Depth Distribution Of Density Research Articles

Svobodnyye korotkoperiodnyye vnutrenniye volny v arkticheskikh moryakh Rossii

Purpose. The aim of the work is to investigate vertical structure and phase characteristics of free shortperiod internal waves (IW), and to assess their dependence on density stratification in the Barents, Kara, Laptev and East Siberian seas. © Букатов А. А., Соловей Н. М., Павленко Е. А., 2021 МОРCКОЙ ГИДРОФИЗИЧЕСКИЙ ЖУРНАЛ том 37 № 6 2021 645 Methods and Results. Solving the main boundary problem of the Sturm-Liouville theory has resulted in calculating the amplitudes of velocity vertical component, own frequencies and periods of the first mode of internal waves. The density field was calculated using the reanalysis data (World Ocean Atlas 2018) on temperature and salinity for 1955–2017 with a resolution 0.25°× 0.25°. The relation between the internal waves’ vertical structure and dispersion features, and the density depth distribution was analyzed. It is shown that the averaged over the sea area depth of the maximum amplitude of the IW velocity vertical component in the Barents and Kara seas is ∼ 90 m in the mid winter and ∼ 75–80 m in summer, and in the Laptev and East Siberian seas – ∼ 60 m throughout the whole year. Conclusions. In the months when the density gradients are maximal, the internal waves of the highest frequency and the shortest period are observed. The maximum water stability in the Barents Sea takes place in July – August, in the Kara Sea – in July – September and November, in the Laptev Sea – in June, November, and in the East Siberian Sea – in July. Just in the same months, the maximum values of the averaged own frequencies, and the minimum values of the averaged own periods and amplitudes of the vertical component of the internal waves’ velocity are observed.

Simple 2D gravity–density inversion for the modeling of the basin basement: example from the Banat area, Serbia

We have developed a technique to calculate lateral density distribution of the sedimentary basin basement by combining linear gravity–density inversion and 2D forward modeling. The procedure requires gravity anomaly data, depth-to-basement data and density data for the sediments (density–depth distribution). Gravity effect of density variations in the basement was extracted from the total gravity anomaly by removing the joint effect of the sediments with vertical density variations and homogeneous basement of average density contrast (calculated by 2D modeling). Gravity effect of the sediments was calculated using depth-to-basement data and density–depth function, based on borehole logging data. Bouguer slab formula was used in order to simplify basement model and calculate the operator for the linear inversion of gravity effect of the basement into lateral density distribution. The results were tested by forward modeling, and differences between observed and modeled gravity data were used for the next iteration of the inversion and correction of density values in each point along the profile. The procedure was tested using synthetic models and field example, and both results were satisfying, especially taking into account the simplicity of the inversion technique. The main problem was the effect of abrupt changes in the basement topography on density distribution, but it was downsized by filtering. Basement density maps were compiled based upon the density distribution along the profiles.

Structural and optical properties of Gd implanted GaN with various crystallographic orientations

Structure, morphology, and optical properties of Gd implanted GaN epitaxial layers were studied for (0001), (11−20), and (11−22) orientations. The GaN layers grown by MOVPE on sapphire were subsequently implanted with 200keV Gd+ ions using fluences of 5×1015 and 5×1016cm−2. Dopant depth profiling was accomplished by Rutherford Back-Scattering spectrometry (RBS). Structural and optical changes during subsequent annealing were characterized by RBS, Raman spectroscopy, and photoluminescence measurements. Post-implantation annealing induced a structural reorganization of GaN structure in the buried layer depending on the introduced disorder level, i.e. depending on the implantation fluence and on crystallographic orientation. The defect density depth distribution was evaluated by RBS. The surface morphology and optical properties depend on particular crystallographic orientation.

Comparative study of threading dislocations in GaN epitaxial layers by nondestructive methods

An investigation of the threading dislocations (TDs) density in two high quality GaN epitaxial layers grown on sapphire (Al2O3) substrate, with the thickness of 300 and 1000nm, respectively, is presented in this paper. In the case of GaN300 sample, taking into account that the finite size effect exerts an increased influence, further advanced methods are necessary to find the correct results besides the standard analysis of the Full Width at Half Maximum (FWHM) of the X-ray rocking curves peaks as in the case of the thicker sample, GaN1000. Thus, we explored the tails of the rocking curves using a universal power law fit and subsequently, we used modified version of the Williamson-Hall plots. Analysis of the XRD profiles allowed us to avoid the overestimation of the threading dislocations density determined by the influence of the correlation between dislocations. Moreover, we successfully separate the contribution of the strain and size broadening based on the analysis of refined Williamson Hall plots and demonstrate the nearly uniform dislocation density depth distribution of the GaN studied films, with no supplementary nucleation or annihilation centers are present inside the epitaxial film using, both grazing incidence and grazing exit configurations of the asymmetric geometry.

Study of the amorphization of surface silicon layers implanted by low-energy helium ions

The structural changes in surface layers of Si(001) substrates subjected to plasma-immersion implantation by (2–5)-keV helium ions to a dose of D = 6 × 1015–5 × 1017 cm–2 have been studied by highresolution X-ray diffraction, Rutherford backscattering, and spectral ellipsometry. It is found that the joint application of these methods makes it possible to determine the density depth distribution ρ(z) in an implanted layer, its phase state, and elemental composition. Treatment of silicon substrates in helium plasma to doses of 6 × 1016 cm–2 leads to the formation of a 20- to 30-nm-thick amorphized surface layer with a density close to the silicon density. An increase in the helium dose causes the formation of an internal porous layer.

Attenuation of free spheroidal oscillations of the Earth after the M = 9 Earthquake in Sumatra and the super-deep Earthquake in the Sea of Okhotsk: I. the Admissible Q-factor range for the fundamental mode and overtones of the free spheroidal oscillations

The problem of reconstructing the depth distribution of density and the depth and frequency dependences of the mechanical Q-factor in the Earth’s mantle from the entire set of the present-day seismic and astrometric data on the travel times and periods of seismic waves and the amplitudes and phases of forced nutations is considered. The solution of the problem is refined by including the new data about the attenuation of the free oscillations of the Earth excited by the Sumatra earthquake (M = 9) and super-deep earthquake in the Sea of Okhotsk. The actual accuracy of the Q-factor is studied in the first part of the paper. To this end, we analyze (1) the convergence of the Q-factor estimated from the time series of different length shifted along the time axis and (2) the convergence of the results based on the different data. Since the accuracy of identifying all the periods and attenuation factors for the free oscillations from the Sumatra earthquake is significantly higher than for the earthquake with M = 9 in Japan, the data are only compared for the Sumatra and Okhotsk events. The signal-to-noise ratio (SNR) is analyzed based on the records from different Global Seismographic Network (GSN) stations including the station in Obninsk, the Kurchatov station in Kazakhstan, and the main ERM and MAJO stations in Japan. It is found that the highest SNR was observed in Obninsk. The inverse problem of reconstructing the density and Q-factor is solved for the frequency dependent real parts of the shear moduli with allowance for the most accurate data about the attenuation factors for the fundamental spheroidal modes of the free oscillations of the Earth.

On the anomalies in gravity associated with lateral inhomogeneities in temperature: 2. Numerical results

In the first part of the paper, we obtained the analytical relationships determining the changes in the topography of the geoid and the component of horizontal displacements of the Earth’s surface, which appear under the action of the point heat source located at the arbitrary depth in the mantle. For the real model of radially heterogeneous Earth with hydrostatic distribution of the initial stresses, the solution of the problem on thermoelastic deformations is represented in the form of spherical expansions with the coefficients determined by the corresponding coefficients of spherical expansions of the product of temperature, bulk modulus, and bulk compression modulus with the same indices. As mentioned in part I, the variation in the external potential is contributed by three effects: the reduction in density in the heated area, the increase in density in the external (not heated) area due to its elastic compression, and the attraction of the near-surface simple layer that is formed due to the change in the shape of the external surface under its elastic deformation. The total effect of these three factors is represented in the form of a spherical series expansion. It is shown that in the limiting case of the high-order spherical functions, the ratios of the radial displacements of the geoid to the radial displacements of the external surface tend to zero. Since at high orders of the spherical functions, the effects of sphericity are negligible, this statement means that at any thermoelastic deformations of the uniform elastic halfspace, the three effects listed above exactly compensate each other. Due to this compensation, the question of the interpretation of the observed relationships between the coefficients of series expansions of the temperature and geoid can only be solved after the detailed numerical calculations, since the arbitrarily small radial inhomogeneities of the medium (e.g., those associated with the depth changes of its rheological properties) are not only capable of significantly changing the magnitude of the radial displacements of the geoid but also altering their sign. Moreover, even in the uniform Earth’s model, the effects of sphericity of its external surface and self-gravitation can also provide a noticeable contribution, which determines the signs of the coefficients in the expansion of the geoid’s shape in the lower-order spherical functions. In order to separate these effects, below we present the results of the numerical calculations of the total effects of thermoelastic deformations for the two simplest models of spherical Earth without and with self-gravitation with constant density and complex-valued shear moduli and for the real Earth PREM model (which describes the depth distributions of density and elastic moduli for the high-frequency oscillations disregarding the rheology of the medium) and the modern models of the mantle rheology. Based on the calculations, we suggest the simplest interpretation of the present-day data on the relationship between the coefficients of spherical expansion of temperature, velocities of seismic body waves, the topography of the Earth’s surface and geoid, and the data on the correlation between the lower-order coefficients in the expansions of the geoid and the corresponding terms of the expansions of horizontal inhomogeneities in seismic velocities. The suggested interpretation includes the estimates of the sign and magnitude for the ratios between the first coefficients of spherical expansions of seismic velocities, topography, and geoid. The presence of this correlation and the relationship between the signs and absolute values of these coefficients suggests that both the long-period oscillations of the geoid and the long-period variations in the velocities of seismic body waves are largely caused by thermoelastic deformations.

The density and Q-factor models based on the new data on the nutations and overtones of the free oscillations of the earth: 1. The analysis of the new GSN data for the Sumatra, Tohoku, and Okhotsk earthquakes

We discuss the problem of the ambiguity of gravity inversion, i.e., finding the depth distribution of density and the depth and frequency dependences of the Q-factor from the entire set of the present-day seismic and astrometric data on the travel times of seismic waves, the periods and attenuation factors of the free oscillations of the Earth, as well as the amplitudes and phases of the forced nutations. In the first part of the paper, we present the new and more accurate determinations of the periods and Q-factors for the fundamental tones and overtones of the spheroidal and toroidal oscillations of the Earth, which have periods longer than 3 min. These determinations are based on analyzing the signals from the Sumatra, Tohoku, and Okhotsk earthquakes of magnitude 9, which were recorded by the stations of the Global Seismographic Network (GSN) in Obninsk and Kazakhstan. It is shown that, although the Okhotsk earthquake had a lower magnitude than the other quakes analyzed (since its seismic source was extremely deep (about 600 km)), the amplitudes of the overtones excited by this event are significantly higher than the amplitudes of the overtones caused by the Sumatra and Tohoku events of magnitude 9. Moreover, the amplitudes of the overtones from the Okhotsk earthquake exceed the amplitudes of the overtones of the free oscillations caused by the other seismic events of magnitude 9 that occurred in the second half of the 20th century. Due to this, the data on the Okhotsk Sea earthquake are of utmost importance for the solution of the inverse problems of reconstructing the vertical profiles of Q-factor in the ultra-low frequency (ULF) range and for reconstructing the vertical distribution of density. Based on the new empirical data, we obtained new and more accurate estimates for the periods and attenuation factors of the free oscillations of the Earth.

Influence of the chemical nature of implanted ions on the structure of a silicon layer damaged by implantation

The influence of the implantation of silicon single crystals by fluorine, nitrogen, oxygen, and neon ions on the distribution of strain and the static Debye-Waller factor in the crystal lattice over the implanted-layer depth has been investigated by high-resolution X-ray diffraction. The density depth distribution in the surface layer of native oxide has been measured by X-ray reflectometry. Room-temperature implantation conditions have ensured the equality of the suggested ranges of ions of different masses and the energies transferred by them to the target. It is convincingly shown that the change in the structural parameters of the radiation-damaged silicon layer and the native oxide layer depend on the chemical activity of the implanted ions.

On the admissible range for the mass and inertia moments of the liquid core: I. Solving the inverse problem of nutations and free oscillations of the Earth by decomposition of mechanical parameters in an orthogonalized basis

The results of solving the inverse problem of forced nutations and free oscillations of the Earth by decomposing the Q-factor and small depth variations in density in a system of orthogonal functions are considered. These functions are determined by orthogonalization of the functional derivatives of the observed parameters with respect to the depth distributions of the sought parameters (assuming there are no distributions of the velocities of body seismic waves Vp and VS with depth and unchanged total mass M and inertia moments I of the Earth). The examples are presented to illustrate the numerical solution of the inverse problem on finding the density distributions in the mantle and core of the Earth using orthogonalization of the integral constraints for the probable depth distributions of density describing the conditions of unchanged M and I, as well as the constraints posed by the data on the periods of the free low-order oscillations of the Earth.

Models of density and mechanical Q-factor distributions according to new data on the nutations and free oscillations of the Earth: 2. Comparison with astrometric data

In the first part of the paper [Molodenskii, 2011], we considered the problem of ambiguity in the solution of the inverse problem of retrieval of density distribution in the Earth’s core and mantle and determination of the Q factors in the mantle from the entire set of modern data on seismic velocities (V p and V S ), the frequencies f i and quality factors Q i of free oscillations of the Earth, and the amplitudes and phases of its forced nutations. We have constructed the model distributions of these parameters, in which the root-meansquared (rms) deviations of all observed values from the predicted ones are much smaller than in the PREM model. Below, we compare the observed amplitudes of the forced nutation with the values predicted by our model. In order to understand how rigid are the constraints imposed by the amplitudes of forced nutation, we not only calculate the deviations of the observed amplitudes of nutation from the predictions by our model but also estimate the changes in these deviations caused by small variations in several parameters of the model. To the parameters to be varied we refer those which have no or barely any effect on the periods and damping constants of free oscillations but have a pronounced effect on the amplitudes of forced nutation. These parameters include (1) the rheological properties of the mantle in the interval of periods from an hour to a day; (2) the dynamical flattening of the liquid core; (3) the dynamic flattening of the solid inner core; (4) the viscosity of the liquid core; and (5) the moment of inertia of the solid inner core. In addition, we estimate the effects of variations in the moment of inertia of the liquid core to be small (±0.2%) and not to affect, within the observation error, the periods of free oscillations. We show that the uncertainty in the model depth distributions of density considerably decreases when the new data on the amplitudes and phases of the forced nutation of the Earth are taken into account. With these data, it is possible to estimate the creep function for the lower mantle in a wide range of periods from a second to a day.

Models of density and mechanical Q-factor distributions according to new data on the nutations and free oscillations of the Earth: 1. Ambiguity in the inverse problem

Ambiguity in the inverse problem of retrieval of the mechanical parameters of the Earth’s shell and core from the set of data on the velocities V p and V S , of longitudinal and transverse seismic body waves, the frequencies f i and quality factors Q i , of free oscillations, and the amplitudes and phases of forced nutation is considered. The numerical experiments show that the inverse problem of simultaneous retrieval of the density profile ρ in the mantle-liquid core system and the mechanical quality factor Q μ of the mantle (if the total mass M and the total mean moment of inertia I of the Earth, and V p and V S are constant at all depths) has most unstable solutions. An example of depth distributions of ρ and Q μ which are alternative to the well-known PREM model is given. In these distributions, the values of M and I and the velocities V p and V S at all depths for the period of oscillations T = 1 s exactly coincide with their counterparts yielded by PREM model (T = 1 s); however, the maximum deviations of the ρ and Q μ profiles from those in the PREM model are about 3% and 40%, respectively; the mass and the moment of inertia of the liquid core are smaller than those for the PREM model by 0.75% and 0.63%, respectively. In this model, the root mean square (rms) deviations of all the measured values of f i and Q i from their values predicted by theory are half to third the corresponding values in the PREM model; the values of Δ for natural frequencies of the fundamental tone and overtones of radial oscillations, the fundamental tones of torsional oscillations, and the fundamental tones of spheroidal oscillations, which are measured with the highest relative accuracy, are smaller by a factor of 30, 6.6, and 2 than those in the PREM model, respectively. Such a large ambiguity in the solution of the inverse problem indicates that the current models of the depth distribution of density have relatively low accuracy, and the models of the depth distribution of the mechanical Q in the mantle are extremely unreliable. It is shown that the ambiguity in the models of depth distribution of density considerably decreases after the new data on the amplitudes and phases of the forced nutation of the Earth are taken into account. Using the same data, one may also refine by several times the recent estimates of the creep function for the lower mantle within a wide interval of periods ranging from a second to a day.

The effects of buoyant crust on the gravitational instability of thickened mantle lithosphere at zones of intracontinental convergence

Using both numerical experiments and approximate linear theory, we examine the stability of a 2-D, three-layered viscous system that represents crust over mantle lithosphere, overlying asthenosphere. If horizontal shortening of lithosphere occurs, as in mountain building, the development of gravitational instability may follow one of two distinct paths. Localized downwelling occurs beneath the region of horizontal shortening and crustal thickening, if the layer representing crust has a large viscosity coefficient, is relatively dense or is thin, relative to the underlying layer that represents mantle lithosphere. Conversely, for a low viscosity ratio or buoyant crust, downwelling flow develops on the flanks of the zone of convergence, and the mantle lithosphere layer thins beneath the central region. Thinning in such a setting would facilitate volcanism and high-temperature metamorphism during the development of a mountain belt. A series of numerical experiments with different density and viscosity structures, including runs with non-Newtonian viscosity, show that this general description is insensitive to minor differences in the depth distributions of density and viscosity. The tendency of structures with relatively thick crustal layers (or relatively thin lithospheric mantle) to favour paired, marginal downwellings may account for sustained volcanism during intracontinental deformation where lithosphere initially is warm, thin and weak. The western part of the Tien Shan in Asia and the region including and surrounding the Alboran Sea illustrate some of the features associated with paired, marginal downwellings. The Western Transverse Ranges of California and the Southern Alps of New Zealand share features associated with single downwelling flow beneath the axes of the belts.

Variability of particulate seawater properties related to bottom mixed layer‐associated internal waves in shallow water on a time scale of hours

To obtain information on relations between internal wave‐controlled hydrographic variability in bottom mixed layers (BMLs) and particle‐associated BML parameters, depth distributions of density, relative turbidity, relative chlorophyll a (Chl a), relative phycoerythrin fluorescence (Phyco), total particulate matter (TPM), particulate carbon (PC), and particulate nitrogen (PN) were obtained at a shallow‐water site in the southwestern Baltic Sea in July 2001 in the course of a temporally highly resolved 1‐d time series. The density distribution showed evidence for a BML and undulations of BML thickness probably caused by near‐inertial internal waves. Relative pigment fluorescence in the BML and in the layer above the BML was inversely coupled and related to the wave. Dense transient PC‐ and PN‐depleted TPM clouds, having the highest TPM loads in the BML, occurred on leading wave faces. Leading wave faces and wave backs are suggested to be locations of preferred vertical exchange between adjacent compartments (surface sediment, BML, layer above BML). Different processes control relative turbidity in the BML (decoupled from Chl a) and in the layer above the BML (coupled to Chl a). Most of the time, spatial variability of the Chl a/Phyco ratio was higher within the BML than in the layer above the BML. The Brunt—Väisälä frequency within the layer above the BML was positively and negatively related to the thickness of the BML and the layer above the BML, respectively. The dataset indicates that the BML itself and in coaction with passing internal waves effectively controls the communication between interior water column and sediment.

Secondary ion yields of C, Si, and Ge in InP, and Cs surface density and concentration, in SIMS

In secondary ion mass spectrometry (SIMS), the relationship between negative secondary ion yield ( γ −) of C, Si, and Ge in an InP substrate and sputtering yield ( Y), and that between the secondary ion yield and the surface density of reactive primary ion Cs ( n Cs(0); zero refers to substrate surface) were examined by changing the incident angle of the primary ion to the surface. The γ − value was derived by dividing the corresponding useful yield by the instrumental transmission factor, which was obtained by measuring the useful yield of an element with high electron affinity, such as fluorine. Monte Carlo simulations using TRIM code and theoretical analysis were performed to obtain the Cs density (atoms/unit volume) depth distribution, n Cs( x), in the sputtered substrate. The density depth distribution was measured directly using SIMS, under conditions where the energy of the O 2 + primary ion was sufficiently reduced. n Cs(0) was obtained by setting x of n Cs( x) to zero. The Cs ions used for sputtering were distributed mostly according to a Gaussian function. The n Cs( x) profile estimated on the basis of the Gaussian distribution showed good accordance with the measured one. At the sputtered surface, n Cs(0) was closely proportional to 1/ Y. The values of γ − for C, Si and Ge changed proportionally to the power of n Cs(0), or 1/ Y. For C, Si, and Ge, the lower the γ −, the more sensitively γ − changed in response to n Cs(0). Furthermore, the composition at the Cs-sputtered surface was examined using Auger electron and wavelength dispersive X-ray spectrometry. These measurements showed that n In(0), n P(0) and n Cs(0) changed almost linearly with 1/ Y InP, suggesting that the Cs surface concentration (at.%), C Cs(0), is proportional not to 1/ Y itself, but to a function of 1/ Y. However, under certain special conditions, C Cs(0) is also proportional to 1/ Y itself, as is n Cs(0).

Relaxation and rocking-curve broadening of strained (Ga,In)As single layers on (001) GaAs

We have measured the lattice relaxation of various strained Ga1−xInxAs layers which are thicker than the equilibrium critical thickness. Samples with a thickness near the energy balance model critical thickness exhibited a large relaxation. We have analyzed the strain relaxation data in a GaInAs/GaAs system using the Dodson–Tsao plastic flow model [Appl. Phys. Lett. 52, 852 (1988)]. It was found that the model provides a reasonably good fit to the data, however, the model parameters have widely different values for the GaInAs/GaAs samples with different mismatches. One parameter of the model shows an approximate inverse-square-law dependence on the misfit. The rocking-curve linewidths are presented for the GaInAs layers. The measured linewidths are discussed in terms of the theoretical linewidth, dynamical x-ray diffraction, and defect density depth distribution.