Flow and dynamic topography from hemispheric heterogeneity in the mantle,

Abstract:

In a coordinate frame with origin at the planet’s center of mass, all hemispheric mass heterogeneities are balanced. Should a mass redistribution occur on this length scale, displacements within the compressible planet would arise that would keep the center of mass (COM) in the celestial orbit. We distinguish two components of such mass anomalies and the corresponding displacements. One is related to the planet’s deformation, and the other to the translation to compensate for the shift of the COM.

We analyze the deformational component to place constraints on the Earth’s rheology and structure. For that we calculate the dynamic topography of a compressible, self-gravitating Earth and compare it with the observed residual topography. The latter is supposedly supported by the mantle flow driven by the interior density heterogeneities (which we estimate from models of Vs and Vp seismic velocity) and associated with the lithospheric plate motion. We analyze the translation-related component by calculating a coordinate frame shift from the hydrostatic to the perturbed state. We perform a Monte-Carlo type inversion fitting the surface dynamic topography to constrain the mantle viscosity profile and the seismic velocity-to-density conversion factors.

Consistently throughout all the inversions, the top boundary for the stiff lower mantle appears within 100 km of 600 km depth. On average, the viscosity contrast between the upper and the lower mantle tends to be 3-4 orders of magnitude. For the ratio of density to seismic anomaly of 0.2 and 0.5 (for Vs and Vp models, respectively), the average upper mantle absolute viscosity tends to be smaller than 3×1019 Pa s with four orders of magnitude viscosity increase across the lower mantle. For a half of that density signal, the upper mantle could reach 3×1020 Pa s requiring less viscosity contrast with the lower mantle -- 2-3 orders of magnitude.

Inversion for Mantle Viscosity Profiles Constrained by Dynamic Topography and the Geoid, and Their Estimated Errors,

Abstract:

We perform a joint inversion of Earth's geoid and dynamic topography for its radial mantle viscosity structure using a number of models of interior density heterogeneities, including an assessment of the error budget.

We identify three classes of errors; those related to the density perturbations used as input, those due to insufficiently constrained observables, and those due to the limitations of our analytical model. We estimate the amplitudes of these errors in the spectral domain. Our minimization function weights the squared deviations of the compared quantities with the corresponding errors, so that the components with more reliability contribute to the solution more strongly than less certain ones. We develop a quasi-analytical solution for mantle flow in a compressible, spherical shell with Newtonian rheology, allowing for continuous radial variations of viscosity, together with a possible reduction of viscosity within the phase change regions due to the effects of transformational superplasticity.

The inversion reveals three distinct families of viscosity profiles, all of which have an order of magnitude stiffening within the lower mantle, followed by a soft D"-layer. The main distinction among the families is the location of the lowest-viscosity region, -- directly beneath the lithosphere, just above 400-km, or just above 670-km depth. All profiles have a reduction of viscosity within one or more of the major phase transformations, leading to reduced dynamic topography, so that whole-mantle convection is consistent with small surface topography.

Models of Isostatic and Dynamic Topography, Geoid Anomalies, and Their Uncertainties.

Abstract:

We calculate global models of topography created by lateral density variations in the crust, the oceanic lithosphere, and the continental tectosphere. The key assumption is that the crust, lithosphere and tectosphere are in isostatic equilibrium. We also calculate the isostatic geoid anomaly that would result from these compensated near-surface density anomalies. We then obtain dynamic topography and dynamic geoid models by subtracting the respective isostatic models from the observed fields.

We investigate two models of the cooling of the oceanic lithosphere - half-space and plate - and estimate the effect of each on the overall dynamic topography.

We estimate the uncertainties in the values of the calculated dynamic topography and geoid by combining the errors in the data and systematic errors. To obtain the spectral coefficients of the fields, we use weighted least-squares inversions. The calculated dynamic topography, the residual geoid, and the errors associated with these fields can be used in studies of mantle dynamics as constraints on convection and mantle rheology.

A model of transformational superplasticity of the upper mantle.

Abstract:

We develop a model of transformational superplasticity of creeping mantle material as it undergoes a solid-solid phase change. By considering various scenarios of the grain-geometry evolution in a polycrystalline composed of two phases of different densities, we estimate the internal stress arising to accommodate the volume change relaxes through reshaping of the grains. We relate the microscopic deviatoric strain rate of the reshaping grains to the macroscopic dilatation rate of the entire composite, where the latter is evaluated both by applying a kinetic theory of the transformation and by implementing the seismically-observed sharpness of the phase-transformation-related density change. We estimate that depending on the grain-geometry, the granularity, and the kinetics, the transformational strain rates can exceed the dilatation ones by an order of magnitude.

We calculate the degree of softening of mantle material which would occur inside the thin phase-change regions located at 400- and 670-km depths. For a power-law rheology, mantle viscosity decreases by up to one to two orders of magnitude within the upper transition, and by two to three orders of magnitude inside the 1-km thick layer at 670-km depth. To account for uncertainties in stress level and grain size, we construct deformation mechanism maps for a three-component mantle and a variety of grain sizes, tectonic stresses, and strain rates. In the low-stress dislocational creep regime, the high transformational stresses place an upper bound on the effective viscosity of the composite.

We calculate the transformational-superplasticity field for a particular mantle flow model and show that variations on the order of one order of magnitude occur at half of the dominant flow wavelength. We reduce the effect of a phase transformation on mantle dynamics to boundary conditions on the vertical and the lateral velocities across the thin two-phase layer. An abrupt change in the azimuthal velocity would facilitate mixing across the phase-change region and cause refraction of the currents passing through this depth. The biggest deviation of the flow velocities occurs within the major up- and down-wellings. We also show that when TS is included, the change in the long-wavelength geoid is comparable to a 50% increase in viscosity of the lower mantle, and the change in the short-wavelength geoid is similar to an extension of the upper mantle low-viscosity zone down to 450-km depth.

Relatively recent construction of the Tien Shan inferred from GPS measurements of present-day crustal deformation rates.

Abstract:

The Tien Shan, the high, seismically active intracontinental belt 1000-2000 km north of the Himalaya, has grown as a result of India's penetration into the rest of Asia. Yet, whereas the crustal shortening (~200 +/- 50 km) and thickening that built the belt has accommodated only a small fraction of India's 2000-3000 km penetration since India and Eurasia collided, we report Global Positioning System (GPS) geodetic measurements that indicate a current shortening rate that is nearly half of India's 44 mm/y convergence rate with Eurasia in this area4. Our measurements demonstrate 13 +/- 2 mm/yr of shortening across the segment of the Tien Shan in Kyrgyzstan and Kazakhstan, ~70% of its width. Extrapolation across the remaining, highest, part suggests a total shortening rate of ~20 mm/yr, which is roughly twice average rates inferred previously from extrapolating Holocene slip rates and from displacements associated with earthquakes in this century. Insofar as this rate applies to late Cenozoic time, it suggests that the rate of mountain building in the Tien Shan has accelerated several fold since the collision at ~ 50-55 Ma. An extrapolation of the current rate suggests that most of the belt has been constructed in the last 10 Myr, perhaps following an apparently abrupt 1-2.5km rise of the Tibetan Plateau and in response to an increased horizontal force applied by a higher plateau to the Tien Shan.

Understanding the effects of mantle compressibility on geoid kernels.

Abstract:

We develop a model of transformational superplasticity of creeping mantle material as it undergoes a solid-solid phase change. By considering various scenarios of the grain-geometry evolution in a polycrystalline composed of two phases of different densities, we estimate the internal stress arising to accommodate the volume change relaxes through reshaping of the grains. We relate the microscopic deviatoric strain rate of the reshaping grains to the macroscopic dilatation rate of the entire composite, where the latter is evaluated both by applying a kinetic theory of the transformation and by implementing the seismically-observed sharpness of the phase-transformation-related density change. We estimate that depending on the grain-geometry, the granularity, and the kinetics, the transformational strain rates can exceed the dilatation ones by an order of magnitude.

We calculate the degree of softening of mantle material which would occur inside the thin phase-change regions located at 400- and 670-km depths. For a power-law rheology, mantle viscosity decreases by up to one to two orders of magnitude within the upper transition, and by two to three orders of magnitude inside the 1-km thick layer at 670-km depth. To account for uncertainties in stress level and grain size, we construct deformation mechanism maps for a three-component mantle and a variety of grain sizes, tectonic stresses, and strain rates. In the low-stress dislocational creep regime, the high transformational stresses place an upper bound on the effective viscosity of the composite.

We calculate the transformational-superplasticity field for a particular mantle flow model and show that variations on the order of one order of magnitude occur at half of the dominant flow wavelength. We reduce the effect of a phase transformation on mantle dynamics to boundary conditions on the vertical and the lateral velocities across the thin two-phase layer. An abrupt change in the azimuthal velocity would facilitate mixing across the phase-change region and cause refraction of the currents passing through this depth. The biggest deviation of the flow velocities occurs within the major up- and down-wellings. We also show that when TS is included, the change in the long-wavelength geoid is comparable to a 50% increase in viscosity of the lower mantle, and the change in the short-wavelength geoid is similar to an extension of the upper mantle low-viscosity zone down to 450-km depth.

Dynamic and static geoid anomalies: regional approach and the errors due to flat-earth bounded region approximation.

Abstract:

Sorry, no abstract is available

Flow and Dynamic Topography from Hemispheric Heterogeneity in the Mantle

Panasyuk, S.V. and R.J. O'Connell, Eos Trans. Am. geophys. Un., 82, SSS, 2000.

Abstract:

In the study of Earth deformations, a mass redistribution that occurs on a hemispheric scale (degree one spherical harmonic) requires a special consideration, because it shifts the center of mass in the coordinate frame of an undisturbed planet. We investigate the response of compressible, self-gravitating Earth to a first order spherical harmonic load and analyze the dynamic topography.

The Earth's observed topography is one example of a surface mass redistribution. The Northern hemisphere of observed Earth topography on average stands nearly 2 km higher than the Southern one. Most of this is due to continental crust and age related lithospheric thickness variations. When these are accounted for, a difference of the order of 200 m remains, supposedly supported by the mantle flow. Models of seismic heterogeneity in the mantle frequently contain large scale hemispheric heterogeneities that correspond to degree one spherical harmonics. These are absent (by definition) from the geoid, which is referred to the center of mass of the Earth, but they will excite flow in the mantle and give rise to dynamic topography.

To facilitate the physical and mathematical interpretation, we consider the deformation and the translation separately. The former is in the physical center of mass coordinate frame. The latter is in the hypothetical center of mass of an undisturbed planet coordinate frame. We consider different surface boundary conditions: free-slip, non-slip, and velocity driven. We derive an analytical solution for deforming sphere and extend our analysis by investigating a more complicated system: PREM-compressible, self-gravitating Earth with the depth variable viscosity. To drive the l=1 flow, we consider several tomography models of Vs and Vp seismic velocity anomalies in the mantle and observed kinematic velocity of the plates. We fit the calculated dynamic topography with the one that is obtained by removing the contribution of crust, lithosphere, and tectosphere from the observed topography. The dynamic topography of l=1 represents the stress magnitudes of the longest wavelength in the deforming mantle.

Constraints on the Density and Viscosity Structure of Earth

Panasyuk, S.V., Ishii, M., O'Connell, R.J., and J. Tromp, Eos Trans. Am. geophys. Un., 81, F17, 1999.

Abstract:

Recent models of lateral variations in density based on Earth's free oscillations enable us to estimate geoid anomalies directly from topographic undulations and volumetric density anomalies and constrain the latter to fit the observed gravitational field. This begs the question: is the density structure consistent with the dynamic Earth? Our objective is to find a viscosity profile that satisfies the observed geoid, boundary topographies, and surface plate velocity.

Traditionally, density heterogeneities have been estimated by scaling seismic velocity anomalies. The direct determination of density allows us to bypass this step. For a compressible, self-gravitating Earth model, we perform two sets of iterative but independent inversions: one for the density structure (using splitting function coefficients of normal modes) and another for the viscosity profile (a non-linear, multi-parameter, constrained inversion weighted by the parameter uncertainty). Both inversions use similar constraints on the geoid and the topography (surface topography is corrected for the isostatic crust; topography of boundaries at 410-km and 670-km are from seismic reflection studies; excess in CMB oblateness is constrained by VLBI measurements). The models explicitly include the observed plate motions. We first focus on the best constrained lower harmonics.

We find a series of plausible viscosity profiles that satisfy the observational constraints. The common, major features are a stiff lower mantle with low viscosity zones at the top and bottom, a weak transition zone with further reduced viscosity within the phase change regions. Inclusion of surface plate motions is critical in complementing the strong degree 2 order 1

The Effect of Plate Associated Flow on the Mantle Convection

Panasyuk, S.V. and R.J. O'Connell, Eos Trans. Am. geophys. Un., 80, S17, 1999.

Abstract:

We investigate consequences of mantle flow associated with plates moving on the Earth's surface. For a compressible, self-gravitating Earth model, we describe the mantle flow as a superposition of two flows: one is driven by the internal density anomalies under the assumption of a no-slip surface and a free-slip core-mantle boundary (cmb); the other is flow resulting from the velocity that matches the observed distribution of the plate motion on the surface. We calculate and analyze the contributions from each source of the flow to the mantle velocities, stresses, geoid, and topography at the surface and cmb.

The plate associated flow in the deeper mantle depends strongly on the mantle viscosity profile assumed. For the low-viscosity asthenosphere models the plate flow dominates in the upper mantle. The internally driven flow dominates the stress field in the mantle. Both fields contribute substantially to the geoid. Since most of the inversions for the mantle viscosity are based on the fit to the geoid, we evaluate the impact of the more realistic boundary conditions (no-slip for the density driven flow in combination with the plate-associated flow) on the inverted viscosity. We carry out a non-linear, multi-parameter, constrained inversion for the mantle viscosity profile based on fits to the geoid and dynamic topography. We use several recent tomographic and slab models to assign the source for the convection,simultaneously invert for velocity-to-density conversion factor for each model, and carry out an error analysis.

We believe that a consistent treatment of the surface boundary conditions (viz. plate motions) is necessary for successful modeling of mantle flow and related phenomena such as the geoid.

Models of Isostatic and Dynamic Topography, Geoid Anomalies, and Their Uncertainties

Panasyuk, S.V. and B.H. Hager,Eos Trans. Am. geophys. Un., 79, F879, 1998.

Abstract:

We calculate global models of topography created by the lateral density variations in the crust, the oceanic lithosphere, and the continental tectosphere. The key assumption is that the crust, lithosphere and tectosphere can be considered as existing in isostatic equilibrium. We also calculate the isostatic geoid anomaly that would result from these compensated near-surface density anomalies. Dynamic topography and dynamic geoid models are then obtained by subtracting the respective isostatic models from the observed fields.

To model the crust, we use the recent CRUST 5.1 model (Mooney et al., 1998); for lithospheric ages, we use a model by Muller et al. (1997); and for the tectosphere, the GTR1 regionalization (Jordan, 1981). We investigate two assumptions about the cooling of the oceanic lithosphere - half-space and plate-like. The effect of each on the overall dynamic topography is investigated for comparison with the results of inverse modeling based on a fit to the geoid and to dynamic topography amplitude.

We estimate the uncertainties in the values of the calculated dynamic topography and geoid by combining the errors of the data and statistical errors. The calculated dynamic topography, the residual geoid, and the errors associated with these fields can be used in studies of mantle dynamics as constraints on convection.

References:

Mooney, W.D., Laske, G., and T.G. Masters, CRUST 5.1: A global Crustal Model at 5x5 degrees, J. Geophys. Res., 103, 727-747, 1998.

Müller, R.D., Roest, W.R., Royer, J.-Y., Gahagan, L.M. and J.G. Sclater, Digital Isochrons of the World's Ocean Floor, J. Geophys. Res., 102, 3211-3214, 1997.

Jordan, T.H., Continents as a chemical boundary layer, Phil. Trans. R. Soc. Lond. A, 301, 359-373, 1981.

What do Global Geoid Models Tell us About the Mantle Viscosity Profile?

Panasyuk, S.V. and B.H. Hager,Eos Trans. Am. geophys. Un., 78, F156, 1997.

Abstract:

Previous investigations of mantle viscosity structure based on models of the nonhydrostatic geoid typically have assumed a particular model of the distribution of internal density anomalies. Densities were typically converted from a seismic velocity anomaly model, assuming a constant of proportionality, and/or from a geodynamical model of subducted slabs. The inferred viscosity profile was very sensitive to the assumed upper mantle density structure, e.g., slabs vs. tomography. We carry out a non-linear, multi-parameter, constrained inversion for the mantle viscosity profile based on fits to the geoid and/or free-air gravity field using tens of models of mantle density heterogeneity from tomographic and slab models. Using a compressible flow formulation, we simultaineously invert for velocity-to-density conversion factors in the upper and lower mantle for each model.

A small number (three) of distinct families of mantle viscosity profiles are chosen by all the models we consider. One has viscosity decreasing through the upper mantle, then increasing into the lower mantle; one has a low viscosity asthenosphere, with viscosity increasing through the transition zone into the lower mantle; one has a high viscosity transition zone, with a lower viscosity in the asthenosphere and lower mantle. These viscosity and density structures provide comparable fits to the geoid, with variance reductions of about 80\% for harmonic degrees 2-6. The velocity/density conversion factor, viscosity near the CMB, and resulting dynamic topography differ from family to family, however, suggesting that multidisciplinary investigations should be able to discriminate among the families of viscosity models.

The broad distribution of initial parameters, large number of inversion runs, and many tomography models investigated allow us to reproduce previous results and to construct robust statistics.

Effects of transformational superplasticity on global mantle circulation

Panasyuk, S.V. and B.H. Hager, EUG, Strasbourg, France, 1997.

Abstract:

We develop a model of transformational superplasticity (TS) of creeping mantle material as it undergoes a solid-solid phase change. By considering various scenarios of grain-geometry evolution in a polycrystalline material composed of two phases of different densities, we suggest that the internal stress arising from the volume change relaxes through reshaping of the grains. We relate the microscopic deviatoric strain rate of the reshaping grains to the macroscopic dilatation rate of the entire composite, where the latter is evaluated both by applying kinetic theory and by implementing the seismically-observed sharpness of the phase-transformation-related density change. We estimate that, depending on the grain-geometry, the granularity, and the kinetics, transformational strain rates can exceed dilatational ones by an order of magnitude.

We calculate the degree of softening of mantle material that would occur inside the thin phase-change regions located at 400- and 670-km depths. For a power-law rheology, mantle viscosity decreases by one to two orders of magnitude within the upper transition, and by two to three orders of magnitude inside the 1-km thick layer at 670-km depth. We calculate the TS-field for a particular mantle flow model and show that effective viscosity variations on the order of one orer of magnitude occur at half of the dominant wavelength for mantle flow. Phase transformations affect mantle flow, introducing jumps in the vertical (due to the density change) and in the lateral (due to the low viscosity) velocities across the two thin layers at 400- and 670-km depth. An abrupt change in the azimuthal velocity would facilitate mixing across the phase-change regions and cause refraction of the currents passing through these depths. The largest velocity deviations occur within the major up- and down-wellings. When TS is included, the change in the geoid is comparable to a 40% increase in viscosity of the lower mantle: the geoid anomalies are affected through the change in the normal stresses at the surface and CMB.

Time changes of geoid and inertia tensor for various models of mantle flow

Steinberger, B.M., Panasyuk, S.V., and R.J. O'Connell,Eos Trans. Am. geophys. Un., 78, F187, 1997.

Abstract:

Over time scales of millions of years, mantle flow may give the dominant contribution to changes of the geoid. We therefore use a mantle flow field consistent with tomographic anomalies and time-dependent plate velocities in order to calculate advection of mantle density heterogeneities and corresponding changes in the geoid. From changes in the spherical harmonic degree two component also changes of the inertia tensor and rotation axis, which will closely follow any imposed changes of the axis of maximum non-hydrostatic moment of inertia, are inferred.

We are able to model a polar wander path that agrees well with paleomagnetic results. This model predicts a present increase of the Earth's flattening with time. Characteristic feature of the successful model is a geoid kernel with opposite signs and roughly equal magnitudes in the upper and lower mantle. Other realistic viscosity models without that feature may yield much faster polar motion. Results are similar for various tomographic models. Flow in the upper mantle (largely related to plate motions) and in the lower mantle (mostly driven by internal density heterogeneities) give contributions to polar motion of similar magnitude. Some of the higher terms will also be discussed. Particularly, results for J_n will be compared with predictions from post-glacial rebound and other available data.

Relatively Recent Construction of the Tien Shan Inferred from GPS Measurements of Recent Crustal Deformation

Hager, B.H. et al.,Eos Trans. Am. geophys. Un., 77, F143, 1996.

Abstract:

The Tien Shan, the high, seismically active intracontinental range 1000-2000 km north of the Himalaya, has grown as a result of India's penetration into the rest of Asia. Yet, whereas the crustal shortening and thickening that built the range (~ 200+/-50 km) has accommodated only a small fraction of India's 2000-3000 km penetration since India and Eurasia collided, our GPS measurements over the past several years suggest a shortening rate that is nearly half of India's 44 mm/yr convergence rate with Eurasia in this area.

Our measurements demonstrate 13+/-2mm/yr of shortening across ~70% of the Tien Shan in Kyrgyzstan and Kazakhstan. Extrapolation across the remaining, highest, part yields a total shortening rate of ~20 mm/yr, which is roughly twice the average rates inferred previously from extrapolating Holocene faulting and from slip associated with earthquakes in this century. Insofar as this rate applies to late Cenozoic time, it suggests that the rate of mountain building in the Tien Shan has accelerated several fold since the collision at 50-55 Ma. An extrapolation of the current rate suggests the bulk of the range has been built in the last 10 Myr, perhaps following the apparently abrupt rise of 1-2.5 km of the Tibetan Plateau, and in response to an increased horizontal force applied by a higher plateau to the Tien Shan.

How transformational superplasticity affects mantle viscosity, large scale flow, slab trajectories and geoid

Panasyuk S.V. and B. H. Hager, Gordon Research Conferences, Composition, structure and dynamics of the Earth's interior, New Hampshire, USA, 1996.

Abstract:

An anomalous softening of polycrystalline material while it undergoes a phase transformation while being subjected to a low deviatoric stress was experimentally documented several decades ago. Later, transformational superplasticity (TS) phenomenon was proposed to be relevant to Earth rocks. Driven by large-scale mantle flow, the material encounters pT-conditions favorable for the phase transformations to occur. External deviatoric stress, in combination with the ongoing reaction, leads to increased strain rate.

We build a qualitative model of TS for mantle material and estimate the reduction in the effective viscosity for both major phase changes at 410-km and 670-km depth. We analyze possible effects of transformation kinetics and constrain it by seismic wave reflectivity data to infer the thickness of the two-phase region. Assuming different types for the grain geometry, we relate the macroscopically observed volumetric strain rate to the overall effective viscosity reduction using recent rheological data and deformational mechanism maps (DMM) technique.

In terms of the large scales, TS can be viewed as a thin low-viscosity layer fixed inside of a convecting high-viscosity shell. To explore the effect on the flow structure, we reduce the complicated dynamics to two boundary conditions on the flow velocities and tie the solutions across the thin phase change region. We apply a stream function technique to separate the effects of the step-like density change from the delta-function-like viscosity reduction. The solution allows us to analyze the problem graphically and to get an explicit factor which represents the "strength" of the low-viscosity layer. The latter shows a wave-length dependence, supporting the idea of a frequency-filtering effect of the phase change region. For a driving density source located between the two major phase changes, TS may result in "plug flow" within the mantle. Changing slab trajectories substantially, TS may help explain the difference in character of tomographic mantle models across '670 and the richness of slab structure revealed by regional tomographic models. Through the modification of the mantle flow, TS reduces the large-scale dynamic topography at the surface and the CMB, leading to a shift of the geoid kernels to more positive values. A hundred times reduction of viscosity by TS is comparable to a moderate (40 per cent) change in the viscosity contrast between the upper and lower mantle.

Transformational superplasticity affects and relates many topics of geophysical science. Accurately accounting for the effect of phase transformations on mantle flow is essential in understanding Earth's viscosity structure.

Reduction of mantle shear viscosity by transformational superplasticity

Panasyuk S.V. and B. H. Hager, EOS Trans. Am. geophys. Un., 76, 578, 1995.

Large deviatoric strain rates from flow through a phase change: implication for the rheology and dynamics of the transition zone

Hager B.H. and S. V. Panasyuk, EOS Trans. Am. geophys. Un., 74, 641, 1994.

Understanding the effects of compressibility of the mantle and core and self-gravitation of the ocean on geoid kernels

Panasyuk S.V. and B. H. Hager, XX International Conference on Mathematical Geophysics, France, 1994.

Constraints on the Dynamic topography of the Canadian shield from geology and geodynamics

Hager B.H., J. P. Grotzinger, S. S. Shapiro, and S. V. Panasyuk, Eos Trans. Am. geophys. Un., 74, 298-299, 1993.

The effect of the assumed g(r) on geoid kernels for compressible and incompressible mantle flow models

Panasyuk, S.V., Forte A.M., and B. H. Hager, Eos Trans. Am. geophys. Un., 74, 558, 1993.

GPS constrains on shortening across the northen Tien Shan of Kazakhstan and Kyrgyzstan

Souter B.J. et al., Eos Trans. Am. geophys. Un., 74, 190, 1993.

Gravity field of Northern Eurasia and P-wave velocity anomalies: Understanding in terms of the dynamic mantle

Kogan M.G. and S. V. Panasyuk, Eos Trans. Am. geophys. Un., 73, 209, 1992.

Longwavelength gravity anomalies over a region of the Earth, understanding in terms of the steady state convection

Panasyuk S.V. and M. G. Kogan, workshop on Numerical Modeling of Lithospheric and Mantle Dynamics, Weilburg, Germany, 1991.

Dynamic and static geoid anomalies: regional approach and the errors due to flat-earth bounded region approximation

Panasyuk S.V. , USSR National School of Young Scientists, Russia, 1990.