A Discussion on the measurement and interpretation of changes of strain in the Earth - Some problems of tilt and strain measurements

1973 ◽  
Vol 274 (1239) ◽  
pp. 203-208 ◽  
Keyword(s):  
Numerical Results ◽  
Quality Test ◽  
Strain Measurements ◽  
The Earth ◽  
Calibration Methods

The importance of calibration methods is emphasized. It is considered that the numerical results obtained for the tidal diurnal tesseral waves provide a quality test for the instruments.

A Discussion on the measurement and interpretation of changes of strain in the Earth - New Zealand Earth strain measurements

1973 ◽  
Vol 274 (1239) ◽  
pp. 311-321 ◽  
Keyword(s):  
New Zealand ◽  
High Precision ◽  
Heavy Rain ◽  
Great Care ◽  
Strain Measurements ◽  
Exposed Site ◽  
The Earth

Three invar wire lever type Earth strain meters are being operated in geophysically interesting areas in New Zealand. T he oldest has been operational since early 1970. The main object of the work has been to detect possible strain changes occurring before an earthquake. None have been detected, the most likely earthquake to have produced an effect before hand having M s = 5.3 and lying at A = 1° from the nearest strain meter. Strain steps accompanying earthquakes appear to be rather smaller than expected. A great deal of information has been accumulated on strains induced by wind and rain at the most exposed site which is but 10 m below the top of a very exposed 300 m hill. Strain changes produced by several days’ heavy rain can, at this site, be as m uch as 3 x 10-6, and this indicates th at great care m ust be taken in interpreting apparent changes in the length of a baseline m easured by high precision surveying.

Forced nutations of the Earth: Influence of inner core dynamics: 2. Numerical results and comparisons

1991 ◽  
Vol 96 (B5) ◽  
pp. 8243 ◽  
Author(s):  
P. M. Mathews ◽  
B. A. Buffett ◽  
T. A. Herring ◽  
I. I. Shapiro
Keyword(s):  
Inner Core ◽  
Numerical Results ◽  
The Earth ◽  
Core Dynamics

Developing Best Practices for Observing Global Surface Shortwave and Longwave Radiation across the Land and Ocean

2020 ◽  
Author(s):  
Robert Weller ◽  
Christian Lanconelli ◽  
Martin Wild ◽  
Joerg Trenmann
Keyword(s):  
Climate Models ◽  
Global Climate ◽  
Surface Radiation ◽  
Global Ocean ◽  
Radiation Balance ◽  
Radiative Fluxes ◽  
Temporal Sampling ◽  
The Earth ◽  
Calibration Methods

<p>In-situ shortwave or solar radiation and longwave or thermal radiation are observed at the earth’s surface on both the land and the ocean.  In addition, satellites are used to develop fields of surface radiation balance.  Planning for the Global Ocean Observing System (GOOS) and the Global Climate Observing System (GCOS) has identified surface heat flux, including the radiative fluxes, as an Essential Ocean Variable (EOV) and Essential Climate Variable (ECV), respectively.  The GOOS and GCOS requirements for surface radiative fluxes (spatial and temporal sampling, accuracies) are summarized here.  Surface radiation sites will continue to be sparse in the future, especially in the ocean; and satellite-derived products developed in concert with in-situ observing system will be important.  To make better progress towards meeting those requirements, we propose the goal of establishing dialog across the different methods of in-situ observing surface radiation and with the remote sensing community.  Objectives of the effort would include sharing knowledge and experience of how to make the observations, documentation of calibration methods, and assessment of the uncertainties to be associated with the different observing methods.  The resulting metadata and quantitative understanding of the different approaches would support improved combination of surface radiation observations across land and sea into homogeneous products at global scale.  At the same time, improved in-situ sampling would help assess and validate climate models and contribute to our understanding of the earth’s energy balance.  We review here the different observing methods now in use on land and at sea and discuss the challenges faced in making the observations.  We also propose future field inter-comparison and standardization of calibration methods to better establish the accuracy and comparability of surface radiation observations on land and at sea.</p>

scholarly journals Observations on the reciprocal influence which magnetic needles exercise over each other, when placed at a given distance within their respective spheres of action, at different positions on the earth; with tables of numerical results obtained at separate stations. Also a method of discovering where certain local influences are acting on the needle, from which may be obtained a proportional correction to be applied to magnetic observations in general

1837 ◽  
Vol 3 ◽  
pp. 282-282
Keyword(s):  
Horizontal Plane ◽  
Numerical Results ◽  
Tabular Form ◽  
Reciprocal Influence ◽  
Material Change ◽  
The Earth ◽  
Freely Suspended

The author, considering it probable that two or more magnetic needles freely suspended at a certain distance in given positions with respect to each other, would develope certain proportionate deflections determined by their position on the earth, made a set of experiments, with a few common compass needles, at Yarmouth, London, and Clifton, which so far confirmed the truth of his conjecture, as to induce him to fix on stations at a greater distance from one another, and to multiply his observations; ascertaining, from time to time, that the magnetic powers of his apparatus had undergone no material change. The results of these observations are given in a tabular form. The author conceives that comparative observations of the amount of deflection produced by one magnet on another, placed in various situations, relative to the meridian, on an horizontal plane, will afford the means of determining the peculiar local influences of the particular situation in which the experiment is made, as distinguished from the general magnetic influence; because the former will act unequally on each magnet, while the latter acts equally on all.

scholarly journals Multiple Scattering Theory for Polycrystalline Materials with Strong Grain Anisotropy: Theoretical Fundamentals and Applications

2019 ◽  
Author(s):  
Huijing He
Keyword(s):  
Grain Size ◽  
Multiple Scattering ◽  
Scattering Theory ◽  
Inner Core ◽  
Numerical Results ◽  
Polycrystalline Materials ◽  
Multiple Scattering Theory ◽  
New Model ◽  
The Earth ◽  
Dispersion And Attenuation

This work is a natural extension of the author’s previous work: “Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications” (arXiv:1706.09137 [physics.geo-ph]), which established the foundation for developing multiple scattering model for heterogeneous elastic continua with either weak or strong fluctuations in mass density and elastic stiffness. Polycrystalline material is another type of heterogeneous materials that widely exists in nature and extensively used in industry. In this work, the corresponding multiple scattering theory for polycrystalline materials with randomly oriented anisotropic crystallites is developed. To validate the theory, the theoretical results for a series of materials such as OFHC copper, 304 stainless steel, and Inconel 600 are compared to experimental measurements and the numerical results obtained using finite element simulations. Detailed analysis shows that the new theory is capable of predicting the dispersion and attenuation of polycrystals with satisfactory accuracy. The results also show the new model can give an estimate on the average grain size with a relative error equal to or less than ten percent. As applications in ultrasonic nondestructive evaluation, we calculated the dispersion and attenuation coefficient of one of the most important polycrystalline materials in aeronautics engineering: high-temperature titanium alloys. The effects of grain symmetry, grain size, and alloying elements on the dispersion and attenuation behaviors are examined. Key information is obtained which has significant implications for quantitatively evaluating the average grain size, monitoring the phase transition, and even estimating gradual change in chemical composition of titanium components in gas turbine engines. For applications in seismology, the velocities and Q-factors for both hexagonal and cubic polycrystalline iron models for the Earth’s uppermost inner core are obtained in the whole frequency range. Using the realistic material parameters of iron under the high temperature and high-pressure conditions calculated from ab initio simulations, the numerical results show that the Q-factors range from 0.001 to 0.05, which shows good agreement with that inferred from real seismic data. The new model predicts the velocity of longitudinal waves varies between ± 1% to ± 5 % relative to the Voight average velocity, while the velocity of transverse waves varies from ± 10% to ± 20%, which gives promising explanation to the abnormally slow transverse velocity observed in practical measurements. The numerical results support the conjecture that the Earth’s uppermost inner core is a solid polycrystalline medium. The comprehensive numerical examples show the new model is capable of capturing the most important scattering features of both ultrasonic and seismic waves with satisfactory accuracy. This work provides a universal, quantitative model for characterization of a large variety of polycrystalline materials. It also can be extended to incorporate more complicated microstructures, including ellipsoidal grains with or without textures, and even multi-phase polycrystalline materials. The new model demonstrates great potential of applications in ultrasonic nondestructive evaluation and inspection of aerospace and aeronautic structures. It also provides a theoretical framework for quantitative seismic data explanation and inversion for the material composition and structural formations of the Earth’s inner core.

Propagation of Torsional Surface Waves in Heterogeneous Half-Space with Irregular Free Surface

2020 ◽  
Vol 9 (2) ◽  
pp. 128-131
Author(s):  
Mahmoud M. Selim
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Half Space ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Surface Irregularity ◽  
Closed Form Solutions ◽  
The Earth ◽  
Waves Propagation ◽  
Torsional Surface Waves

This study is an attempt to show the impacts of free surface irregularity on the torsional surface waves propagating in heterogeneous, elastic half-space. The surface irregularity is taken in the parabolic form at the surface of the half-space. The governing equation and corresponding closed form solutions are derived. Then, the phase velocity of torsional surface waves is obtained analytically and the influences of surface irregularity are studied in detail. Numerical results analyzing the torsional surface waves propagation are discussed and presented graphically. The analytical solutions and numerical results reveal that, the surface irregularity and heterogeneity have notable effects on the torsional surface waves propagation in the elastic half-space. Since the Earth crust is heterogeneous medium with irregular surface, thus it is important to consider the effects of heterogeneity and surface irregularity on velocity of torsional surface waves propagating in the Earth medium.

scholarly journals The boundary integral method for the D.C. geoelectric problem in the 3-layered earth with a prismoid inhomogeneity in the second layer

2012 ◽  
Vol 42 (4) ◽  
pp. 313-343 ◽  
Author(s):  
Milan Hvoždara
Keyword(s):  
Integral Method ◽  
Apparent Resistivity ◽  
Boundary Integral Equations ◽  
Sedimentary Basins ◽  
Boundary Integral ◽  
Numerical Results ◽  
Boundary Integral Method ◽  
Layered Earth ◽  
The Earth ◽  
Schlumberger Array

Abstract The paper presents algorithm and numerical results for the boundary integral equations (BIE) method of the forward D.C. geoelectric problem for the three-layered earth which contains the prismoidal body with sloped faces in the second layer. This situation occurs in the sedimentary basins. Although the numerical calculations are more complicated in comparison with faces orthogonal to the x, y, z axes, the generalization to the sloped faces enables treatment of the anomalous fields for the bodies of more general shapes as rectangular prisms. The graphs with numerical results present isoline maps of the perturbing potential as well as the resistivity profiles when the source field is due to the pair of D.C. electrodes at the surface of the earth. Also presented apparent resistivity curves for the Schlumberger array AMNB sounding.

scholarly journals Comparison of accelerometer data calibration methods used in thermospheric neutral density estimation

2018 ◽  
Vol 36 (3) ◽  
pp. 761-779 ◽  
Author(s):  
Kristin Vielberg ◽  
Ehsan Forootan ◽  
Christina Lück ◽  
Anno Löcher ◽  
Jürgen Kusche ◽  
...  
Keyword(s):  
Solar Activity ◽  
Radiation Pressure ◽  
Precise Orbit Determination ◽  
High Solar Activity ◽  
Neutral Density ◽  
Accelerometer Data ◽  
The Earth ◽  
Calibration Methods ◽  
Leo Satellites ◽  
Gravity Recovery

Abstract. Ultra-sensitive space-borne accelerometers on board of low Earth orbit (LEO) satellites are used to measure non-gravitational forces acting on the surface of these satellites. These forces consist of the Earth radiation pressure, the solar radiation pressure and the atmospheric drag, where the first two are caused by the radiation emitted from the Earth and the Sun, respectively, and the latter is related to the thermospheric density. On-board accelerometer measurements contain systematic errors, which need to be mitigated by applying a calibration before their use in gravity recovery or thermospheric neutral density estimations. Therefore, we improve, apply and compare three calibration procedures: (1) a multi-step numerical estimation approach, which is based on the numerical differentiation of the kinematic orbits of LEO satellites; (2) a calibration of accelerometer observations within the dynamic precise orbit determination procedure and (3) a comparison of observed to modeled forces acting on the surface of LEO satellites. Here, accelerometer measurements obtained by the Gravity Recovery And Climate Experiment (GRACE) are used. Time series of bias and scale factor derived from the three calibration procedures are found to be different in timescales of a few days to months. Results are more similar (statistically significant) when considering longer timescales, from which the results of approach (1) and (2) show better agreement to those of approach (3) during medium and high solar activity. Calibrated accelerometer observations are then applied to estimate thermospheric neutral densities. Differences between accelerometer-based density estimations and those from empirical neutral density models, e.g., NRLMSISE-00, are observed to be significant during quiet periods, on average 22 % of the simulated densities (during low solar activity), and up to 28 % during high solar activity. Therefore, daily corrections are estimated for neutral densities derived from NRLMSISE-00. Our results indicate that these corrections improve model-based density simulations in order to provide density estimates at locations outside the vicinity of the GRACE satellites, in particular during the period of high solar/magnetic activity, e.g., during the St. Patrick's Day storm on 17 March 2015.

The influence of the re-radiation of the earth on the motion of the artificial satellites

1966 ◽  
Vol 25 ◽  
pp. 345-354 ◽  
Author(s):  
L. Sehnal
Keyword(s):  
Orbital Period ◽  
Numerical Results ◽  
Disturbing Function ◽  
Artificial Satellites ◽  
Orbital Elements ◽  
Lagrangian Equations ◽  
The Earth

The components of the pressure of the radiation, reflected from the Earth, are derived. The two cases, when the satellite does or does not enter the Earth's shadow are investigated. The components of the disturbing function are derived and can be used in computing the perturbations of the orbital elements by the Lagrangian equations. The results are used for the computation of the changes of the orbital period and some numerical results are given.

A Discussion on the measurement and interpretation of changes of strain in the Earth - The use of ground strain measurements in civil engineering

1973 ◽  
Vol 274 (1239) ◽  
pp. 421-428 ◽  
Keyword(s):  
Civil Engineering ◽  
Field Conditions ◽  
Strain Measurements ◽  
The Earth ◽  
Safety And Stability ◽  
Natural Strains

Strains of the ground are of increasing importance in civil engineering for as projects get larger the strains they induce often exceed the natural strains. For the engineer to ensure the safety and stability of a structure and its surroundings he must be able to predict and, if need be, control the strains. Our approach is to measure the deformations in specific cases and to use the information to gain a better understanding of ground behaviour, to determine parameters of the ground to use in prediction and to check the safety and design of the project. It demands simple and sensitive instruments that can be used reliably under rigorous field conditions. Examples of recent studies are given.

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