THE APPARENT RESISTIVITY TENSOR

Geophysics ◽  
1977 ◽  
Vol 42 (6) ◽  
pp. 1258-1261 ◽  
Author(s):  
H. M. Bibby
Keyword(s):  
Electric Field ◽  
Apparent Resistivity ◽  
Geometric Mean ◽  
Field Station ◽  
Tensor Invariants ◽  
Resistivity Tensor ◽  
Reduced Data

The scalar apparent resistivity was originally defined for simple linear electrode resistivity arrays such as Wenner and Schlumberger arrays. With the extension of resistivity surveying into bipole‐dipole arrays, several different and not obviously related definitions of apparent resistivity have been used by different authors despite similar field procedure. In this note we show that when a pair of current sources (or quadripole source) is used, and the corresponding electric field vectors are measured at each field station, the most comprehensive expression of the reduced data is as an apparent resistivity tensor. Other definitions of apparent resistivity can be simply related to this tensor. For example, the quadripole‐quadripole apparent resistivity of Doicin (1976) is one of the tensor invariants; the maximum and minimum resistivities defined by the rotating dipole method of Furgerson and Keller (1975) can be simply derived, and their geometric mean is shown to be the quadripole‐quadripole value.

Analysis of multiple‐source bipole‐quadripole resistivity surveys using the apparent resistivity tensor

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 972-983 ◽  
Author(s):  
H. M. Bibby
Keyword(s):  
Electric Field ◽  
Apparent Resistivity ◽  
Extreme Values ◽  
Strong Dependence ◽  
Current Source ◽  
The Body ◽  
Multiple Source ◽  
Tensor Invariants ◽  
Resistivity Tensor ◽  
Receiver Array

Measurements of apparent resistivity made using the bipole‐dipole method depend upon the location and orientation of the current source relative to the body under study. Although it has been recognized that this dependence on orientation can be partially overcome by use of two current bipoles with different orientations, no agreement on the method of analysis of multiple source surveys has been reached. The most general form of presentation of such results is an apparent resistivity tensor. Various rotation invariants derived from the apparent resistivity tensor can be regarded as mean values of apparent resistivity, independent of the direction of the electric field, thus greatly reducing the “false anomalies” typical of single‐source bipole‐dipole survey results. Two of the tensor invariants obey the principle of reciprocity: if the roles of the current and potential electrodes are interchanged, the invariants are unchanged. The properties of the apparent resistivity tensor are demonstrated for selected simple models. For a horizontally layered medium, when the receiver array is far from the current source, the tensor is symmetric and has invariants which depend only on the distance from the current source. The extreme values of apparent resistivity occur when the electric field vector is tangential and radial relative to the current source. These extreme values correspond to the Schlumberger apparent resistivity and the “polar” dipole apparent resistivity, respectively. Lateral discontinuities in resistivity are modeled with both a single vertical discontinuity and a hemispherical model. The source‐dependent variations in the apparent resistivity derived from a single‐current bipole are greatly reduced in plots of the tensor invariants. For a vertical discontinuity, the tensor trace (the sum of the diagonal elements) is close to the resistivity underlying the receiver site, whereas for a hemisphere, the square root of the tensor determinant gives the best representation. Near lateral discontinuities in resistivity, the apparent resistivity tensor indicates strong dependence of apparent resistivity on the direction of the measured electric field. This apparent anisotropy can be used as an indicator of such discontinuities, yielding both position and orientation of the discontinuity.

scholarly journals STRUCTURE OF FREEZING TALIK UNDER LAKE AT THE PARISENTO FIELD STATION (GYDAN PENINSULA) ACCORDING TO ELECTRICAL RESISTIVITY TOMOGRAPHY

2019 ◽  
Vol 2 (2) ◽  
pp. 103-110
Author(s):  
Alexandr Shein ◽  
Vladimir Olenchenko ◽  
Yaroslav Kamnev ◽  
Anton Sinitskiy
Keyword(s):  
Electrical Resistivity ◽  
Apparent Resistivity ◽  
Electrical Resistivity Tomography ◽  
Two Dimensional ◽  
Resistivity Tomography ◽  
Field Station ◽  
Approximate Rate

The article presents the results of studies of freezing talik under lake with using of electrical resistivity tomography. The research was conducted on one of paleolake – khasyrey. The measurements performed in two perpendicular profiles by pole-dipole array with a maximum spacing of 435 m. According to results of two-dimensional inversion, an area of low electrical resistivity of rocks at a depth of 25-30 m associated with a freezing talik under lake was identified. It was determined that the depth of freezing within drained lake for the period from 1996 to 2018 is 17-22 m. The approximate rate of freezing is 1 m/year. Formation of talik have a resistance of 5-15 Ω·m. Frozen formations in the contours of young paleolake have apparent resistivity hundreds Ω·m. Within the boundaries of the more ancient khasyrey apparent resistivity of the frozen rocks up to several thousand Ω·m.

The Effects of 3D Electrical Anisotropy on Magnetotelluric Responses: Synthetic Case Studies

2018 ◽  
Vol 23 (1) ◽  
pp. 61-75
Author(s):  
Wenxin Kong ◽  
Changhong Lin ◽  
Handong Tan ◽  
Miao Peng ◽  
Tuo Tong ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Finite Difference Method ◽  
Apparent Resistivity ◽  
Electrical Anisotropy ◽  
Staggered Grid ◽  
Qualitative And Quantitative ◽  
Resistivity Tensor ◽  
Quantitative Analyses ◽  
Prism Model ◽  
Euler’S Angles

Using the staggered-grid finite difference method, a numerical modeling algorithm for a 3D arbitrary anisotropic Earth is implemented based on magnetotelluric (MT) theory. After the validation of this algorithm and comparison with predecessors, it was applied to several qualitative and quantitative analyses containing electrical anisotropy and a simple 3D prism model. It was found that anisotropic parameters for ρ 1 , ρ 2 , and ρ 3 play almost the same role in affecting 3D MT responses as in 1D and 2D without considering three Euler's angles α S , α D , and α L . Significant differences appear between the off-diagonal components of the apparent resistivity tensor and also between the diagonal components in their values and distributing features under the influence of 3D anisotropy, which in turn help to identify whether the MT data are generated from 3D anisotropic earth. Considering the deflecting effects arising from the inconsistency between the anisotropy axes and the measuring axes, some strategies are also provided to estimate the deflecting angles associated with anisotropy strike α S or dip α D , which may be used as initial values for the 3D anisotropy inversion. [Figure: see text]

TELLURIC SOUNDING—A MAGNETOTELLURIC METHOD WITHOUT MAGNETIC MEASUREMENTS

Geophysics ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 185-191 ◽  
Author(s):  
S. H. Yungul
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Magnetic Measurements ◽  
Sedimentary Basins ◽  
Base Station ◽  
Primary Objective ◽  
Field Station ◽  
Field Operation ◽  
Resistivity Log ◽  
The Magnetic Field

The basic theory and objectives of telluric sounding (TS) are about the same as those of the well‐known method of magnetotelluric sounding (MTS) (Cagniard, 1953). Both methods make use of the natural electromagnetic phenomena known as geomagnetic micropulsations to obtain crude “resistivity logs” from the surface down to great depths, without drilling, if the subsurface has mild structures, low dips, and lateral continuity in the electrical resistivity. Let the x-y plane of the Cartesian coordinates represent the surface of the earth. With MTS, the field operation consists of simultaneously recording the time variations of an arbitrary x component of the electric field, [Formula: see text], called a tellurogram, and that of the y component of the magnetic field, [Formula: see text], called a magnetogram, both at the same point where the downward information is desired. The main difficulty is in the measurement of the magnetic field variations with sufficient accuracy. The measurement of the electric field variations is very simple and expeditious. TS bypasses this difficulty, because it does not require the measurement of the magnetic field. With TS, the field operation requires two electric field recording units. One of these units remains at a “base station” where the subsurface is known from a well log, while the second unit is placed at a “field station” where one wishes to explore the subsurface. Thus, for each sounding, one obtains two simultaneous tellurograms. These are Fourier analyzed. The ratios of the electric field amplitudes as a function of frequency, combined with the resistivity log at the base station, furnish the MTS‐type data at the field station that are interpreted in the usual manner to yield a crude resistivity log at the field station. The primary objective of TS is the exploration of sedimentary basins. It may be preferable to MTS in certain cases and vice versa; it is not meant to replace MTS. The theoretical basis and the procedures of TS are discussed in this paper.

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.

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.

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