A method for analyzing long-term (1997–2025) continuous records of low-frequency global seismic noise measured at a network of 229 broadband seismic stations distributed across the Earth’s surface is proposed in this study. The method is based on the use of nonlinear multifractal and entropy statistics, evaluated daily in successive time intervals, of first-principal component analysis, correlation analysis, and parametric models of point process intensity. The relationships between changes in seismic noise properties and the response of noise properties to the irregularity of the Earth’s rotation with the sequence of strong earthquakes, including those of a predictive nature, are investigated.

This study addresses the solution of inverse problems in exploration geophysics using machine learning methods that involve reusing a trained model for different cases. At the same time, inverse problems are characterized by ill-posedness, for the reduction of which an approach is considered based on the indirect use of a priori information by taking it into account when forming a training sample through using narrow models of the media that describe some certain class of geological sections. However, this approach requires obtaining a separate solution for each case, with generation of a separate training dataset and training of a separate machine learning model (or set of models), which reduces usability and increases computational costs. Therefore, in order to reduce the computational cost, this study proposes to use transfer learning methods, which involve training base models on large datasets and fine-tuning them on limited datasets. This work is devoted to the study of the applicability of the transfer learning method in relation to inverse problems of gravimetry, magnetometry and magnetotelluric sounding, as well as their integration.

An estimate of the trigger effect of the proton flux on seismicity was obtained. The proton flux time series with a time step of 5 min, 2000–2024, was analyzed. In each time interval of 5 days, statistics of the proton flux time series were calculated: mean values, logarithm of kurtosis, spectral slope, singularities spectrum support width, wavelet-based entropy, and the Donoho–Johnston wavelet-based index. For each of the used statistics, time points of local extrema were found, and for each pair of time sequences of proton flux statistics and earthquakes with a magnitude of at least 6.5 in sliding time windows, the “advance measures” of each time sequence relative to the other were estimated using a model of the intensity of interacting point processes. The difference between the “direct” measure of the advance of time points of local extrema of proton flux statistics relative to the time moments of earthquakes and the “inverse” measure of the advance was calculated. The maximum proportion of the intensity of seismic events for which the proton flux was a trigger was estimated as 0.28 for using the points of the local minima of the singularities spectrum support width.

The relationship between the seismic regime and humidity, pressure, temperature, and wind speed measured at a network of stations on the Japanese islands was studied for the period from 1973 to 2025. For each of the parameters, weighted average time series were constructed using the principal component method and then subjected to wavelet decomposition. For wavelet decomposition levels, the amplitudes of the envelopes and the points of their local extrema were found and compared with the times at which earthquakes occurred. The problem of estimating an advanced measure of envelope extremum points relative to earthquake moments was considered using a model of interacting point processes. For a sequence of 213 strong earthquakes with a magnitude of at least 6.5, the same numbers for the largest local maxima and the smallest local minima were selected for the extrema of the envelope amplitude of each parameter. It turned out that the largest advance measures occurred for the seventh level of decomposition (the period from 16 to 32 days). Two advance mechanisms were identified: one mechanism is associated with the trigger effect of cyclones on seismicity, and the second is associated with the occurrence of atmospheric earthquake precursors.

This study investigates the hypothesis that meteorological anomalies may precede earthquake events. Long-term time series of observations for air temperature, atmospheric pressure and precipitation at a meteorological station in Kamchatka are considered. Time series are subjected to Huang decomposition into sequences of levels of empirical oscillation modes (intrinsic mode functions—IMFs), forming a set of orthogonal components with decreasing average frequency. For each IMF level, the instantaneous amplitudes of envelopes are calculated using the Hilbert transform. A comparison with the earthquake sequence is made using a parametric model of the intensity of two interacting point processes, which allows one to quantitatively estimate the “measure of the lead” of the time instants of the compared sequences. For each IMF level, the number of time moments of the largest local maxima of instantaneous amplitudes which is equal to the number of earthquakes is selected. As a result of the analysis, it turned out that for the sixth IMF level (periods of 8–16 days), the “lead measure” of the instantaneous amplitude maxima of meteorological parameters in comparison with earthquake time moments significantly exceeds the inverse lead, which confirms the existence of prognostic changes in meteorological parameters in the problem of “atmosphere–lithosphere” interaction. This study reveals that certain meteorological anomalies can be a precursor for seismic activity.

We consider 3-component records of the magnetic field strength with a time step of 1 min at 153 stations of the INTERMAGNET network for 31 years, 1991-2021. Data analysis is based on the calculation of pairwise correlation coefficients between wavelet coefficients in successive time windows 1 day long (1440 min counts). To describe the state of the magnetic field, the maxima of the average values of all pairwise correlation coefficients between stations were chosen, calculated over all detail levels of the wavelet decomposition and over all components of the magnetic field strength vector. The daily time series of such maxima is called wavelet correlation. The division of the network stations into 7 clusters is considered, and a time series of wavelet correlations is calculated for each cluster. In a sliding time window with a length of 365 days, correlation measures of synchronization of wavelet correlations from different clusters are calculated, which are compared with the strongest earthquakes with a magnitude of at least 8.5. For the global time series of wavelet correlations, the method of influence matrices is used to study the relationship between the maximum correlation responses to a change in the length of the day and a sequence of earthquakes with a magnitude of at least 7. As a result of the analysis, precursor effects are identified, and the important role of the Maule earthquake in Chile on February 27, 2010 in the behavior of the response of magnetic field (c) 2024 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Previously, it was shown that integration (joint use of data) of several geophysical methods allows one to obtain a higher quality of the solution of the inverse problem of exploration geophysics in comparison with the individual use of each of these methods. However, there may be a situation when for some measurement points there is no data from one of the geophysical methods used. At the same time, the data spaces of different integrated geophysical methods are interconnected. Therefore, the missing data of one method can be recovered from the known data of another one by constructing a preliminary adaptive mapping of one of the spaces to another. In this study, we investigate the solution of the inverse problem with integration of geophysical methods on the recovered data obtained based on noise addition during training of the neural networks performing the mapping from the data space of the method(s) with all data present to the data space of the method with missing data.

A method is proposed for analyzing the tremor of the earth's surface, measured by GPS, in order to highlight prognostic effects. The method is applied to the analysis of daily time series of vertical displacements in Japan. The network of 1047 stations is divided into 15 clusters. The Huang Empirical Mode Decomposition (EMD) is applied to the time series of the principal components from the clusters, with subsequent calculation of instantaneous amplitudes using the Hilbert transform. To ensure the stability of estimates of the waveforms of the EMD decomposition, 1000 independent additive realizations of white noise of limited amplitude were averaged before the Hilbert transform. Using a parametric model of the intensities of point processes, we analyze the connections between the instants of sequences of times of the largest local maxima of instantaneous amplitudes, averaged over the number of clusters and the times of earthquakes in the vicinity of Japan with minimum magnitude thresholds of 5.5 for the time interval 2012-2023. It is shown that the sequence of the largest local maxima of instantaneous amplitudes significantly more often precedes the moments of time of earthquakes (roughly speaking, has an "influence") than the reverse "influence" of earthquakes on the maxima of amplitudes.

This study is devoted to solving inverse problems of exploration geophysics, which consist in reconstructing the spatial distribution of the properties of the medium in the thickness of the earth from the geophysical fields measured on its surface. We consider the methods of gravimetry, magnetometry, and magnetotelluric sounding, as well as their integration, i.e. simultaneous use of data from several geophysical methods to solve the inverse problem. To implement such integration, in our previous studies we have proposed a parameterization scheme that describes a layered geophysical model with fixed layer properties, in which the determined parameters were the positions of the boundaries between the layers. In the present study, this parameterization scheme is complicated so that the properties of the layers vary from pattern to pattern in the data set. To improve the quality of neural network solution of the described inverse problem, we consider an approach based on the use of a priori information about the physical properties of the layers, in which this information is used directly as additional input features for the neural network.

Abstract We consider 3-component records of the magnetic field strength with a time step of 1 minute at 153 stations of the INTERMAGNET network for 31 years, 1991–2021. Data analysis is based on the calculation of pairwise correlation coefficients between wavelet coefficients in successive time windows 1 day long (1440 minute counts). To describe the state of the magnetic field, the maxima of the average values of all pairwise correlation coefficients between stations were chosen, calculated over all detail levels of the wavelet decomposition and over all components of the magnetic field strength vector. The daily time series of such maxima is called wavelet correlation. The division of the network stations into 7 clusters is considered, and a time series of wavelet correlations is calculated for each cluster. In a sliding time window with a length of 365 days, correlation measures of synchronization of wavelet correlations from different clusters are calculated, which are compared with the strongest earthquakes with a magnitude of at least 8.5. For the global time series of wavelet correlations, the method of influence matrices is used to study the relationship between the maximum correlation responses to a change in the length of the day and a sequence of earthquakes with a magnitude of at least 7. As a result of the analysis, precursor effects are identified, and the important role of the Maule earthquake in Chile on February 27, 20210 in the behavior of the response of magnetic field for the preparation of strong seismic events is shown.

In this paper, we consider a neural network solution of the inverse problem (IP) of magnetotelluric sounding (MTS) which consists in constructing the electrical conductivity distribution in the Earth's interior from the values of the electromagnetic field components measured on its surface. It has a high input dimension (thousands of features), so it is necessary to reduce the input data dimension to achieve a more accurate and stable solution while reducing computational complexity. Neighboring measurement points and neighboring frequencies carry similar information dictating the need to use a selection method that considers this feature. The present work is devoted to the study of a method based on the iterative selection of features with the highest correlation with respect to the target variable and the exclusion of features with high cross-correlation. This method was compared with the traditional selection method, the cross-correlation filter.

The inverse problem (IP) of exploration geophysics consists in reconstructing the spatial distributionf of the properties of the medium in the Earth’s interior from measurements on its surface. This IP is a non-linear ill-posed ill-conditioned problem with high dimensionality both by input and by output. One of the approaches free of many shortcomings inherent for traditional methods of IP solving, is the use of artificial neural networks (NN). In this study, it has been suggested to use an integration of geophysical methods to improve the quality of the solution obtained by NN. The considered model combines three geophysical methods: gravimetry, magnetometry, and magnetotellurics. The problem considered is that of determining the structural boundaries separating the geological layers with constant values of the parameters: density in gravimetry, magnetization in magnetometry, electrical resistivity in magnetotellurics. In this study, a four-layer 2D model was considered. It is demonstrated that integration of geophysical methods provides significantly better results that use of each of the methods separately. It is also shown that in some cases it is also possible to improve the quality of the IP solution using multitask learning—simultaneous determination of the positions of two or all three layer boundaries.

This study is devoted to the inverse problems of exploration geophysics, which consist in reconstructing the spatial distribution of the properties of the medium in the Earth’s thickness from the geophysical fields measured on its surface. We consider the methods of gravimetry, magnetometry, and magnetotelluric sounding, as well as their integration, i.e. simultaneous use of data from several geophysical methods to solve the inverse problem. In their previous studies, the authors have shown that the integration of geophysical methods allows improving the quality of the solution of the inverse problem in comparison with the individual use of each of them. One of the obstacles to using the integration of geophysical methods can be the situation when for some measurement points there is no data from one of the geophysical methods used. At the same time, the data spaces of different integrated geophysical methods are interconnected, and the values of the observed quantities (fields) for one of the methods can be possibly recovered from the known values of the observed quantities of another geophysical method by constructing a preliminary adaptive mapping of one of the spaces to another. In this study, we investigate the neural network recovery of missing data of one geophysical method from the known data of another one and compare the quality of the solution of the inverse problem on full and on recovered data.

In their previous studies, the authors have shown that the integration of geophysical methods allows improving the quality of the solution of an inverse problem of exploration geophysics in comparison with the individual use of each of them. However, in practice, it is possible that for some measurement points, data from one of the geophysical methods used is missing. In this study, we investigate an approach associated with neural network recovery of the missing data of one geophysical method from the known data of another, and their further joint application to solve the inverse problem. In addition, we explore the effectiveness of applying multitask learning approach at the data recovery stage for the subsequent solution of the inverse problem.

The inverse problems of exploration geophysics are to reconstruct the spatial distribution of the properties of the medium in the Earth's thickness from the geophysical fields measured on its surface. In particular, this paper deals with the problems of gravimetry, magnetometry, and magnetotelluric sounding, as well as their integration, i.e., the simultaneous use of several geophysical fields to restore the desired distribution. To implement the integration, a 4-layer 2D model was used, where the inverse problem was to determine the lower boundary of the layers, and each layer was characterized by variable values of the depth of the lower boundary along the section and fixed values of density, magnetization, and resistivity, both for the layer and for the entire data set. To implement the neural network solution of the inverse problem, a data set was generated by solving the direct problem, where for each pattern, the distribution of layer depth values was set randomly in a given range and with a given step, i.e. it took discrete values from a certain set. In this paper, we consider an approach involving the use of neural networks to solve the problem of multiclass classification, where class labels correspond to discrete values of the determined layer depths. The results of the solution are compared with the results of the solution of the same inverse problem in the formulation of the regression problem, in terms of the error in determining the depth of the layers.

In the present study, using the inverse problem (IP) of magnetotelluric sounding (MTS) as an example, we consider the use of neural networks to solve high-dimensional coefficient inverse problems. To reduce the incorrectness, a complex approach is considered related to the use of narrow classes of geological models, with prior selection of the model class by solving the classification problem by MTS data. Within the framework of this approach, the actual direction of work is to reduce the volume of calculations when re-building the system for another set of geological models. This goal can be achieved by selecting the essential features. The present paper is devoted to the study of the applicability of various selection methods to the MTS IP. Also, in this paper we consider taking into account domain knowledge about the studied object in the process of selection of essential features using methods such as wrapper.

The article deals with a priori and a posteriori characteristics of a degree of practical stability (practical uniqueness) of solutions to nonlinear inverse problems in geoelectrics. Numerical values of moduli of continuity of direct and inverse operators and their modifications are used as criteria of a degree of practical stability. Examples of calculation of a priori and a posteriori characteristics of a degree of practical stability of inverse problems for standard models which are used in geoelectrics are given. A dependence of characteristics of a degree of practical stability on accuracy of a descrip-tion and on input data structure, volume and level of error is examined. The obtained numerical esti-mations of a degree of practical stability of approximate solutions to inverse problems do not depend on the algorithm applied for their solving. This allows estimating accuracy and reliability of the geo-physical data interpretation results objectively.