Nikolay I. Khokhlov

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• PhD
• Senior Researcher at Moscow Institute of Physics and Technology

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...

Nowadays, solving seismic exploration problems requires taking into account the scattering of seismic waves at boundaries and contact boundaries of complex shape. For the subsequent solution of inverse problems, it is important to save computing resources as much as possible. A way to do this while saving the accuracy of calculations is to use Chim...

A new approach is considered for increasing the order of accuracy of the grid-characteristic method in the region of coefficient jumps. The approach is based on piecewise polynomial interpolation for schemes of the second and third orders of accuracy for the case where the interface between the media is consistent with a finite-difference grid. The...

Introduction. Seismic exploration in conditions of heterogeneity of the environment is an urgent topic for the oil and gas industry. Consequently, the development of numerical methods for solving the direct problem of seismic exploration remains relevant as a necessary link in the development and improvement of methods for solving the inverse probl...

Wave perturbations propagating through heterogeneous media with porous inclusions are numerically simulated, and an explicit description of porous heterogeneities is considered. The method of overlapping meshes is proposed for an explicit description of heterogeneities. The arising systems of partial differential equations are solved numerically by...

Our work is devoted to the numerical solution of direct problems of non-destructive testing of rails in a full-wave three-dimensional formulation. The complexity of this class of problems is due to the high frequencies of the waves, which imposes a limitation on the step size of the computational grid, including along the rail, as well as the compl...

Interest in computational methods for calculating wave scattering from fractured geological clusters is due to their application in processing and interpreting the data obtained during seismic prospecting of hydrocarbon and other mineral deposits. In real calculations, numerical methods on structured, regular (Cartesian) computational grids are use...

Nowadays, traditional hydrocarbon reserves are depleted. The search for and production of oil and gas in hard-to-reach fields require the development of appropriate computing technologies. Therefore, there is a need to develop novel high-precision computational methods that make it possible to more accurately take into account the features of the g...

A mathematical model of a homogeneous geological medium with methane cavities was developed. Based on the results of the calculations, wave patterns of the distribution of the velocity modulus in the models and seismograms of the recording of various velocity components on the receivers of reflected signals were obtained. The simulation results dem...

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-...

This paper considers numerical simulation of acoustic waves in heterogeneous two-dimensional (2D) media by the grid-characteristic method. We present a novel high-order compact numerical scheme that accurately handles discontinuous material parameters. We present one-dimensional and 2D formulations and discuss their programming implementation. The...

Hydraulic fracturing is the method, used during the seismic works on hydrocarbon’s extraction. It is necessary to control the properties of the fracture to provide the maximum safety and productivity of the works. The main problem is to obtain the data from the direct modelling, based on which the inverse problem is lately solved. In this paper we...

The Arctic shelf zone is a very important region in our country due to the huge amounts of hydrocarbons, located there. The exploration of this region is difficult because of the presence of lots of various ice constructions, in particular, ice fields. While carrying out the seismic prospecting works, the reflected waves from the ice field contribu...

Reconstruction of rock boundaries plays an important role in seismic exploration of minerals. Seismic data processing requires multiple solutions to the corresponding direct problem. Therefore, it is of interest to develop numerical methods for solving direct problems of seismic exploration, taking into account curvilinear boundaries of rocks and s...

The paper considers a software package designed to simulate the propagation of dynamic wave disturbances in heterogeneous media. One of the main features of the considered software package is numerical algorithms with an explicit selection of inhomogeneities. Within the framework of the work, such inhomogeneities as pores, fractures and interfaces...

This note summarizes some preliminary results on the fast solution of the coefficient inverse problem for the Helmholtz equation, given measured pressure in a set of observation points. The Helmholtz equation is the model PDE for the harmonic problem of the linear theory of elasticity, and this work is a move in that direction. The problem has been...

Geological fracture zones play an important role in determining the amount of deposits in oil and gas fields. In practice, for modeling wave scattering in fractured zones, numerical methods are usually used on structured computational meshes to save computational resources. However, these numerical methods can only calculate wave scattering on crac...

In this paper, an acoustic approximation is considered, which allows to describe the propagation of longitudinal waves in geological media. For the two-dimensional case, a compact numerical scheme is described that provides an increased approximation order on a two-point spatial stencil. To construct it, we used the method of splitting along coordi...

An efficient solution of the three-dimensional Helmholtz equation is known to be crucial in many applications, especially geophysics. In this paper, we present and test two preconditioning approaches for the discrete problem resulting from the second order finite-difference discretization of this equation. The first approach combines shifted-Laplac...

The problem of detecting the hydrocarbon deposits in the heterogeneous media is very important and difficult for solving. We suppose the grid-characteristic method of the third order of accuracy for solving the problem of the direct modeling of the seismic waves spread in such a medium with the presence of gas cavities and without them. The numeric...

Heterogeneous media with fractured geological structures are widely spread, and therefore, they need a very careful exploration. In this work, we present the results of modeling the seismic waves spread through the homogeneous and heterogeneous media with single fractures and fracture clusters using the grid-characteristic method. We analyze the se...

We present the solution to the problem of detecting the gas layers in the Arctic conditions through the numerical modelling of the seismic waves spread in the heterogeneous media. The grid-characteristic method of the third order of accuracy is used in all the computations. We build the models with the different numbers of the gas layers and analyz...

In this chapter, we investigate the use of GPUs to speed up the matrix–vector product within an iterative integral equation (IE) solver. Our implementation is based on CUDA. Numerical experiments suggest that GPU computing can accelerate the performance of the solver by a factor of 70 for the single-precision arithmetic and by a factor of 30 for th...

This work aims to find the optimal algorithm of computational load distribution for parallel modeling of objects using multiple grids. Reducing of calculation time will be achieved by reducing the amount of information transmitted between processes through contact surfaces. For testing effectiveness of the algorithms, an elastic wave propagation mo...

Schoenberg’s mathematical model of fractured geological media has been widely used in studies related to seismic exploration of oil fields. This paper proposes to use this model for computing wave processes in geological media by the grid-characteristic method. In that case, the sought-for functions are components of the velocity vector and stress...

The Arctic region contains lots of underground gas layers closed from the outside. In case of their opening, the gas is of great danger for the surface buildings and drilling equipment. In this work, we observe the main dangerous gas reservoirs – gas cavities and methane bombs. We build the mathematical models of these heterogeneities and presented...

The paper is devoted to the numerical simulation of mechanical destruction of icebergs under man-made intense explosive influences. Icebergs pose a significant threat to offshore facilities, offshore oil platforms, ships, and bottom pipelines. One way to reduce the probability of collision is to detonate the iceberg. This work is dedicated to the c...

This work is devoted to the numerical solution of the acoustic problem. It has a lot of important applications, for example, direct and inverse problems of the seismic survey process. The grid-characteristic approach was used to transform the problem into a set of independent linear transport equations. In one-dimensional case explicit numerical sc...

The article describes the method of calculating the wave field of reflected waves of a certain type of re-reflection from localized target objects. A special feature of the method is the combination of the wave field continuation operator calculated by means of layer-by-layer recalculation based on the Kirchhoff integral and the finite-difference o...

This paper presents a novel approach to modeling the propagation of seismic waves in a medium containing subvertical fractured inhomogeneities, typical for mineralization zones. The developed method allows us to perform calculations on a structural computational grid, which avoids the construction of unstructured grids. For the calculations, the gr...

In this paper, we develop a general approach to integrating petrophysical models in 3D seismic full‐waveform inversion based on the Gramian constraints. In the framework of this approach, we present an example of the frequency‐domain P‐wave velocity inversion guided by an electrical conductivity model. In order to introduce a coupling between the t...

The volume of oil deposits directly depends on the characteristics of the fractured zones. Therefore, it is very important to be able to accurately determine their geometric position, type of filler (water, oil, air), spatial orientation. For these purposes, numerical methods are used to interpret seismic data. The task is complicated by the fact t...

Today the Arctic region exploration is one of the most important courses for research in our country because large amounts of unexplored oil and gas deposits are located there. Large deposits of hydrocarbons are situated in water areas of the North seas. Gas explosions complicate the development of hydrocarbon deposits in these water areas. They oc...

Gas emissions occur quite often in the North seas while carrying out oil-extracting works in the area. It is very important to be able to forecast such gas accumulations spread for further taking appropriate measures to avoid such emissions. This chapter represents the results of modeling of the spread of seismic waves in the layered structure of s...

This work is devoted to the numerical solution of the linear hyperbolic transport equation. The importance of this topic is explained by the wide variety of possible applications: seismic survey of oil and gas deposits, seismic resistance of ground facilities estimation, hydrodynamic simulation. In one-dimensional case, a class of two-point compact...

We consider application of Message Passing Interface (MPI) to parallelize a numerical code that solves the seismic wave equation with the grid-characteristic method. The problem is time reducing of communication between MPI processes during computation. The solution to this problem is of great interest, when multiple computational grids are involve...

We consider an application of the Message Passing Interface (MPI) technology for parallelization of the program code which solves equation of the linear elasticity theory. The solution of this equation describes the propagation of elastic waves in demormable rigid bodies. The solution of such direct problem of seismic wave propagation is of interes...

This paper introduces a novel method of modeling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear elastic media (e.g., longitudinal, transverse, Stoneley, Rayl...

Seismic survey process is the common method of prospecting and exploration of deposits: oil and natural gas. Invented at the beginning of the XX century, it has received significant development and is currently used by almost all service oil companies. Its main advantages are the acceptable cost of fieldwork (in comparison with drilling wells) and...

In this chapter, the application of the grid-characteristic method to solving seismic prospecting problems is considered. The characteristic seismogeological models, including Marmousi and SEG/EAGE Salt Model, are considered, wave patterns and seismograms are presented. The cases of 2D and 3D modelling, curvilinear boundaries between geological lay...

Two approaches to the calculation of air subdomains are compared in this paper, i.e. the use of imaginary points and explicit allocation. They are completely mathematically equivalent to each other, but there is a difference in their complexity of implementation, complexity of parallelization and computational resources needed for performing calcul...

In this paper, we propose a method for calculating the impact of a damaged wheel with a flat spot on a rail. The method allows us to take into account different degrees of the wheelset damage, various types of train cars, locomotives and rails, distance between sleepers, weather conditions, and features of enclosing geological medium. Combined calc...

Today the Arctic is one of the most important regions, where lots of oil and gas deposits are located. The Arctic contains different ice formations that give rise to problems of the North seas’ exploring. The models ought to simulate the situations with the presence of ice constructions and oil slices. The main goal is to find the difference betwee...

Numerical modeling of dynamic wave processes in heterogeneous media allows to investigate the earthquake stability of different constructions. The aim of this work is to study the earthquakes’ impact on the ground buildings and underground facilities. The use of grid-characteristic method makes possible to take into account the physics of arising w...

The paper presents the results of application of a grid-characteristic method to simulation of wave processes in media with linearly-elastic and acoustic layers on the example of seismic exploration of the Arctic shelf. The grid-characteristic method correctly describes the contact and boundary conditions. The results of numerical simulation are pr...

This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative sol...

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 analy...

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown i...

This paper touches upon the computer simulation of the propagation of elastic waves in three-dimensional multilayer fractured media. The dynamic processes are described using the defining system of equations in the partial derivatives of the deformed solid mechanics. The numerical solution of this system is carried out via the grid-characteristic m...

The influence of the Chelyabinsk meteorite’s bow shock wave on the Earth’s surface is modeled. For solving the problem, a 3D statement is considered for its gas-dynamic and seismic parts. The determining equations of a gas-dynamic model and a seismic model are Euler equations with respect to the radiation heat exchange and the equations of linear e...

Over the past 160 years, railways are one of the main elements of the top track structure throughout the world. They serve to direct the wheels when they move and directly perceive and transmit pressure to the underlying elements. Despite all the efforts of engineers, karst cavities can form under the rails due to severe operating conditions. One o...

The attention to Arctic shelf is explained by the real need of exploration and development of oil-fields and gas-fields. The computer modeling is a single appropriate approach because the physical experiments in Arctic are expensive and sometimes difficult or impossible to make. In this research, the wave processes during seismic exploration of Arc...

A class of two-point compact difference schemes of the second–third orders of accuracy on a twopoint coordinate stencil is considered for a one-dimensional transfer equation. All difference schemes are based on interpolation polynomials constructed on a given stencil. Based on the behaviour of the solution and the character of interpolation polynom...

We present a parallel algorithm for solution of the three-dimensional Helmholtz equation in the frequency domain using volume-integral equations. The algorithm is applied to seismic forward modeling. The method of integral equations reduces the size of the problem by dividing the geologic model into the anomalous and background parts, but leads to...

Рассматривается применение метода интегральных уравнений (ИУ) к сейсмическому 3D полноволновому обращению. Продемонстрировано, что использование итеративного солвера, в котором операция умножения на матрицу системы реализована через быстрое преобразование Фурье, позволяет использовать метод ИУ для решения задача большого размера. С целью уменьшения...

This paper develops a new approach to 3D full-waveform inversion of the acoustic field data. This approach is based on a novel technique to compute the data gradient in the framework of seismic full-waveform inversion carried out in the frequency domain. The quasi-analytical (QA) approximation, which was initially developed for electromagnetic fiel...

A numerical solution of a 3D linear transport equation on parallelepipedic computational grids is considered. By the technique of splitting in coordinates, compact grid-characteristic schemes of higher orders of accuracy are generalized to the 3D case. The influence of particular steps of the computational algorithm on the accuracy of the resulting...

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 w...

The aim of this work is the numerical simulation of wave propagation in media with linear-elastic and acoustic layers as exemplified by the seismic prospecting problems in the Arctic region and the explosive impact on an iceberg. The complete system of equations describing the state of a linearly elastic body and the system of equations describing...

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 a...

This paper is concerned with CUDA and OpenCL technologies used to solve seismic problems in elastic media. We solve the problem of the dynamic wave disturbances spreading in geologic environment in an elastic approach in the two-dimensional case. A grid-characteristic method is used for numerical solution. Performance of problem solving algorithm w...