Study on the Response of a Multicomponent Induction Logging Tool in Deviated and Layered Anisotropic Formations by Using Numerical Mode Matching Method

Wang, Hongnian; Tao, Honggen; Jing-Jin, Yao; Chen, Guibo; Yu, Shou-Wen

doi:10.1002/cjg2.1305

Cited by 19 publications

(19 citation statements)

References 12 publications

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“…Since all naturally occurring media possess diagonalizable material tensors, this constraint is not a practical concern and thus warrants no further discussion. 5 c o (m/s) is the speed of light in free space, μ o (H/m) is the free space magnetic permeability, and o = 1 μoc 2 o (F/m) is the free space electric permittivity. 6 Field quantities exhibiting purely spatial dependence have calligraphic script and are denoted spatial quantities.…”

Section: Formulation Overviewmentioning

confidence: 99%

“…To invert apparent conductivity from the received magnetic field, formula (18) of Ref. [5] is used. Figure 7 corresponds to the sonde in a homogeneous, uniaxial medium with varying α; agreement is excellent.…”

Section: B Triaxial Induction Sondementioning

confidence: 99%

“…The study of electromagnetic fields produced by dipole sources in planar-stratified environments with anisotropic layers is pertinent to many applications such as geophysical prospection [1][2][3][4][5][6][7], microwave remote sensing [8], groundpenetrating radar [9,10], optical field focusing [11], antenna design [12,13], microwave circuits [14], and plasma physics [15]. For this problem class, one can exploit the planar symmetry and employ pseudoanalytical approaches based upon embedding spectral Green's function kernels within Fourier-type integrals to compute the space-domain fields [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments

2014

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We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary and independent anisotropy in both its (complex) permittivity and permeability tensors. Among the salient features of our formulation are (i) computation of eigenmodes (characteristic plane waves) supported in arbitrarily anisotropic media in a numerically robust fashion, (ii) implementation of an hp-adaptive refinement for the numerical integration to evaluate the radiation and weakly evanescent spectra contributions, and (iii) development of an adaptive extension of an integral convergence acceleration technique to compute the strongly evanescent spectrum contribution. While other semianalytic techniques exist to solve this problem, none have full applicability to media exhibiting arbitrary double anisotropies in each layer, where one must account for the whole range of possible phenomena (e.g., mode coupling at interfaces and nonreciprocal mode propagation). Brute-force numerical methods can tackle this problem but only at a much higher computational cost. The present formulation provides an efficient and robust technique for field computation in arbitrary planar-stratified environments. We demonstrate the formulation for a number of problems related to geophysical exploration.

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Section: Formulation Overviewmentioning

confidence: 99%

Section: B Triaxial Induction Sondementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments

2014

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“…The response of both a conventional induction logging tool and multi-component induction logging tool in radially stratified media within the V-shaped channel can be simulated by using Eq. (6) [17,18] .…”

Section: Magnetic-current-source Dyadic Green's Functions In Radiallymentioning

confidence: 99%

Simulating the Response of Induction Logging‐While‐Drilling Tools by Vector Eigenfunction Expansion Formulae of Dyadic Green's Functions

Wei¹,

Wang²,

Ou³

2011

Chinese J of Geophysics

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The vector eigenfunction expansion formulae of magnetic-current-source dyadic Green's functions for a perfect electric conduction wedge model in cylindrical coordinate system are adopted to compute the response of an induction logging-while-drilling tool within the collar's V-shaped channel. It has shown from computation that the influence of the change of the V-shaped channel's angle on different components of electromagnetic fields is different. If only a conventional induction logging tool is used, the channel's angle should be as small as possible in order to increase the signal's intensity fully. If a multi-component induction logging tool is used, the value of the channel's angle should be selected compromisingly. Since the received signal's intensity will change when the tool is in the V-shaped channel with different angle, the criterion should be fixed on the basis of the V-shaped channel's angle when the formation's apparent conductivity is calibrated. It has also shown that different components of electromagnetic fields rely differently on the azimuth angle, and that the influence of the invasion zone's conductivity on different components of the received signal is also different, thus the radial depth of exploration is different for different components of the received signal.

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“…In order to efficiently demonstrate the responses of multicomponent tools, the analytic algorithm in a cylindrically layered medium [12] and semi-analytic method in horizontal stratified formation have been applied [13,14] . These algorithms are indeed efficient, but they cannot yet be applied to solve the responses in entirely 3-D anisotropic formation such as a dipping formation with varying bed thicknesses and invasions.…”

Section: Introductionmentioning

confidence: 99%

The 3‐D Finite Difference Time Domain Algorithm of Responses of Multi‐component Electromagnetic Well Logging in a Deviated and Layered Anisotropic Formation

Yu¹,

Wang²,

Chen³

et al. 2009

Chinese J of Geophysics

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In this paper, we advance an algorithm of numerical modeling for responses of multicomponent electromagnetic well logging in a deviated and layered anisotropic formation through the 3‐D finite difference time domain approach (FDTD). First, we use a Yee's staggered grid and linear interpolation formula to discretize the Maxwell equation in the time domain in an anisotropic medium and determine the non‐defined components of electromagnetic (EM) field in the staggered grid in order to obtain the time recursive equation of the EM field on all staggered grids in an arbitrary anisotropic media. At the same time, area weighted average and transformation matrix are utilized to calculate the effective conductive tensors on the grids, and an absorbing boundary condition is executed to reduce the reflection of outer‐boundary on the base of uniaxial anisotropic perfectly matched layer (UPML). Then, we apply three mutually orthogonal transmitter coils with a singlefrequency sinusoidal current to excite EM fields in the time domain and extract the amplitude and phase of EM from the EM field through a special two‐equation and two‐unknown (2E2U) approach to obtain the responses of multicomponent EM propagation logging tool. Finally, by numerical results we validate the algorithm and examine systematically the influence of changes in bed thickness, formation dipping angle and radius of invasion zones on responses of the tool.

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Study on the Response of a Multicomponent Induction Logging Tool in Deviated and Layered Anisotropic Formations by Using Numerical Mode Matching Method

Cited by 19 publications

References 12 publications

Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments

Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments

Simulating the Response of Induction Logging‐While‐Drilling Tools by Vector Eigenfunction Expansion Formulae of Dyadic Green's Functions

The 3‐D Finite Difference Time Domain Algorithm of Responses of Multi‐component Electromagnetic Well Logging in a Deviated and Layered Anisotropic Formation

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