We introduce a novel method for developing the training dataset for the Numerical Dispersion Mitigation network (NDM-net), aimed at diminishing numerical inaccuracies in seismic modeling. Our strategy involves using a limited set of seismograms, produced with coarse and fine grids, to train the network. This training enables the network to transform less accurate coarse-grid data into higher-quality fine-grid data. Subsequently, the network is employed on a more extensive set of seismograms, initially computed with the coarse grid, to lower numerical errors. Creating the training dataset is the most demanding aspect of this method, requiring a balance between the number of seismograms used and maintaining training effectiveness. We propose a method to create the training dataset that maintains a specific Hausdorff distance with the complete dataset. However, this distance can vary based on the seismic-geological model used in simulations. Our work shows that an adaptive approach in setting the Hausdorff distance limit is more advantageous than a fixed limit, as it reduces the training dataset size without compromising accuracy.
Quasistatic Biot equations in the frequency domain are applied to model low-frequency loading of the fractured porous rock sample. We approximate Biot equations by a finite-difference scheme on the staggered grid, defining different field components at different grid points. To solve the resulting system of linear algebraic equations (SLAE) with more than 106 unknown values, we use an iterative method (Biconjugate gradient stabilized method, BCGStab) with a preconditioner based on field-split approach to divide equations into two groups. The first group describes solid deformation, and the second group describes fluid transport. Numerical experiments demonstrate fast convergence of the iterative process for applied method and its advantages in the case of large computational grid in comparison with direct method.
The solutions of many spatially discretized problems, related with computational geophysics, are presented as 𝑢 = 𝑓(𝐴)𝜑, where 𝐴 ∈ 𝑹𝑁×𝑁, 𝜑 ∈ 𝑹𝑁, 𝑓 is a function. We consider approximations to 𝑢 on the basis of Galerkin approach for polynomial and rational Krylov subspaces. We describe the corresponding computational methods – the ones of Lanczos and rational Arnoldi, and also their application to solving some problems of computational geophysics (in the area of electrologging, thermal logging, electrical prospecting). The aim of this review paper is to instruct the reader to apply the methods described here to his applied problems.
A mathematical model of a blocky-layered medium with thin layers is considered. This model describes elastic deformations of both blocks and interlayers. The viscoelastic properties of the interlayer materials are taken into account in order to describe wave attenuation. Wave fields excited in a blocky medium are investigated. The results of numerical simulation are compared with experimental data.
We present a numerical approach to simulate the two-phase flows. The approach is based on the phase-field method where the phase is defined by the concentration function. This function smoothly varied from zero to one to distinguish between the phases. However, the phase interface is substituted by a thin enough layer where the phases are artificially mixed. Such representation of the phases simplifies evaluation of the interfacial tension and approximation of the wetting angles when the finite differences are used to approximate the problem. We verified the approach over a series of tests.
A technology for transient electromagnetic monitoring of permafrost is being scientifically substantiated to prevent man-made accidents and environmental disasters. Methods for fast 1D and 3D modeling of pulse signals have been developed. We have created a procedure for transforming the signals into apparent electrical resistivities, and implemented a data inversion algorithm using the Sumudu transform and artificial neural networks. Based on modeling of the signals in realistic geoelectric models with permafrost, the capability of monitoring the state of frozen soil by changes in the signals has been shown. Full-scale experiments with a prototype of a transient monitoring system have been successfully completed.
The spatial microstructure of the Bazhenov Formation samples was studied according to FIB-SEM data to prepare a digital model and calculate filtration-capacitance properties. Digital core modeling is aimed at complementing traditional laboratory studies of rock samples with computational experiment capabilities and allows not only to predict the amount of hydrocarbons that can be extracted from a field, but also to plan optimal methods for its development. The possibilities of digital core technology have been tested on highly permeable rocks, while for non-traditional ones there are still questions about the choice and description of a porous medium, primarily related to the need to switch to the submicron and nano scale. The present study shows the difficulties associated with the preparation of a digital model based on FIB-SEM material of the Bazhenov Formation, as well as modeling and validation of properties.
This paper provides a description and software implementation of an algorithm for numerical simulation of uniaxial loading of porous media. The algorithm is based on the method of bonded discrete elements, in which the environment is represented as a set of interacting particles. The purpose of this study is to systematically study the influence of input parameters on the strength characteristics of the resulting material. A series of numerical experiments is presented for various combinations of tangential stiffness, bond length, and particle friction coefficient at the microlevel. Based on the obtained stress-strain curves, the values of Young's modulus and compressive strength of the body were calculated. It is shown that compressive strength of the material shows a linear increase with increasing bond length and tangential stiffness, and a quadratic dependence with increasing friction coefficient. Young's modulus tends to increase for all varied parameters. However, it seems impossible to establish any specific dependencies using the number of statistical realizations used in the work.
The general concept of a multiscale modeling approach for solving geomechanics problems is presented. It is based on the solution of a system of poroelastoplasticity equations taking into account changes in macroparameters during the development of deformation as a result of the evolution of the internal structure of the geomedium under the influence of load. Macroparameters are refined by modeling the deformation of selected smaller-scale areas. A feature of the presented approach is the absence of a fixed mesovolume to clarify the parameters. This mesovolume is determined depending on the stress-strain state of the macroscopic region.
The article discusses the basis of the recently discovered fan mechanism of rock rupture at seismogenic depths of the Earth's crust, creating faults with high permeability. A phenomenal feature of the fan mechanism is the ability to create new faults in strong rocks at abnormally low shear stresses and provide high fault velocity up to supersonic, which makes it the most dangerous earthquake mechanism. It is shown that this mechanism can be activated artificially for various purposes, for example, when creating deep collectors for petro-thermal power plants and to increase oil recovery from hardto-recover reserves.
