A new singularity-free analytical formula has been developed for the gravity field of arbitrary 3D polyhedral mass bodies with horizontally and vertically varying density contrast using third-order polynomial functions. First, the observation sites are moved to the origin of the coordinate system. Then, the volume and surface integral theorems are invoked successively to transform the volume integrals into surface integrals over polygonal faces and into line integrals over the edges of the polyhedral mass bodies. Furthermore, singularity-free closed-form solutions are derived for these line integrals over the edges. Thus, the observation sites can be located inside, on, or outside the 3D distributions. A synthetic prismatic mass body is adopted to verify the accuracy and singularity-free property of our newly developed analytical expressions. Excellent agreements are obtained between our solutions and other published closed-form solutions with relative errors in the order of ${10}^{-12}\%$ to ${10}^{-13}\%$. In addition, an octahedral model and a near-Earth asteroid model are used to verify the accuracy of the presented method for complicated target structures by comparing the results with those from a high-order Gaussian quadrature approach.

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.

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.