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Previous inversions of surface magnetometric resistivity (MMR) could obtain only the ratio, not the absolute value of earth electrical conductivity. In this paper, instead of solving Poisson's equation, the magnetic fields generated by low frequency alternating current(AC) line are looked as MMR data and calculated from electric-type Helmholtz's equation in frequency domain, so that the absolute conductivity could be taken into account. Forward modeling scheme is adapted from staggered-grid finite-difference method. Inversion algorithm is non-linear conjugate gradient (NLCG). The magnetic field perpendicular to line source is selected as observed data. To improve depth resolution, we introduce a model reconstruction strategy based on reference model. In the strategy, the upper portion of the resultant model from previous inversion is replaced by a homogeneous layer to construct a new model to trigger next inversion. The thickness of the homogeneous layer is called reconstruction depth, it is equal to the depth where the models difference between last two iterations after the run of the i th inversion is almost none-zero. The reconstruction could be applied until the model difference is almost zero or the difference of model differences between two adjacent inversions is less than a predefined threshold. Inversion results from synthetic and real data have proved that the proposed multi-reconstruction inversion strategy is able to obtain absolute resistivity, as well as enhance the deep resolution of surface MMR data inversion .

The computationally expensive cost and complexity are practical challenges in solving the three-dimensional (3-D) inverse problem in the time domain, and many real-world surveys are still inverted in one dimension (1-D). We present a new way to invert transient electromagnetic (TEM) data from a rectangular fixed loop to image subsurface electrical conductivity, which overcomes this limitation and permits efficient implementation of the inversion process on a personal computer. A TEM signal was transformed to the real and imaginary components of a frequency-domain (FD) electromagnetic (EM) response. The transformation was performed by a regularization inversion method. The recovered FD EM response was used as the data for the 3-D inversion. The forward problem and sensitivity were solved by using a staggered-grid finite-difference technique in the FD, and the background Green's function was carried out using the virtual interface method. The non-linear conjugate gradient method (NLCG) was employed to solve the 3-D inverse problem. A synthetic example revealed the basic functionality of the approach, and the FD inversion of a TEM field dataset acquired in the northeastern Qinshui Basin, Shanxi Province, China demonstrated a real-world application. Our inversion approach is general and suitable for different-type sources, such as a vertical magnetic dipole or horizontal electric dipole .

In this paper, we introduce a technique to obtain smoother C-responses in geomagnetic depth sounding. Instead of frequency by frequency, C-responses in entire frequency range are estimated simultaneously. In order to do so, after obtaining the spectrum of Hy and Hz, the equations relating C-response with Hy and Hz are combined for a batch frequency to form a linear equation set, from which, incorporating the requirement of smooth constraint on C-responses, we could define a regularized least-squared inversion problem. And to minimize influence of noise, data squared coherencies between Z and H signals are used to weight prediction error in order to suppress unreliable data. Synthetic data tests indicate that using the optimal regularization parameter determined by V-curve method other than L-curve method, regularization method could produce rather smooth C-responses from noise interfered signals. C-responses in Northeast China are thus obtained and then 1-D inversion is applied, from the obtained electrical and combining the Global and regional tomographic results, it is speculated that the stagnant plate in MTZ leads the high conductivity anomaly in Northeast China.

Wide applications of time-domain electromagnetic (TEM) data require 3D inversion. A possible strategy is to use the developed 3D inversion algorithms in frequency-domain (FD) electromagnetic (EM) methods. Thus, the key of the strategy is how to transform the time-domain ([Formula: see text]-[Formula: see text]) EM signal into the FD. An inversion algorithm has been developed to transform the [Formula: see text]-[Formula: see text] signal into a corresponding FD response. In this method, a step-off current is presumed. Under this assumption, the Fourier transform relating the EM FD response to the [Formula: see text]-[Formula: see text] signal becomes a sine or cosine transformation. Using the polynomial approximation method, the transformation turns into a linear equation. From a set of [Formula: see text]-[Formula: see text] signals, FD responses could be obtained by solving these linear equations in the least-squares sense. To reduce the nonuniqueness of the solution, and enhance the solution stability, an additional smoothness constraint on the FD response is imposed, thus converting the minimization problem into a regularization inversion problem. The algorithm is applied to synthetic and field vertical magnetic data in the in-loop TEM surveying mode. The numerical results show that in the entire audio-frequency range, the relative errors between the inversed and theoretical FD responses of the real and imaginary parts are almost all less than 1%, with the largest discrepancy of 5% occurring at high frequencies. There are two significances behind our work: First, the possibility of accurately transforming [Formula: see text]-[Formula: see text] response into FD response in audio-frequency range is coming into true, thereby (from the mathematical perspective) implementing the equivalence between the responses of the EM method in the time domain and the FD. Second, the algorithm provides a new approach to interpret TEM data in 3D mode by using developed 3D FEM inversion techniques.

We present a method to unify the calculation of Green’s functions for an electromagnetic (EM) transmitting source embedded in a homogeneous stratified medium. A virtual interface parallel to layer interfaces is introduced through the source location. The potentials for Green’s function are derived by decomposing the partial wave solutions to Helmholtz’s equations into upward and downward within boundaries. The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level. The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface. Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters, whereas the kernel connected with the stratified media stays unchanged. Hence, the present method can be easily applied to EM transmitting sources with little modification. The application of the proposed method to the marine controlled-source electromagnetic method (MCSEM) demonstrates its simplicity and flexibility.