We present a finite‐element algorithm for computing MT responses for 3D conductivity structures. The governing differential equations in the finite‐element method are derived from the T–Ω Helmholtz decomposition of the magnetic field H in Maxwell's equations, in which T is the electric vector potential and Ω is the magnetic scalar potential. The Coulomb gauge condition on T necessary to obtain a unique solution for T is incorporated into the magnetic flux density conservation equation. This decomposition has two important benefits. First, the only unknown variable in the air is the scalar value of Ω. Second, the curl–curl equation describing T is only defined in the earth. By comparison, the system of curl–curl equations for H and the electric field E are singular in the air, where the conductivity σ is zero. Although the use of a small but nonzero value of σ in the air and application of a divergence correction are usually necessary in the E or H formulation, the T–Ω method avoids this necessity. In the finite‐element approximation, T and Ω are represented by the edge‐element and nodal‐element interpolation functions within each brick element, respectively. The validity of this modeling approach is investigated and confirmed by comparing modeling results with those of other numerical techniques for two 3D models.

I present a method for calculating frequency-domain electromagnetic responses caused by a dipole source over a 2-D structure. In modeling controlled-source electromagnetic data, it is usual to separate the electromagnetic field into a primary (background) and a secondary (scattered) field to avoid a source singularity, and only the secondary field caused by anomalous bodies is computed numerically. However, this conventional scheme is not effective for complex structures lacking a simple background structure. The present modeling method uses a pseudo-delta function to distribute the dipole source current, and does not need the separation of the primary and the secondary field. In addition, the method employs an isoparametric finite-element technique to represent realistic topography. Numerical experiments are used to validate the code. Finally, a simulation of a source overprint effect and the response of topography for the long-offset transient electromagnetic and the controlled-source magnetotelluric measurements is presented.

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SUMMARY In controlled‐source electromagnetic measurements in the near zone or at low frequencies, the real (in‐phase) frequency‐domain component is dominated by the primary field. However, it is the imaginary (quadrature) component that contains the signal related to a target deeper than the source–receiver separation. In practice, it is difficult to measure the imaginary component because of the dominance of the primary field. In contrast, data acquired in the time domain are more sensitive to the deeper target owing to the absence of the primary field. To estimate the frequency‐domain responses reliably from the time‐domain data, we have developed a Fourier transform algorithm using a least‐squares inversion with a smoothness constraint (smooth spectrum inversion). In implementing the smoothness constraint as a priori information, we estimate the frequency response by maximizing the a posteriori distribution based on Bayes' rule. The adjustment of the weighting between the data misfit and the smoothness constraint is accomplished by minimizing Akaike's Bayesian Information Criterion (ABIC). Tests of the algorithm on synthetic and field data for the long‐offset transient electromagnetic method provide reasonable results. The algorithm can handle time‐domain data with a wide range of delay times, and is effective for analysing noisy data.

Three different-scale electromagnetic (EM) measurements have been performed in the Kujukuri coastal plain, southeast Japan, to investigate the distribution of saline groundwater. The three techniques were audio-frequency magnetotelluric (AMT), transient electromagnetic (TEM), and small loop-loop EM measurements. The resistivity sections estimated from these data sets reveal three independent resistivity distributions extending to different depths. The AMT method reveals a regional-scale resistivity distribution across the plain to a maximum depth of approximately [Formula: see text] and the existence of deep conductive zones, which are inferred to be associated with fossil seawater trapped in a Pleistocene formation. The TEM results show a medium-scale resistivity distribution to depths of approximately [Formula: see text], in which two shallow conductive zones are recognized. It is concluded that these features are caused by present seawater intrusion and high-salinity salt-marsh deposits formed during sporadic marine regressions. The small loop-loop EM method provided a shallow resistivity profile that highlights the conductive salt-marsh deposits and resistive sandy ridges. Although these resistivity sections correspond to different depth ranges, the overlapping portions of the sections are very consistent with one another. These EM methods are useful in detecting and interpreting important resistivity features. Taking the geologic evolution of the coastal plains into consideration is crucial when interpreting resistivity profiles such as these, and our results suggest that the presence of fossil seawater is an important factor controlling resistivity at a variety of depths.