scispace - formally typeset
Search or ask a question
Journal ArticleDOI

3D controlled-source electromagnetic modeling in anisotropic medium using edge-based finite element method

01 Dec 2014-Computers & Geosciences (Pergamon Press, Inc.PUB1185Elmsford, NY, USA)-Vol. 73, pp 164-176
TL;DR: The method uses the edge-based vector basis functions, which automatically enforce the divergence free conditions for electric and magnetic fields, which is effective in modeling the seafloor bathymetry using hexahedral mesh.
About: This article is published in Computers & Geosciences.The article was published on 2014-12-01 and is currently open access. It has received 85 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.

Summary (3 min read)

1. Introduction

  • For accurate interpretation of the subsurface structure using the MCSEM method, the bathymetry effect should be accurately simulated.
  • The edge-based finite element method uses vector basis functions defined on the edges of the corresponding elements.
  • More advanced preconditioners based on the approximated inverse of the stiffness matrix can be used to speed up the solvers.

4. Comparison with semi-analytical solution for a horizontally layered geoelectrical model

  • The frequency of the harmonic electric source is 0.5 Hz.
  • The grid is refined nearby the source, target layer and the surface of observation (see Fig. 3).
  • Fig. 4 shows a comparison of the anomalous electric field between the finite element solution and the 1D semi-analytical solution.
  • One can see that the finite element results are in a good agreement with the semi-analytical solution.
  • For this model with the specified source configuration, the y component of secondary electric field, the x and z components of secondary magnetic field are equal to 0 at y¼0.

5. Model of an off-shore hydrocarbon reservoir

  • Hz, which is a typical frequency for marine CSEM.
  • The EM receivers are located on the seafloor.
  • The sparsity pattern for the finite element stiffness matrix is shown in panel (a) of Fig.
  • From this figure, one can see that the matrix is very sparse, although the problem size is huge.
  • In the second model, the authors consider an anisotropic background conductivity and isotropic anomalous conductivity for the reservoir.

5.1. Model 1: isotropic background and isotropic reservoir

  • The numerical result obtained by the edge-based finite element method was compared with the integral equation solution.
  • One can clearly see an anomaly around x¼2 km where the offset is about 5 km.
  • Due to the page limits, the authors will only show the numerical modeling result for the frequency of 1 Hz in the following sections.
  • Due to the page limits, the authors only show a comparison of the convergences of QMR, GMRES and BiCGSTAB solvers for Model 1.
  • It took about 20 min to solve this model using the finite element method and about 3 min for the integral equation method on a PC with 2.6 GHz CPU.

5.2. Model 2: anisotropic background with isotropic reservoir

  • In a marine environment, the conductivity of sediments shows a strong transverse anisotropy due to the process of sedimentation with the longitudinal conductivity being larger than the transverse conductivity (Ellis et al., 2010; Ramananjaona et al., 2011).
  • The macroanisotropy is mainly caused by thin layering when bulk resistivity is measured so that the electric current prefers to travel parallel to the bedding planes (Ellis et al., 2010).
  • This transverse anisotropy could have a strong effect on the primary field and the anomalous field could also be distorted significantly.
  • The conductivity of seawater and air stays unchanged compared to the previous model.
  • As in the previous model, the authors compare the finite element result with the integral equation solution.

5.3. Model 3: isotropic background with anisotropic reservoir

  • In practical applications of the MCSEM method, not only the conductivity of the sea-bottom sediments, but also the reservoir conductivity can be anisotropic.
  • The reservoir anisotropy is usually weak in comparison to the background conductivity anisotropy (Brown et al., 2012).
  • The authors can see that the result obtained by the integral equation method is practically the same as the finite element solution for the anisotropic reservoir model.
  • Ex components of the background and total electric field with the frequency of 1 Hz.
  • The total memory requirement for solving this problem using finite element and integral equation methods were practically the same as for Model 1.

5.4. Model 4: anisotropic background with anisotropic reservoir

  • Finally, the authors study Model 4 having transverse anisotropy of both the background and reservoir conductivities.
  • Hz, with the anomaly observed around a point x¼3 km, which corresponds to the 6 km offset.
  • The total memory requirement of this problem for finite element and integral equation methods are the same as Model 1.
  • The effect of the anisotropy of background conductivity is manifested by shifting the anomaly to larger offset, while the increase of the anisotropy coefficient of the reservoir increases the amplitude of the anomaly without shifting the anomaly significantly.
  • Thus, their numerical modeling results confirm ones again that quantitative interpretation of the MCSEM data requires taking into account the effect of anisotropy on the observed data.

6. Modeling the effect of the bathymetry on the EM data

  • One of the advantages of the edge-based finite element method is its ability to model the bathymetry effect on the EM data.
  • Fig. 23 shows the hexahedral grid for the bathymetry model without a reservoir in the X–Z section at y¼0.
  • Fig. 26 shows a comparison of the anomalous field at y¼0 along the bathymetry, with the frequency of 1 Hz, computed using both the edge-based finite element and integral equation methods.
  • One can see that the results produced by these two methods show a good agreement.
  • Some minor difference may be related to the staircase approximation used in the integral equation method.

7. Conclusions

  • The authors have developed an edge-based finite element algorithm to solve the diffusive electromagnetic problem in the 3D anisotropic medium.
  • The authors use the edge-based vector basis functions, which automatically enforce the divergence free conditions for electric and magnetic fields.
  • The sparse finite element system is solved using the quasiminimum residual method with a Jacobian preconditioner.
  • The results of numerical study confirm the accuracy and the efficiency of a new code.

Did you find this useful? Give us your feedback

Figures (29)
Citations
More filters
Journal ArticleDOI
TL;DR: An edge-based finite element method for 3D CSEM modeling which is effective in modeling complex geometry such as bathymetry and capable of dealing with anisotropic conductivity is developed.

66 citations


Cites background or methods from "3D controlled-source electromagneti..."

  • ...The electric field inside each element can be represented as: ∑ EE N= .e i i e i e =1 6 (7) The vector basis functions are continuous on element boundaries and the continuity conditions are imposed directly (Jin, 2002, 2014; Silva et al., 2012; Cai et al., 2014, 2015)....

    [...]

  • ...The iterative solvers were widely used for solving 3D EM forward modeling problem for less memory requirement (Axelsson, 1994; Badea et al., 2001; Cai et al., 2014; Freund and Nachtigal, 1991; Puzyrev et al., 2013; Saad, 2003)....

    [...]

  • ...For simplicity, we consider our coordinate axes coincide with the principal axes of the conductivity tensor (Cai et al., 2014)....

    [...]

  • ...…online 22 November 2016 crossmark have observed that the edge-based FE starts to gain more interests from geophysical community (Mitsuhata and Uchida, 2004; Nam et al., 2007; Mukherjee and Everett, 2011; Schwarzbach et al., 2011; Silva et al., 2012; Kordy et al., 2016; Cai et al., 2014, 2015)....

    [...]

Journal ArticleDOI
TL;DR: In this article, the vector finite-element (FE) method was used to solve the linear system of equations generated by FE analysis for fixed-and moving-loop configurations, where the right side is different for every transmitter loop but for which the coefficient matrix is unchanged.
Abstract: Unstructured tetrahedral grids with local refinement facilitate the use of total-field solution approaches to geophysical electromagnetic (EM) forward problems. These approaches, when combined with the vector finite-element (FE) method and with refinement near transmitters and receivers, can give accurate solutions and can easily handle realistic models with complex geometry and topography. We have applied this approach to 3D forward modeling for fixed- and moving-loop configurations. MUMPS, a direct solver, was used to solve the linear system of equations generated by FE analysis. A direct solver is particularly suited to the moving-loop configuration for which the right side is different for every transmitter loop, but for which the coefficient matrix is unchanged. Therefore, the coefficient matrix need only be factorized once, and then the system can be solved efficiently for all different right sides. We compared our results with several typical scenarios from the literature: a conductive bric...

54 citations

Journal ArticleDOI
TL;DR: The custEM toolbox as mentioned in this paper is a toolbox for the simulation of complex 3D controlled-source electromagnetic (CSEM) problems, which is based on the open-source toolbox custEM.
Abstract: We have developed the open-source toolbox custEM (customizable electromagnetic modeling) for the simulation of complex 3D controlled-source electromagnetic (CSEM) problems. It is based on t...

46 citations


Cites methods from "3D controlled-source electromagneti..."

  • ...Um et al. (2013) and Cai et al. (2014) successfully implement iterative solution techniques for the ill-conditioned system of equations on tetrahedral and hexahedral meshes, respectively....

    [...]

Journal ArticleDOI
TL;DR: An automatic mesh adaptation strategy for a given frequency and specific source position is presented and a scalability study based on fundamental metrics for high-performance computing (HPC) architectures is presented.

39 citations

Journal ArticleDOI
TL;DR: In this article, the effects of anisotropic media on the strengths and the diffusion patterns of time-domain airborne EM responses were modeled by edge-based finite-element method and the Backward Euler scheme was adopted to discretize the timedomain diffusion equation for electric field.

35 citations

References
More filters
Book
09 Jun 2003
TL;DR: In this paper, the conjugate gradients method is used to solve singular systems with Krylov subspace information, and the solution of f (A)x = b with k-subspace information is given.
Abstract: Preface 1. Introduction 2. Mathematical preliminaries 3. Basic iteration methods 4. Construction of approximate solutions 5. The conjugate gradients method 6. GMRES and MINRES 7. Bi-conjugate gradients 8. How serious is irregular convergence? 9. BI-CGSTAB 10. Solution of singular systems 11. Solution of f (A)x = b with Krylov subspace information 12. Miscellaneous 13. Preconditioning References Index.

665 citations

Journal ArticleDOI
TL;DR: Early development of marine electromagnetic methods, dating back about 80 years, was driven largely by defense/military applications, and use for these purposes continues to this day as mentioned in this paper, although the hydrocarbon exploration industry was aware of this work, the shallow-water environments being explored at that time were not ideally suited for its use.
Abstract: Early development of marine electromagnetic methods, dating back about 80 years, was driven largely by defense/military applications, and use for these purposes continues to this day. Deepwater, frequency-domain, electric dipole-dipole, controlled-source electromagnetic (CSEM) methods arose from academic studies of the oceanic lithosphere in the 1980s, and although the hydrocarbon exploration industry was aware of this work, the shallow-water environments being explored at that time were not ideally suited for its use. Low oil prices and increasingly successful results from 3D seismic methods further discouraged investment in costly alternative geophysical data streams. These circumstances changed in the late 1990s, when both Statoil and ExxonMobil began modeling studies and fieldtrials of CSEM surveying in deep water (around 1000 m or deeper), specifically for characterizing the resistivity of previously identified drilling targets. Trials offshore Angola in 2000–2002 by both these companies showed that ...

412 citations

Journal Article
TL;DR: In this paper, the Tikhonov-Cagnard approach linearity of relationships between components of the magnetotelluric field electromagnetic fields in a horizontally homogenous medius electromagnetic fields, in horizontally inhomogeneous media was used to interpret the MT data interpretation of MVP and GDS data.
Abstract: Part 1 Electrical methods in geophysics: in the beginning the mind set and the future. Part 2 General concepts of electromagnetic field behaviour: Maxwell's equations diffusing electromagnetic fields static electromagnetic fields quasi-stationary electromagnetic fields. Part 3 Properties of rocks and minerals: properties and units properties in a parametric sense properties in an existential sense geoelectrical mesostructures and megastructures electrical properties of the atmosphere and the ocean. Part 4 Electromagnetic environment of planet Earth: Earth currents of external origin industrial noise atmospheric electric sources mechanically generated electric fields extraneous sources of electric fields electromagnetic fields generated by the oceans. Part 5 Direct current and induced polarization methods: point and dipole sources on a uniform Earth electric fields in one-dimensional Earth structures fields of a point source for two- and three-dimensional structures vertical electric sounding and apparent resistivity induced polarization magnetic field measurements. Part 6 Natural-field electromagnetic methods: the Tikhonov-Cagniard approach linearity of relationships between components of the magnetotelluric field electromagnetic fields in a horizontally homogenous medius electromagnetic fields in horizontally inhomogeneous media magnetotelluric and magnetovariational survey methods data reduction interpretation of MT data interpretation of MVP and GDS data. Part 7 Controlled source electromagnetic methods: principles of controlled source electromagnetic methods electromagnetic sounding electromagnetic profiling. Part 8 Modelling and simulation: exact analytical solutions for special cases thin sheet models the integral equation method finite difference modelling finite element method physical and analog modelling other approaches to modelling. Part 9 Insensitivity and ambiguity: insensitivity for a laterally uniform Earth ambiguity for a laterally uniform Earth. Part 10 Practical aspects of data acquisition: sources detection of electric and magnetic fields sampling filtering survey design. Part 11 Interpretation: rules, intuition and pragmatic interpretation pseudo-inversion of soundings by transformation inversion continuation of electromagnetic fields electromagnetic migration comprehensive three-dimensional interpretation. Part 12 Other platforms, other methodologies: airborne electromagnetic (AEM) methods marine electrical surveys bore hole assisted methods spontaneous polarization (SP) method ground penetrating radar (GPR) the piezoelectric method (PEP). Part 13 A baker's dozen of case histories: minerals exploration - Que River Deposit, Tasmania, Australia physical volcanology - Oshima volcano, Japan groundwater exploration - Apodi Valley, Rio Grande do Norte, Brazil. (Part Contents).

320 citations


"3D controlled-source electromagneti..." refers methods in this paper

  • ...Controlled-source electromagnetic (CSEM) method has been widely used in geophysical exploration on land for decades (Ward and Hohmann, 1988; Zhdanov and Keller, 1994)....

    [...]

  • ...For such an isotropic model, the anomalous field caused by the target layer can be computed semi-analytically using the Hankel transform (Ward and Hohmann, 1988; Anderson, 1989; Zhdanov and Keller, 1994; Guptasarma and Singh, 1997)....

    [...]

Book
20 May 2009
TL;DR: In this article, the authors present the state-of-the-art electromagnetic (EM) theories and methods employed in EM geophysical exploration, including direct current (DC), induced polarization (IP), magnetotelluric (MT), and controlled-source electromagnetic (CSEM) methods.
Abstract: In this book the author presents the state-of-the-art electromagnetic (EM) theories and methods employed in EM geophysical exploration. The book brings together the fundamental theory of EM fields and the practical aspects of EM exploration for mineral and energy resources. This text is unique in its breadth and completeness in providing an overview of EM geophysical exploration technology. The book is divided into four parts covering the foundations of EM field theory and its applications, and emerging geophysical methods. Part I is an introduction to the field theory required for baseline understanding. Part II is an overview of all the basic elements of geophysical EM theory, from Maxwell's fundamental equations to modern methods of modeling the EM field in complex 3-D geoelectrical formations. Part III deals with the regularized solution of ill-posed inverse electromagnetic problems, the multidimensional migration and imaging of electromagnetic data, and general interpretation techniques. Part IV describes major geophysical electromagnetic methods-direct current (DC), induced polarization (IP), magnetotelluric (MT), and controlled-source electromagnetic (CSEM) methods-and covers different applications of EM methods in exploration geophysics, including minerals and HC exploration, environmental study, and crustal study. * Presents theoretical and methodological findings, as well as examples of applications of recently developed algorithms and software in solving practical problems * Describes the practical importance of electromagnetic data through enabling discussions on a construction of a closed technological cycle, processing, analysis and three-dimensional interpretation * Updates current findings in the field, especially with MT, magnetovariational and seismo-electrical methods and the practice of 3D interpretations

256 citations


"3D controlled-source electromagneti..." refers background or methods in this paper

  • ...The low frequency electromagnetic field, considered in geophysical application, satisfies the following Maxwell's equations (Zhdanov, 2009):...

    [...]

  • ...In the anomalous field formulation of diffusive EM field problem, the total field is decomposed into background and anomalous fields (Zhdanov, 2009)...

    [...]

  • ...The node-based finite element method was applied in the past to model EM data by solving the coupled equations for the vector and scalar potentials and also by solving Maxwell's equations for electric and magnetic fields (e.g., Zhdanov, 2009)....

    [...]

  • ...…in anisotropic medium The low frequency electromagnetic field, considered in geophysical application, satisfies the following Maxwell's equations (Zhdanov, 2009): ωμ∇ × = iE H (1)0 σ∇ × = + ¯H J E (2)s where we adopt the harmonic time dependence ω−e i t , ω is the angular frequency, μ0 is the…...

    [...]

  • ...In the anomalous field formulation of diffusive EM field problem, the total field is decomposed into background and anomalous fields (Zhdanov, 2009) = +E E E , (5)b a σ σσ Δ¯ = ¯ + ¯....

    [...]

PatentDOI
Leonard J. Srnka1
TL;DR: In this paper, the location of and average earth resistivities above, below, and horizontally adjacent to the subsurface geologic formation are first determined using geological and geophysical data in the vicinity of the SINR.
Abstract: A method for surface estimation of reservoir properties, wherein location of and average earth resistivities above, below, and horizontally adjacent to the subsurface geologic formation are first determined using geological and geophysical data in the vicinity of the subsurface geologic formation. Then dimensions and probing frequency for an electromagnetic source are determined to substantially maximize transmitted vertical and horizontal electric currents at the subsurface geologic formation, using the location and the average earth resistivities. Next, the electromagnetic source is activated at or near surface, approximately centered above the subsurface geologic formation and a plurality of components of electromagnetic response is measured with a receiver array. Geometrical and electrical parameter constraints are determined, using the geological and geophysical data. Finally, the electromagnetic response is processed using the geometrical and electrical parameter constraints to produce inverted vertical and horizontal resistivity depth images. Optionally, the inverted resistivity depth images may be combined with the geological and geophysical data to estimate the reservoir fluid and shaliness properties.

205 citations

Frequently Asked Questions (2)
Q1. What have the authors contributed in "3d controlled-source electromagnetic modeling in anisotropic medium using edge-based finite element method" ?

This paper presents a linear edge-based finite element method for numerical modeling of 3D controlledsource electromagnetic data in an anisotropic conductive medium. The authors use a nonuniform rectangular mesh in order to capture the rapid change of diffusive electromagnetic field within the regions of anomalous conductivity and close to the location of the source. 

Future work will be aimed at the implementation of the high order finite elements and at the use of the unstructured tetrahedral and hexahedron meshes to include seafloor bathymetry and complex geoelectrical structures in the modeling of the MCSEM data.