scholarly journals Some theoretical aspects of the two-level magnetovariational method

1997 ◽  
Vol 40 (6) ◽  
Author(s):  
M. Vellante
Keyword(s):  
Magnetic Field ◽  
Transfer Function ◽  
Apparent Resistivity ◽  
Vertical Component ◽  
Horizontal Magnetic Field ◽  
Source Field ◽  
Earth Models ◽  
The Vertical Distribution ◽  
Magnetic Field Variations

We discuss some theoretical aspects of the two-level magnetovariational method for the determination of the underground electrical structure. The properties of two new apparent resistivity functions, respectively depending on gain and phase of the transfer function of the horizontal magnetic field variations between the Earth's surface and a given depth, are examined for two-layer Earth models. The effects of a finite wavelength of the source field are also investigated. It is shown that the measurement of the attenuation of the magnetic vertical component generated by an inhomogeneous source field can provide further information on the vertical distribution of the Earth's conductivity. In particular, it is shown that the measurement of the transfer function of both vertical and horizontal components between two levels can be used to estimate the average conductivity of the interlying medium.

Magnetic Field Variations in Alaska: Recording Space Weather Events on Seismic Stations in Alaska

2020 ◽  
Vol 110 (5) ◽  
pp. 2530-2540 ◽  
Author(s):  
Adam T. Ringler ◽  
Robert E. Anthony ◽  
David C. Wilson ◽  
Abram C. Claycomb ◽  
John Spritzer
Keyword(s):  
Magnetic Field ◽  
Ground Motion ◽  
Space Weather ◽  
Vertical Component ◽  
Environmental Data ◽  
Magnetic Data ◽  
Seismic Stations ◽  
Weather Events ◽  
S Period ◽  
Magnetic Field Variations

ABSTRACT Seismometers are highly sensitive instruments to not only ground motion but also many other nonseismic noise sources (e.g., temperature, pressure, and magnetic field variations). We show that the Alaska component of the Transportable Array is particularly susceptible to recording magnetic storms and other space weather events because the sensors used in this network are unshielded and magnetic flux variations are stronger at higher latitudes. We also show that vertical-component seismic records across Alaska are directly recording magnetic field variations between 40 and 800 s period as opposed to actual ground motion during geomagnetic events with sensitivities ranging from 0.004 to 0.48  (m/s2)/T. These sensitivities were found on a day where the root mean square variation in the magnetic field was 225 nT. Using a method developed by Forbriger (2007, his section 3.1), we show that improving vertical seismic resolution of an unshielded sensor by as much as 10 dB in the 100–400 s period band using magnetic data from a collocated three-component magnetometer is possible. However, due to large spatial variations in Earth’s magnetic field, this methodology becomes increasingly ineffective as the distance between the seismometer and magnetometer increases (no more than 200 km separation). A potential solution to this issue may be to incorporate relatively low-cost magnetometers as an additional environmental data stream at high-latitude seismic stations. We demonstrate that the Bartington Mag-690 sensors currently deployed at Global Seismographic Network sites are not only acceptable for performing corrections to seismic data, but are also capable of recording many magnetic field signals with similar signal-to-noise ratios, in the 20–1000 s period band, as the observatory grade magnetometers operated by the U.S. Geological Survey Geomagnetism Program. This approach would densify magnetic field observations and could also contribute to space weather monitoring by supplementing highly calibrated magnetometers with additional sensors.

Non-linear waves interactions in rotating shallow water magnetohydrodynamics

2020 ◽  
Author(s):  
Dmitry Klimachkov ◽  
Arakel Petrosyan
Keyword(s):  
Magnetic Field ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Plasma Layer ◽  
Vertical Component ◽  
Vertical Magnetic Field ◽  
Amplitude Equations ◽  
Horizontal Magnetic Field ◽  
Non Linear ◽  
Poincare Waves

<p>This study is devoted to the development of the nonlinear theory of the magneto-Poincare waves and magnetostrophic waves in rotating layers of astrophysical and space plasma in the shallow-water approximation. These waves determine the large-scale dynamics of the various astrophysical and space objects such as solar tachocline, as well as  magnetoactive atmospheres of exoplanets trapped by tides of a carrier star, neutron stars atmospheres and the flows in accretion disks of neutron stars. For this purpose we derived magnetohydrodynamic shallow water equations with a rotation and presence of an external vertical magnetic field. The system is obtained from conventional magnetohydrodynamic equations for incompressible inviscid heavy plasma layer with free surface in an external vertical magnetic field. The pressure is assumed to be hydrostatic, and the height of the plasma layer is considered to be much smaller than horizontal scales of the flow. The magnetohydrodynamic equations in the shallow-water approximation play equally important role in the space and astrophysical plasma flows like classical shallow-water equations in the fluid dynamics of a neutral fluid. The magnetohydrodynamic shallow water equations with an external vertical magnetic field are modified by supplementing them with the equation for the vertical component of the magnetic field and divergence-free condition for magnetic field contains its vertical component. Thus the velocity field remains two-dimensional while the magnetic field becomes three-dimensional. It is shown that the presence of a vertical magnetic field significantly changes the dynamics of the wave processes in astrophysical plasma compared to the neutral fluid and plasma layer in a horizontal magnetic field.  We have investigated the interaction of Magneto-Poincare waves and magnetostrophic waves in the magnetohydrodynamic shallow water flows in external vertical magnetic field and in horizontal (toroidal and poloidal) magnetic field. In the absence of the horizontal magnetic field the dynamics of plasma appears to be similar to the neutral fluid dynamics and it is shown that there are four-waves interactions in this case. Using the asymptotic multiscale method we obtained the non-linear amplitude equations for the three interacting Magneto-Poincare waves and magnetostrophic waves. The analysis of the amplitude equations shows that there are two types of instabilities for four different types of three-waves configurations. These instabilities occur in both cases: in the external vertical magnetic field and in the horizontal magnetic field. For all types of instabilities the growth rates are found. In the absence of the vertical magnetic field we obtained the non-linear amplitude equations for the four interacting waves. It is shown that the resulting system of equations has the first integrals that describe the mechanism of energy transfer among interacting waves of small amplitude. This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</p>

Extracting geoelectrical maps from vintage very-low-frequency airborne data, tipper inversion, and interpretation: A case study from northern Sweden

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. B135-B147 ◽  
Author(s):  
Sayyed Mohammad Abtahi ◽  
Laust Börsting Pedersen ◽  
Jochen Kamm ◽  
Thomas Kalscheuer
Keyword(s):  
Magnetic Field ◽  
Apparent Resistivity ◽  
Vertical Component ◽  
Low Frequency ◽  
High Resistivity ◽  
Clear Correlation ◽  
Northern Sweden ◽  
Very Low Frequency ◽  
Basaltic Composition ◽  
The Magnetic Field

In 1985, the mining company Luossavaara-Kiirunavaara Aktiebolag collected airborne very-low-frequency (VLF) data in northern Sweden. The operators stored only the vertical component and the total magnetic field, which at that time were believed to be sufficient for qualitative interpretation. Therefore, the data could not be directly used for quantitative tensor VLF processing and inversion. To avoid the costs of resurveying, we have developed a novel technique to estimate the tippers from the measured VLF data by computing anomalous and normal parts of the horizontal components of the magnetic field from two transmitters separately. Retrieval of the normal horizontal components was possible because one component of the horizontal magnetic field was used as the phase reference during the measurements. Additionally, we have determined how the approximate apparent resistivity suitable for data visualization can be computed from the components of the magnetic field assuming an average normal resistivity of the subsurface. Maps of apparent resistivity combined with topography show a clear correlation between high topography and high resistivity, whereas conductive zones are found in valleys in between. More importantly, the 3D model inverted from the calculated tippers shows excellent agreement with a map of the surface geology. Based on this comparison, some less resistive zones can be related to fluids in fractures and others can be related to mineralized contact zones. We suggest to focus further exploration on conductive zones surrounding areas with basaltic composition.

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

Two-dimensional oscillation of convection roll in a finite liquid metal layer under a horizontal magnetic field

2021 ◽  
Vol 911 ◽  
Author(s):  
Y. Tasaka ◽  
T. Yanagisawa ◽  
K. Fujita ◽  
T. Miyagoshi ◽  
A. Sakuraba
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Metal Layer ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Convection Roll

Abstract

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

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