Magnetic object localization techniques have significant applications in automated surveillance and security systems, such as aviation aircrafts or underwater vehicles. In this letter, a practical localization algorithm was presented to determine the center coordinates and magnetic moments of multiple underwater magnetic objects using a combination of the magnetic field vector and its gradient tensor data. It formulates the localization of underwater magnetic objects into a nonlinear problem, which was solved by the Levenberg-Marquardt algorithm. The regularization parameters in the nonlinear problem were adaptively varied in terms of information of the Jacobian matrix. Good initial values of the center coordinates and magnetic moments of this nonlinear problem were automatically determined by a novel and analytical single-object localization algorithm based on magnetic field vector and its gradient tensor. Simulations with two and three underwater objects were adopted to study the feasibility of the magnetic gradiometry technique in multiple underwater objects localization. We have demonstrated that our algorithm can produce reliable results to locate multiple underwater magnetic objects.

Magnetotelluric (MT) method is widely used for revealing deep electrical structure. However, natural MT signals are susceptible to cultural noises. In particular, the existing data-processing methods usually fail to work when MT data are contaminated by persistent or coherent noises. To improve the quality of MT data collected with strong ambient noises, we propose a novel time-series editing method based on the improved shift-invariant sparse coding (ISISC), a data-driven machine learning algorithm. First, a redundant dictionary is learned autonomously from the raw MT data. Second, cultural noises are reconstructed using the learned dictionary and the orthogonal matching pursuit (OMP) algorithm. Finally, the de-noised MT data are obtained by subtracting the reconstructed cultural noises from the raw MT data. The synthetic data, field experimental data and measured data are tested to verify the effectiveness of the newly proposed method. The results show that our new scheme can effectively remove strong cultural noises and has better adaptability and efficiency than the predefined dictionary-based methods. The method can be used as an alternative when a remote reference station is not available.

Traditional gradient-based inversion methods usually suffer from the problems of falling into local minima and relying heavily on initial guesses. Deep-learning methods have received increasing attention due to their excellent nonlinear fitting ability. However, given the recent application of deep-learning methods in the field of magnetotelluric (MT) inversion, there are currently challenges associated with achieving high inversion resolution and extracting sufficient features. We develop a neural network model (called MT2DInv-Unet) based on the deformable convolution for 2D MT inversion to approximate the nonlinear mapping from the MT response data to the resistivity model. The deformable convolution is achieved by adding an offset to each sample point of the conventional convolution operation, which extracts hidden relationships and allows the flexible adjustment of the size and shape of the feature region. Meanwhile, we design the network structure with multiscale residual blocks, which effectively extract the multiscale features of the MT response data. This design not only enhances the network performance but also alleviates issues such as vanishing gradients and network degradation. The results of synthetic models indicate that our network inversion method has stable convergence, good robustness, and generalization performance, and it performs better than the fully convolutional neural network and U-Net network. Finally, the inversion results of field data show that MT2DInv-Unet can effectively obtain a reliable underground resistivity structure and has a good application prospect in MT inversion.

SUMMARY: The fast and accurate 3-D magnetotelluric (MT) forward modelling is core engine of the interpretation and inversion of MT data. In this study, we develop an improved extrapolation cascadic multigrid method (EXCMG) to solve the large sparse complex linear system arising from the finite-element (FE) discretization on non-uniform orthogonal grids of the Maxwell’s equations using potentials. First, the vector Helmholtz equation and the scalar auxiliary equation are derived from the Maxwell’s equations using Coulomb-gauged potentials. The weighted residual method is adopted to discretize the weak formulation and assemble the FE equation. Secondly, carefully choosing the preconditioned complex stable bi-conjugate gradient method (BiCGStab) as multigrid smoother, we develop an improved EXCMG method on non-uniform grids to solve the resulting large sparse complex non-Hermitian linear systems. Finally, several examples including three standard testing models (COMMEMI3D-1, COMMEMI3D-2 and DTM1.0) and a topographic model are used to validate the accuracy and efficiency of the proposed multigrid solver. Numerical results show that the proposed EXCMG algorithm greatly improves the efficiency of 3-D MT forward modelling, is more efficient than some existing solvers, such as Pardiso, incomplete LU factorization preconditioned biconjugate gradients stabilized method (ILU-BiCGStab) and flexible generalized minimum residual method with auxiliary space Maxwell preconditioner (FGMRES-AMS), and capable to simulate large-scale problems with more than 100 million unknowns.

We present a novel algorithm to locate multiple underwater objects in real time using gravity field vector and gravity gradient tensor signals. This algorithm formulates the task of localization of multiple underwater objects into a regularized nonlinear problem, which is solved with the standard Levenberg–Marquardt algorithm. The regularization parameters are estimated by cross validation. The initial coordinates and masses of these underwater objects are automatically determined by solving a single-object localization problem. A synthetic navigation model with two underwater objects was adopted to validate the proposed algorithm. The results show that it has good stability and antinoise ability for multiple underwater objects localizations.