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...

Abstract-In this paper, we developed a general framework for the inversion of electromagnetic measurements in cases where parametrization of the unknown configuration is possible. Due to the ill-posed nature of this nonlinear inverse scattering problem, this parametrization approach is needed when the available measurement data are limited and measurements are only carried out from limited transmitter-receiver positions (limited data diversity). By carrying out this parametrization, the number of unknown model parameters that need to be inverted is manageable. Hence the Newton based approach can advantageously be used over gradient-based approaches. In order to guarantee an error reduction of the optimization process, the iterative step is adjusted using a line search algorithm. Further unlike the most available Newton-based approaches available in the literature, we enhanced the Newton based approaches presented in this paper by constraining the inverted model parameters with nonlinear transformation. This constrain forces the reconstruction of the unknown model parameters to lie within their physical bounds. In order to deal with cases where the measurements are redundant or lacking sensitivity to certain model parameters causing non-uniqueness of solution, the cost function to be minimized is regularized by adding a penalty term. One of the crucial aspects of this approach is how to determine the regularization parameter determining the relative importance of the misfit between the measured and predicted data and the penalty term. We reviewed different approaches to determine this parameter and proposed a robust and simple way of choosing this regularization parameter with aid of recently developed multiplicative regularization analysis. By combining all the techniques mentioned above we arrive at an effective and robust parametric algorithm. As numerical examples we present results of electromagnetic inversion at induction frequency in the deviated borehole configuration. 266Habashy and Abubakar

We present 2.5D fast and rigorous forward and inversion algorithms for deep electromagnetic (EM) applications that include crosswell and controlled-source EM measurements. The forward algorithm is based on a finite-difference approach in which a multifrontal LU decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single-source experiment for each frequency of operation. When the size of the linear system of equations is large, the use of this noniterative solver is impractical. Hence, we use the optimal grid technique to limit the number of unknowns in the forward problem. The inversion algorithm employs a regularized Gauss-Newton minimization approach with a multiplicative cost function. By using this multiplicative cost function, we do not need a priori data to determine the so-called regularization parameter in the optimization process, making the algorithm fully automated. The algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image. To increase the robustness of the algorithm, we also constrain the minimization and use a line-search approach to guarantee the reduction of the cost function after each iteration. To demonstrate the pros and cons of the algorithm, we present synthetic and field data inversion results for crosswell and controlled-source EM measurements.

We introduce a novel approximation to numerically simulate the electromagnetic response of point or line sources in the presence of arbitrarily heterogeneous conductive media. The approximation is nonlinear with respect to the spatial variations of electrical conductivity and is implemented with a source‐independent scattering tensor. By projecting the background electric field(i.e., the electric field excited in the absence of conductivity variations) onto the scattering tensor, we obtain an approximation to the electric field internal to the region of anomalous conductivity. It is shown that the scattering tensor adjusts the background electric field by way of amplitude, phase, and cross‐polarization corrections that result from frequency‐dependent mutual coupling effects among scatterers. In general, these three corrections are not possible with the more popular first‐order Born approximation. Numerical simulations and comparisons with a 2.5‐dimensional finite difference code show that the new approximation accurately estimates the scattered fields over a wide range of conductivity contrasts and scatterer sizes and within the frequency band of a subsurface electromagnetic experiment. Furthermore, the approximation has the efficiency of a linear scheme such as the Born approximation. For inversion, we employ a Gauss‐Newton search technique to minimize a quadratic cost function with penalty on a spatial functional of the sought conductivity model. We derive an approximate form of the Jacobian matrix directly from the nonlinear scattering approximation. A conductivity model is rendered by repeated linear inversion steps within range constraints that help reduce nonuniqueness in the minimization of the cost function. Synthetic examples of inversion demonstrate that the nonlinear approximation reduces considerably the execution time required to invert a large number of unknowns using a large number of electromagnetic data.