than did natural cooling, and resulted in significant oxidation with the consequent modification of some magnetic properties and the formation of another reversed TRM component. The subdivision of titanomagnetite grains by oxidation along fractures decreased its effective grain size and caused an apparent increase in its magnetic intensity, in addition to a slight increase in its resistance to alternating field demagnetization. The χ-phase associated with the reversed NRM component, with 0.42 > Xilm 0.31, became Fe-enriched during the earlier stages of heat treatment. It is suggested that after heating at 600°C for two hours or more, this χ-phase exsolves as titanohematite with Xilm < 0.33. The ferrian ilmenite host is consequently enriched in Ti, and another χ-phase much closer in composition to the host generates a reversed TRM component with Tb < 200°C. 相似文献
11.
The high-pressure and temperature phase transformations of MgSiO 3 have been investigated in a diamond-anvil cell coupled with laser heating from 150 to 300 kbar at 1000–1400°C. X-ray diffraction study of the quenched samples reveals that the sequence of phase transformations for this compound is clinoenstatite → β-Mg 2SiO 4 plus stishovite → Mg 2SiO 4(spinel) plus stishovite → ilmenite phase → perovskite phase with increasing pressure. The hexagonal form of MgSiO 3 observed by Kawai et al. is demonstrated to have the ilmenite structure and the “hexagonal form” of MgSiO 3 observed by Ming and Bassett is shown to be predominantly the orthorhombic perovskite phase plus the ilmenite phase. The mixture of oxides, periclase plus stishovite, reported by Ming and Bassett was not observed in this study. The very wide stability field for the ilmenite phase of MgSiO 3 found in this study suggests that this phase is of importance in connection with the observed rapid increase of velocity in the transition zone of the earth's mantle. On the basis of the extremely dense-packed structure of the perovskite phase of MgSiO 3, this phase should be the most important component for the lower mantle. 相似文献
12.
Phase relations in the system Mg 4Si 4O 12-Mg 3Al 2Si 3O 12 were examined at pressures of 19-27 GPa and relatively low temperatures of 800-1000 °C using a multianvil apparatus to clarify phase transitions of pyroxene-garnet assemblages in the mantle. Both of glass and crystalline starting materials were used for the experiments. At 1000 °C, garnet solid solution (s.s.) transforms to aluminous ilmenite s.s. at 20-26 GPa which is stable in the whole compositional range in the system. In Mg 4Si 4O 12-rich composition, ilmenite s.s. transforms to a single-phase aluminous perovskite s.s., while Mg 3Al 2Si 3O 12-rich ilmenite s.s. dissociates into perovskite s.s. and corundum s.s. These newly determined phase relations at 1000 °C supersede preliminary phase relations determined at about 900 °C in the previous study. The phase relations at 1000 °C are quite different from those reported previously at 1600 °C where garnet s.s. transforms directly to perovskite s.s. and ilmenite is stable only very close to Mg 4Si 4O 12. The stability field of Mg 3Al 2Si 3O 12 ilmenite was determined at 800-1000 °C and 25-27 GPa by reversed phase boundaries. In ilmenite s.s., the a-axis slightly increases but the c-axis and molar volume decrease substantially with increasing Al 2O 3 content. Enthalpies of ilmenite s.s. were measured by differential drop-solution calorimetry method using a high-temperature calorimeter. The excess enthalpy of mixing of ilmenite s.s. was almost zero within the errors. The measured enthalpies of garnet-ilmenite and ilmenite-perovskite transitions at 298 K were 105.2±10.4 and 168.6±8.2 kJ/mol, respectively, for Mg 4Si 4O 12, and 150.2±15.9 and 98.7±27.3 kJ/mol, respectively, for Mg 3Al 2Si 3O 12. Thermodynamic calculations using these data give rise to phase relations in the system Mg 4Si 4O 12-Mg 3Al 2Si 3O 12 at 1000 and 1600 °C that are generally consistent with those determined experimentally, and confirm that the single-phase field of ilmenite expands from Mg 4Si 4O 12 to Mg 3Al 2Si 3O 12 with decreasing temperature. The earlier mentioned phase relations in the simplified system as well as those in the Mg 2SiO 4-Fe 2SiO 4 system are applied to estimate mineral proportions in pyrolite as a function of depth along two different geotherms: one is a horizontally-averaged temperature distribution in a normal mantle, and the other being 600 °C lower than the former as a possible representative geotherm in subducting slabs. Based on the previously described estimated mineral proportions versus depth along the two geotherms, density and compressional and shear wave velocities are calculated as functions of depth, using available mineral physics data. Along a normal mantle geotherm, jumps of density and velocities at about 660 km corresponding to the post-spinel transition are followed by steep gradients due to the garnet-perovskite transition between 660 and 710 km. In contrast, along a low-temperature geotherm, the first steep gradients of density and velocities are due to the garnet-ilmenite transition between 610 and 690 km. This is followed by abrupt jumps at about 690 km for the post-spinel transition, and steep gradients between 700 and 740 km that correspond to the ilmenite-perovskite transition. In the latter profile along the low-temperature geotherm, density and velocity increases for garnet-ilmenite and ilmenite-perovskite transitions are similar in magnitude to those for the post-spinel transition. The likely presence of ilmenite in cooler regions of subducting slabs is suggested by the fact that the calculated velocity profiles along the low-temperature geotherm are compatible with recent seismic observations indicating three discontinuities or steep velocity gradients at around 600-750 km depth in the regions of subducting slabs. 相似文献
13.
The paper presents an experimental study on the influence of the grain size distribution curve on dynamic soil properties. More than 160 resonant column tests with additional P-wave measurements have been performed on 27 different grain size distribution curves of a quartz sand. While the small-strain shear modulus Gmax has been discussed by Wichtmann and Triantafyllidis [1] the present paper focusses on P-wave velocity vP, on the small-strain constrained elastic modulus Mmax and on Poisson's ratio ν . It is demonstrated that while vP and Mmax do not significantly depend on mean grain size d50 in the investigated range, they decrease with increasing coefficient of uniformity Cu= d60/ d10 of the grain size distribution curve. Poisson's ratio does also not depend on d50 but increases with increasing Cu. An empirical formula similar to Hardin's equation has been developed for Mmax, considering the influence of the grain size distribution curve. It predicts quite well the experimental data. 相似文献
14.
Natural “monalbite” (MA) has been observed on a submicron-scale in jadeite along with high albite (HA) and low albite (LA) in jadeite quartzite in the Dabie ultrahigh-pressure (UHP) metamorphic terrane, China. Transmission electron microscope (TEM) observation of inclusions in jadeite crystals has revealed mineral phases with C2/ m and C1? structures. The cell parameters of the C2/ m crystal structure correspond to those of MA, whereas the cell parameters of C1? structure are identical to those of HA and LA. The existence of the C2/ m structure shows that the jadeite underwent partial change to MA on a submicron-scale during retrograde metamorphism. Albite transformation twinning of HA suggests the transformation of MA into HA. MA occurrence provides powerful evidence of high-temperature metamorphism during exhumation, probably above 930 °C. The preservation of MA may be due to the armouring by the jadeite and implies a very rapid cooling (quenching) during retrogression. 相似文献
15.
Ultrasonic data for the velocities of the low- and high-pressure polymorphs of germanate compounds undergoing the pyroxene-garnet (CaGeO 3, CdGeO 3) and pyroxene-ilmenite (MgGeO 3, MnGeO 3) phase transformations have been determined as a function of pressure to 7.5 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 60 kbar. These transitions are characterized by the following velocity (υ)-density (ρ) relationships: (1) the velocity jumps are comparable in percentage magnitude to the density jumps, with the exception of shear velocity for the pyroxene-ilmenite transition; (2) the ratio (υ p/υ s) of the compressional to shear velocity is constant or increases slightly across the transitions; and (3) low slopes (linear or logarithmic) on υ-ρ diagrams. The observed relationships (1) and (2) are similar to those for the coesite-stishovite transition, but are in marked contrast with those from the olivine-spinel and olivine-beta phase transformations. Coordination changes are thus important factors to be considered in establishing velocity-density systematics governing polymorphic transitions. The υ-ρ changes across the pyroxene-garnet and pyroxene-ilmenite transitions are also distinctly smaller than those produced by compression or thermal expansion of a homogeneous material or by varying composition at constant mean atomic weight. Systematic trends in the elastic properties for isostructural sequences support the concept of germanates as models for the elasticity of their silicate analogues; this scheme is applied to estimate the bulk moduli of the garnet (1.80 Mbar) and ilmenite (2.11 Mbar) polymorphs of MgSiO 3. 相似文献
16.
The results of studying the composition of hydrocarbon gases (C 1–C 5) and organic matter in bottom sediments of the Ivankovo Reservoir in 1995, 2004, and 2005 are given. The methods used in the study include vapor-phase gas chromatography, instrumental pyrolysis gas chromatography, and mass-spectrometry for determining organic carbon δ 13C org. The gas field of bottom sediments in different regions of the reservoir varies widely in terms of gas saturation and the spectrum of hydrocarbon gases. This suggests the heterogeneous composition of organic matter in the sediments and different conditions of its input and transformation processes. The gases were found to contain saturated hydrocarbons from methane to pentane C 1–C 5, including isomers i-C 4 and i-C 5 and unsaturated compounds C 2–C 4. A correlation was found to exist between methane distribution and the distribution of its more high-molecular homologues, which confirms their genetic relationship in bottom sediments. The obtained results show an increase in the rate of microbiological processes and organic matter transformation for most regions in the Ivankovo Reservoir. The only exceptions are the zones of Moshkovichskii Bay and the sections at Gorodnya and Konakovo, where technogenic organic matter is being accumulated. The high information value of hydrocarbon gases as biogeochemical markers of the sources of organic matter and the rates of its transformation is demonstrated. The isotopic composition of organic-matter carbon in the bottom sediments of the Ivankovo Reservoir δ 13C varies from ?26.21 to ?30.86‰. 相似文献
17.
The parameters of the earthquake that took place February 3, 2015, near the city of Sumy, Ukraine, were calculated from an analysis of records obtained by both Russian and Ukrainian seismic stations (Poltava, Skvira, Nikolaev, Dneropetrovsk, and Desna). The calculated hypocenter depth of 54 km was verified by several approaches: isolation of deep PP, SP phases from the records of remote stations and solution of the kinematic problem for the Poltava station. The focal mechanism as shear with a complex fault component was determined by the first arrivals of P-waves. The data on the azimuthal travel-time curve confirm the focal mechanism. We have calculated the earthquake parameters; they are as follows: length gap L1 = 8.08 km, L2 = 6.68 km, a destruction rate of C = 2 km/s. We have obtained the dynamic parameters of the event. The calculated fault length ( L = 5.46 km) within the accuracy limits of the method coincides with the early result obtained by the azimuthal travel-time curve. On the basis of these results, we suggest that elastic energy release and formation of the dislocations in the earthquake source occurred on a smooth, prefractured fault (σ r > 0). Association of the hypocenter with the tectonic node of the northern marginal fault of the Dnieper–Donets graben and northern branch of Kryvyi Rih–Kremenchuk suture confirm this. Here, we observe a considerable Moho depth, structural alteration, and high gradients of the temperature and magnetic and electric rock properties in the lower Earth’s crust and upper mantle. These circumstances are favorable for the earthquake occurring here. 相似文献
18.
Reviewing 92 measurements of lunar sample dielectric constant versus density at frequencies above 100 kHz, gives the relation K′ = (1.93 ± 0.17) p by regression analysis, where K′ is the dielectric constant of a soil or solid at a density of pg/cm 3. This formula is the geometric mean between the dielectric constant of vacuum (1) and the zero porosity dielectric constant of lunar material. Similarly, the loss tangent ( D) can be described by D = [(0.00053 ± 0.00056) + (0.00025 ± 0.00009)C]p where D is the loss tangent at density pg/cm 3 with C percent of total FeO + TiO 2 (approximately proportional to ilmenite content). Using the density versus depth relations derived from lunar surface core tubes, and from laboratory studies of lunar soil compression gives a model of the dielectric properties as a function of depth in the lunar regolith. The dielectric constant increases smoothly with depth, as a function of the soil compaction only. The loss tangent, however, is more sensitive to the ilmenite content than it is to density. Neither dielectric constant nor loss tangent varies significantly with the temperature observed in a lunar day. 相似文献
19.
In a diamond-anvil press coupled with YAG laser heating, the spinels of Co 2GeO 4 and Ni 2GeO 4 have been found to disproportionate into their isochemical oxide mixtures at about 250 kbar and 1400–1800°C in the same manner as their silicate analogues. At about the same P-T conditions MnGeO 3 transforms to the orthorhombic perovskite structure (space group Pbnm); the lattice parameters at room temperature and 1 bar are a0 = 5.084 ± 0.002, b0 = 5.214 ± 0.002, and c0 = 7.323 ± 0.003Å with Z = 4 for the perovskite phase. The zero-pressure volume change associated with the ilmenite-perovskite phase transition in MnGeO 3 is ?6.6%. Mn 2GeO 4 disproportionates into a mixture of the perovskite phase of MnGeO 3 plus the rocksalt phase of MnO at P = 250kbar and T = 1400–1800°C. The concept of utilizing germanates as high-pressure models for silicates is valid in general. The results of this study support the previous conclusion that the lower mantle comprises predominantly the orthorhombic perovskite phase of ferromagnesian silicate. 相似文献
20.
—We investigate a new nonlinear inversion method for low frequencies to determine the bulk and shear modulus as well as the material density and the location of subsurface inhomogeneities. The solution is a direct exact nonlinear inversion of single scattered waves containing near- and far-field terms for incident P and scattered P and S waves, allowing for inversion of parameters in the vicinity and at distance from the sources and receivers. Because the approach is based on single scattering theory, the range of application includes single strong scattering anomalies of various sizes like magma chambers, gas- or fluid-filled cavities, or buried near-surface obstacles. The replacement of the material properties by a new set of parameters, referred to as scattering factors, allows the inverse problem to be solved analytically. The nonlinear nature of the scattering problem is investigated and implications for the inversion process are discussed. The deviations in the elastic parameters as a function of the scattering factors show a strong asymmetry about zero, and therefore linearized approximations will perform differently, depending on the sign of the perturbation. Based on the low frequency (Rayleigh) approximation, we introduce and evaluate a pair of approximations (Mie) derived by numerical and analytical integration of the Rayleigh approximation. Both approximations are based on the underlying principle of subdividing the inhomogeneities into a number of small noninteracting parts and subsequent integration over the total volume, thus increasing the Rayleigh limit and producing better resolution of the parameter estimates during the inversion. The two Mie approximations, when evaluated as a function of scattering angle and distance, produce similar results in the mid- and far-field of the inhomogeneity and reveal better resolution than the Rayleigh approximation. For three anomalies of ± 50% in bulk modulus, shear modulus, and density, the relative error between the exact solution and the two Mie approximations remains below 10%, 20%, and 30%, respectively, for values of k p R < 3.0, where R is the radius of the heterogeneity. However, smaller errors for individual cases are found for values up to k p R≈ 4.5. The performance of the inversion based on the analytically and the numerically integrated Mie approximation is tested for single parameter perturbations, revealing reliable and stable inversion results for the bulk and the shear modulus, reasonable results for the density, and crosstalk between the shear modulus and the density. The results show well-defined locations of the anomalies and slight deviations in the estimates of their magnitudes, which can be explained by amplitude and phase deviations between the analytical solution used for forward modeling and the approximations used for the inversion. The analytical Mie approximation provides a fast means to estimate elastic parameters compared to the more time consuming numerically integrated approximation, while the latter can be applied to more arbitrarily shaped inhomogeneities. 相似文献
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