The problem of the earth's density variation*

1940 ◽  
Vol 30 (3) ◽  
pp. 235-250 ◽  
Author(s):  
K. E. Bullen
Keyword(s):  
Density Distribution ◽  
Finite Strain ◽  
Density Variation ◽  
Central Core ◽  
Lower Portion ◽  
Gravitational Attraction ◽  
Earth’S Mantle ◽  
The Mean

Summary The present paper examines the problem of the earth's density variation and includes a quantitative discussion of the errors likely to be involved. Figures are given for the density distribution of the earth's outer mantle, and it is shown that all these are probably accurate within about 0.05 gm/cm.3 On the figures presented, the density in the earth's mantle ranges from 3.32 gm/cm.3 at the base of the crustal layers to 5.68 gm/cm.3 at the base of the mantle. The mean density of the central core is shown to be 10.7 gm/cm.3 within an error of order 0.1 gm/cm.3 Application of equations derived by Birch from Murnaghan's theory of finite strain indicates agreement with the density figures found, but it is to be noted that the rigidity of the lower portion of the earth's mantle appears to increase more slowly with increase of depth than would be consistent with the equations of Birch. Values which are expected to need very little future amendment are also given for the pressure and gravitational attraction within the earth's mantle.

The density variation of the earth's central core*

1942 ◽  
Vol 32 (1) ◽  
pp. 19-29
Author(s):  
K. E. Bullen
Keyword(s):  
Pure Iron ◽  
Outer Boundary ◽  
Density Variation ◽  
Central Core ◽  
Good Precision ◽  
Wide Margin ◽  
The Core ◽  
The Earth ◽  
The Mean ◽  
Published Paper

ABSTRACT A detailed analysis of the problem of the earth's density variation has been extended to the earth's central core. It is shown that in the region between the outer boundary of the core and a distance of about 1400 km. from the earth's center the density ranges from 9.4 gm/cm.3 to 11.5 gm/cm.3 within an uncertainty which, if certain general assumptions are true, does not exceed 3 per cent. The density and pressure figures are, moreover, compatible with the existence of fairly pure iron in this part of the earth. The result for the earth's outer mantle as given in a previously published paper, together with those in the present paper, are found to give with good precision the density distribution in a region occupying 99 per cent of the earth's volume. Values of the density within 1400 km. of the earth's center are subject, however, to a wide margin of uncertainty, and there appears to be no means of resolving this uncertainty for the present. The most that can be said is that the mean density in the latter region is greater than 12.3 gm/cm.3 and may quite possibly be several gm/cm.3 in excess of this figure. In the present paper figures are also included for the variation of gravity and the distribution of pressure within the central core. The gravity results are shown to be subject to an appreciable uncertainty except within about 1000 km. of the outer boundary of the core, but the pressure results are expected to be closely accurate at all depths.

scholarly journals High Ripple-Density Resolution for Discriminating Between Rippled and Nonrippled Signals: Effect of Temporal Processing or Combination Products?

2021 ◽  
Vol 25 ◽  
pp. 233121652110101
Author(s):  
Dmitry I. Nechaev ◽  
Olga N. Milekhina ◽  
Marina S. Tomozova ◽  
Alexander Y. Supin
Keyword(s):  
Low Frequency ◽  
Noise Signal ◽  
Density Variation ◽  
Choice Procedure ◽  
Masker Level ◽  
Reference Signals ◽  
Forced Choice Procedure ◽  
The Mean ◽  
Density Resolution

The goal of the study was to investigate the role of combination products in the higher ripple-density resolution estimates obtained by discrimination between a spectrally rippled and a nonrippled noise signal than that obtained by discrimination between two rippled signals. To attain this goal, a noise band was used to mask the frequency band of expected low-frequency combination products. A three-alternative forced-choice procedure with adaptive ripple-density variation was used. The mean background (unmasked) ripple-density resolution was 9.8 ripples/oct for rippled reference signals and 21.8 ripples/oct for nonrippled reference signals. Low-frequency maskers reduced the ripple-density resolution. For masker levels from −10 to 10 dB re. signal, the ripple-density resolution for nonrippled reference signals was approximately twice as high as that for rippled reference signals. At a masker level as high as 20 dB re. signal, the ripple-density resolution decreased in both discrimination tasks. This result leads to the conclusion that low-frequency combination products are not responsible for the task-dependent difference in ripple-density resolution estimates.

scholarly journals Characterizing Mat Formation of Bamboo Fiber Composites: Horizontal Density Distribution

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1198
Author(s):  
Yu’an Hu ◽  
Mei He ◽  
Kate Semple ◽  
Meiling Chen ◽  
Hugo Pineda ◽  
...  
Keyword(s):  
Density Distribution ◽  
Fiber Composite ◽  
Fiber Composites ◽  
Density Variation ◽  
Bamboo Fiber ◽  
Wood Composites ◽  
Forming Process ◽  
Bamboo Culm ◽  
Basic Understanding ◽  
Panel Thickness

Bamboo fiber composite (BFC) is a unidirectional and continuous bamboo fiber composite manufactured by consolidation and gluing of flattened, partially separated bamboo culm strips into thick and dense panels. The composite mechanical properties are primarily influenced by panel density, its variation and uniformity. This paper characterized the horizontal density distribution (HDD) within BFC panels and its controlling factors. It revealed that HDD follows a normal distribution, with its standard deviation (SD) strongly affected by sampling specimen size, panel thickness and panel locations. SD was lowest in the thickest (40 mm) panel and largest-size (150 × 150-mm2) specimens. There was also a systematic variation along the length of the BFC due to the tapering effect of bamboo culm thickness. Density was higher along panel edges due to restraint from the mold edges during hot pressing. The manual BFC mat forming process is presented and found to effectively minimize the density variation compared to machine-formed wood composites. This study provides a basic understanding of and a quality control guide to the formation uniformity of BFC products.

scholarly journals The Elastic Properties of β-Mg2SiO4 Containing 0.73 wt.% of H2O to 10 GPa and 600 K by Ultrasonic Interferometry with Synchrotron X-Radiation

Minerals ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 209
Author(s):  
Gabriel D. Gwanmesia ◽  
Matthew L. Whitaker ◽  
Lidong Dai ◽  
Alwin James ◽  
Haiyan Chen ◽  
...  
Keyword(s):  
Finite Strain ◽  
Seismic Velocity ◽  
Strain Analysis ◽  
Data Sets ◽  
Third Order ◽  
Data Set ◽  
Earth’S Mantle ◽  
Ultrasonic Interferometry ◽  
Linear Fit ◽  
Derivatives Of

We measured the elastic velocities of a synthetic polycrystalline β-Mg2SiO4 containing 0.73 wt.% H2O to 10 GPa and 600 K using ultrasonic interferometry combined with synchrotron X-radiation. Third-order Eulerian finite strain analysis of the high P and T data set yielded Kso = 161.5(2) GPa, Go = 101.6(1) GPa, and (∂Ks/∂P)T = 4.84(4), (∂G/∂P)T = 1.68(2) indistinguishable from Kso = 161.1(3) GPa, Go = 101.4(1) GPa, and (∂Ks/∂P)T = 4.93(4), (∂G/∂P)T = 1.73(2) from the linear fit. The hydration of the wadsleyite by 0.73 wt.% decreases Ks and G moduli by 5.3% and 8.6%, respectively, but no measurable effect was noted for (∂Ks/∂P)T and (∂G/∂P)T. The temperature derivatives of the Ks and G moduli from the finite strain analysis (∂KS/∂T)P = −0.013(2) GPaK−1, (∂G/∂T)P = −0.015(0.4) GPaK−1, and the linear fit (∂KS/∂T)P = −0.015(1) GPaK−1, (∂G/∂T)P = −0.016(1) GPaK−1 are in agreement, and both data sets indicating the |(∂G/∂T)P| to be greater than |(∂KS/∂T)P|. Calculations yield ∆Vp(α-β) = 9.88% and ∆VS(α-β) = 8.70% for the hydrous β-Mg2SiO4 and hydrous α-Mg2SiO4, implying 46–52% olivine volume content in the Earth’s mantle to satisfy the seismic velocity contrast ∆Vs = ∆VP = 4.6% at the 410 km depth.

scholarly journals Determination of the Mean Number of Bonds per snow grain And of the Dependence of the Tensile Strength of Snow on Stereological Parameters

1978 ◽  
Vol 20 (83) ◽  
pp. 329-341 ◽  
Author(s):  
H. Gubler
Keyword(s):  
Tensile Strength ◽  
Density Distribution ◽  
Structural Parameters ◽  
Theoretical Density ◽  
Thin Sections ◽  
Distribution Parameters ◽  
The Mean ◽  
Fundamental Units ◽  
Effective Distribution

AbstractA theoretical density distribution of the Dumber of bonds per grain as a function of the mean number of bonds per grain is derived from the assumption of randomness and isotropy of grain and grain-bond location and orientation. The knowledge of the theoretical density distribution allows the determination of the effective distribution parameters from section planes or thin sections. The concept of the fundamental unit to describe the strength of snow is introduced. Structural parameters developed on the basis of the fundamental units show improved correlations with the tensile strength.

scholarly journals A NEW PERSPECTIVE FOR PHYSICAL HEIGHTS IN BRAZIL

2019 ◽  
Vol 25 (1) ◽  
Author(s):  
Fabio Luiz Albarici ◽  
Ismael Foroughi ◽  
Gabriel do Nascimento Guimarães ◽  
Marcelo Santos ◽  
Jorge Trabanco
Keyword(s):  
Mass Density ◽  
Density Variation ◽  
Mean Value ◽  
South American ◽  
Normal Height ◽  
Rigorous Definition ◽  
The Mean ◽  
Orthometric Heights ◽  
New Perspective ◽  
Definition Of

Abstract The physical heights definition of heights, proposed by Helmert in 1890 is one of the commonly used heights systems in practice. In Helmert’s definition, the mean value of gravity along plumbline is computed by simplifying the topography with a Bouguer shell containing masses with mean density value. Although this approximation might be accurate enough many purposes, a more rigorous definition can be determined by considering the effects of terrain, topographic mass density variation, and masses contained in the geoid the mean gravity value along the plumbline. The purpose of this paper is to compute the corrections for the Helmert’s definition of the orthometric heights to obtain the rigorous orthometric heights in the state of São Paulo and adjacent states and to evaluate these corrections. The heights system used in Brazil (until July 2018) and some South American countries is normal-orthometric heights, therefore the corrections needs to be applied accordingly. Our numerical results show that there are significant differences between the normal-orthometric and rigorous orthometric heights, with maximum values of ~ 0.4 m, minimum of ~ -0.8 m and mean value of ~ -0.32 m. There are larger differences between normal-orthometric and normal height than the ones between normal and rigorous definition of orthometric heights.

Hypophosphatasia: Evaluation of Size and Mineral Density of Exfoliated Teeth

2016 ◽  
Vol 40 (6) ◽  
pp. 496-502 ◽  
Author(s):  
S Hayashi-Sakai ◽  
N Numa-Kinjoh ◽  
M Sakamoto ◽  
J Sakai ◽  
J Matsuyama ◽  
...  
Keyword(s):  
Density Distribution ◽  
Primary Teeth ◽  
Micro Ct ◽  
Micro Computed Tomography ◽  
Mineral Density ◽  
Normal Range ◽  
Mean Values ◽  
Present Patient ◽  
Ct Analysis ◽  
The Mean

Objective: Most cases of hypophosphatasia (HPP) exhibit early loss of primary teeth. Results of micro-computed tomography (micro-CT) analysis of teeth with HPP have not yet been reported. The purpose of the present study was to describe the size and mineral density distribution and mapping of exfoliated teeth with HPP using micro CT. Study design: Seven exfoliated teeth were obtained from a patient with HPP. Exfoliated teeth sizes were measured on micro CT images and mineral densities of the mandibular primary central incisors were determined. Results: Partial dentures were fabricated for the patient to replace the eight primary teeth which had exfoliated. Most primary teeth sizes were within the normal range. The mean values of enamel and dentin mineral densities in teeth with HPP were 1.35 and 0.88 g/cm3, respectively, in the mandibular primary central incisors. Conclusion: Mineral density distribution and mapping revealed that the values in teeth with HPP were lower than the homonymous teeth controls in all regions from the crown to apex. Furthermore, it was demonstrated that the differences between HPP and controls were larger on the crown side and the differences tended to converge on the apex side. These results suggested that the present patient showed mild hypomineralization in the primary dentition.

Training-dependent changes of red cell density and erythrocytic oxygen transport

1983 ◽  
Vol 55 (5) ◽  
pp. 1403-1407 ◽  
Author(s):  
H. Mairbaurl ◽  
E. Humpeler ◽  
G. Schwaberger ◽  
H. Pessenhofer
Keyword(s):  
Density Distribution ◽  
Cell Density ◽  
Training Status ◽  
Red Cell ◽  
Transport Parameters ◽  
Trained Subjects ◽  
O2 Transport ◽  
The Mean ◽  
Fitness Training ◽  
2,3 Dpg

Prolonged endurance training causes a decreased O2 affinity of Hb, which is due to an increase in erythrocyte 2,3-diphosphoglycerate (2,3-DPG) concentration. Possible mechanisms were studied in 20 males with varying degrees of fitness. Training status was tested by ergometry. Red cell density and O2 transport parameters were determined before this test. The O2 tension at 50% O2 saturation of Hb (P50) was higher in the more fit subjects (+1.3 mmHg) and the 2,3-DPG concentration was higher (+2.3 mumol/g Hb) in this group. The mean density was significantly lower in fit subjects (1.1002 g/ml) as compared with less fit subjects (1.1056 g/ml), indicating a lower mean age. Density distribution curves show that in the fit subjects more young erythrocytes were in blood and that the very old erythrocytes were missing. After correction for the differences in the density distribution, no differences in the P50 value and 2,3-DPG concentration between less fit and fit subjects were found. Therefore, the decreased Hb-O2 affinity after training can be explained by the presence of more young erythrocytes in the blood of trained subjects. The magnitude of this effect correlates with the training status.

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