Acoustic 3D modeling by the method of integral equations

Malovichko, Mikhail; Хохлов, Н. И.; Yavich, N.; Zhdanov, Michael S.

doi:10.1016/j.cageo.2017.11.015

Cited by 14 publications

(15 citation statements)

References 24 publications

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“…The details of the numerical method and its parallel implementation can be found in Malovichko et al . ().…”

Section: Forward Modellingmentioning

confidence: 97%

“…In this case, the Green's function is given by a numerical Hankel transform of an analytically computed kernel (for example, Malovichko et al . ; the Appendix). In the two special cases, which are the constant velocity model,

c_{b} = const

, and the half‐space model,

c_{b} false(z \geq 0 false) = normalconst normaland c_{b} false(z < 0 false) = 0

, the solution to the Green's function simplifies even more to a closed‐form expressions.…”

Section: Forward Modellingmentioning

confidence: 99%

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Incorporating known petrophysical model in the seismic full‐waveform inversion using the Gramian constraint

Malovichko

Хохлов

Yavich

et al. 2020

Geophysical Prospecting

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A B S T R A C TIn this paper, we develop a general approach to integrating petrophysical models in three-dimensional 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 two models, we minimize the corresponding Gramian functional, which is included in the Tikhonov parametric functional. We demonstrate that in the case of a single-physics inversion guided by a model of different physical type, the general expressions of the Gramian functional and its gradients become simple and easy to program. We also prove that the Gramian functional has a nonnegative quadratic form, so it can be easily incorporated in a standard gradient-based minimization scheme. The developed new approach of seismic inversion guided by the known petrophysical model has been validated by three-dimensional inversion of synthetic seismic data generated for a realistic three-dimensional model of the subsurface.

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“…The details of the numerical method and its parallel implementation can be found in Malovichko et al . ().…”

Section: Forward Modellingmentioning

confidence: 97%

c_{b} = const

, and the half‐space model,

c_{b} false(z \geq 0 false) = normalconst normaland c_{b} false(z < 0 false) = 0

, the solution to the Green's function simplifies even more to a closed‐form expressions.…”

Section: Forward Modellingmentioning

confidence: 99%

Incorporating known petrophysical model in the seismic full‐waveform inversion using the Gramian constraint

Malovichko

Хохлов

Yavich

et al. 2020

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recall that we have three systems S i (i = 1, 2, 3) depending on the already quoted cases in (19)(20)(21)(22). According to these cases, we explore the rest of the equations in system (26) as follows.…”

Section: Non-linear System Resolutionmentioning

confidence: 99%

“…In financial sector the problem of pricing puttable convertible bonds is investigated and modeled as an integral equation by [37]. An acoustic problem arising from Geosciences was investigated by [19] and the mathematical formulation yielded an integral equation. In [34] authors modeled a Convection-diffusion problem using the integral equation.…”

Section: Introductionmentioning

confidence: 99%

Solution of a Non-Classical Integral Equation Modeling a Rotating Thin Rod Under Some Constraints and Technical Feasibility

Hidri

Gazdar

2020

IEEE Access

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In this paper, a mechanical system composed of a thin rotating rod under some constraints is considered. For this system, the total torque of the gravity forces is fixed and the unknown function to be determined is the mass density of the rod. This kind of problem is faced in several engineering applications as in aerospace. The resulting problem is formulated as a non classical integral equation, where the conventional methods of resolution do not apply. Therefore, a special treatment is required to solve the obtained integral equation. First, the obtained integral equation is transformed into a system of mixed integral and linear differential equations with two unknown functions. The latter transformation allows the inspiration of the general expression of the requested functions. Consequently, a highly non linear system with several unknowns is obtained. During the resolution of the latter system several mathematical technics are used. After applying all these technics an analytical solution of the studied integral equation is obtained. Finally, the technical feasibility from an engineering viewpoint of the production of a thin rod with the obtained mass density function is briefly discussed. In this context, the Functionally Graded Material is proposed as a material satisfying the obtained mass density function.

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“…An experimental verification of this model was made in [3]. Numerical simulation of wave propagation a is well-studied area in general, with many approaches proposed to date, such as the most popular finite-difference time-marching schemes [4,5], the spectral elements [6,7], discontinuous Galerkin [8], Helmholtz finite-difference [9,10] or integral-equation solvers [11,12], etc. Still, the development of the numerical methods for modeling the fractured heterogeneities is an area of active research.…”

Section: Introductionmentioning

confidence: 99%

Novel Approach to Modeling the Seismic Waves in the Areas with Complex Fractured Geological Structures

Хохлов

Stognii

2020

Minerals

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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 grid-characteristic method is used. We also present a comparison of the proposed method with the one described at earlier works and discuss the areas of its practical application. As an example, the numerical results for a cluster of subvertical fractures are given. A new approach for modeling fractures makes it quite easy to incorporate fractured objects into the seismic models and perform calculations without using algorithms on unstructured and curved grids.

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Acoustic 3D modeling by the method of integral equations

Cited by 14 publications

References 24 publications

Incorporating known petrophysical model in the seismic full‐waveform inversion using the Gramian constraint

Incorporating known petrophysical model in the seismic full‐waveform inversion using the Gramian constraint

Solution of a Non-Classical Integral Equation Modeling a Rotating Thin Rod Under Some Constraints and Technical Feasibility

Novel Approach to Modeling the Seismic Waves in the Areas with Complex Fractured Geological Structures

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