Influence of permeability on wave-tilt of EM waves

1982 ◽  
Vol 19 (6) ◽  
pp. 1323-1325 ◽  
Author(s):  
Ramesh P. Singh ◽  
Tarkeshwar Lal
Keyword(s):  
Half Space ◽  
Magnetic Permeability ◽  
Pronounced Effect ◽  
Earth Model ◽  
Theoretical Studies ◽  
Computational Results ◽  
Frequency Range ◽  
Magnetic Wave ◽  
Homogeneous Half Space ◽  
Wave Tilt

Theoretical studies on the influence of magnetic permeability on the amplitude and phase of electric and magnetic wave-tilt have been carried out in the frequency range 102–106 Hz over a homogeneous half-space Earth model. Computational results show a pronounced effect of magnetic permeability on the amplitude of wave-tilt measurements.

Wave-tilt characteristics of TE-mode waves

1981 ◽  
Vol 18 (2) ◽  
pp. 382-385 ◽  
Author(s):  
Ramesh P. Singh ◽  
Tarkeshwar Lal
Keyword(s):  
Dielectric Constants ◽  
Phase Changes ◽  
Earth Model ◽  
Frequency Range ◽  
Homogeneous Half Space ◽  
Te Mode ◽  
Tm Mode ◽  
Displacement Currents ◽  
Lower Frequency Region ◽  
Wave Tilt

The dependence of TE-mode wave-tilt on frequency and altitude of measurement, and the resistivity and dielectric constants of the ground have been investigated. Computational results showing the influence of these parameters on the amplitude and phase of the wave-tilt over a homogeneous half-space earth model have been presented. In contrast to TM-mode waves, the wave-tilt effects for TE-mode are stronger in the lower frequency region. In the lower frequency range, the amplitude decreases with the increase in resistivity of the ground, whereas it increases for an increase in dielectric constant value. When the displacement currents are ignored, the magnitude of amplitude of wave-tilt is reduced considerably. The altitude of measurement has minimal effect on the amplitude, but the phase changes appreciably in some cases.

Crustal deformation by earthquakes and explosions

1970 ◽  
Vol 60 (1) ◽  
pp. 193-215 ◽  
Author(s):  
Ari Ben-Menahem ◽  
Allon Gillon
Keyword(s):  
Half Space ◽  
Crustal Deformation ◽  
Surface Deformation ◽  
Epicentral Distance ◽  
Single Layer ◽  
Strike Slip ◽  
Earth Model ◽  
Homogeneous Half Space ◽  
Layer 2 ◽  
A New Technique

abstract Static displacements were calculated for an earth model which consists of a single layer of thickness H overlying a homogeneous half space. Localized sources simulating earthquake and explosion foci are placed at depths h=H2andh=32H. The ensuing surface deformation is evaluated as a function of the epicentral distance for a typical continental crust model. A new technique is used for the quadrature of the displacement integrals. By this method one is able to calculate 1000 layer-integrals of the type F m n ( x , t ) = ∫ 0 ∞ y n e − x y J m ( t y ) d y 1 + ( A + B y 2 ) e − 2 y + D e − 4 y , with an accuracy of 0.1 per cent, in less than 2 minutes. It is found that for epicentral distances r > 20H the displacements decay like (r/H)−α where 2 < α < 5. For compressional and strike-slip displacements at all depths and for dip-slip source above the layer, 2 < α < 3. For a dip-slip source located below the layer, 3 < α < 5. Maximal displacements for wr, ur, ux, uy and uz occur at approximately r ≃ 0.8h and decay with source's-depth like h−3/2.

Inversion of slingram electromagnetic induction data using a Born approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. E201-E212 ◽  
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Born Approximation ◽  
High Efficiency ◽  
Three Dimensions ◽  
Background Model ◽  
Desktop Computer ◽  
Near Surface ◽  
Homogeneous Half Space ◽  
Integral Equation Formulation ◽  
Forward Operator

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

Airborne resistivity and susceptibility mapping in magnetically polarizable areas

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 502-511 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Half Space ◽  
Magnetic Permeability ◽  
Apparent Resistivity ◽  
Dynamic Range ◽  
Single Frequency ◽  
Measured Signal ◽  
Apparent Permeability ◽  
Quadrature Component ◽  
New Methods ◽  
Quadrature Response

The apparent resistivity technique using half‐space models has been employed in helicopter‐borne resistivity mapping for twenty years. These resistivity algorithms yield the apparent resistivity from the measured in‐phase and quadrature response arising from the flow of electrical conduction currents for a given frequency. However, these algorithms, which assume free‐space magnetic permeability, do not yield a reliable value for the apparent resistivity in highly magnetic areas. This is because magnetic polarization also occurs, which modifies the electromagnetic (EM) response, causing the computed resistivity to be erroneously high. Conversely, the susceptibility of a magnetic half‐space can be computed from the measured EM response, assuming an absence of conduction currents. However, the presence of conduction currents will cause the computed susceptibility to be erroneously low. New methods for computing the apparent resistivity and apparent magnetic permeability have been developed for the magnetic conductive half‐space. The in‐phase and quadrature responses at the lowest frequency are first used to estimate the apparent magnetic permeability. The lowest frequency should be used to calculate the permeability because this minimizes the contribution to the measured signal from conduction currents. Knowing the apparent magnetic permeability then allows the apparent resistivity to be computed for all frequencies. The resistivity can be computed using different methods. Because the EM response of magnetic permeability is much greater for the in‐phase component than for the quadrature component, it may be better in highly magnetic environments to derive the resistivity using the quadrature component at two frequencies (the quad‐quad algorithm) rather than using the in‐phase and quadrature response at a single frequency (the in‐phase‐quad algorithm). However, the in‐phase‐quad algorithm has the advantage of dynamic range, and it gives credible resistivity results when the apparent permeability has been obtained correctly.

Numerical seismograms obtained using ω-κ integrals, for a point P source in a vertically inhomogeneous anelastic model

1996 ◽  
Vol 86 (3) ◽  
pp. 750-760
Author(s):  
F. Abramovici ◽  
L. H. T. Le ◽  
E. R. Kanasewich
Keyword(s):  
Half Space ◽  
Homogeneous Layer ◽  
Variable Step Size ◽  
Step Size ◽  
Adaptive Process ◽  
Cpu Time ◽  
Homogeneous Half Space ◽  
Linear Layer ◽  
Variable Step ◽  
Viscoelastic Layers

Abstract This article presents some numerical experiments in using a computer program for calculating the displacements due to a P source in a vertically inhomogeneous structure, based on the Fourier-Bessel representation. The structure may contain homogeneous, inhomogeneous, elastic, or viscoelastic layers. The source may act in any type of sublayer or in the half-space. Synthetic results for the simple case of a homogeneous layer overlaying a homogeneous half-space compare favorably with computations based on the Cagniard method. Numerical seismograms for an elastic layer having velocities and density varying linearly with depth were computed by integrating numerically the governing differential systems and compared with results based on the Haskell model of splitting the linear layer in homogeneous sublayers. Even an adaptive process with a variable step size based on the Haskell model has a poorer performance on the accuracy-cpu time scale than numerical integration.

Surface-wave dispersion computations

1970 ◽  
Vol 60 (2) ◽  
pp. 321-344 ◽  
Author(s):  
Fred Schwab ◽  
Leon Knopoff
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Wave Dispersion ◽  
Reduction Technique ◽  
Surface Wave Dispersion ◽  
Single Precision ◽  
Homogeneous Half Space ◽  
Full Control ◽  
Significant Figures ◽  
Rayleigh Wave Dispersion

abstract Fundamental-mode Love- and Rayleigh-wave dispersion computations for multilayered, perfectly-elastic media were studied. The speed of these computations was improved, and the accuracy brought under full control. With sixteen decimal digits employed in these computations, fifteen significant-figure accuracy was found possible with Love waves and twelve to thirteen figure accuracy with Rayleigh waves. In order to ensure that the computed dispersion is correct to a specified accuracy, say σ significant figures, (σ + 1)/4 wavelengths of layered structure must be retained above a homogeneous half-space. To this accuracy, the homogeneous half-space is a sufficient model of the true layering it replaces. Using this result, it was possible to refine the usual layer-reduction technique so as to ensure retention of the specified accuracy while employing reduction. With this reduction technique in effect, and with σ specified below single-precision accuracy, the program can be run entirely in single precision; the specified accuracy is maintained without overflow or loss-of-precision problems being encountered during calculations.

Boundary-Element Modeling of 3-D Poroelastic Half-Space Dynamics

2014 ◽  
Vol 1040 ◽  
pp. 881-885 ◽  
Author(s):  
Leonid A. Igumnov ◽  
Svetlana Litvinchuk ◽  
Andrey Petrov ◽  
Alexander A. Belov
Keyword(s):  
Boundary Element Method ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Half Space ◽  
Material Model ◽  
Direct Approach ◽  
Computational Results ◽  
Element Modeling ◽  
Base Functions ◽  
Space Dynamics

A direct approach of the boundary element method for treating 3-D boundary-value problems of poroelastodynamics is considered. Biot’s material model with four unknown base functions is used. Computational results for the surface responses of displacements and pore pressures as functions of a force acting on a half-space weakened by a cavity are presented.

Stress relaxation in a semi-infinite viscoelastic earth model

1973 ◽  
Vol 63 (6-1) ◽  
pp. 2145-2154
Author(s):  
Martin Rosenman ◽  
Sarva Jit Singh
Keyword(s):  
Free Surface ◽  
Stress Relaxation ◽  
Half Space ◽  
Epicentral Distance ◽  
Strike Slip ◽  
Strike Slip Fault ◽  
Earth Model ◽  
Contour Maps ◽  
Surface Stresses ◽  
Stress Components

Abstract Expressions for quasi-static surface stresses resulting from a finite, rectangular, vertical, strike-slip fault in a Maxwellian viscoelastic half-space are derived. Variation of the stresses with time and epicentral distance is studied. Contour maps are obtained in some representative cases. It is found that all nonvanishing stress components at the free surface die exponentially with time. This is in contrast to the behavior of the displacements and strains which, in general, do not vanish for large times.

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