Synthesis and crystal-chemical characterization of MgSiO3 perovskite

The orthorhombic MgSiO₃ perovskite has been synthesized with the aid of a double-stage split-sphere-type high-pressure apparatus at about 280 kbar and 1000°C. The unit cell dimensions are: a = 4.7754(3)Å, b = 4.9292(4)Å and c = 6.8969(5)Å with the probable space group Pbnm. Calculated density is 4.108 g cm^?3. Crystal structure determination has been carried out by means of both the geometrical simulation (DLS) technique and the ordinary powder X-ray analysis. The results indicate that the MgSiO₃ perovskite is closer to the ideal perovskite than ScAlO₃ perovskite.     

Elasticity of MgSiO3 in the ilmenite phase

The single-crystal elastic moduli of the ilmenite phase of MgSiO₃ have been determined from Brillouin spectroscopy. They are: C₁₁ = 472, C₁₂ = 168, C₃₃ = 382, C₁₃ = 70, C₄₄ = 106, C₁₄ = ?27, C₆₆ = 152 and C₂₅ = ?24 in GPa. These elastic properties are consistent with a structural mechanical model where the silicon octahedra are very stiff under compression and shear. This latter property yields an unexpectedly high shear modulus for the magnesium silicate ilmenite as compared with analogue compounds. The further transformation to perovskite will probably be associated with a significant increase in elastic properties since the strong silicon polyhedra form a structural network in this phase. The transformation of spinel and stishovite to ilmenite is associated with a slight density increase and a slight decrease in acoustic velocities. This transformation will probably not produce a seismic discontinuity even if it does occur in the Earth's mantle.     

High-pressure phases of Co2GeO4, Ni2GeO4, Mn2GeO4 and MnGeO3: implications for the germanate-silicate modeling scheme and the Earth's mantle

In a diamond-anvil press coupled with YAG laser heating, the spinels of Co₂GeO₄ and Ni₂GeO₄ 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 MnGeO₃ 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 MnGeO₃ is ?6.6%. Mn₂GeO₄ disproportionates into a mixture of the perovskite phase of MnGeO₃ 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.     

Elasticity of the ilmenite - perovskite phase transformation in CdTiO3

Ultrasonic data for the velocities of the ilmenite and perovskite polymorphs of CdTiO₃ 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 CdTiO₃ 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 CaSiO₃ (2.7 Mbar) and MgSiO₃ (2.8 Mbar).     

Elasticity of aluminate,titanate, stannate and germanate compounds with the perovskite structure

Ultrasonic data for the velocities of a large number of perovskite-structure compounds have been determined as a a function of pressure to 6 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 100 kbar in solid-media devices: ScAlO₃, GdAlO₃, SmAlO₃, EuAlO₃, YAlO₃, CdTiO₃, CdSnO₃, CaSnO₃ and CaGeO₃. The elasticity data for these orthorhombic and cubic perovskites define systematic patterns on bulk modulus (K_S)-volume (V_O) and bulk sound velocity (υ_φ—mean atomic weight (M) diagrams which are insensitiv to the details of cation chemistry and crystallographic structure. These isostructural trends are used to estimate K_S = 2.5 ± 0.3 Mbar and υ_φ = 7.9 ± 0.4 km/s for the perovskite polymorph of MgSiO₃. On a Birch diagram of veloc vs. density, the perovskite data define linear trends which lead to erroneous estimates of velocity for MgSiO₃ unless specific account is taken of ionic radius effects in isomorphic substitutions.     

The high-pressure phases of MgSiO3

The high-pressure and temperature phase transformations of MgSiO₃ 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-Mg₂SiO₄ plus stishovite → Mg₂SiO₄(spinel) plus stishovite → ilmenite phase → perovskite phase with increasing pressure. The hexagonal form of MgSiO₃ observed by Kawai et al. is demonstrated to have the ilmenite structure and the “hexagonal form” of MgSiO₃ 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 MgSiO₃ 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 MgSiO₃, this phase should be the most important component for the lower mantle.     

Elasticity of (Mg, Fe)(Si, Al)O3-perovskite at high pressure

The most abundant mineral on Earth has a perovskite crystal structure and a chemistry that is dominated by MgSiO₃ with the next most abundant cations probably being aluminum and ferric iron. The dearth of experimental elasticity data for this chemically complex mineral limits our ability to calculate model seismic velocities for the lower mantle. We have calculated the single crystal elastic moduli (c_ij) for (Mg, Fe^3 +)(Si, Al)O₃ perovskite using density functional theory in order to investigate the effect of chemical variations and spin state transitions of the Fe³⁺ ions. Considering the favored coupled substitution of Mg²⁺-Si^4 + by Fe³⁺-Al³⁺, we find that the effect of ferric iron on seismic properties is comparable with the same amount of ferrous iron. Ferric iron lowers the elastic moduli relative to the Al charge-coupled substitution. Substitution of Fe³⁺ for Al³⁺, giving rise to an Fe/Mg ratio of 6%, causes 1.8% lower longitudinal velocity and 2.5% lower shear velocity at ambient pressure and 1.1% lower longitudinal velocity and 1.8% lower shear velocity at 142 GPa. The spin state of the iron for this composition has a relatively small effect (< 0.5% variation) on both bulk modulus and shear modulus.     

Silicate perovskites: A review

Since the first discovery of silicate perovskites at high pressures and high temperatures in the laboratory in 1974, silicate perovskites have probably become the most studied materials in the geophysical community during the past decade or so and it is nearly established that these silicates are the most abundant materials making up the bulk of the Earth. There are basically two groups of silicate perovskites. Ferromagnesian silicates with or without Al₂O₃ crystallizing in a common orthorhombic perovskite structure at high pressures and temperatures (HPT) are preservable at ambient conditions. Silicates of large cations such as Ca and Na crystallizing in an ideal cubic perovskite structure at HPT cannot be preserved at ambient conditions. Thus, the lattice parameters, crystal structure, thermal expansion and compressional data have been studied, both experimentally and theoretically, mainly for orthorhombic silicate perovskites, and for MgSiO₃ in particular. For MgSiO₃ perovskite, the recommended lattice parameters area=4.777±0.003,b=4.931±0.003 andc=6.899±0.004 Å; bulk modulusB ₀=2.4±0.2 Mbar; and volume thermal expansivity =(3±1)×10^–5 deg^–1 at ambient conditions. Cubic CaSiO₃ perovskite is probably less compressible than orthorhombic MgSiO₃ perovskite. The lattice parameters of MgSiO₃ perovskite increase linearly with increasing contents of both FeSiO₃ and Al₂O₃, forming limited solid solutions. The degree of distortion of orthorhombic silicate perovskites does not appear to change at HPT.     

High-temperature elasticity of the fluorite-structure compounds CaF2, SrF2 and BaF2

The elastic moduli of single-crystal CaF₂, SrF₂ and BaF₂ have been determined by the ultrasonic pulse superposition technique as a function of temperature from T = 298 to T = 650°K. These new data are consistent with other data obtained by ultrasonic pulse techniques in the region of room temperature and are superior to previous high-temperature data from resonance experiments. The elastic moduli (c) are represented by quadratic functions in T over the experimental temperature range with the curvature in the same sense for all the moduli. Evaluation of the temperature derivatives of the elastic moduli at constant volume indicates that the dominant temperature effect is extrinsic for (?K_S/?T)_P and intrinsic for (?μ/?T)_P, where K_S and μ are the isotropic bulk and shear moduli, respectively. For the series CaF₂SrF₂BaF₂, |(?c/?T)_p| decreases with increasing molar volume for all moduli; however there are no theoretical or empirical grounds on which to derive a simple relationship between (?c/?T)_P and crystallographic parameters.     

Elasticity of (Mg0.83,Fe0.17)O ferropericlase at high pressure: ultrasonic measurements in conjunction with X-radiation techniques

The elasticity of ferropericlase with a potential mantle composition of (Mg_0.83,Fe_0.17)O is determined using ultrasonic interferometry in conjunction with in situ X-radiation techniques (X-ray diffraction and X-radiography) in a DIA-type cubic anvil high-pressure apparatus to pressures of 9 GPa (NaCl pressure scale) at room temperature. In this study, we demonstrate that it is possible to directly monitor the specimen length using an X-ray image technique and show that these lengths are consistent with those derived from X-ray diffraction data when no plastic deformation of the specimen occurs during the experiment. By combining the ultrasonic and X-ray diffraction data, the adiabatic elastic bulk (K_S) and shear (G) moduli and specimen volume can be measured simultaneously. This enables pressure scale-free measurements of the equation of state of the specimen using a parameterization such as the Birch-Murnaghan equation of state. The elastic moduli determined for (Mg_0.83,Fe_0.17)O are K_S0=165.5(12) GPa, G₀=112.4(4) GPa, and their pressure derivatives are K_S0′=4.17(20) and G₀′=1.89(6). If these results are compared with those for MgO, they demonstrate that K_S0 and K_S0′ are insensitive to the addition of 17 mol% FeO, but G₀ and G₀′ are reduced by 14% and 24%, respectively. We calculate that the P and S wave velocities of a perovskite plus ferropericlase phase assemblage with a pyrolite composition at the top of the lower mantle (660 km depth) are lowered by 0.8 and 2.3%, respectively, when compared with those calculated using the elastic properties of end-member MgO. Consequently, the magnitudes of the calculated wave velocity jumps across the 660 km discontinuity are reduced by about 11% for P wave and 20% for S wave, if this discontinuity is considered as a phase transformation boundary only (ringwoodite→perovskite+ferropericlase).     

Elastic properties of the olivine and spinel polymorphs of Mg2GeO4, and evaluation of elastic analogues

The single-crystal elastic moduli of the olivine and spinel phases of Mg₂GeO₄ have been measured using Brillouin scattering spectra. The moduli for the olivine phase are: C₁₁ = 3.12, C₂₂ = 1.87, C₃₃ = 2.17, C₆₆ = 0.71, C₂₃ = 0.66, C₃₁ = 0.65 and C₁₂ = 0.60. The moduli for the spinel phase are: C₁₁ = 3.00, C₄₄ = 1.26 and C₁₂ = 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.     

Synthesis of a perovskite-type polymorph of CaSiO3

Synthetic crystalline (wollastonite) and glass forms of CaSiO₃ have been compressed to loading pressures above 160 kbar and heated to about 1500° C by a laser in a diamond-anvil cell. After cooling, an X-ray diffraction study carried out whilst the sample was maintained at high pressure revealed that it had transformed to a cubic perovskite-type 3olymorph with a = 3.485 ± 0.008A?. After release of pressure, however, the sample showed a mixture of glass plus a few weak lines corresponding to ε-CaSiO₃ which is thus interpreted as a retrogressive transition product. The density of the perovskite polymorph of CaSiO₃ is about 9.2% greater than that of an isochemical mixture of CaO + SiO₂ (stishovite) at about 160 kbar.     

High-pressure reconnaissance investigation in the system Mg3Al2Si3O12-Fe3Al2Si3O12

Two synthetic end-members and two natural solid solutions of the system Mg₃Al₂Si₃O₁₂-Fe₃Al₂Si₃O₁₂ have been found to display successive phase transformations at increasingly high pressures when they were compressed in a diamond-anvil cell and heated with a YAG laser to temperatures of approximately 1400–1800°C. X-ray diffraction studies of the quenched samples show that the iron-rich garnets apparently first transform to a garnet-related high-pressure phase, then disproportionate into a mixture of magnesiowüstite plus an unknown phase(s). The latter phase(s) may further transform to a still denser unknown phase(s). The ultimate high-pressure phase may be a perovskite-like structure as was previously found for the magnesium-rich garnets. One of the unknown phases may be the high-pressure phase of Al₂O₃ · nSiO₂ compounds. Magnesium-rich garnets display similar phase transformations as do the iron-rich garnets with the exception of the garnet-related high-pressure phase. These results disagree with a previous interpretation for the high-pressure phase of iron-silicate garnets recovered in shock-wave experiments reported by Ahrens and Graham (1972).     

In situ measurements of sound velocities and densities across the orthopyroxene → high-pressure clinopyroxene transition in MgSiO3 at high pressure

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 (V_P and V_S) for both ortho- and high-pressure clino-MgSiO₃ 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 K_S=156.7(8) GPa, G = 98.5(4) GPa and their pressure derivatives are K_S′=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.     

Phase transition in CaSiO3 perovskite

A phase transition in pure CaSiO₃ perovskite was investigated at 27 to 72 GPa and 300 to 819 K by in-situ X-ray diffraction experiments in an externally-heated diamond-anvil cell. The results show that CaSiO₃ perovskite takes a tetragonal form at 300 K and undergoes phase transition to a cubic structure above 490–580 K in a pressure range studied here. The transition boundary is strongly temperature-dependent with a slightly positive dT / dP slope of 1.1 (± 1.3) K/GPa. It is known that the transition temperature depends on Al₂O₃ content dissolved in CaSiO₃ perovskite [Kurashina et al., Phys. Earth Planet. Inter. 145 (2004) 67–74]. The phase transition in CaSiO₃(+ 3 wt.% Al₂O₃) perovskite therefore could occur in a cold subducted mid-oceanic ridge basalt (MORB) crust at about 1200 K in the upper- to mid-lower mantle. This phase transition is possibly ferroelastic-type and may cause large seismic anomalies in a wide depth range.     

High-pressure phase transformations in the system CaSiO3-Al2O3

Phase assemblages for five selected compositions in the system CaSiO₃-Al₂O₃ have been investigated in the pressure range 100–300 kbar and at about 1000°C in a diamond-anvil press coupled with laser heating. At pressures below about 250 kbar, the assemblage of grossularite plus corundum is stable for compositions containing more than 25 mole% Al₂O₃. Above about 250 kbar, phase assemblages for the latter compositions are truncated by those in the join CaAl₂O₄-SiO₂. Garnet solid solutions are stable between about 10 and 25 mole% Al₂O₃. Grossularite transforms to a new tetragonal form at pressures greater than about 250 kbar, but the stability field for the garnet solid solutions extends to pressures up to about 300 kbar. The perovskite modification appears to be stable at pressures above about 150 kbar, but is probably limited to nearly pure CaSiO₃ composition. Phase behaviour for calcium-bearing silicates or aluminosilicates in the lower mantle are apparently more complicated than was suggested earlier.     

Phase relations and equation-of-state of aluminous Mg-silicate perovskite and implications for Earth's lower mantle

We have investigated the effect of Al³⁺ on the room-temperature compressibility of perovskite for stoichiometric compositions along the MgSiO₃-AlO_1.5 join with up to 25 mol% AlO_1.5. Aluminous Mg-perovskite was synthesized from glass starting materials, and was observed to remain a stable phase in the range of ∼30-100 GPa at temperatures of ∼2000 to 2600 K. Lattice parameters for orthorhombic (Pbnm) perovskite were determined using in situ X-ray diffraction at SPring8, Japan. Addition of Al³⁺ into the perovskite structure increases orthorhombic distortion and unit cell volume at ambient conditions (V₀). Compression causes anisotropic decreases in axial length, with the a axis more compressive than the b and c axes by about 25% and 3%, respectively. The magnitude of orthorhombic distortion increases with pressure, but aluminous perovskite remains stable to pressures of at least 100 GPa. Our results show that substitution of Al³⁺ causes a mild increase in compressibility, with the bulk modulus (K₀) decreasing at a rate of −67±35 GPa/X_Al. This decrease in K₀ is consistent with recent theoretical calculations if essentially all Al³⁺ substitutes equally into the six- and eight-fold sites by charge-coupled substitution with Mg²⁺ and Si⁴⁺. In contrast, the large increase in compressibility reported in some studies with addition of even minor amounts of Al is consistent with substitution of Al³⁺ into six-fold sites via an oxygen-vacancy forming substitution reaction. Schematic phase relations within the ternary MgSiO₃-AlO_1.5-SiO₂ indicate that a stability field of ternary defect Mg-perovskite should be stable at uppermost lower mantle conditions. Extension of phase relations into the quaternary MgSiO₃-AlO_1.5-FeO_1.5-SiO₂ based on recent experimental results indicates the existence of a complex polyhedral volume of Mg-perovskite solid solutions comprised of a mixture of charge-coupled and oxygen-vacancy Al³⁺ and Fe³⁺ substitutions. Primitive mantle with about 5 mol% AlO_1.5 and an Fe³⁺/(Fe³⁺+Fe²⁺) ratio of ∼0.5 is expected to be comprised of ferropericlase coexisiting with Mg-perovskite that has a considerable component of Al³⁺ and Fe³⁺ defect substitutions at conditions of the uppermost lower mantle. Increased pressure may favor charge-coupled substitution reactions over vacancy forming reactions, such that a region could exist in the lower mantle with a gradient in substitution mechanisms. In this case, we expect the physical and transport properties of Mg-perovskite to change with depth, with a softer, probably more hydrated, defect dominated Mg-perovskite at the top of the lower mantle, grading into a stiffer, dehydrated, charge-coupled substitution dominated Mg-perovskite at greater depth.     

Structure constraints and instability leading to the post-perovskite phase transition of MgSiO3

Recent experience with Rietveld refinement of structural analogues and literature surveys, suggests anion–anion repulsion limits the stability of the perovskite phase, including in the MgSiO₃ perovskite to post-perovskite transition. Assuming rigid octahedral coordination, still to be tested experimentally, the critical point where intra- and inter-octahedral anion–anion distances are equal provides a useful metric for predicting the pressure of the perovskite/post-perovskite transition and the Clapeyron slope of the phase boundary, once pressure and temperature derivatives of relevant structure parameters are known. The inter-octahedral anion–anion distances and the polyhedral volume ratio are rigorously formulated as a function of octahedral rotation in this work, assuming the orthorhombic (Pbnm) perovskite structure, where regular octahedra share each corner and conform to the in- and anti-phase rotation schemes designated by space group symmetry. These mathematical expressions are consistent with structure data from 70 perovskite-structured materials surveyed in the literature at ambient as well as extreme conditions and define structure constraints, such as the minimum polyhedral volume ratio, which must be reached before the phase transition to the post-perovskite structure-type can proceed. The formalism we present is general for perovskite (Pbnm) and dependent on the accuracy with which structures can be determined from, sometimes compromised, high pressure diffraction data.     

Orthorhombic perovskite phases observed in olivine,pyroxene and garnet at high pressures and temperatures

Ferromagnesian silicate olivines, pyroxenes and garnets with Mg/(Mg + Fe)?0.3 (molar) have been found to transform to high-pressure phases characterized by the orthorhombic perovskite structure when compressed to pressures above 250 kbar in a diamond-anvil press and heated to temperatures above 1,000°C with a YAG laser. The zero-pressure density of the perovskite phase of (Mg,Fe)SiO₃ is about 3–4% greater than that of the close-packed oxides, rocksalt plus stishovite. For (Mg,Fe)₂SiO₄ compounds, the perovskite plus rocksalt phase assemblage is 2–3% denser than the mixed oxides. The experimental synthesis of such high-density perovskite phases in olivine, pyroxene and garnet compounds suggests that (Mg,Fe)SiO₃-perovskite is the dominant mineral phase in the earth's lower mantle.     

Inversion of normal moveout for monoclinic media1

Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide-azimuth reflection data (combined with known vertical velocity or reflector depth) or multi-azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media. In order to facilitate the inversion procedure, we introduce a Thomsen-style parametrization for monoclinic media that includes the vertical velocities of the P-wave and one of the split S-waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal-moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε^(1,2), δ^(1,2,3) and γ^(1,2)) analogous to those defined by Tsvankin for the higher-symmetry orthorhombic model. The parameters ε^(1,2), δ^(1,2) and γ^(1,2) are primarily responsible for the pure-mode NMO velocities along the coordinate axes x₁ and x₂ (i.e. in the shear-wave polarization directions). The remaining coefficient δ⁽³⁾ is not constrained by conventional-spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ^(1,2,3) which control the rotation of the P-, S₁- and S₂-wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P-wave NMO ellipse and shear-wave polarization directions was recently observed on field data by Pérez et al. Our parameter-estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P-, S₁- and S₂-waves. A Dix-type representation of the NMO velocity of mode-converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS₁- and PS₂-waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.