Tensor Invariants for Gravitational Curvatures

2021 ◽  
Author(s):  
Xiao-Le Deng ◽  
Wen-Bin Shen ◽  
Meng Yang ◽  
Jiangjun Ran
Keyword(s):  
Gravity Field ◽  
Gravity Gradient ◽  
Additional Information ◽  
Tensor Invariants ◽  
Global Gravity ◽  
Potential Applications ◽  
Gravitational Curvatures ◽  
Definition Of ◽  
Elemental Mass ◽  
Derivatives Of

<p>The tensor invariants (or invariants of tensors) for gravity gradient tensors (GGT, the second-order derivatives of the gravitational potential (GP)) have the advantage of not changing with the rotation of the corresponding coordinate system, which were widely applied in the study of gravity field (e.g., recovery of global gravity field, geophysical exploration, and gravity matching for navigation and positioning). With the advent of gravitational curvatures (GC, the third-order derivatives of the GP), the new definition of tensor invariants for gravitational curvatures can be proposed. In this contribution, the general expressions for the principal and main invariants of gravitational curvatures (PIGC and MIGC denoted as I and J systems) are presented. Taking the tesseroid, rectangular prism, sphere, and spherical shell as examples, the detailed expressions for the PIGC and MIGC are derived for these elemental mass bodies. Simulated numerical experiments based on these new expressions are performed compared to other gravity field parameters (e.g., GP, gravity vector (GV), GGT, GC, and tensor invariants for the GGT). Numerical results show that the PIGC and MIGC can provide additional information for the GC. Furthermore, the potential applications for the PIGC and MIGC are discussed both in spatial and spectral domains for the gravity field.</p>

Antarctica crustal model by means of the Bayesian gravity inversion

2020 ◽  
Author(s):  
Martina Capponi ◽  
Daniele Sampietro
Keyword(s):  
Gravity Field ◽  
Gravity Data ◽  
Mass Density ◽  
Geophysical Methods ◽  
Gravity Inversion ◽  
Inversion Algorithm ◽  
Global Gravity ◽  
Uniqueness Of The Solution ◽  
Definition Of ◽  
Regional Gravity

<p>The Antarctica crustal structure is still not completely unveiled due to the presence of thick ice shields all over the continent which prevent direct in situ measurements. In the last decades, various geophysical methods have been used to retrieve information of the upper crust and sediments distribution however there are still regions, especially in central Antarctica, where our knowledge is limited. For these kind of situations, in which the indirect investigation of the subsurface is the only valuable solution, the gravity data are an important source of information. After the recent dedicated satellite missions, like GRACE and GOCE, it has been possible to obtain global gravity field data with spatial resolution and accuracy almost comparable to those of local/regional gravity acquisitions, paving the way to new geophysical applications. The new challenge today is the capability to invert such gravity data on large areas with the aim to obtain a 3D density model of the Earth crust. This is in fact a problem characterized by intrinsic instability and non-uniqueness of the solution that to be solved requires the definition of strong constrains and numerical regularization.</p><p>In this work the authors propose the application of a Bayesian inversion algorithm to the Antarctica continent to infer a model of mass density distribution. The first operation is the definition of an initial geological model in terms of geological horizons and density. These two variables are considered as random variables and, within the iterative procedure based on Markov Chain Monte Carlo methods, they are adjusted in such a way to fit the gravity field on the surface. The test performed show that the method is capable of retrieving an estimated model consistent with the prior information and fitting the gravity observations according to their accuracy.</p>

scholarly journals DETERMINISTICALLY-MODIFIED INTEGRAL ESTIMATORS OF GRAVITATIONAL TENSOR

2015 ◽  
Vol 21 (1) ◽  
pp. 189-212 ◽  
Author(s):  
Mohsen Romeshkani ◽  
Mehdi Eshagh
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Physical Geodesy ◽  
Gravity Models ◽  
Satellite Mission ◽  
Satellite Gravity ◽  
Global Gravity ◽  
Gravimetric Data ◽  
Derivatives Of ◽  
Terrestrial Data

The Earth's global gravity field modelling is an important subject in Physical Geodesy. For this purpose different satellite gravimetry missions have been designed and launched. Satellite gravity gradiometry (SGG) is a technique to measure the second-order derivatives of the gravity field. The gravity field and steady state ocean circulation explorer (GOCE) is the first satellite mission which uses this technique and is dedicated to recover Earth's gravity models (EGMs) up to medium wavelengths. The existing terrestrial gravimetric data and EGM scan be used for validation of the GOCE data prior to their use. In this research, the tensor of gravitation in the local north-oriented frame is generated using deterministically-modified integral estimators involving terrestrial data and EGMs. The paper presents that the SGG data is assessable with an accuracy of 1-2 mE in Fennoscandia using a modified integral estimatorby the Molodensky method. A degree of modification of 100 and an integration cap size of for integrating terrestrial data are proper parameters for the estimator.

scholarly journals Identification of Ransiki fault segment in South Manokwari Regency, West Papua Province, Indonesia based on analysis of a high-resolution of global gravity field: Implications on the Earthquake Source Parameters

2021 ◽  
Vol 873 (1) ◽  
pp. 012048
Author(s):  
Richard Lewerissa ◽  
Nur Alzair ◽  
Laura Lapono
Keyword(s):  
Gravity Field ◽  
Source Parameters ◽  
Bouguer Anomaly ◽  
Earthquake Source ◽  
Gravity Gradient ◽  
Gravity Inversion ◽  
Fault Segment ◽  
Global Gravity ◽  
Earthquake Source Parameters ◽  
West Papua

Abstract The province of West Papua in Indonesia is an area crossed by three major faults, including Sorong, Koor, and Ransiki, leading to the collision of Australia, the Pacific, and Eurasia. In the past, there have been strong and damaging earthquakes on these faults, manly Ransiki fault in the South Manokwari regency. Identification of the Ransiki fault segment was conducted by geological subsurface modeling using the earth gravity field of the Global Gravity Map (GGM) based on satellite measurements implicates for earthquake source parameters. The GGM is seen as a solution for the unavailability of direct measurements in the region. The gravity field analysis begins with data reduction using SRTM2gravity as modern terrain correction to obtain a complete Bouguer anomaly. Furthermore, the gravity gradient approach through vertical and horizontal gradients, analytical signal, and the tilt angle are applied to emphasize a contact or fault structures that are not visible using a 2D fast Fourier transform. Overall, the gravity gradient analysis obtained results that were compatible with the alignment of the Ransiki fault segment which direction of the northwest to south. The gravity inversion produces a geological subsurface model that clearly shows the Ransiki fault segment, associated with a low rock density distribution, thought to the Befoor formation and quaternary sediments, located between high-density rocks correlated to Arfak volcanic rocks as a basement.

An Analysis of the Demand for Reporting on Internal Control

2000 ◽  
Vol 14 (3) ◽  
pp. 325-341 ◽  
Author(s):  
Heather M. Hermanson
Keyword(s):  
Decision Making ◽  
Financial Reporting ◽  
Internal Control ◽  
Operational Definition ◽  
Financial Statement ◽  
Individual Investors ◽  
Internal Auditors ◽  
Additional Information ◽  
User Groups ◽  
Definition Of

The purpose of this study is to analyze the demand for reporting on internal control. Nine financial statement user groups were identified and surveyed to determine whether they agree that: (1) management reports on internal control (MRIC) are useful, (2) MRICs influence decisions, and (3) financial reporting is improved by adding MRICs. In addition, the paper examined whether responses varied based on: (1) the definition of internal control used (manipulated as broad, operational definition vs. narrow, financial-reporting definition) and (2) user group. The results indicate that financial statement users agree that internal controls are important. Respondents agreed that voluntary MRICs improved controls and provided additional information for decision making. Respondents also agreed that mandatory MRICs improved controls, but did not agree about their value for decision making. Using a broad definition of controls, respondents strongly agreed that MRICs improved controls and provided a better indicator of a company's long-term viability. Executive respondents were less likely to agree about the value of MRICs than individual investors and internal auditors.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

scholarly journals Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation

1999 ◽  
Vol 123 (4) ◽  
pp. 535-541 ◽  
Author(s):  
L. Saggere ◽  
S. Kota
Keyword(s):  
Compliant Mechanisms ◽  
Shape Change ◽  
Synthesis Method ◽  
Elastic Equilibrium ◽  
Body Motion ◽  
Motion Generation ◽  
Generation Task ◽  
Potential Applications ◽  
Flexible Segment ◽  
Definition Of

Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

Combining the deep Earth and lithospheric gravity field to study the density structure of the upper mantle

2021 ◽  
Author(s):  
Bart Root ◽  
Javier Fullea ◽  
Jörg Ebbing ◽  
Zdenek Martinec
Keyword(s):  
Gravity Field ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Field Data ◽  
Wavelength Region ◽  
Density Structure ◽  
Long Wavelength ◽  
Global Gravity ◽  
Deep Earth

<p>Global gravity field data obtained by dedicated satellite missions is used to study the density distribution of the lithosphere. Different multi-data joint inversions are using this dataset together with other geophysical data to determine the physical characteristics of the lithosphere. The gravitational signal from the deep Earth is usually removed by high-pass filtering of the model and data, or by appropriately selecting insensitive gravity components in the inversion. However, this will remove any long-wavelength signal inherent to lithosphere. A clear choice on the best-suited approach to remove the sub-lithospheric gravity signal is missing. </p><p>Another alternative is to forward model the gravitational signal of these deep situated mass anomalies and subtract it from the observed data, before the inversion. Global tomography provides shear-wave velocity distribution of the mantle, which can be transformed into density anomalies. There are difficulties in constructing a density model from this data. Tomography relies on regularisation which smoothens the image of the mantle anomalies. Also, the shear-wave anomalies need to be converted to density anomalies, with uncertain conversion factors related to temperature and composition. Understanding the sensitivity of these effects could help determining the interaction of the deep Earth and the lithosphere.</p><p>In our study the density anomalies of the mantle, as well as the effect of CMB undulations, are forward modelled into their gravitational potential field, such that they can be subtracted from gravity observations. The reduction in magnitude of the density anomalies due to the regularisation of the global tomography models is taken into account. The long-wavelength region of the density estimates is less affected by the regularisation and can be used to fix the mean conversion factor to transform shear wave velocity to density. We present different modelling approaches to add the remaining dynamic topography effect in lithosphere models. This results in new solutions of the density structure of the lithosphere that both explain seismic observations and gravimetric measurements. The introduction of these dynamic forces is a step forward in understanding how to properly use global gravity field data in joint inversions of lithosphere models.</p>

Sign in / Sign up

Export Citation Format

Share Document