There are many occasions on which the magnetotelluric impedance tensor is affected by local galvanic distortion (channelling) of electric currents arising from induction in a conductive structure which is approximately two‐dimensional (2‐D) on a regional scale. Even though the inductive behavior is 2‐D, the resulting impedance tensor can be shown to have three‐dimensional (3‐D) behavior. Conventional procedures for rotating the impedance tensor such as minimizing the mean square modulus of the diagonal elements do not in general recover the principal axes of induction and thus do not recover the correct principal impedances but rather linear combinations of them. This paper presents a decomposition of the impedance tensor which separates the effects of 3‐D channeling from those of 2‐D induction. Where the impedance tensor is actually the result of regional 1‐D or 2‐D induction coupled with local frequency independent telluric distortion, the method correctly recovers the principal axes of induction and, except for a static shift (multiplication by a frequency independent real constant), the two principal impedances. Also obtained are two parameters (twist and shear), which partially describe the effects of telluric distortion. It is shown that the tensor operator which describes the telluric distortions can always be factored into the product of three tensor sub‐operators (twist, shear, local anisotropy) and a scalar. This product factorization allows assimilation of local anisotropy, if present, into the regional anisotropy. The method of decomposition is given in the paper along with a discussion of the improvements obtained over the conventional method and an example with real data.

we introduced the IEBA and IQA algorithms and discussed their convergence properties. In addition, it was shown a linear operator updates the IEBA state, while that of the IQA is updated nonlinearly. The linearity of the IEBA causes one to recognize the divergency of the IEBA within its execution.We have employed the algorithms to solve 2D TM scattering problems. The numerical examples presented in this article and several other examples illustrate the IEBA and IQA are convergent and fast for the practical low-frequency applications (induction frequency range). In such applications, the IQA presents remarkable rate of convergence in comparison with the HOGEBA and it yields sufficient accuracy for 3-6 iterations. As the frequency is increased, the IEBA and IQA tend to become divergent. However, the IQA is convergent for wider range of frequency, object size, and object contrast. Also, the convergence rate of the IQA is superior to that of the HOGEBA for many cases and in overall; the IQA seems to be an efficient and accurate alternative to the high-order approximations.Our formula should be assessed with incorporation of other approximations, such as the tensor version of QA [3] and the DTA [9]. Furthermore, all algorithms should be implemented not only for 2D TM cases but also for 2D TE and 3D scattering problems. Then, a comparative study is conducted to find out the advantages and drawbacks of the algorithms. This is our future work. -3]. Accurate largesignal model for multi-cell high power HBT devices is of great importance in designing circuits such as power amplifiers where several cells are used at the output stage to deliver the required amount of power. The on-wafer characterization of high power active devices is laborious [4] and has limited accuracy in measuring RF performances such as power gain. This is mainly due to the elevated junction temperature of such devices when biased with high voltages. In addition, commonly used lumped model does not accurately predict the small-signal characteristics of multi-cell HBTs, particularly at higher frequencies where the equivalent electrical circuit of such devices exhibits a distributed nature [5,6]. As reported in [7][8][9][10], small-size HBTs (low power devices) can be easily characterized, and the lumped equivalent circuit is adequate to predict their small-signal characteristics over extended frequency ranges. High-power HBTs are usually composed of several identical elementary cells connected in parallel.Each of these cells can be considered as a small-size HBT and consequently can be modeled by a lumped equivalent circuit. Therefore, it is more appropriate to derive the multi-cell HBT model by scaling up the elementary-cell device model. CHARACTERIZED HBT DEVICESTwo GaAsHBT devices were characterized to illustrate in detail the proposed modeling approach. The first device is a small-size GaAsHBT (HBT1) composed of an elementary-cell ( Fig. 1). The second device is a large-size GaAsHBT (HBT2) composed of three cells (Fig. 2). Figure 1 shows the physi...

An outcropping hemispherical inhomogeneity embedded in a two‐dimensional (2-D) earth is used to model the effects of three‐dimensional (3-D) near‐surface electromagnetic (EM) “static” distortion. Analytical solutions are first derived for the galvanic electric and magnetic scattering operators of the heterogeneity. To represent the local distortion by 3-D structures of fields which were produced by a large‐scale 2-D structure, these 3-D scattering operators are applied to 2-D electric and magnetic fields derived by numerical modeling to synthesize an MT data set. Synthetic noise is also included in the data. These synthetic data are used to study the parameters recovered by several published methods for decomposing or parameterizing the measured MT impedance tensor. The stability of these parameters in the presence of noise is also examined. The parameterizations studied include the conventional 2-D parameterization (Swift, 1967), Eggers’s (1982) and Spitz’s (1985) eigenstate formulations, LaTorraca et al.’s (1986) SVD decomposition, and the Groom and Bailey (1989) method designed specifically for 3-D galvanic electric scattering. The relationships between the impedance or eigenvalue estimates of each method and the true regional impedances are examined, as are the azimuthal (e.g., regional 2-D strike, eigenvector orientation and local strike) and ellipticity parameters. The 3-D structure causes the conventional 2-D estimates of impedances to be site‐dependent mixtures of the regional impedance responses, with the strike estimate being strongly determined by the orientation of the local current. For strong 3-D electric scattering, the local current polarization azimuth is mainly determined by the local 3-D scattering rather than the regional currents. There are strong similarities among the 2-D rotation estimates of impedance and the eigenvalue estimates of impedance both by Eggers’s and Spitz’s first parameterization as well as the characteristic values of LaTorraca et al. There are striking similarities among the conventional estimate of strike, the orientations given by the Eggers’s, Spitz’s (Q), and LaTorraca et al.’s decompositions, as well as the estimate of local current polarization azimuth given by Groom and Bailey. It was found that one of the ellipticities of Eggers, LaTorraca et al., and Spitz is identically zero for all sites and all periods, indicating that one eigenvalue or characteristic value is linearly polarized. There is strong evidence that this eigenvalue is related to the local current. For these three methods, the other ellipticity differs from zero only when there are significant differences in the phases of the regional 2-D impedances (i.e., strong 2-D inductive effects), implying the second ellipticity indicates a multidimensional inductive response. Spitz’s second parameterization (U), and the Groom and Bailey decomposition, were able to recover information regarding the actual regional 2-D strike and the separate character of the 2-D regional impedances. Unconstrained, both methods can suffer from noise in their ability to resolve structural information especially when the current distortion causes the impedance tensor to be approximately singular. The method of Groom and Bailey, designed specifically for quantifying the fit of the measured tensors to the physics of the parameterization, constraining a model, and resolving parameters, can recover much of the information in the two regional impedances and some information about the local structure.

Vertical spatial sensitivity and effective depth of exploration (d e ) of low-induction-number (LIN) instruments over a layered soil were evaluated using a complete numerical solution to Maxwell's equations. Previous studies using approximate mathematical solutions predicted a vertical spatial sensitivity for instruments operating under LIN conditions that, for a given transmitter-receiver coil separation (s), coil orientation, and transmitter frequency, should depend solely on depth below the land surface. When not operating under LIN conditions, vertical spatial sensitivity and d e also depend on apparent soil electrical conductivity (s a ) and therefore the induction number (b). In this new evaluation, we determined the range of s a and b values for which the LIN conditions hold and how d e changes when they do not. Two-layer soil models were simulated with both horizontal (HCP) and vertical (VCP) coplanar coil orientations. Soil layers were given electrical conductivity values ranging from 0.1 to 200 mS m 21. As expected, d e decreased as s a increased. Only the least electrically conductive soil produced the d e expected when operating under LIN conditions. For the VCP orientation, this was 1.6s, decreasing to 0.8s in the most electrically conductive soil. For the HCP orientation, d e decreased from 0.76s to 0.51s. Differences between this and previous studies are attributed to inadequate representation of skin-depth effect and scattering at interfaces between layers. When using LIN instruments to identify depth to water tables, interfaces between soil layers, and variations in salt or moisture content, it is important to consider the dependence of d e on s a .

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