Magnetotelluric responses of three‐dimensional bodies in layered earths

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1517-1533 ◽  
Author(s):  
Philip E. Wannamaker ◽  
Gerald W. Hohmann ◽  
Stanley H. Ward
Keyword(s):  
Electric Field ◽  
Apparent Resistivity ◽  
Three Dimensional ◽  
Wave Impedance ◽  
Transverse Magnetic ◽  
Small Scale ◽  
Low Frequencies ◽  
High Frequencies ◽  
Large Structures ◽  
The Earth

The electromagnetic fields scattered by a three‐dimensional (3-D) inhomogeneity in the earth are affected strongly by boundary charges. Boundary charges cause normalized electric field magnitudes, and thus tensor magnetotelluric (MT) apparent resistivities, to remain anomalous as frequency approaches zero. However, these E‐field distortions below certain frequencies are essentially in‐phase with the incident electric field. Moreover, normalized secondary magnetic field amplitudes over a body ultimately decline in proportion to the plane‐wave impedance of the layered host. It follows that tipper element magnitudes and all MT function phases become minimally affected at low frequencies by an inhomogeneity. Resistivity structure in nature is a collection of inhomogeneities of various scales, and the small structures in this collection can have MT responses as strong locally as those of the large structures. Hence, any telluric distortion in overlying small‐scale extraneous structure can be superimposed to arbitrarily low frequencies upon the apparent resistivities of buried targets. On the other hand, the MT responses of small and large bodies have frequency dependencies that are separated approximately as the square of the geometric scale factor distinguishing the different bodies. Therefore, tipper element magnitudes as well as the phases of all MT functions due to small‐scale extraneous structure will be limited to high frequencies, so that one may “see through” such structure with these functions to target responses occurring at lower frequencies. About a 3-D conductive body near the surface, interpretation using 1-D or 2-D TE modeling routines of the apparent resistivity and impedance phase identified as transverse electric (TE) can imply false low resistivities at depth. This is because these routines do not account for the effects of boundary charges. Furthermore, 3-D bodies in typical layered hosts, with layer resistivities that increase with depth in the upper several kilometers, are even less amenable to 2-D TE interpretation than are similar 3-D bodies in uniform half‐spaces. However, centrally located profiles across geometrically regular, elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic (TM) algorithm, which implicitly includes boundary charges in its formulation. In defining apparent resistivity and impedance phase for TM modeling of such bodies, we recommend a fixed coordinate system derived using tipper‐strike, calculated at the frequency for which tipper magnitude due to the inhomogeneity of interest is large relative to that due to any nearby extraneous structure.

Removal of static shift in two dimensions by regularized inversion

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2102-2106 ◽  
Author(s):  
Catherine deGroot‐Hedlin
Keyword(s):  
Electric Fields ◽  
Apparent Resistivity ◽  
Skin Depth ◽  
Two Dimensions ◽  
Small Scale ◽  
Low Frequencies ◽  
Near Surface ◽  
Regularized Inversion ◽  
Conductivity Anomalies ◽  
Local Distortions

A common problem in magnetotelluric (MT) sounding is the presence of static shifts in the data, i.e., a vertical shifting of the log‐apparent‐resistivity versus period curves relative to regional values (Jones, 1988; Jiracek, 1990; Berdichevsky et al., 1989). These static shifts are due to the presence of small‐scale, shallow conductivity anomalies near the measurement site. Electric charge builds up on near‐surface anomalies that are small in comparison to the skin depth of the electromagnetic (EM) fields. The charge buildup produces a perturbation of the measured electric fields from their regional values that persists to arbitrarily low frequencies. Incorrect removal of these local distortions leads to incorrect interpretation of the deeper targets of investigation.

scholarly journals Beam Patterns of the Five-hundred-metre Aperture Spherical Telescope

2013 ◽  
Vol 30 ◽  
Author(s):  
B. Dong ◽  
J. L. Han
Keyword(s):  
Structural Parameters ◽  
Power Level ◽  
Three Dimensional ◽  
High Gain ◽  
Main Beam ◽  
Frequency Range ◽  
Ray Method ◽  
Low Frequencies ◽  
High Frequencies ◽  
Beam Patterns

AbstractThe Five-hundred-metre Aperture Spherical Telescope (FAST) is being constructed in China. With an illuminated aperture of 300-m diameter, it will be the most sensitive single-dish radio telescope in the world. We calculate the beam patterns, gains, and efficiencies of the FAST at 200 MHz, 1.4 GHz, and 3 GHz. A program is developed to calculate the structural parameters and construct the FAST models. The three-dimensional beam patterns are calculated by utilising the shooting and bouncing ray method. We show that, with a coaxial horn feed, the FAST has a beam pattern of high gain and reasonably low first sidelobe over the frequency range of 200 MHz to 3 GHz. Compared with an ideal 300-m parabolic reflector, the un-illuminated spherical part of the FAST would make the power level near both sides of the main beam rise by at least 20 dB and the efficiency tends to decrease at high frequencies. At a zenith angle of 0°, its efficiencies at 200 MHz, 1.4 GHz, and 3 GHz are 71.72%, 66.94%, and 57.55%, respectively. We conclude that the FAST is an excellent telescope at low frequencies. At high frequencies, the triangular spherical panels and the gaps between panels are important factors that affect the performance of the FAST.

Transient electromagnetic inversion: A remedy for magnetotelluric static shifts

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1242-1250 ◽  
Author(s):  
Louise Pellerin ◽  
Gerald W. Hohmann
Keyword(s):  
Electric Field ◽  
Apparent Resistivity ◽  
Parametric Representation ◽  
Impedance Tensor ◽  
Static Shift ◽  
Electrode Arrays ◽  
Data Set ◽  
Low Frequencies ◽  
Transient Electromagnetic ◽  
Correction Scheme

Surficial bodies can severely distort magnetotelluric (MT) apparent resistivity data to arbitrarily low frequencies. This distortion, known as the MT static shift, is due to an electric field generated from boundary charges on surficial inhomogeneities, and persists throughout the entire MT recording range. Static shifts are manifested in the data as vertical, parallel shifts of log‐log apparent resistivity sounding curves, the impedance phase being unaffected. Using a three‐dimensional (3-D) numerical modeling algorithm, simulated MT data with finite length electrode arrays are generated. Significant static shifts are produced in this simulation; however, for some geometries they are impossible to identify. Techniques such as spatial averaging and electromagnetic array profiling (EMAP) are effective in removing static shifts, but they are expensive, especially for correcting a previously collected MT data set. Parametric representation and use of a single invariant quantity, such as the impedance tensor determinant, are only useful in limited circumstances and can lead the MT interpreter astray. Transient electromagnetic (TEM) sounding data are relatively inexpensive to collect, do not involve electric field measurements, and are only affected at very early times by surficial bodies. Hence, using TEM data acquired at the same location provides a natural remedy for the MT static shift. We describe a correction scheme to shift distorted MT curves to their correct values based on 1-D inversion of a TEM sounding taken at the same location as the MT site. From this estimated 1-D resistivity structure an MT sounding is computed at frequencies on the order of 1 Hz and higher. The observed MT curves are then shifted to the position of the computed curve, thus eliminating static shifts. This scheme is accurate when the overlap region between the MT and TEM sounding is 1-D, but helpful information can be gleaned even in multidimensional environments. Other advantages of this scheme are that it is straightforward to ascertain if the correction scheme is being accurately applied and it is easy to implement on a personal computer.

Hydrodynamic Flows in Electrowetting

2008 ◽  
Author(s):  
Sung Hee Ko ◽  
Horim Lee ◽  
Kwan Hyoung Kang
Keyword(s):  
Electric Field ◽  
High Speed ◽  
Strong Electric Field ◽  
Electrical Signal ◽  
Droplet Surface ◽  
Electrohydrodynamic Flow ◽  
Low Frequencies ◽  
High Frequencies ◽  
Steady Streaming ◽  
Flow Generation

In this work, we found experimentally that there exist fairly strong fluid flows in AC electrowetting, which can be utilized as a means to mix the fluids in EWOD-based micro-devices. We visualized the internal flow. There may exist two distinct flow-generation mechanisms; one is the droplet oscillation, and the other is the electrohydrodynamic flow. The flow pattern is significantly dependent on the applied AC frequency. At low frequencies (represented here by 1 kHz), the center of the vortices is located somewhat randomly and the flow directs upward near the symmetric axis. At high frequencies (represented by 128 kHz), however, a pair of vortices having quite a regular structure is clearly visible and the flow directs downward near the symmetric axis. The flow patterns are strongly dependent on the position of the point electrode. The droplet surface undergoes a periodic oscillation (visualized by a high-speed camera) with a frequency exactly twice the frequency of applied electrical signal. The oscillating interface can generate a steady streaming. However the numerical results show that there exists no electric field at low AC frequencies. On the contrary, there exists quite a strong electric field inside the droplet at high frequencies. It means the electrohydrodynamic flow cannot be generated at the low frequency region, and the droplet oscillation might cause the flow generation at low frequencies. We also demonstrated the flow can be beneficially utilized as a mixing method.

Numerical study of deformations induced by ac electric field in insulating flexoelectric nematic layers

2011 ◽  
Vol 19 (1) ◽  
Author(s):  
G. Derfel ◽  
M. Buczkowska
Keyword(s):  
Liquid Crystals ◽  
Electric Field ◽  
Time Dependence ◽  
Critical Frequency ◽  
Numerical Study ◽  
Dielectric Anisotropy ◽  
Low Frequencies ◽  
High Frequencies ◽  
Ac Electric Field ◽  
Time Period

AbstractThe influence of the frequency f of applied ac electric field on the time dependence of electric field induced deformations of homeotropic nematic layers is studied numerically. Three kinds of nematic liquid crystals were considered: non-flexoelectric nematic with negative dielectric anisotropy, Δɛ < 0dielectrically compensated nematic (Δɛ = 0) possessing flexoelectric properties determined by the positive sum of flexoelectric coefficients e = e11 + e33 > 0nematic characterised by both Δɛ < 0 and e > 0.It was found that at sufficiently low frequencies, the deformations varied with time. The deformations of purely dielectric nature had the period 1/(2f). When the frequency was increased, a stationary director distribution was achieved, determined by the rms value of the ac voltage. The time period of purely flexoelectric distortions was equal to 1/f. There was a well defined cut-off frequency above which these deformations vanished. In the case of dielectrically anisotropic and flexoelectric nematic, the flexoelectric contribution vanished above a critical frequency and the deformation of dielectric nature stabilized at high frequencies.

Frequency Dependence of Electrorheological (ER) Effect and Its Relationship to Dielectric and Electrical Properties in Ba1-xSrxTiO3 Suspensions

2005 ◽  
Vol 19 (07n09) ◽  
pp. 1443-1448 ◽  
Author(s):  
Yasuhito Misono ◽  
Shoichi Furukawa ◽  
Hitomi Yosinaga ◽  
Junko Sugiyama ◽  
Keishi Negita
Keyword(s):  
Electrical Conductivity ◽  
Electrical Properties ◽  
Dielectric Permittivity ◽  
Field Strength ◽  
Electric Field ◽  
Frequency Dependence ◽  
Applied Electric Field ◽  
Electrode Polarization ◽  
Low Frequencies ◽  
High Frequencies

Varying the electric field strength (E), the ER effect, the dielectric permittivity, and the electrical conductivity were simultaneously measured on the Ba 0.75 Sr 0.25 TiO 3 suspension. It was found that at high E the ER effect increased with the frequency (f), while at low E it once decreased and then increased with increase in f. At high E, the dielectric permittivity at low frequencies was much larger than that at high frequencies, indicating that an electrode polarization was formed as a result of accumulations of ions, which were dissociated from the liquid at high E, near the electrodes. This electrode polarization was further confirmed in the time dependence of the electrical conductivity after the electric field was switched on. From these results it is suggested that the E-dependent frequency dependence of the ER effect may be due to the electrode polarization, which causes larger shielding of the applied electric field at lower f while smaller shielding at higher f.

Dynamics of uncharged colloidal inclusions in polyelectrolyte hydrogels

2011 ◽  
Vol 669 ◽  
pp. 298-327 ◽  
Author(s):  
ALIASGHAR MOHAMMADI ◽  
REGHAN J. HILL
Keyword(s):  
Ionic Strength ◽  
Electric Field ◽  
Reference Frame ◽  
Particle Surface ◽  
Fixed Charge ◽  
Particle Displacement ◽  
Restoring Force ◽  
Low Frequencies ◽  
High Frequencies ◽  
Dynamic Mobility

We calculate the dynamics of an uncharged colloidal sphere embedded in a quenched polyelectrolyte hydrogel to (i) an oscillatory (optical and magnetic) force, as adopted in classical micro-rheology, and (ii) an oscillatory electric field, as adopted in electrical micro-rheology and electro-acoustics. The hydrogel is modelled as a linearly elastic porous medium with the charge fixed to the skeleton and saturated with a Newtonian electrolyte; and the colloidal inclusion is modelled as a rigid, impenetrable sphere. The dynamic micro-rheological susceptibility, defined as the ratio of the particle displacement to the strength of an applied oscillatory force, depends on the fixed-charge density and ionic strength and is bounded by the limits for incompressible and uncharged, compressible skeletons. Nevertheless, the influences of fixed charge and ionic strength vanish at frequencies above the reciprocal draining time, where the polymer and the electrolyte hydrodynamically couple as a single incompressible phase. Generally, the effects of fixed charge and ionic strength are small compared with, for example, the influences of polymer slip at the particle surface. The electrical susceptibility, defined as the ratio of the particle displacement to the strength of an applied oscillatory electric field, is directly influenced by charge at all frequencies, irrespective of skeleton compressibility. At low frequencies, polymer charge modulates the driving (electro-osmotic) and restoring (electrostatically enhanced elastic) forces, whereas charge has no influence on the restoring force at high frequencies where dilational strain is suppressed by hydrodynamic coupling with the electrolyte. In striking contrast to charged inclusions in uncharged hydrogels (Wang & Hill, J. Fluid Mech., vol. 640, 2009, pp. 357–400), the electrical susceptibility at high frequencies is independent of electrolyte concentration. Rather, the dynamics primarily reflect the elastic modulus, charge and hydrodynamic permeability, with a relatively weak dependence on particle size. Interestingly, the dynamic mobility in the zero-momentum reference frame, which is central to the electro-acoustic response, is qualitatively different from the dynamic mobility in the skeleton-fixed reference frame. Finally, we propose a phenomenological harmonic-oscillator model to address – in an approximate manner – the dynamics of charged particles in charged hydrogels. This shows that particle dynamics at low frequencies are dominated by particle charge, whereas high-frequency dynamics are dominated by hydrogel charge.

The use of quad–quad resistivity in helicopter electromagnetic mapping

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 459-467 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Apparent Resistivity ◽  
Single Frequency ◽  
Magnetic Polarization ◽  
Phase Component ◽  
Misleading Information ◽  
High Frequencies ◽  
Quadrature Component ◽  
The Earth ◽  
The Impact ◽  
Dependent Choice

The apparent resistivity from a helicopter-borne frequency-domain electromagnetic (EM) system is typically obtained from the in-phase and quadrature responses arising from the flow of conduction currents in the earth. The most commonly used resistivity algorithms, derived from half-space models and using single-frequency data, do not account for magnetic polarization and consequently do not yield a reliable value for apparent resistivity in highly magnetic areas. This is because magnetic polarization modifies the EM response, causing the computed resistivity to be erroneously high. The impact of magnetic permeability on the EM response is much greater for the in-phase component than for the quadrature component. If magnetic polarization is to be ignored, the calculation of the apparent resistivity using the quadrature component at two frequencies (the quad–quad algorithm) is less subject to error from magnetic polarization than if the in-phase and quadrature responses at a single frequency are used (the in-phase–quad algorithm). The quad–quad algorithm, however, can display undesirable behavior for large induction numbers, i.e., when conductivities and frequencies are large. Determining which algorithm is optimum is a data-dependent choice, which, of course, is area dependent. We have studied the behavior of the quad–quad (apparent) resistivity and its comparison to in-phase–quad resistivity to determine the conditions under which the use of quad–quad resistivity is appropriate. For a two-layer earth, the behavior of the quad–quad resistivity depends mainly upon the ratio of the lower frequency fL to the upper-layer resistivity ρ1. If this ratio is low, the quad–quad resistivity will behave well. In areas yielding a high value of the ratio fL/ρ1, the quad–quad resistivity may lie outside of the range of the true resistivities of the earth and therefore provide misleading information. Our studies therefore suggest that the quad–quad resistivity algorithm should be avoided in areas where the ratio is large, i.e., when using high frequencies in conductive areas. The term large is relative. For a two-layer case, for example, the use of quad–quad resistivity is only recommended for magnetic areas where fL/ρ1 < 500 Hz/ohm-m, when conductive cover exists, and where fL/ρ1 < 50 Hz/ohm-m when a conductive basement underlies resistive cover. In spite of these limitations, quad–quad resistivity is often preferable to in-phase–quad resistivity in highly magnetic areas.

scholarly journals Artificial Electric Field Algorithm with Greedy State Transition Strategy for Spherical Multiple Traveling Salesmen Problem

2022 ◽  
Vol 15 (1) ◽  
Author(s):  
Jian Bi ◽  
Guo Zhou ◽  
Yongquan Zhou ◽  
Qifang Luo ◽  
Wu Deng
Keyword(s):  
Electric Field ◽  
Traveling Salesman Problem ◽  
State Transition ◽  
Three Dimensional ◽  
Traveling Salesman ◽  
Dimensional Sphere ◽  
Transition Strategy ◽  
The Earth ◽  
Multiple Traveling Salesman Problem ◽  
The Traveling Salesman Problem

AbstractThe multiple traveling salesman problem (MTSP) is an extension of the traveling salesman problem (TSP). It is found that the MTSP problem on a three-dimensional sphere has more research value. In a spherical space, each city is located on the surface of the Earth. To solve this problem, an integer-serialized coding and decoding scheme was adopted, and artificial electric field algorithm (AEFA) was mixed with greedy strategy and state transition strategy, and an artificial electric field algorithm based on greedy state transition strategy (GSTAEFA) was proposed. Greedy state transition strategy provides state transition interference for AEFA, increases the diversity of population, and effectively improves the accuracy of the algorithm. Finally, we test the performance of GSTAEFA by optimizing examples with different numbers of cities. Experimental results show that GSTAEFA has better performance in solving SMTSP problems than other swarm intelligence algorithms.

The Effect of Roughness Features on Mos Surface Electric Field and Fowler-Nordheim Tunneling Behavior

1997 ◽  
Vol 473 ◽  
Author(s):  
Heng-Chih Lin ◽  
Edwin C. Kan ◽  
Toshiaki Yamanaka ◽  
Simon J. Fang ◽  
Kwame N. Eason ◽  
...  
Keyword(s):  
Electric Field ◽  
Three Dimensional ◽  
Tunneling Current ◽  
Gate Oxide ◽  
Oxide Thickness ◽  
Interface Roughness ◽  
Normal Electric Field ◽  
Surface Electric Field ◽  
Tunneling Behavior ◽  
Nordheim Tunneling

ABSTRACTFor future CMOS GSI technology, Si/SiO2 interface micro-roughness becomes a non-negligible problem. Interface roughness causes fluctuations of the surface normal electric field, which, in turn, change the gate oxide Fowler-Nordheim tunneling behavior. In this research, we used a simple two-spheres model and a three-dimensional Laplace solver to simulate the electric field and the tunneling current in the oxide region. Our results show that both quantities are strong functions of roughness spatial wavelength, associated amplitude, and oxide thickness. We found that RMS roughness itself cannot fully characterize surface roughness and that roughness has a larger effect for thicker oxide in terms of surface electric field and tunneling behavior.

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