Electromagnetic field anomalous

Background (normal) and anomalous parts of the electromagnetic field... 

The electromagnetic field in the model described above can be presented as a sum of the background (normal) and anomalous fields ... 

In order to develop the numerical analogs of the electromagnetic field integral representations, we have to discretize, also, the field components and the Green s tensors within the anomalous domain D of integration. We can treat all integral representations, considered in this chapter, as operators acting on the vector functions, x,... 

Let us introduce a notation d for an electric or magnetic vector of the anomalous part of tiic observed data. This vector contains the components of tlic anomalous electric and/or magnetic fields at the receivers. The discrete forward modeling problem for the electromagnetic field based on the QA approximation can be expressed by the following matrix operations ... 

However, equation (10.4) is ill-posed, because it is non-unique and unstable. We have already discussed in Chapter 1 that there are nonradiating sources of electromagnetic field. For example, consider Maxwell s equations (9.3) for an anomalous field ... 

In this section we introduce first the migrated anomalous electromagnetic field and show how it can be calculated from the anomalous field. In the following sections we will demonstrate the connections between the migrated electromagnetic fields and the solution of the electromagnetic inverse problem. 

We can extend the integral representations in the frequency domain, formulae (9.37) of Chapter 9, to the time domain. As a result, the anomalous electromagnetic field in the model can be expressed as an integral over the anomalous domain D of the product of the corresponding Green s tensors and excessive currents An (E -I- E ) ... 

The perturbations of anomalous electric and magnetic fields in the time domain can be expressed through the perturbation of the conductivity 6a using the integral formulae similar to equations (9.51) and (9.52) for electromagnetic field perturbation in the frequency domain ... 

We can use Dirichlet boundary-value conditions (12.7), asymptotic boundary conditions (12.8), or absorbing boundary conditions in the formulation of the boundary-value problem for the anomalous electromagnetic field. 

Similar to an electromagnetic field (see Chapter 9), the total wavefield in the model described above can be represented as a sum of two parts, the incident p (background) field p r,w) and the scattered (anomalous) field p (r,cu),... 

The ideas of iterative Born inversion, introduced in Chapter 10 for an electromagnetic field, can be extended to wavefield inversion as well. Following the basic principles of this method, we first write the original integral equations for the acoustic or vector wavefields (14.20) and (14.81) as the domain equations for the wavefield inside the anomalous domain D ... 

Other landmark achievements of QED attributable to radiative effects include the explanation and calculation of the anomalous magnetic moment of fhe electron, and the Lamb shift in atomic hydrogen [1]. In order to treat processes involving the interaction of electromagnetic fields with atoms and molecules, the latter containing bound electrons moving at a small fraction... 

The basis of surface enhanced optical absorption is the so-called "anomalous absorption". To observe anomalous absorption an absorbing colloid or colloid layer is positioned in a defined distance to a metal mirror and illuminated from the colloid side. At a certain distance of the colloid or absorbing layer to the mirror the incident fields has the same phase as the electromagnetic field that is reflected by the mirror at the position of the absorbing colloid particle (or colloid particle layer). The set-up is described as a reflection interference system, which feedback mechanism strongly enhances the absorption coefficient of the absorbing colloid (layer). 

Figures 10-5 - 10-6 present the results of inversion for an xy polarized field using, respectively, the iterative Born and the diagonalized quasi-analytical (DQA) inversion methods, with focusing. Both methods produce good results. Note that inversion of theoretical MT data takes just few minutes on a personal computer. A remarkable fact is that it is possible for this polarization to separate the upper and lower parts of the dike. The position and shape of the dike are also reconstructed quite well. However, the resistivity of the dike is not recovered correctly, which is a common problem in nonlinear inversion. The first method (iterative Born inversion) underestimates the anomalous conductivity, while the second (DQA inversion) produces a more correct result. The reason for the underestimation of the conductivity by the iterative Born inversion is very simple. The linearized response, which is used in this technique, usually overestimates the anomalous field, which results in an underestimation of the conductivity in inversion. The quasi-analytical approximation produces a more accurate electromagnetic response, so the inversion works more accurately as well.

The definition of the electromagnetic migration field in time domain was introduced in the monograph by Zhdanov (1988). According to this definition, the migration field is the solution of the boundary value problem for the adjoint Maxwell s equations. For example, we can introduce the migration anomalous field E ", H " as the field, determined in reverse time t = —t, whose tangential components are equal to the anomalous field in reverse time at the surface of the earth S... 

Similar to the field separation into the background and anomalous parts, one can represent the electromagnetic potentials as the sums of the corresponding potentials for the background and anomalous fields ... 

The behavior of electromagnetic waves in normal metals at ordinary temperatures and microwave frequencies is quite adequately described by the classical treatment based on MaxwelPs equations and Ohm s law. At low temperatures this is no longer true even though MaxwelPs equations are still valid, Ohm s law is inadequate to describe the relation between high frequency electric currents and fields in metals. According to classical theory, the surface resistance R is inversely proportional to the square root of the dc conductivity cr. Consequently, as the temperature is lowered and o- increases, the classical theory predicts that R cc. This is not borne out in practice, as will be seen by referring to Fig, 1. The ordinate is IR the observed surface conductance, and the abscissa is proportional to c T. Initially the behavior is classical and as the temperature is lowered. As the dc conductivity becomes larger, however, I does not increase proportionately and in the low temperature limit it becomes independent of a (and temperature). This phenomenon is known as the anomalous skin effect. The experimental data shown are due to Chambers [1]. The solid curve is the curve predicted from the theory of Reuter and Sondheimer [2],... 

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