Controlled source tensor magnetotellurics

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1456-1461 ◽  
Author(s):  
Xiaobo Li ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Transfer Functions ◽  
Unit Vector ◽  
Impedance Tensor ◽  
Wave Excitation ◽  
Controlled Source ◽  
Practice Analysis ◽  
Homogeneous Half Space ◽  
Dipole Sources ◽  
Layered Half Space

Impedance tensor and tipper vectors, known to connect the electromagnetic surface components for plane‐wave excitation, are shown to be uniquely defined for horizontal electric or horizontal magnetic dipole sources. Two independent source polarizations are needed for their estimation in practice. Analysis of impedance tensors and tipper vectors for a layered half‐space shows that the impedance tensor can be antidiagonalized by rotating the measurement system so that one of the measurement directions coincides with the direction to the transmitter dipole. The tipper vector points towards the transmitter dipole. In the static limit, all transfer functions are real, and simple analytic results for a homogeneous half‐space show that impedance elements are proportional to the inverse of the product of conductivity and distance between source and receiver, while the tipper vector is a unit vector pointing towards the transmitter dipole.

The electromagnetic response of an azimuthally anisotropic half‐space

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1462-1473 ◽  
Author(s):  
Xiaobo Li ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Transfer Functions ◽  
Hankel Transform ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Impedance Tensor ◽  
Fracture Zones ◽  
Transform Method ◽  
Homogeneous Half Space ◽  
Horizontal Electric Dipole

Fracture zones are pervasive in crystalline areas. When the earth is seen over a sufficiently large volume fracture zones may be too thin to be individually identified. If they have preferred directions in that volume, the volume can be considered to be an azimuthally anisotropic medium. We have formulated the electromagnetic fields induced by a horizontal electric dipole on the surface of a homogeneous half‐space with azimuthally anisotropic conductivity. The field components are expressed by the two‐dimensional Fourier transform which can be computed by a fast Hankel transform method. The impedance tensor and tipper functions of controlled source tensor magnetotellurics are derived by exciting the dipole source in two different directions. We show the behavior of impedance tensor, tipper functions and their derived quantities: rotational invariants and Parkinson vectors. All transfer functions clearly show anisotropic characteristics. Contours of rotationally invariant apparent resistivities and phases for fixed frequencies are elongated in the direction of maximum conductivity, and Parkinson’s vectors tend to point in the same direction.

Groundwater exploration using combined controlled-source and radiomagnetotelluric techniques

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. G8-G15 ◽  
Author(s):  
Laust B. Pedersen ◽  
M. Bastani ◽  
L. Dynesius
Keyword(s):  
Transfer Functions ◽  
Three Dimensional ◽  
Groundwater Exploration ◽  
Impedance Tensor ◽  
Two Dimensional ◽  
Controlled Source ◽  
Reflection Seismic ◽  
Seismic Sections ◽  
Clay Layers ◽  
Clay Lenses

Radiomagnetotelluric (RMT) (14–250 kHz) combined with controlled-source magnetotelluric (CSMT) (1–12 kHz) measurements were applied to the exploration of groundwater located in sandy formations at depths as great as 20 m below thick clay lenses. A combination of approximately 30 radio frequencies and controlled-source frequencies is essential for penetrating the thick clay layers. The electromagnetic transfer functions of impedance tensor and tipper vectors point toward a structure that is largely two-dimensional, although clear three-dimensional effects can be observed where the sandy formation is close to the surface. The determinant of the impedance tensor was chosen for inversion using two-dimensional models. The final two-dimensional model fits the data to within twice the estimated standard errors, which is considered quite satisfactory, given that typical errors are on the level of 1% on the impedance elements. Comparison with bore-hole results and shallow-reflection seismic sections show that the information delivered by the electromagnetic data largely agrees with the former and provides useful information for interpreting the latter by identifying lithological boundaries between the clay and sand and between the sand and crystalline basement.

Arbitrary Load Distribution on a Layered Half Space

2000 ◽  
Vol 122 (4) ◽  
pp. 672-681 ◽  
Author(s):  
N. Schwarzer
Keyword(s):  
Half Space ◽  
Load Distribution ◽  
Elastic Field ◽  
Stress Fields ◽  
Method Of Images ◽  
Elementary Functions ◽  
Homogeneous Case ◽  
Arbitrary Load ◽  
Homogeneous Half Space ◽  
Layered Half Space

This paper develops a method which allows one to calculate the complete elastic field (stress field and displacements) of layered materials of transverse and complete isotropy under given load conditions. It is assumed that the layered body consists of an infinite half-space and various infinite planes which are all ideally bonded to each other. Thus, the interfaces are parallel to the surface of the resulting “coated half space.” The approach is based on the method of images in classical electrostatics. The final solution for an arbitrary load problem can be presented as a series of potential functions, where corresponding functions may be interpreted as “image loads” the analogous to “image charges.” The solution for the elastic field for any arbitrary stress distribution on the surface of the coated half space can be obtained in a relatively straightforward manner by using the method described here as long as the corresponding solution for the homogeneous half space is known. Further, if this solution of the homogeneous case may be expressed in terms of elementary functions, then the solution for the coated half space is elementary, too. Explicit formulas for the stress fields for some particular examples are given. [S0742-4787(00)01204-2]

An efficient method for computing Green's functions for a layered half-space with sources and receivers at close depths

1994 ◽  
Vol 84 (5) ◽  
pp. 1456-1472 ◽  
Author(s):  
Yoshiaki Hisada
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Point Sources ◽  
Asymptotic Solutions ◽  
Reflection And Transmission ◽  
Reflection And Transmission Coefficient ◽  
Dipole Sources ◽  
Coefficient Method ◽  
Layered Half Space

Abstract We propose an analytical method to compute efficiently the displacement and stress of static and dynamic Green's functions for viscoelastic layered half-spaces. When source and receiver depths are close, it is difficult to compute Green's functions of the layered half-space, because their integrands, whose variable of integration is the horizontal wavenumber, oscillate with only slowly decreasing amplitude. In particular, when the depths are equal, it is extremely difficult to compute the stress Green's functions, because their integrands oscillate with increasing amplitude. To remedy this problem, we first derive the asymptotic solutions, which converge to the integrands of Green's functions with increasing wavenumber. For this purpose, we modify the generalized R/T (reflection and transmission) coefficient method (Luco and Apsel; 1983) to be completely free from growing exponential terms, which are the obstacles to finding the asymptotic solutions. By subtracting the asymptotic solutions from the integrands of the corresponding Green's functions, we obtain integrands that converge rapidly to zero. We can, therefore, significantly reduce the range of wavenumber integration. Since the asymptotic solutions are expressed by the products of Bessel functions and simple exponential functions, they are analytically integrable. Finally, we obtain accurate Green's functions by adding together numerical and analytical integrations. We first show this asymptotic technique for Green's functions due to point sources, and extend it to Green's functions due to dipole sources. Finally, we demonstrate the validity and efficiency of our method for various cases.

Fast programs for layered half-space problems

1967 ◽  
Vol 57 (6) ◽  
pp. 1299-1315
Author(s):  
M. J. Randall
Keyword(s):  
Half Space ◽  
Matrix Method ◽  
Transfer Functions ◽  
Synthetic Seismograms ◽  
Time Function ◽  
Source Time Function ◽  
Fast Computer ◽  
The Matrix ◽  
Crustal Reflection ◽  
Layered Half Space

Abstract Knopoff's matrix method for the solution of P-SV problems has been somewhat simplified and modified to take account of oceanic structures. Advantage has been taken of a method of separating the frequency-dependent operations from the matrix multiplications to obtain very fast computer programs for calculating Rayleigh dispersion, crustal reflection functions, and crustal transfer functions. Applications include Rayleigh dispersion inversion, QitR, inversion, crustal investigations using pP, crustal transfer corrections to amplitude observations, and the construction of synthetic seismograms for investigation of the source time-function.

An efficient method for computing Green's functions for a layered half-space with sources and receivers at close depths (part 2)

1995 ◽  
Vol 85 (4) ◽  
pp. 1080-1093
Author(s):  
Yoshiaki Hisada
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Efficient Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
New Method ◽  
Direct Wave ◽  
Transmitted Waves ◽  
Dipole Sources ◽  
Layered Half Space

Abstract In this study, we improve Hisada's (1994) method to efficiently compute Green's functions for viscoelastic layered half-spaces with sources and receivers located at equal or nearly equal depths. Compared with Hisada (1994), we can significantly reduce the range of wavenumber integration especially for the case that sources and receivers are close to the free surface or to boundaries of the source layer. This can be done by deriving analytical asymptotic solutions for both the direct wave and the reflected/transmitted waves from the boundaries, which are neglected in Hisada (1994). We demonstrate the validity and efficiency of our new method for several cases. The FORTRAN codes for this method for both point and dipole sources are open to academic use through anonymous FTP.

Reply to L. Szarka by the authors

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 727-729
Author(s):  
L. C. Bartel ◽  
R. D. Jacobson
Keyword(s):  
Half Space ◽  
Near Field ◽  
Three Dimensional ◽  
Far Field ◽  
Audio Frequency ◽  
Opportunity To Respond ◽  
Controlled Source ◽  
Electrical Structure ◽  
Homogeneous Half Space ◽  
Correction Scheme

We welcome the opportunity to respond to comments by Szarka on our recent paper. The main points he raised on our near‐field correction scheme for controlled‐source audio‐frequency magnetotelluric (CSAMT) data are the application of the correction scheme and the near‐field/far‐field demarcation in the presence of layers and the application in the presence of electrical structure beneath the transmitter location. In our paper, we addressed the application for three‐dimensional electrical structure beneath the receiver location with the transmitter over a homogeneous half‐space. In this reply we wish to clarify these points and point out possible limitations of our correction scheme.

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