The article proposes an approach to optimize the division of initial data into training and test subsets for modeling the spatial distribution of a component using artificial neural networks (ANN). This approach takes into account the spatial irregularities and the scatter values of the modeled component. Data were obtained during soil screening of urban areas in the Russian subarctic zone: Tarko-Sale and Noyabrsk cities. For modeling, the chemical element chromium (Cr) was chosen. On Tarko-Sale, areas with an abnormally high value of the modeled element were discovered. On Noyabrsk, no anomalies in Cr values were detected. Using the feedforward neural network multilayer perceptron (MLP) method, Cr spatial distribution in the surface soil layer is constructed. The MLP structure was chosen by computer simulation based on minimizing the root mean square error (RMSE). Comparison of the models that use random division of the initial data into a training and test subset, and models that are based on the proposed approach was performed. For each approach, the mean absolute error (MAE), RMSE, and the mean square relative error (RMSRE) were calculated. For both areas, models using the proposed approach showed more accurate results (up to 50% improvement).

Theoretical basis and its mathematical model for local correlation of two spatial variables have been developed. It reflects coherent change of values depending on the spatial position. The proposed method is based on the representation of spatial variables in the form of continuous fields and their gradients’ comparison. Local correlation algorithm has been developed and used for the automatic creation of correlation surfaces. The technology has been tested on the areal lithogeochemical surveying data. It also can be used for the processing of any other spatially distributed data.

The Tsaga gabbro-labradorite massif (the Kola Peninsula) shows possibilities of applying the complex interpretation of geophysical data in order to construct a structural-geological model of the intrusion and find the direction of future exploration work. The observed fields Δg and ΔZ (the survey scales were 1:100 000 and 1:50 000), results of seismic surveys and petrophysical data have been used. The studies have been carried out using numerical modeling, which for the first time made it possible to obtain quantitative estimates of the geological and structural position of Tsaga containing complex iron-titanium-vanadium ores. The undertaken studies, including correlation methods and transformations of the gravitational field, indicated that the massif looks like a plate-like body with the thickness of up to 3,5 km, continuing in the northeast and east directions beyond the known boundaries. In addition, we have identified 10 areas in its near-surface part, where widespread rocks with the anomalous density of 3,06-3,20 g/cm³ and the thickness of 0,8-1,1 km occur. They practically reach the surface and can host a titan-magnetite mineralization. The obtained results allow us to significantly expand the massif prospects to iron-titanium oxide ores using the identified areas where the high-density rocks were found.

Currently, computer control methods for such complex systems as natural water bodies are in demand. The aim of this work was to model the ecosystem of the shallow water section of the Volgograd reservoir using geoinformation technologies. The criteria for determining shallow water zones are formulated. Geoinformation technologies are used as a tool of ordering and systematization for heterogeneous data obtained in the course of environmental monitoring. We used geocoding to bind model elements to the selected study area. The paper presents an analysis of the basic principles of the model to describe the ecosystem. The main components of the simulated ecosystem and the relationship between them are characterized. The importance of obtaining spatial data for creating a computer model of the ecosystem is explained. The paper uses the author’s hardware that allows describing water bodies using sensors of geolocation and echolocation. The technique of point-by-point scanning of the bottom configuration is described. The method of registration, transmission and processing of this data is shown. The paper describes the work of the author’s software package that allows you to organize the data to create files that can be used in the program Matlab. As a result of the field study, data on the state of the model shallow water area were collected; geodatabases with information about the object under study were created, obtained with the help of hardware. Geoinformation modeling of the shallow section «Black waters» of the left Bank of the Volgograd reservoir near Marx with the use of Matlab tools is carried out. Geoinformation components, graphics and animation, algorithms of simulation modeling of the ecosystem in the study area are implemented. The accelerated change of the ecosystem of this shallow water is noted. The computer model made it possible to establish the relationship between the configuration of the bottom and the transfer of sediments, which entails changes in the ecosystem of the reservoir, such as algae overgrowth. In turn, the increase in the number of aquatic plants leads to waterlogging.

Application of methods of mathematical physics and logical approximations to the solution of problems of distribution of temperature fields between a trend of the rising mantle-crust migrant (plume) and surrounding medium is considered. The four-dimensional problem (x, y, z, time) is reduced to the two-dimensional problem (x, time) for a particular, but the most common, case of the symmetry of the plume around the central axis and the uniform nature of its rise. A software Vladi Gear 3.0 for thermodynamic calculations in the range «plume adiabat–regional geotherms» that implements the described transformation, is developed. The analogy of the vertical thermal interaction of time layers with the internal friction (viscosity) of the medium is shown. This analogy can be used in the calculations of convective heat and mass transfer.

The study of the dynamics of the deltas of the northern rivers is complicated by a number of circumstances: a) the slowed rates of the processes occurring in the cryolithozone condition determine the small variability of the deltas; b) the shortness of the season of possible observations after the completion of the spring flood and before the formation of snow cover limits the choice of suitable shooting dates by the end of July–August–September; c) cloudiness shielding, weather conditions drastically reduce the choice of images. Remote studies of the dynamics of the northern deltas over the past half century are based on images from the Landsat satellite; to assess the current state of the deltas, images from the Sentinel satellite with the best resolution and frequency of shooting are used. To ensure the comparability of images obtained by different imaging systems, they are mutually geometrical (transformed) and brightness (brought to a common division by brightness levels) matching, selection of comparable spectral channels is performed. Based on the analysis of the spectral brightness curves of the main objects studied, the survey channels that are most informative for the study of delta dynamics are determined. To select the optimal method of automated isolation of coastlines, several methods of computer separation of water and land objects were tested: clustering into two levels using the entire set of spectral channels; the same for the most informative channels in the near and middle infrared spectrum; creating index images (water index options). Due to the complexity of eliminating the errors that remain with these methods, the luminance quantization of images in the near infrared zone is considered optimal, allowing the use of best-resolution images and sequentially refining the brightness level chosen for dividing based on comparing the quantization results with the original synthesized images. The Landsat-7 images of 1999 and Sentinel-2B 2017 in the near infrared zone, quantized to brightness levels «water»–«land», obtained a raster image of the Yenisei delta with contours of water appearing at the land (erosion of the coast) and land formation at the water location (accumulation of sediments). On its basis, maps of the delta dynamics are compiled. Three types of maps of different scales and contents reflecting the dynamics of the Yenisei delta are proposed.