Gravitational potential changes of a spherically symmetric earth model caused by a surface load

1998 ◽  
Vol 23 (1) ◽  
pp. 47-52 ◽  
Author(s):  
W. Sun ◽  
L.E. Sjöberg
Keyword(s):  
Gravitational Potential ◽  
Earth Model ◽  
Surface Load ◽  
Spherically Symmetric

Accretion onto a Black Hole

2014 ◽  
Author(s):  
Charles D. Bailyn
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Gas Flow ◽  
Gravitational Potential Energy ◽  
Spherically Symmetric ◽  
Potential Well ◽  
Accretion Flows ◽  
Flow Geometry

This chapter explores the ways that accretion onto a black hole produces energy and radiation. As material falls into a gravitational potential well, energy is transformed from gravitational potential energy into other forms of energy, so that total energy is conserved. Observing such accretion energy is one of the primary ways that astrophysicists pinpoint the locations of potential black holes. The spectrum and intensity of this radiation is governed by the geometry of the gas flow, the mass infall rate, and the mass of the accretor. The simplest flow geometry is that of a stationary object accreting mass equally from all directions. Such spherically symmetric accretion is referred to as Bondi-Hoyle accretion. However, accretion flows onto black holes are not thought to be spherically symmetric—the infall is much more frequently in the form of a flattened disk.

scholarly journals Reservoir Induced Deformation Analysis for Several Filling and Operational Scenarios at the Grand Ethiopian Renaissance Dam Impoundment

2020 ◽  
Vol 12 (11) ◽  
pp. 1886
Author(s):  
Austin Madson ◽  
Yongwei Sheng
Keyword(s):  
Large Scale ◽  
Elastic Response ◽  
Deformation Analysis ◽  
Earth Model ◽  
Spherically Symmetric ◽  
Operational Strategies ◽  
Surface Models ◽  
Elevation Difference ◽  
Reservoir Inflow ◽  
Elastic Responses

Addressing seasonal water uncertainties and increased power generation demand has sparked a global rise in large-scale hydropower projects. To this end, the Blue Nile impoundment behind the Grand Ethiopian Renaissance Dam (GERD) will encompass an areal extent of ~1763.3 km2 and hold ~67.37 Gt (km3) of water with maximum seasonal load changes of ~27.93 (41% of total)—~36.46 Gt (54% of total) during projected operational scenarios. Five different digital surface models (DSMs) are compared to spatially overlapping spaceborne altimeter products and hydrologic loads for the GERD are derived from the DSM with the least absolute elevation difference. The elastic responses to several filling and operational strategies for the GERD are modeled using a spherically symmetric, non-rotating, elastic, and isotropic (SNREI) Earth model. The maximum vertical and horizontal flexural responses from the full GERD impoundment are estimated to be 11.99 and 1.99 cm, regardless of the full impoundment period length. The vertical and horizontal displacements from the highest amplitude seasonal reservoir operational scenarios are 38–55% and 34–48% of the full deformation, respectively. The timing and rate of reservoir inflow and outflow affects the hydrologic load density on the Earth’s surface, and, as such, affects not only the total elastic response but also the distance that the deformation extends from the reservoir’s body. The magnitudes of the hydrologic-induced deformation are directly related to the size and timing of reservoir fluxes, and an increased knowledge of the extent and magnitude of this deformation provides meaningful information to stakeholders to better understand the effects from many different impoundment and operational strategies.

Developing an open-source 3D glacial isostatic adjustment modeling code using ASPECT

2020 ◽  
Author(s):  
Maaike Weerdesteijn ◽  
Clinton Conrad ◽  
John Naliboff ◽  
Kate Selway
Keyword(s):  
Open Source ◽  
Sea Level ◽  
Material Properties ◽  
Adaptive Mesh Refinement ◽  
Earth Model ◽  
Surface Load ◽  
Glacial Isostatic Adjustment ◽  
Ice Load ◽  
Isostatic Adjustment ◽  
Ice Cap

<p>Models of Glacial Isostatic Adjustment (GIA) processes are useful because they help us understand landscape evolution in past and current glaciated regions. Such models are sensitive to ice and ocean loading as well as to Earth material properties, such as viscosity. Many current GIA models assume radially-symmetric (layered) viscosity structures, but viscosity may vary laterally and these variations can have large effects on GIA modeling outputs. Here we present the potential of using ASPECT, an open-source finite element mantle-convection code that can handle lateral viscosity variations, for GIA modeling applications. ASPECT has the advantage of adaptive mesh refinement, making it computationally efficient, especially for problems such as GIA with large variations in strain rates. Furthermore, ASPECT is open-source, as will be the GIA extension, making it a valuable future tool for the GIA community.</p><p> </p><p>Our GIA extension is benchmarked using a similar case as in Martinec et al. (GJI, 2018), such that the performance of our GIA code can be compared to other GIA codes. In this case, a spherically symmetric, five-layer, incompressible, self-gravitating viscoelastic Earth model is used (Spada et al, GJI 2011). The surface load consists of a spherical ice cap centered at the North pole, and is applied as a Heaviside loading. The ice load remains constant with time, and thus we have not yet implemented the full sea level equation (SLE). Beyond this benchmark, we have incorporated lateral viscosity variations underneath the ice cap, to demonstrate the ability of efficiently implementing laterally-varying material properties in ASPECT.</p><p> </p><p>We show the possibilities, capabilities, and potential of ASPECT for GIA modeling. In the near future we will further develop the code with the sea level equation and an ocean basin, and will explore ASPECT’s current capability of using time-varying distributed surface loads. These functions will allow for modeling of GIA for realistic ice load scenarios imposed above potentially complex earth structures.</p>

scholarly journals Trajectory around a spherically symmetric non-rotating black hole

2011 ◽  
Vol 89 (6) ◽  
pp. 689-695 ◽  
Author(s):  
Sumanta Chakraborty ◽  
Subenoy Chakraborty
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Test Particle ◽  
Effective Potential ◽  
Particle Motion ◽  
Spherically Symmetric ◽  
Rotating Black Hole

The trajectory of a test particle or a photon around a general spherical black hole is studied, and bending of the light trajectory is investigated. A pseudo-Newtonian gravitational potential describing the gravitational field of the black hole is determined and is compared with the related effective potential for test particle motion. As an example, results are presented for a Reissner–Nordström black hole.

scholarly journals On the application of a particular form of the gravitational potential

2003 ◽  
pp. 39-42 ◽  
Author(s):  
Slobodan Ninkovic
Keyword(s):  
Gravitational Potential ◽  
Stellar System ◽  
Spherically Symmetric ◽  
Good Agreement

A formula, already existing in the literature, describing the gravitational potential of a spherically symmetric stellar system is analyzed. Some interesting cases of comparison with empirical formulae are presented. A good agreement is found.

Anomalously large near-field Rayleight waves excited by the 1992 Landers, California, earthquake

1994 ◽  
Vol 84 (3) ◽  
pp. 751-760
Author(s):  
Tatsuhiko Hara ◽  
Robert J. Geller
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Epicentral Distance ◽  
Moment Tensor ◽  
Near Field ◽  
Strike Slip ◽  
Field Amplitude ◽  
Earth Model ◽  
Symmetric Model ◽  
Spherically Symmetric

Abstract The epicenter of the Landers, California, earthquake (28 June 1992; MW = 7.3) was located near the TERRAscope network of broadband seismic stations. The direct Rayleigh wave arrivals, R1, were clipped, and the first two later arrivals, R2 and R3, were contaminated by the waves from a large aftershock, but, as reported by Kanamori et al. (1992a), the amplitudes of R4 and later great circle Rayleigh wave arrivals (fundamental mode spheroidal free oscillations) are about 10 times larger than predicted by synthetic seismograms for a spherically symmetric earth model. We show that, for the moment tensor of the Landers event (predominantly vertical strike slip), the amplitudes of synthetics at the TERRAscope stations for a laterally heterogeneous, rotating, elliptical model are about 10 times greater than those for a spherically symmetric model. Because the anomaly ratio is sensitive to both the source model and the three-dimensional (3D) earth model, we do not attempt to reproduce the exact anomaly ratios recorded by the various stations. To explain the existence of near-field amplitude anomalies in general, we use the first-order Born approximation to find the perturbation to the synthetic seismogram resulting from lateral heterogeneity, ellipticity, and the earth's rotation. In a coordinate system with the source on the z axis a point-source strike-slip earthquake on a vertical fault plane in a spherically symmetric medium excites Rayleigh waves with azimuthal order ±2 only; these waves have a near-field vertical displacement of zero at the source; the displacement increases with the square of epicentral distance for any given azimuth. Coupling as a result of asphericity allows such a source to excite Rayleigh waves with azimuthal order zero, whose near-field amplitude is independent of epicentral distance, thereby generating large near-field amplitude anomalies. We conduct numerical experiments to study the influence of various parameters on near-field amplitude anomalies.

The impact of crustal structures on multiple frequency and waveform tomography of Antarctica

2020 ◽  
Author(s):  
Maria Tsekhmistrenko ◽  
Sergei Lebedev
Keyword(s):  
Upper Mantle ◽  
Body Wave ◽  
Earth Model ◽  
Spherically Symmetric ◽  
Mantle Structure ◽  
Multiple Frequency ◽  
S Wave ◽  
Wave Tomography ◽  
Waveform Tomography ◽  
The Impact

<p>We present two preliminary tomography models of Antarctica using seismic data recorded globally since 1994. Through combined efforts, several seismic broadband arrays have been deployed in Antarctica in previous decades, enabling the generation of two types of tomography models in this study: a multiple-frequency body-wave tomography and a waveform tomography model. Altogether, more than 2000 global events are collected resolving this region in great detail.</p><p>Crustal correction is crucial in seismic tomography, as it can cause the crustal smearing or leakage of shallow heterogeneities into the deep mantle. In global multiple-frequency tomography, synthetic seismograms are calculated on a spherically symmetric earth model (e.g. PREM, IASP91) in which effects of the crust, ellipticity, and topography are neglected. At a later stage, corrections are applied to the measured traveltimes to account for the known deviations from spherically symmetric earth models.</p><p>In waveform tomography, the crust has a significant impact on the Rayleigh and Love wave speeds. We invert for the crustal structure and explicitly account for its highly non-linear effects on seismic waveforms. Here, we implement a flexible workflow where different 3D reference crustal models can be plugged in. We test this using the CRUST2.0 and CRUST1.0 models.</p><p>In this study, we quantify the effects of these crustal models on two types of inversion techniques with a focus on the mantle structure beneath Antarctica. We compare the mantle structures beneath Antarctica imaged by a multiple-frequency body-wave tomography technique (e.g., Hosseini et al, 2019) and a waveform tomography method (Lebedev et al. 2005; Lebedev and van der Hilst 2008) using CRUST1.0 and CRUST2.0.</p><p>References:<br>K. Hosseini, K. Sigloch, M. Tsekhmistrenko, A. Zaheri, T. Nissen-Meyer, H. Igel, Global mantle structure from multifrequency tomography using P, PPand P-diffracted waves, Geophysical Journal International, Volume 220, Issue 1, January 2020, Pages 96–141, https://doi.org/10.1093/gji/ggz394</p><p>S. Lebedev, R. D. Van Der Hilst, Global upper-mantle tomography with the automated multimode inversion of surface and S-wave forms. Geophysical Journal International, Volume 173, Issue 2, May 2008, Pages 505–518, https://doi.org/10.1111/j.1365-246X.2008.03721.x</p><p>A. J. Schaeffer, S. Lebedev, Global shear speed structure of the upper mantle and transition zone, Geophysical Journal International, Volume 194, Issue 1, 1 July 2013, Pages 417–449, https://doi.org/10.1093/gji/ggt095</p>

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