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Intense methane emission from permafrost soil into the atmosphere has long been observed in Arctic shelf and coastal zones. Due to the potential danger of this phenomenon for the environment and infrastructure, there is a need for periodic monitoring of gas pockets, including by means of land seismic exploration. In the present paper, this process is studied using numerical simulation methods. In order to reflect the main specific features of the region, a model of layered permafrost sandy soil with curved boundaries between the layers is constructed. Vertical and horizontal gas migration is represented by an increase in the number of methane reservoirs. The hyperbolic equations of linear elasticity are used as a governing system. The problem is solved by applying the grid-characteristic method in the two-dimensional case. The elastic parameters of the layers are specified in each grid cell. Wave structures exhibited by the resulting synthetic wave patterns and seismograms are analyzed in detail, allowing the direction of gas migration to be determined. The results can be used to interpret similar in situ measurements. [ABSTRACT FROM AUTHOR]

An explicit-implicit scheme is constructed for the numerical solution of the system of equations governing an elastoviscoplastic continuous medium with softening. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations, which contain a small relaxation time parameter in the denominator of the nonlinear free terms. Accurate formulas for correcting the stress deviators after the elastic computation step are derived in the case of a linear viscosity function and a nonlinear softening law. The resulting solutions of the implicit approximation for the stress deviators of the elastoviscoplastic system admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of numerical solutions to ill-posed elastoplastic systems with softening. [ABSTRACT FROM AUTHOR]

This paper presents a novel numerical method for the Newton seismic full-waveform inversion (FWI). The method is based on the full-space approach, where the state, adjoint state, and control variables are optimized simultaneously. Each Newton step is formulated as a PDE-constrained optimization problem, which is cast in the form of the Karush–Kuhn–Tucker (KKT) system of linear algebraic equitations. The KKT system is solved inexactly with a preconditioned Krylov solver. We introduced two preconditioners: the one based on the block-triangular factorization and its variant with an inexact block solver. The method was benchmarked against the standard truncated Newton FWI scheme on a part of the Marmousi velocity model. The algorithm demonstrated a considerable runtime reduction compared to the standard FWI. Moreover, the presented approach has a great potential for further acceleration. The central result of this paper is that it establishes the feasibility of Newton-type optimization of the KKT system in application to the seismic FWI. [ABSTRACT FROM AUTHOR]

The goal of this study is to develop and apply a grid-characteristic numerical algorithm for determining damage to an offshore object (ice island) by computing seismic wave propagation from an earthquake hypocenter located at a depth of several kilometers taking into account specific features of the Northern Seas (shallow depths). The grid-characteristic method on combined grids is used for this purpose. A single run involves more than 25 separate grids differing from each other in the system of equations to be solved, the type of the numerical scheme, and the step sizes in coordinates. Some of these grids make up a set of embedded hierarchical ones with a multiple step in coordinate, while the others are conformal to each other. Additionally, an improved nonreflecting condition is used, which assumes a sharp increase in the step size in coordinate and the application of a dissipative difference scheme. Special attention is given to the computational algorithms used on the boundaries and interfaces of the separate grids, which make it possible to implement the proposed approach with the use of the grid-characteristic method on combined grids. [ABSTRACT FROM AUTHOR]

The distribution of the dynamic load on railroad track caused by a moving heavy train is numerically simulated. The track is represented as a multilayered linear elastic medium. A complete system of equations describing the state of a linear elastic body and a system of continuum mechanics equations are solved. The grid-characteristic method is used, which ensures the formulation of correct contact and boundary conditions. Analytical expressions taking into account the impact of damaged wheels on rails are derived, and corresponding boundary conditions are developed and numerically implemented. [ABSTRACT FROM AUTHOR]

Abstract: A key difficulty faced when grid-characteristic methods on tetrahedral meshes are used to compute structures of complex geometry is the high computational cost of the problem. Formally, grid-characteristic methods can be used on any tetrahedral mesh. However, a direct generalization of these methods to tetrahedral meshes leads to a time step constraint similar to the Courant step for uniform rectangular grids. For computational domains of complex geometry, meshes nearly always contain very small or very flat tetrahedra. From a practical point of view, this leads to unreasonably small time steps (1-3 orders of magnitude smaller than actual structures) and, accordingly, to unreasonable growth of the amount of computations. In their classical works, A.S. Kholodov and K.M. Magomedov proposed a technique for designing grid-characteristic methods on unstructured meshes with the use of skewed stencils. Below, this technique is used to construct a numerical method that performs efficiently on tetrahedral meshes. [ABSTRACT FROM AUTHOR]

Abstract: Wave processes occurring in a fractured rock material in seismic exploration are numerically simulated and studied. The grid-characteristic method on hexahedral grids is extended to construct a seismic image of a fractured elastic medium (i.e., the positions of the reflecting layers under the daytime surface). The underlying idea is that the method is applied to both direct and adjoint problems (in the latter problem, seismometer data recorded on the daytime surface are transformed into corresponding seismic sources). In this case, a seismic image is obtained as the convolution of the direct and adjoint fields. Numerical computations are used to produce synthetic seismograms (time dependences of point oscillations on the daytime surface) for rock materials with gas-saturated and liquid-saturated cracks. The inhomogeneities are explicitly described (at the stage of hexahedral grid generation) and the stressed state on their boundaries is updated at every time step (by solving a contact discontinuity problem). The algorithm is used to construct seismic images for media. An analysis of the results yields information not only on the locations of the cracks, but also on their spatial orientations. [ABSTRACT FROM AUTHOR]

The grid-characteristic method on a sequence of embedded hierarchical grids is used to study the reflection and diffraction of elastic seismic waves propagating from an earthquake hypocenter to the Earth's surface. More specifically, the destruction caused by seismic waves in complex heterogeneous structures, such as multi-story buildings, is analyzed. This study is based on computer modeling with the use of the grid-characteristic method, which provides a detailed description of wave processes in heterogeneous media, takes into account all types of emerging waves, and relies on algorithms that perform well on the boundaries of the integration domain and material interfaces. Applying a sequence of hierarchical grids makes it possible to simulate seismic wave propagation from an earthquake hypocenter to ground facilities of interest-multi-story buildings-and to investigate their seismic resistance. [ABSTRACT FROM AUTHOR]

Elastic wave propagation in a porous medium is numerically studied by applying the grid-characteristic method. On the basis of direct measurements of reflected and transmitted wave amplitudes, the reflection and decay coefficients are investigated as depending on the degree of porosity (percentage of the pore volume) and on the type of the filling substance (solid, liquid, or nothing). The reflection and decay coefficients are shown to be closely related to the porosity of the medium, which can be used in geological applications (estimation of porosity) and engineering applications (acoustic response attenuation). [ABSTRACT FROM AUTHOR]

The goal of this paper is the numerical solution of direct problems concerning hydrocarbon seismic exploration on the Arctic shelf. The task is addressed by solving a complete system of linear elasticity equations and a system of acoustic field equations. Both systems are solved by applying the grid-characteristic method, which takes into account all wave processes in a detailed and physically correct manner and produces a solution near the boundaries and interfaces of the integration domain, including the interface between the acoustic and linear elastic media involved. The seismograms and wave patterns obtained by numerically solving these systems are compared. The effect of ice structures on the resulting wave patterns is examined. [ABSTRACT FROM AUTHOR]

For wave propagation in heterogeneous media, we compare numerical results produced by grid-characteristic methods on structured rectangular and unstructured triangular meshes and by a discontinuous Galerkin method on unstructured triangular meshes as applied to the linear system of elasticity equations in the context of direct seismic exploration with an anticlinal trap model. It is shown that the resulting synthetic seismograms are in reasonable quantitative agreement. The grid-characteristic method on structured meshes requires more nodes for approximating curved boundaries, but it has a higher computation speed, which makes it preferable for the given class of problems. [ABSTRACT FROM AUTHOR]

The article presents biography of Oleg Mikhailovich Belotserkovskii, a researcher and educator of the Russian Academy of Sciences. Topics discussed include his education at the Faculty of Physics and Technology of Moscow State University; his birth in a family of teachers in Livny, Oryol; and Belotserkovskii's research interests in physics and turbulence. It also mentions the Joukowski Prize and gold medal "For the Best Study in Aviation Theory won by him.

Seismic responses from fractured geological layers are mathematically simulated by applying the grid-characteristic method on unstructured tetrahedral meshes with the use of high-performance computer systems. The method is intended for computing complicated spatial dynamical processes in complex heterogeneous media and is characterized by exact formulation of contact conditions. As a result, it can be applied to the simulation of seismic exploration problems, including in regions with a large number of inhomogeneities, examples of which are fractured structures. The use of unstructured tetrahedral meshes makes it possible to specify geological cracks of various shapes and spatial orientations. As a result, problems are solved in a formulation maximally close to an actual situation. A cluster of computers is used to improve the accuracy of the computation by optimizing its duration. [ABSTRACT FROM AUTHOR]

Results of the numerical simulation of mechanical processes occurring in biological tissues under dynamic actions are presented. The grid-characteristic method on unstructured grids is used to solve the system of equations of mechanics of deformable solids; this method takes into account the characteristic properties of the constitutive system of partial differential equations and produces adequate algorithms on interfaces between media and on the boundaries of integration domains. [ABSTRACT FROM AUTHOR]

Wave propagation in fractured rock in the course of seismic exploration is studied. The grid-characteristic method on hexahedral meshes is extended to the case of an elastic medium with empty and fluid-saturated cracks. The crack effect on wave propagation in the medium is taken into account by introducing cracks at the stage of grid generation with boundary conditions and conditions on the crack edges specified in explicit form. This method is used to obtain wave patterns near an extended inclined crack. The problem of numerically computing the seismic effect produced by a cluster of vertical and subvertical cracks is given in a complete three-dimensional formulation. The structure of the resulting pattern and the influence exerted by the crack-filling substance on the signal recorded on the surface are examined. [ABSTRACT FROM AUTHOR]

A combined method blending the advantages of smoothed particles hydrodynamics (SPH) and the grid-characteristic method (GCM) is proposed for simulating elastoplastic bodies. Various grid methods, including the GCM, have long been used for the numerical simulation of elastoplastic media. This method applies to the simulation of wave processes in elastic media, including elastic impacts, in which case an advantage is the use of moving tetrahedral meshes. Additionally, fracture processes can be simulated by applying various fracture criteria. However, this is a technically complicated task with the accuracy of the results degrading due to the continual updating of the grid. A more suitable approach to the simulation of processes involving substantial fractures and deformations is based on SPH, which is a meshless method. However, this method also has shortcomings: it produces spurious modes, and the simulation of oscillations requires particle refinement. Thus, two families of methods are available that are optimal as applied to two different groups of problems. However, a realworld problem can frequently be a mixed one, which requires a substantial tradeoff in the numerical methods applied. Aimed at solving such problems, a combined GCM-SPH method is developed that blends the advantages of two constituting techniques and partially eliminates their shortcomings. [ABSTRACT FROM AUTHOR]

The goal of this paper is to develop a grid-characteristic method intended for high-performance computer systems and implemented on unstructured tetrahedral hierarchical meshes with the use of a multiple time step and high-order interpolation, including interpolation with a limiter, piecewise parabolic interpolation, and monotone interpolation. The method is designed for simulating complex three-dimensional dynamical processes in heterogeneous media. It involves accurately stated contact conditions and produces physically correct solutions of problems in seismology and seismic exploration. Hierarchical meshes make it possible to take into account numerous inhomogeneous inclusions (cracks, cavities, etc.) and to solve problems in a real-life formulation. The grid-characteristic method enables the use of a multiple time step. As a result, the computation time is considerably reduced and the efficiency of the method is raised. The method is parallelized on a computer cluster with an optimal use of system resources. [ABSTRACT FROM AUTHOR]

Seismic activity in homogeneous and layered enclosing rock masses is studied. A numerical mechanical-mathematical model of a hypocenter is proposed that describes the whole range of elastic perturbations propagating from the hypocenter. Synthetic beachball plots computed for various fault plane orientations are compared with the analytical solution in the case of homogeneous rock. A detailed analysis of wave patterns and synthetic seismograms is performed to compare seismic activities in homogeneous and layered enclosing rock masses. The influence exerted by individual components of a seismic perturbation on the stability of quarry walls is analyzed. The grid-characteristic method is used on three-dimensional parallelepipedal and curvilinear structured grids with boundary conditions set on the boundaries of the integration domain and with well-defined contact conditions specified in explicit form. [ABSTRACT FROM AUTHOR]

The deformation and wave processes induced by collisions of an impactor with deformable layered targets of various configurations are analyzed. The numerical solution of such problems is associated with an adequate treatment of wave processes in a continuous medium, which is an especially difficult task in the case of layered targets. To deal with the former problem, it is proposed to use adaptive Lagrangian triangular meshes. Wave processes are simulated using the grid-characteristic method, which can serve as a basis for algorithms that do not fail near the boundary of the computational domain and at numerous material interfaces. Additionally, hybrid and hybridized grid-characteristic schemes are applied that substantially improve numerical solutions with steep gradients (discontinuous solutions). These methods provide an adequate treatment of wave processes in layered targets (wave reflection and refraction at contact surfaces, secondary-wave interaction, changes in the conditions on these boundaries, etc.). [ABSTRACT FROM AUTHOR]

A two-dimensional mathematical model of the mechanical response of a human head to a shock action is proposed. It describes the spatial distribution of the mechanical loads on the brain. Some numerical results obtained using the grid characteristic methods on unstructured triangular grids are presented. [ABSTRACT FROM AUTHOR]