Modeling large‐scale geoelectrical structures with inhomogeneous backgrounds using the integral equation method: applications to the bathymetry effect study in marine CSEM data

2006 ◽  
Author(s):  
Ken Yoshioka ◽  
Michael S. Zhdanov
Keyword(s):  
Integral Equation ◽  
Large Scale ◽  
Integral Equation Method ◽  
Effect Study ◽  
Equation Method ◽  
Geoelectrical Structures ◽  
Marine Csem

scholarly journals On the applicability of a renormalized Born series for seismic wavefield modelling in strongly scattering media

2019 ◽  
Vol 17 (2) ◽  
pp. 277-299 ◽  
Author(s):  
Xingguo Huang ◽  
Morten Jakobsen ◽  
Ru-Shan Wu
Keyword(s):  
Integral Equation ◽  
Frequency Domain ◽  
Large Scale ◽  
Integral Equation Method ◽  
Equation Method ◽  
Scattering Media ◽  
Matrix Vector Multiplication ◽  
Born Series ◽  
And Inversion ◽  
Matrix Vector

Abstract Scattering theory is the basis for various seismic modeling and inversion methods. Conventionally, the Born series suffers from an assumption of a weak scattering and may face a convergence problem. We present an application of a modified Born series, referred to as the convergent Born series (CBS), to frequency-domain seismic wave modeling. The renormalization interpretation of the CBS from the renormalization group prospective is described. Further, we present comparisons of frequency-domain wavefields using the reference full integral equation method with that using the convergent Born series, proving that both of the convergent Born series can converge absolutely in strongly scattering media. Another attractive feature is that the Fast Fourier Transform is employed for efficient implementations of matrix–vector multiplication, which is practical for large-scale seismic problems. By comparing it with the full integral equation method, we have verified that the CBS can provide reliable and accurate results in strongly scattering media.

scholarly journals The volume integral equation method in magnetostatic problem

2019 ◽  
Vol 27 (1) ◽  
pp. 60-69
Author(s):  
Pavel G Akishin ◽  
Andrey A Sapozhnikov
Keyword(s):  
Integral Equation ◽  
Large Scale ◽  
Singular Integrals ◽  
Integral Equation Method ◽  
Equation Method ◽  
Matrix Elements ◽  
System Matrix ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Volume Integral Equation Method

This article addresses the issues of volume integral equation method application to magnetic system calculations. The main advantage of this approach is that in this case finding the solution of equations is reduced to the area filled with ferromagnetic. The difficulty of applying the method is connected with kernel singularity of integral equations. For this reason in collocation method only piecewise constant approximation of unknown variables is used within the limits of fragmentation elements inside the famous package GFUN3D. As an alternative approach the points of observation can be replaced by integration over fragmentation element, which allows to use approximation of unknown variables of a higher order.In the presented work the main aspects of applying this approach to magnetic systems modelling are discussed on the example of linear approximation of unknown variables: discretisation of initial equations, decomposition of the calculation area to elements, calculation of discretised system matrix elements, solving the resulting nonlinear equation system. In the framework of finite element method the calculation area is divided into a set of tetrahedrons. At the beginning the initial area is approximated by a combination of macro-blocks with a previously constructed two-dimensional mesh at their borders. After that for each macro-block separately the procedure of tetrahedron mesh construction is performed. While calculating matrix elements sixfold integrals over two tetrahedra are reduced to a combination of fourfold integrals over triangles, which are calculated using cubature formulas. Reduction of singular integrals to the combination of the regular integrals is proposed with the methods based on the concept of homogeneous functions. Simple iteration methods are used to solve non-linear discretized systems, allowing to avoid reversing large-scale matrixes. The results of the modelling are compared with the calculations obtained using other methods.

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