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Enhancing the reliability of inversion results has always been a prominent issue in the field of geophysics. In recent years, data-driven inversion methods leveraging deep neural networks (DNNs) have gained prominence for their ability to address non-uniqueness issues and reduce computational costs compared to traditional physically model-driven methods. In this study, we propose a GMNet machine learning method, i.e., a CNN-based inversion method for gravity and magnetic field data. This method relies more on data-driven training, and in the prediction phase after the model is trained, it does not heavily depend on a priori assumptions, unlike traditional methods. By forward modeling gravity and magnetic fields, we obtain a substantial dataset to train the CNN model, enabling the direct mapping from field data to subsurface property distribution. Applying this method to synthetic data and one-field data yields promising inversion results. [ABSTRACT FROM AUTHOR]

This article deals with the question of the unique solvability of systems of linear algebraic equations, to the solution of which many inverse problems of geophysics are reduced as a result of discretization when applying the methods of integral equations or integral representations. Examples are given of degenerate and nondegenerate systems of different dimensions that arise in the processing of magnetometric and gravimetric data from experimental observations. Conclusions are drawn about the methods for constructing the optimal grid of experimental observation points. [ABSTRACT FROM AUTHOR]

A new technique for three-dimensional surface reconstruction of relatively smooth surface topography using the scanning electron microscopy with backscattered electron detector is considered. Experiments show high effectiveness of the method. [ABSTRACT FROM AUTHOR]

Retrieval of magnetization parameters using magnetic tensor gradient measurements receives attention in recent years. Determination of subsurface properties from the observed potential field measurements is referred to as inversion. Little regularizing inversion results using full tensor magnetic gradient modeling so far has been reported in the literature. Traditional magnetic inversion is based on the total magnetic intensity (TMI) data and solving the corresponding mathematical physical model. In recent years, with the development of the advanced technology, acquisition of the full tensor gradient magnetic data becomes available. In this paper, we study invert the magnetic parameters using the full tensor magnetic gradient data. A sparse Tikhonov regularization model is established. In solving the minimization model, the conjugate gradient method is addressed. Numerical and field data experiments are performed to show feasibility of our algorithm. [ABSTRACT FROM AUTHOR]

The initial-boundary value problems for a Sobolev equation with exponential nonlinearities, classical, and nonclassical boundary conditions are considered. For this model, which describes processes in crystalline semiconductors, the blow-up phenomena are studied. The sufficient blow-up conditions and the blow-up time are analyzed by the method of the test functions. This analytical a priori information is used in the numerical experiments, which are able to determine the process of the solution's blow-up more accurately. The model derivation and some questions of local solvability and uniqueness are also discussed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]