Geophysical Problems Research Articles

Nonlocal theory of propagation and reflection of plane waves in higher order thermo diffusive semiconducting medium

The present article is related to propagation and reflection of elastic wave through a nonlocal generalized thermo-diffusive semiconducting elastic solid. The non-local theory is employed to study the wave behavior. Three phase lag model with higher order fractional order derivative is incorporated to discuss heat propagation through the medium, in addition with two phase lags diffusion equation. The Helmholz vector rule is applied to decompose the system into longitudinal and transverse components. The frequency dispersion relation indicates the presence of four coupled longitudinal and one un-coupled shear vertical wave. The speed of the waves is plotted against angular frequency for local and nonlocal medium. The cutoff frequency of the waves is also depicted graphically. The longitudinal P-wave is taken to be an incident wave at the free surface of the solid to compute the reflection coefficients. The influences of fractional order and nonlocal parameters on amplitude ratios are also studied. The effect of these parameters is found to be significant. The results are proved in the context of energy conservation. The results obtained from the current investigation are very useful for scientists working on problems of geophysics and various fields of mechanics.

On torsional wave in void type porous layers between viscoelastic and piezoelectric media with parabolic irregularity

The viscoelastic earth model is increasingly utilized by seismologists for studying surface seismic wave propagation through Earth’s porous crustal regions such as granular materials, including rock, soils, and synthetic porous bodies. The present study characterizes torsional wave propagation in an irregular void-type porous layer sandwiched between an initially stressed inhomogeneous viscoelastic layer and a piezoelectric substratum. Displacement fields for the layer and half spaces are obtained separately using a variable separable technique, whereas volume fraction and electric potential field are derived for layer and substratum, respectively using the matrix calculus approach. Dispersion relations have been derived for both electrically open and short circuit conditions and agree with standard results. Particular cases have been deduced to validate the finding of the study with literature results. Effects of change in relevant parameters such as initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity and dissipation factor have been analyzed on the phase velocity of the torsional wave through various plots and summarized in a tabular form for ready reference to researchers. Analysis of the present geophysical problem may be useful in characterizing torsional velocity in porous silicate rocks which are abundantly found in the transition zone between oceanic and continental crust called Conrad discontinuity. Highlights Torsional propagation in a void-type porous layer crammed between an initially stressed inhomogeneous viscoelastic layer and piezoelectric half-space has been investigated. Variable separable technique, the matrix calculus approach is used for computing the displacement fields of respective media. A comparative study has been carried out for both electrically open and short conditions. The impact of pertinent parameters including initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity, and dissipation factor on the phase velocity of the torsional wave has been examined.

Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method

A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty.

Sensing prior constraints in deep neural networks for solving exploration geophysical problems

One of the key objectives in geophysics is to characterize the subsurface through the process of analyzing and interpreting geophysical field data that are typically acquired at the surface. Data-driven deep learning methods have enormous potential for accelerating and simplifying the process but also face many challenges, including poor generalizability, weak interpretability, and physical inconsistency. We present three strategies for imposing domain knowledge constraints on deep neural networks (DNNs) to help address these challenges. The first strategy is to integrate constraints into data by generating synthetic training datasets through geological and geophysical forward modeling and properly encoding prior knowledge as part of the input fed into the DNNs. The second strategy is to design nontrainable custom layers of physical operators and preconditioners in the DNN architecture to modify or shape feature maps calculated within the network to make them consistent with the prior knowledge. The final strategy is to implement prior geological information and geophysical laws as regularization terms in loss functions for training the DNNs. We discuss the implementation of these strategies in detail and demonstrate their effectiveness by applying them to geophysical data processing, imaging, interpretation, and subsurface model building.

3-D Crosswell electromagnetic inversion based on IRLS norm sparse optimization algorithms

Due to the complexity of underground reservoir distribution and the non-uniqueness of geophysical inverse problems, there is still a lack of practical and effective cross-well electromagnetic inversion methods. Our goal is to develop an efficient method to reduce the non-uniqueness of the physical property model recovered in the inversion. Based on a defined framework, we propose a 3-D crosswell electromagnetic sparse inversion based on iterative reweighted least squares (IRLS) method. We perform the inversion using a hybrid norm formulation, where the lp-norm (0 ≤ p ≤ 1) sparse optimization problem can be transformed into a series of weighted l2-norm optimization problems. Compared with the traditional norm inversion method, the sparse inversion method can make more effective use of the known physical information and obtain more accurate abnormal body position and shape. Finally, the effectiveness of sparse inversion method is verified by model test and inversion of measured data in mining area.

3-D gravity inversion for the basement relief reconstruction through modified success-history-based adaptive differential evolution

SUMMARY A gravity inversion procedure using the success-history-based adaptive differential evolution (SHADE) algorithm is presented to reconstruct the 3-D basement relief geometry in sedimentary basins. We introduced exponential population size (number) reduction (EPSR) to reduce the computational cost and used self-adaptive control parameters to solve this highly nonlinear inverse problem. Model parametrization was carried out by discretizing the sedimentary cover via juxtaposed right prisms, each placed below each observation point. Resolvability characteristics of the 3-D inverse problem were revealed through some cost function topography landscapes. The fine-tuned control parameter namely, population number allowed us to get best benefit from the algorithm. Additionally, a stabilizing function as a relative constraint was used to avoid undesired effects originated from the ill-posedness of the problem. In the synthetic data cases, the strategy we propose outperformed the linear population number reduction strategy which has won various IEEE–CEC competitions so far. Thorough uncertainty assessments via probability density function and principal component analysis demonstrated the solidity of the obtained inverse models. In the real data case, residual gravity anomalies of two well-known major grabens of Aegean Graben System (Türkiye), calculated thanks to the finite element method, were inverted. It was determined that the inverse solutions obtained for these basement reliefs, whose depths are still controversial, are statistically reliable. Moreover, these depths were found to be less than the depths reported in most previous studies. We conclude that the SHADE using EPSR strategy that we propose is a powerful alternative inversion tool for highly nonlinear geophysical problems.

A general method for extracting the amplitude spectrum of the seismic wavelet from the seismic traces

When solving geophysical problems using reflection seismology, extracting the amplitude spectrum of the seismic wavelet (ASSW) from a seismic trace is the basis for many downstream works, such as deconvolution and sparse reflection coefficient inversion. This paper pertains to statistical methods for estimating ASSW, that is, separating the scattering effect of the formation from the amplitude spectrum of a seismic trace to obtain a band-limited ASSW. Common methods assume the reflection coefficient sequence (RCS) is white, making them unsatisfactory in many cases. Gao et al (2017 Inverse Problems 33 085005) proposed an ASSW extraction method based on contraction operator mapping (COM method) and experimentally proved it effective for non-white RCSs. However, this method is only valid for unimodal ASSW, which makes it unsuitable for most sources. We propose a general method for estimating ASSW which does not require the whiteness assumption of the RCS and does not restrict the specific form of ASSW. We show that the COM method has function representation limitations and redefines a new operator, proving that it is also a contractive mapping. Our method can be regarded as a general form of the COM method, filling the theoretical gap that existing methods cannot be applied to non-white RCS and non-unimodal ASSW. It provides a general method for the estimation of ASSW. We thoroughly verify this generality by simulating different source types while considering wavelet attenuation. Compared with the COM method, the proposed method has absolute advantages.

Течение пандемии COVID-19 2020-2022 гг.: описание методами математической статистики и дискретного математического анализа

The paper describes the course of the COVID-19 pandemic using a combination of mathematical statistics and discrete mathematical analysis (DMA) methods. The method of regression derivatives and FCARS algorithm as components of DMA will be for the first time tested outside of geophysics problems. The algorithm is applied to time series of the number of new cases of COVID-19 infections per day for some regions of Russia and the Republic of Austria. This allowed to assess the nature and anomalies of pandemic spread as well as restrictive measures and decisions taken in terms of the administration of countries and territories. It was shown that these methods can be used to identify time intervals of change in the nature of the incidence rate and areas with the most severe course of the epidemic. This made it possible to identify the most significant restrictive measures that allowed to reduce the growth of the disease.

A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation

AbstractThe Kuroshio Current in the North Pacific displays path changes on an interannual‐to‐decadal time scale. In an idealized barotropic quasi‐geostrophic model of the double‐gyre wind‐driven circulation under stochastic wind‐stress forcing, such variability can occur due to transitions between different equilibrium states. The high‐dimensionality of the problem makes it challenging to determine the probability of these transitions under the influence of stochastic noise. Here we present a new method to estimate these transition probabilities, using a Dynamical Orthogonal (DO) field approach. In the DO approach, the solution of the stochastic partial differential equations system is decomposed using a Karhunen–Loève expansion and separate problems arise for the ensemble mean state and the so‐called time‐dependent DO modes. The original method is first reformulated in a matrix approach which has much broader application potential to various (geophysical) problems. Using this matrix‐DO approach, we are able to determine transition probabilities in the double‐gyre problem and to identify transition paths between the different states. This analysis also leads to the understanding which conditions are most favorable for transition.

Quantitative interpretation of geoelectric inverted data with a robust probabilistic approach

The nonuniqueness of the solution to the geophysical inverse problem can lead to misinterpretation while characterizing the subsurface. To tackle this situation, ground-truth information from excavations and wells can be used to improve, calibrate, and interpret inverted models. We refer to quantitative interpretation as the decision analysis based on probability theory, which is focused on solving a classification problem. First, we present a probabilistic approach to classify the different types of materials or “categories” observed in borehole logs using multiple data sources: inverted 2D electrical resistivity tomography and induced polarization data and the positions ( x, z) of these boreholes. Then, using the Bayes’ rule and permanence of ratios, we compute the joint conditional probabilities of each category, given all data sources in the whole inverted model domain. We validate this approach with synthetic data modeling for a complex anthropogenic-geologic scenario and using real data from an old landfill. Afterward, we assess the performance of the probabilistic approach for classification and compare it with the machine learning algorithm of multilayer perceptron (MLP). In addition, we analyze the effect that the different data sources and the number of boreholes (and their distribution) have on both approaches with the synthetic case. Our results indicate that the MLP performance is better for delineating the different categories where the lateral contrasts in the synthetic resistivity model are small. Nevertheless, the classification obtained with the probabilistic approach using real data seems to provide a more geologically realistic distribution. We conclude that the probabilistic approach is robust for classifying categories when high spatial heterogeneity is expected and when ground-truth data are limited or not sparsely distributed. Finally, this approach can be easily extended to integrate multiple geophysical methods and does not require the optimization of hyperparameters as for MLP.

Gaussian active learning on multi-resolution arbitrary polynomial chaos emulator: concept for bias correction, assessment of surrogate reliability and its application to the carbon dioxide benchmark

Surrogate models are widely used to improve the computational efficiency in various geophysical simulation problems by reducing the number of model runs. Conventional one-layer surrogate representations are based on global (e.g. polynomial chaos expansion, PCE) or on local kernels (e.g., Gaussian process emulator, GPE). Global representations omit some details, while local kernels require more model runs. The existing multi-resolution PCE is a promising hybrid: it is a global representation with local refinement. However, it can not (yet) estimate the uncertainty of the resulting surrogate, which techniques like the GPE can do. We propose to join multi-resolution PCE and GPE s into a joint surrogate framework to get the best out of both worlds. By doing so, we correct the surrogate bias and assess the remaining uncertainty of the surrogate itself. The resulting multi-resolution emulator offers a pathway for several active learning strategies to improve the surrogate at acceptable computational costs, compared to the existing PCE-kriging approach it adds the multi-resolution aspect. We analyze the performance of a multi-resolution emulator and a plain GPE using didactic test cases and a CO2 benchmark, that is representative of many alike problems in the geosciences. Both approaches show similar improvements during the active learning, but our multi-resolution emulator leads to much more stable results than the GPE. Overall, our suggested emulator can be seen as a generalization of multi-resolution PCE and GPE concepts that offers the possibility for active learning.

Building a model of the Earth's gravitational field within the Caribbean Sea based on satellite altimetry data

Methods for processing measurement information collected over the past 30 years by altimetry spacecraft with various measurement technologies and orbit characteristics are systematized and described. The description and classification of measurement information files is given. Based on the removal-recovery method, a software package for determining the characteristics of the gravitational field and the figure of the Earth by satellite altimetry has been developed. On the example of a geologically complex and seismically active region (the Caribbean Sea), a model of the gravity field (gravity anomalies) was constructed and its accuracy characteristics were evaluated. The calculated standard deviation of gravity anomalies from the data of the EGM2008 global model does not exceed 4 mGal in the open sea and 14 mGal in the coastal zone, which corresponds to the international level. At the moment, a digital interactive gravity model of the Global Ocean is used to solve applied problems of geophysics and geology, in particular, to forecast oil and gas fields.

Reliable amortized variational inference with physics-based latent distribution correction

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges by pretraining a neural network that acts as a surrogate conditional distribution that approximates the posterior distribution not only for one instance of the observed data but also for the distribution of the data pertaining to a specific inverse problem. When fed previously unseen data, the neural network — in our case, a conditional normalizing flow — provides the posterior samples at virtually no cost. However, the accuracy of amortized variational inference relies on the availability of high-fidelity training data, which seldom exist in geophysical inverse problems because of the earth’s heterogeneous subsurface. In addition, the network is prone to errors if evaluated over data that are not drawn from the training data distribution. As such, we have aimed to increase the resilience of amortized variational inference in the presence of moderate data distribution shifts. We achieve this via a correction to the conditional normalizing flow’s latent distribution that improves the approximation to the posterior distribution for the data at hand. The correction involves relaxing the standard Gaussian assumption on the latent distribution and parameterizing it via a Gaussian distribution with an unknown mean and (diagonal) covariance. These unknowns are then estimated by minimizing the Kullback-Leibler divergence between the corrected and the (physics-based) true posterior distributions. Although generic and applicable to other inverse problems by means of a linearized seismic imaging example, we find that our correction step improves the robustness of amortized variational inference with respect to changes in the number of seismic sources, noise variance, and shifts in the prior distribution. This approach, given noisy seismic data simulated via the linearized Born modeling, provides a seismic image with limited artifacts and an assessment of its uncertainty at approximately the same cost as five reverse time migrations.

Model-constrained and data-driven double-supervision acoustic impedance inversion

Seismic impedance inversion is an important technique for structure identification and reservoir prediction. Model-based and data-driven impedance inversion are the commonly used inversion methods. In practice, the geophysical inversion problem is essentially an ill-posedness problem, which means that there are many solutions corresponding to the same seismic data. Therefore, regularization schemes, which can provide stable and unique inversion results to some extent, have been introduced into the objective function as constrain terms. Among them, given a low-frequency initial impedance model is the most commonly used regularization method, which can provide a smooth and stable solution. However, this model-based inversion method relies heavily on the initial model and the inversion result is band limited to the effective frequency bandwidth of seismic data, which cannot effectively improve the seismic vertical resolution and is difficult to be applied to complex structural regions. Therefore, we propose a data-driven approach for high-resolution impedance inversion based on the bidirectional long short-term memory recurrent neural network, which regards seismic data as time-series rather than image-like patches. Compared with the model-based inversion method, the data-driven approach provides higher resolution inversion results, which demonstrates the effectiveness of the data-driven method for recovering the high-frequency components. However, judging from the inversion results for characterization the spatial distribution of thin-layer sands, the accuracy of high-frequency components is difficult to guarantee. Therefore, we add the model constraint to the objective function to overcome the shortages of relying only on the data-driven schemes. First, constructing the supervisor1 based on the bidirectional long short-term memory recurrent neural network, which provides the predicted impedance with higher resolution. Then, convolution constraint as supervisor2 is introduced into the objective function to guarantee the reliability and accuracy of the inversion results, which makes the synthetic seismic data obtained from the inversion result consistent with the input data. Finally, we test the proposed scheme based on the synthetic and field seismic data. Compared to model-based and purely data-driven impedance inversion methods, the proposed approach provides more accurate and reliable inversion results while with higher vertical resolution and better spatial continuity. The inversion results accurately characterize the spatial distribution relationship of thin sands. The model tests demonstrate that the model-constrained and data-driven impedance inversion scheme can effectively improve the thin-layer structure characterization based on the seismic data. Moreover, tests on the oil field data indicate the practicality and adaptability of the proposed method.

Generalized statistics: Applications to data inverse problems with outlier-resistance.

The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood estimators associated with generalized Gaussian distributions in the context of Rényi, Tsallis and Kaniadakis statistics. In this regard, we analytically analyze the outlier-resistance of each proposal through the so-called influence function. In this way, we formulate inverse problems by constructing objective functions linked to the maximum likelihood estimators. To demonstrate the robustness of the generalized methodologies, we consider an important geophysical inverse problem with high noisy data with spikes. The results reveal that the best data inversion performance occurs when the entropic index from each generalized statistic is associated with objective functions proportional to the inverse of the error amplitude. We argue that in such a limit the three approaches are resistant to outliers and are also equivalent, which suggests a lower computational cost for the inversion process due to the reduction of numerical simulations to be performed and the fast convergence of the optimization process.

Methods of Pulse Neutron Probing in Geological and Geophysical Investigations

. The problem of introducing pulse neutron probing in the process of geological and geophysical studies has been updated. The main factors that increase the sensitivity and information content of pulse methods in comparison with stationary neutron methods have been considered. It has been shown that the efficiency of pulse neutron probing depends on the length of the probe, time and energy characteristics of the equipment used. The principal features of various modifications of pulse neutron probing for solving geological and geophysical problems have been noted. The aspects of the efficient use of pulse modification in neutron gamma-ray spectrometry and inelastic scattering of fast neutrons have been discussed. Improved modifications of neutron probing based on the complex application of instrumental signals arising from inelastic scattering of fast and radiative capture of thermal neutrons have been proposed

Dust Settling From Turbulent Layers in the Free Troposphere: Implications for the Saharan Air Layer

AbstractDesert dust accounts for a substantial fraction of the total atmospheric aerosol loading. It produces important impacts on the Earth system due to its nutrient content and interactions with radiation and clouds. However, current climate models greatly underestimate its airborne lifetime and transport. For instance, super coarse Saharan dust particles (with diameters greater than 10 µm) have repeatedly been detected in the Americas, but models fail to reproduce their transatlantic transport. In this study, we investigated the extent to which vertical turbulent mixing in the Saharan Air Layer (SAL) is capable of delaying particle deposition. We developed a theory based on the solution to a one‐dimensional dust mass balance and validated our results using large‐eddy simulation (LES) of a turbulent shear layer. We found that eddy motion can increase the lifetime of suspended particles by up to a factor of 2 when compared with laminar flows. Moreover, we found that the increase in a lifetime can be reliably estimated solely as a function of the particle Peclet number (the ratio of the mixing timescale to the settling timescale). By considering both the effects of turbulent mixing and dust asphericity, we explained to a large extent the presence of super coarse Saharan dust in the Caribbean observed during the Saharan Aerosol Long‐Range Transport and Aerosol‐Cloud‐Interaction Experiment (SALTRACE) field campaign. The theory for the lifetime of coarse particles in turbulent flows developed in this study is also expected to be applicable in other similar geophysical problems, such as phytoplankton sinking in the ocean mixed layer.

SeisDeNet: an intelligent seismic data Denoising network for the internet of things

Deep learning (DL) has attracted tremendous interest in various fields in last few years. Convolutional neural networks (CNNs) based DL architectures have been successfully applied in computer vision, medical image processing, remote sensing, and many other fields. A recent work has proved that CNNs based models can also be used to handle geophysical problems. Due to noises in seismic signals acquired by geophone equipment this kind of important multimedia resources cannot be effectively utilized in practice. To this end, from the perspective of seismic exploration informatization, this paper takes informatization data in seismic signal acquisition and energy exploration field using cutting-edge technologies such as Internet of things and cloud computing as the research object, presenting a novel CNNs based seismic data denoising (SeisDeNet) architecture is suggested. Firstly, a multi-scale residual dense (MSRD) block is built to leverage the characteristics of seismic data. Then, a deep MSRD network (MSRDN) is proposed to restore the noisy seismic data in a coarse-to-fine manner by using cascading MSRDs. Additionally, the denoising problem is formulated into predicting transform-domain coefficients, by which noises can be further removed by MSRDNs while richer structure details are preserved comparing with the results in spatial domain. By using synthetic seismic records, public SEG and EAGE salt and overthrust seismic model and real field seismic data, the proposed method is qualitatively and quantitatively compared with other leading edge schemes to evaluate it performance, and some results shows that the proposed scheme can produce data with higher quality evaluation while maintaining far more useful data comparing with other schemes. The feasibility of this approach is confirmed by the denoising results, and this approach is shown to be promising in suppressing the seismic noise automatically.

Assessment of the liquefaction potential of the Arifiye (Sakarya) region with multidisciplinary geoscience approaches in the GIS environment

The severity of damage under building load during an earthquake, one of the most critical geophysical and geotechnical engineering problems, varies according to soil types. Therefore, the liquefaction problem constitutes an essential phenomenon, especially for the settlements located on alluvial units in high seismicity regions. This study used standard penetration test (SPT), and share wave velocity (Vs) based approaches to evaluate the liquefiability in the Arifiye region in the North Anatolian Fault Zone (NAFZ) with 40 drillings and 35 seismic measurements considering the Izmit (Mw: 7.4) and Mudurnu (Mw: 7.0) earthquake scenarios. In this context, three different approaches (Liquefaction potential index (LPI), Ishihara boundary curve (IB), and Ishihara-inspired index (LPIISH)) were employed. The maps from these assessments were prepared in the Geographic Information System (GIS) environment. It was determined for the study area that the lakeside and northern part of the NAFZ linearity, which has a very shallow groundwater table and low Vs values, are vulnerable to liquefaction hazards for all approaches. On the contrary, the south part of the NAFZ linearity is defined as non-liquefiable. Although the Vs and SPT-based LPI maps considerably overlapped, some differences in LPI values emphasized the importance of integrated use of the geophysical and geotechnical methods. Hence, liquefaction analysis with different approaches will enable it to operate according to the most cautious situation in risk management.

Investigation of the influence of space weather on the occurrence of geoinduction currents in the middle latitudes

The study of physical processes based on geomagnetic induction currents among the geophysical problems of the last decade is one of the main problems of fundamental research. Consideration of geomagnetic-induced current as a threatening "shock" aspect originally took place in the NASA project "life with a star", and one of the main results of this working group was that the problems of geomagnetic-induced current must be solved in combination with science and methods. In the proposed work, calculations were carried out using a model of the same type, the model of which is based on the fundamental laws. The retrospective analysis of the geophysical situation for 2016-2021 was carried out on the basis of the data of the Alma-Ata geomagnetic observatory. For all the considered events, the GIC values were calculated and the peculiarities of the occurrence of GIC at middle latitudes were studied. Of all the events studied for 2016-2021, 25 events were identified. Among these events: 1 large geomatnetic storm, 1 medium geomagnetic storm, 5 substorms and 18 weak geomagnetic storms. For these events, the following was identified. During a large geomagnetic storm, the GIC amplitude value was I=0.4mA. During an average magnetic storm I=0.14mA. During a storm with a sudden onset induced current amplitude I=0.75mA. During weak magnetic storms, the amplitude values varied within (0.06 - 0.15)mA. In general, it can be seen, that the GIC amplitude values depend on the intensity of the geomagnetic storm. However, there are some exceptions. For example, a storm with a sudden onset according to the planetary index refers to weak geomagnetic storms, however, the GIC value turned out to be greater than the GIC induced during a large geomagnetic storm. At the same time, we also considered substorms. During substorms, currents of the order of 0.07-0.13mA were induced.