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.

The magnetotelluric (MT) data collected in an ore-concentration area are extremely vulnerable to all kinds of noise pollution. However, separating real MT signals from strong noise is still a difficult problem, and the noise in MT data is quite distinct from clean data in morphological features. By performing the signal-noise identification and data prediction, we develop a deep learning method to denoise MT data containing strong noise. First, we use the convolutional neural network (CNN) to learn the feature differences between the samples of massive noise and clean data and use the learned features to realize signal-noise identification of the measured data. Second, we use the measured clean data obtained by CNN identification to train the long short-term memory (LSTM) neural network and perform the prediction denoising of the noisy data. The simulation results clearly demonstrate the following two facts: (1) the predicted data output from LSTM basically matches the time-frequency domain features of the real data and (2) our CNN method performs significantly better than the features parameter classification method in dealing with signal-noise identification. In addition, the validity of our method is verified by the processing results of the measured data.

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.

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.

It is well known that a magnetotelluric (MT) signal with high signal-to-noise ratio is an important prerequisite for correct interpretation of subsurface structures. However, MT signals collected in the environment of strong cultural noise often are of low data quality due to noise pollution, which seriously affects the accuracy of interpretation. As can be seen from the MT time-domain waveform, the noise is highly energetic, diverse, and random. This means MT denoising methods should have strong applicability to guarantee accurate and effective separation of MT signal from noise data. Therefore, we propose a deep-learning-based data nonlinear mapping method for MT signal-to-noise separation. First, this method focuses on learning the nonlinear mapping relationship between a large amount of noise data and the corresponding noise contour by using the convolutional neural network (CNN) in advance. Then, the mapping transformation of noise data to noise contour in the measured data is realized by CNN model. Specifically, based on the features of MT noise data, we construct a large amount of training data very close to it by mathematical functions. At the same time, we also select some of the measured data to be added to the training set. This not only expands the amount and diversity of the training set but also improves the adaptability of CNN when dealing with complex data. Finally, we evaluate the denoising performance of the proposed method in terms of time-domain waveforms, apparent resistivity-phase curves, and polarization directions before and after denoising. The processing results of the simulated data and the measured data collected in Luzong area have verified the feasibility and effectiveness of the proposed method in MT data denoising.