Marine Controlled-source Electromagnetic Responses Research Articles

Analyzing the effect of dipping anisotropy on 3D marine controlled-source electromagnetic response based on a goal-oriented adaptive finite element method

This paper presents a goal-oriented adaptive edge-based finite element (FE) algorithm for modelling marine controlled-source electromagnetic (CSEM) responses in three-dimensional (3-D) dipping anisotropic conductive media. We adopt the secondary field formulation for quasi-static Maxwell's equations to avoid the source singularity. The algorithm is implemented on unstructured tetrahedral grids, which allow for the simulation of complex model geometries, including tilted electrical interfaces and bathymetry. We validate the adaptive finite element code against a one-dimensional (1-D) layered model with vertical anisotropy. Further, we compare the 3-D FE numerical solutions with those obtained by a 2-D FE code for a two-dimensional dipping anisotropic model. The modelling results from the new 3-D FE algorithm are in good agreement with both the analytical solutions derived from the 1-D code and the numerical results from the anisotropic 2-D FE algorithm. We then use the algorithm to simulate the marine CSEM responses over different anisotropic 3-D models, including an anisotropic reservoir, anisotropic surrounding sediments, and an anisotropic overburden, and performed a detailed analysis of the effect of VTI, HTI, and TTI anisotropy on 3-D marine CSEM response. The modelling results illustrate that marine CSEM responses are considerably influenced by various anisotropic parameters, but to different extents. The research on different types of anisotropy within different media can help us avoid the misinterpretation of marine CSEM data when processing and interpreting of the measured geophysical electromagnetic data.

Forward calculation of 3D controlled-source electromagnetic responses based on joint application of secondary field and coupled potential formulations

In the traditional framework of 3D controlled-source electromagnetic (CSEM) modeling, either the field formulation or the coupled potential formulation is implemented. We have developed an improved algorithm that can calculate the 3D CSEM responses based on a joint application of the secondary field and secondary coupled potential formulations. The vector finite-element method is implemented for the discretization of the curl-curl equation of the secondary field. The vector and nodal elements are implemented simultaneously for the discretization of the coupled potential formulation. We use the stiffness matrix resulting from the coupled potential formulation to construct an efficient preconditioner, which is used for the solution of the linear system of equations obtained based on the secondary field formulation. The linear system of the equations could be solved efficiently by the quasiminimum residual method within several hundred iterations with the constructed preconditioner. We compare different modeling schemes to calculate the CSEM responses for a horizontally layered earth model excited by an electric dipole and find that the iteration process of the improved algorithm converges faster on average than other modeling schemes for the frequency band considered. Thus, the least computation time can be obtained over the frequency band for the improved algorithm compared with other modeling schemes, with the same level of accuracy reached. We further verify the efficiency of the algorithm through a small-scale 3D earth model excited by a magnetic dipole. Finally, we illustrate the performance of the algorithm with two 3D subsurface models, including a land-based model and a marine disk model. By comparison with published work, it is illustrated that our algorithm can efficiently calculate accurate land-based and marine CSEM responses with the new constructed preconditioner implemented.

A goal-oriented adaptive finite-element approach for 3-D marine controlled-source electromagnetic problems with general electrical anisotropy

SUMMARY We present a goal-oriented adaptive finite-element algorithm for accurately modelling marine controlled-source electromagnetic responses in 3-D media with general electrical anisotropy. We formulate the primal boundary value problem in terms of the total electric field for general applications. Following the goal-oriented adaptivity concept, the dual problem is derived from a functional designed to measure the data errors of interest in light of the data quality. We approximate the solutions to the primal and dual formulations using the edge finite-element method on tetrahedral grids for a flexible treatment of complex geological settings and survey geometries. To control the mesh adaptation, we develop a reliable residual-type a posteriori error estimation that takes account of the volumetric residual and the numerical discontinuity of the normal component of the electrical current density and that of the tangential component of the magnetic field with respect to non-smooth and anisotropic coefficients. We demonstrate the proposed modelling solver on 1-D MCSEM scenarios with varying degrees of electrical anisotropy. The comparison with goal-oriented adaptivity results obtained from other three commonly used error indicators shows that our approach is robust in dealing with both moderate and strong electrical anisotropy. After that, we constructed a 3-D hydrocarbon-bearing reservoir model with slope seafloor topography and tilted transverse isotropy in the background to examine our algorithm for the case of multiple sources. Finally, we implement a sensitivity analysis procedure to evaluate the resolution of the electrical anisotropy. The quantitative results indicate limitations and preferences of conventional MCSEM data in resolving anisotropic models, providing fundamental insights for inversion based data interpretation.

3-D Marine CSEM Forward Modeling With General Anisotropy Using an Adaptive Finite-Element Method

To investigate the effect of azimuthal anisotropy on frequency-domain marine controlled-source electromagnetic (CSEM) responses, an adaptive edge-based finite-element (FE) modeling algorithm is presented in this letter. The 3-D algorithm is capable of dealing with generally anisotropic conductive media. It is implemented on unstructured tetrahedral grids, which allow for complex model geometries. The accuracy of the FE solution is controlled through adaptive mesh refinement, which is performed iteratively until the solution converges to the desired accuracy tolerance. The algorithm is validated against the quasi-analytic solutions for a 1-D layered model with anisotropy. We then simulate the marine CSEM responses over a set of 3-D anisotropic models and illustrate that the azimuthal anisotropy has a considerable influence on both the inline and broadside marine CSEM responses but to different extents.

Impacts of complex geological structures on marine controlled-source electromagnetic responses

Folds and faults are the most common types of basic structures in geological formations. Marine controlled-source electromagnetic (CSEM) data are strongly affected by folds, faults and other complex irregular geological structures in subsea geo-environments because of their electrical anisotropy and the bathymetry generated by these types of structures. In this work, we investigate the effects of two typical geological structures, folds and faults, on marine CSEM responses by using an adaptive finite-element modeling approach. The adoption of unstructured tetrahedral grids in our code easily allows the inclusion of complex model geometries so that natural environments can be mapped into the model realistically. For the fold models, we investigate the impacts of anticlines, synclines and mixed anticline-syncline-type structures; numerical results indicate that both anticlines and synclines can produce considerable negative electromagnetic anomalies, which may be neutralized to a certain extent by the positive electromagnetic anomalies of a highly resistive target reservoir. The response curve of a syncline displays a “W” shape whose central part consisting of rising positive anomalies may be mistaken as the response of a highly resistive reservoir when interpreting CSEM data. Furthermore, the negative anomalies caused by the anticlines/synclines increase with the increasing inclination of their limbs. For the fault models, we investigate the effects of horsts and grabens on marine CSEM responses and results show that the responses of horsts/grabens can be large enough to mask the target reservoir's response. We conclude that folds and faults clearly have to be taken into account to avoid the misinterpretation of marine CSEM data.

Finite Element Simulation of 3-D Marine Controlled Source Electromagnetic Fields in Anisotropic Media with Unstructured Tetrahedral Grids

Marine controlled-source electromagnetic (CSEM) method has proved to be a powerful tool and found its increasing applications for offshore resource exploration and tectonic studies. However, bathymetric variations and anisotropic structures encountered in practical measurements have posed challenges for reliable interpretation of marine CSEM data collected in increasingly complex geologic settings. In this study, we present a Finite element (FE) based forward algorithm for simulating 3-D marine CSEM responses in geologic settings characterized with rough bathymetry and electrical anisotropy. Unstructured tetrahedral meshes are employed to permit precise descriptions of arbitrary seafloor topography. After validating the accuracy of the algorithm, we investigate the effects of bathymetric variations and complicated electric anisotropy separately and jointly on marine CSEM responses. Numerical results have demonstrated that both the bathymetry and electrical anisotropy can cause significant distortions on marine CSEM responses, but to different extent. The effects of full electrical anisotropy and bathymetry have to be taken into consideration for reliable interpretations of marine CSEM data in practice.

Fictitious wave domain modelling and analysis of marine CSEM data

SUMMARY Modelling marine controlled-source electromagnetic (CSEM) responses in the fictitious time domain is a novel approach, which facilitates the full exploration of EM diffusive properties in the fictitious wave domain (FWD). Concepts, such as reflections, refractions, diffractions and transmissions, which are used for the analysis of elastic wave propagation can thus be adopted in FWD for interpreting CSEM data. In this paper, we use a high-order finite difference time domain (FDTD) algorithm for modelling marine CSEM responses in both the fictitious time domain and the diffusive frequency domain. A complex frequency shifted perfectly matched layer (CFS–PML) boundary condition is adopted to the FDTD modelling. We demonstrate the performance of the CFS–PML boundary condition and validate the high-order FDTD code in the FWD with the half-space sea water model and in the frequency domain with the 1-D canonical reservoir model. We investigate and analyse the propagation characteristics of electromagnetic fields in the FWD, where we apply wave propagation concepts to interpret marine CSEM data. Similarities between wave and field propagations relevant for marine CSEM data are demonstrated through several 1-D to 3-D numerical examples.

3-D Marine Controlled-Source Electromagnetic Modeling in Electrically Anisotropic Formations Using Scattered Scalar–Vector Potentials

Marine controlled-source electromagnetic (CSEM) method has become a popular technique for offshore hydrocarbon exploration. It has been well recognized that marine CSEM data are strongly affected by electrical anisotropy of geologic formations in practice. Here, we present a robust and efficient finite volume algorithm for simulating marine CSEM responses in 3-D arbitrarily anisotropic formations. The algorithm is based on scattered scalar–vector potentials which improve the ill-conditioning of the resulting linear system by deflating the null space of the curl operator, and a conservative volume averaging scheme is utilized for the discretization of arbitrary electrical anisotropy. The accuracy of our algorithm is validated against quasi-analytic solutions for a layered vertical transverse isotropic reservoir model. It is then demonstrated by numerical results that the marine CSEM fields are significantly affected by the anisotropic conductivity tensor, and neglect of the full anisotropy of geologic formations may cause misleading data interpretation.

2.5D marine CSEM modeling in the frequency-domain based on an improved interpolation scheme at receiver positions

In the marine controlled-source electromagnetic (CSEM) survey, the receivers are usually placed at the seafloor. The resistivity contrast between the seawater and seafloor sediments is large, which can cause difficulties in numerical modeling of CSEM fields at receiver locations. In this paper, we present an improved interpolating method for calculating electric and magnetic fields at the seafloor with a resistivity contrast. This method is applied to the 2. 5 dimensional (2. 5D) frequency-domain CSEM modeling with towed transmitters and receivers located at the seafloor. Considering the discontinuity of the normal electric fields, we use the normal current electric density for interpolation. We simulate the 2. 5D marine CSEM responses by the staggered finite-difference (SFD) method with Fourier transform to the strike direction. The final SFD equations are solved by the direct solver MUMPS (MUltifrontal Massively Parallel Sparse direct Solver). To avoid the source singularities, the secondary-field approach is used and the primary fields excited by the electric dipole source can be calculated quasi-analytically for the one-dimensional (1D) layered background model. We focus on interpolating of electric and magnetic fields in the wavenumber domain to the receiver locations at the seafloor interface between the conductive seawater and resistive seafloor formation. The secondary electric and magnetic fields are used for interpolation instead of the total fields for high numerical accuracy. After performing the inverse Fourier transform to the wavenumbers, the electric and magnetic fields in the space domain are obtained. To check the accuracy of our 2. 5D marine CSEM SFD modeling algorithm with the improved receiver interpolating technique, we compare our results with both the 1D analytical results and the adaptive finite element results. The SFD numerical results are approved to be accurate. We also compare the numerical accuracy between our improved interpolation scheme and others, i.e., the conventional linear interpolation and the rigorous interpolation. The proposed interpolation only utilizes the nodes below/above the seafloor interface, and is proved to be much more accurate than the other two interpolating methods used.

Splitting marine controlled-source electromagnetic responses into sea and subseafloor contributions: Grounding the air wave

We have found how the effects of the air wave in marine controlled-source electromagnetic (CSEM) methods gradually vanish in the sea for shallow waters, and how at the same time they gradually grow below the seafloor, in an effort to comprehend existing detectability definitions. The transition from sea to land is smooth because the sea becomes a thin conductive layer when the water depth is smaller than the skin depth in the sea. We consider the problem of detecting resistive layers at depth associated with hydrocarbon reservoirs, particularly in shallow-water explorations and, specifically, on how the air wave affects detection. Our analysis is based on an integral representation of the electric field in terms of its sensitivity to changes in the electrical conductivity of a 1D profile. Two-dimensional images of the integrands are obtained by plotting the integrand as a function of depth for different offsets. Results include the expected growth of the inhibiting effect of the sea as the water depths decrease. However, we also find that this happens up to a point and that from then on its effect decreases to zero. Regarding the resistive layer at depth, its importance grows to a constant as the water depth decreases to zero. As a function of offsets, there appear first the direct current effects. The induction zone is next and is dominated by contributions from the underlying formations. The third zone, which corresponds to the air wave, is largely dominated by contributions from the sea. The fourth and last zone is the plane-wave asymptote. All four classical zones identified in marine CSEM are also present in land CSEM.

Accurate Interpolation at Receiver Positions: A Novel Method for Frequency-Domain Marine CSEM Finite-Difference Modelling

We present an accurate interpolating method for calculating electric and magnetic fields at the seafloor with a resistivity contrast. This method is applied to the three-dimensional (3D) frequency-domain marine controlled-source electromagnetic (CSEM) modeling with the towed transmitters and receivers located at the seafloor. We simulate the 3D marine CSEM responses by the staggered finite-difference method with a direct solver. The secondary-field approach is used for avoiding the source singularities and the primary fields excited by the electric dipole source could be calculated quasi-analytically for the one-dimensional layered background. Therefore, in this study, we focus on interpolating of electric and magnetic fields to the receiver locations at the seafloor interface between the conductive seawater and resistive seafloor formation. Considering the discontinuity of the normal electric fields, we use the normal current electric density for interpolation. The secondary electric and magnetic fields are also used for interpolation instead of the total fields for high numerical accuracy. The proposed interpolation only utilizes the nodes below/above the seafloor interface and is approved to be much more accurate than other tested interpolating methods, i.e., the conventional linear interpolation and the rigorous interpolation.

Efficient simulation of marine controlled source electromagnetic responses for axisymmetric scatter by using numerical mode matching approach

Horizontal disk, sphere, and spherical crown are a very important type of scatter in geophysics research. In the marine environment, a disk-like scatter can be used to describe several resistive targets, e.g., basaltic sills and stratigraphic hydrocarbon reservoirs while spherical crown can be used to approximately depict the topography of interface for basement rock. This type of scatter has characteristics of axisymmetrical distribution of the conductivity. If some approaches can be established to efficiently simulate the marine controlled source electromagnetic (MCSEM) response to this scatter, it will be meaningful to investigate the nature of MCSEM responses in complex formation and to build appropriate method of processing and explaining MCSEM data. In this paper, the resistive scatters are approximated by one or several horizontal concentric disks with different radii and thickness values, based on the axially symmetrical spatial distribution of conductivity. Then, a combination of these concentric disks with air, sea water and surrounding beds will construct a horizontally stratified inhomogeneous formation with common axis-center, whose spatial distribution of conductivity is layered in the vertical direction and axisymmetric in the horizontal direction. Based on the approximations mentioned above, the computation of MCSEM response excited by horizontal electrical dipole (HED) located at the z-axis is entirely transformed into two axially symmetrical problems for the Fourier harmonic components of the electromagnetic (EM) fields. The differential operators about the horizontal magnetic components and transformation of horizontal electrical components and other EM components from horizontal magnetic components are derived. Then, the numerical mode matching approach is extended to the simulation of the EM field and three-dimensional (3D) MCSEM responses excited by the HED in the formation. The procedure for solving the EM field is presented. The semi-analytic solution of EM field in the whole space is obtained to efficiently and numerically model MCSEM response in the complex formation. Finally, the efficiency and accuracy of the present method are demonstrated numerically. The characteristics of 3D MCSEM responses in three different cases are further investigated.

Efficient simulation of three-dimensional marine controlled-source electromagnetic response in anisotropic formation by means of coupled potential finite volume method

A coupled potential finite volume method for simulation of three-dimensional marine controlled-source electromagnetic (CSEM) response in anisotropic formation is developed. To circumvent ill-conditioning and convergence problems, Maxwell's equations are reformulated into coupled scalar-vector potentials with Coulomb gauge and its complement by applying a Helmholtz decomposition to the electric field. Yee's staggered girds, finite volume averaging and interpolation techniques are used to make the Helmholtz equations discrete. The resulting sparse and complex linear system in large-scale models is solved by a direct solver PARDISO. In order to improve the accuracy of the near field results without significantly reducing the computational efficiency, a method using difference fields is proposed to reduce the source singularity effect of anisotropic formation. The anisotropic modeling examples show that marine CSEM response is predominantly sensitive to reservoir vertical resistivity, not to reservoir horizontal resistivity, provided that the reservoir are thin and high-resistive; but the marine CSEM response is sensitive to both horizontal and vertical resistivity of the overburden on top of the reservoir.

Adaptive finite element modeling of marine controlled-source electromagnetic fields in two-dimensional general anisotropic media

In this paper, we extend the scope of numerical simulations of marine controlled-source electromagnetic (CSEM) fields in a particular case of anisotropy (dipping anisotropy) to the general case of anisotropy by using an adaptive finite element approach. In comparison to a dipping anisotropy case, the first order spatial derivatives of the strike-parallel components arise in the partial differential equations for generally anisotropic media, which cause a non-symmetric linear system of equations for finite element modeling. The adaptive finite element method is employed to obtain numerical solutions on a sequence of refined unstructured triangular meshes, which allows for arbitrary model geometries including bathymetry and dipping layers. Numerical results of a 2D anisotropic model show both anisotropy strike and dipping angles have great influence on the marine CSEM responses.

The marine controlled source electromagnetic response of a steel borehole casing: applications for the NEPTUNE Canada gas hydrate observatory

ABSTRACTGas hydrates are a potential energy resource, a possible factor in climate change and an exploration geohazard. The University of Toronto has deployed a permanent seafloor time‐domain controlled source electromagnetic (CSEM) system offshore Vancouver Island, within the framework of the NEPTUNE Canada underwater cabled observatory. Hydrates are known to be present in the area and due to their electrically resistive nature can be monitored by 5 permanent electric field receivers. However, two cased boreholes may be drilled near the CSEM site in the near future. To understand any potential distortions of the electric fields due to the metal, we model the marine electromagnetic response of a conductive steel borehole casing. First, we consider the commonly used canonical model consisting of a 100 Ωm, 100 m thick resistive hydrocarbon layer embedded at a depth of 1000 m in a 1 Ωm conductive host medium, with the addition of a typical steel production casing extending from the seafloor to the resistive zone. Results show that in both the frequency and time domains the distortion produced by the casing occurs at smaller transmitter‐receiver offsets than the offsets required to detect the resistive layer. Second, we consider the experimentally determined model of the offshore Vancouver Island hydrate zone, consisting of a 5.5 Ωm, 36 m thick hydrate layer overlying a 0.7 Ωm sedimentary half‐space, with the addition of two borehole casings extending 300 m into the seafloor. In this case, results show that the distortion produced by casings located within a 100 m safety zone of the CSEM system will be measured at 4 of the 5 receivers. We conclude that the boreholes must be positioned at least 200 m away from the CSEM array so as to minimize the effects of the casings.

Simulation of marine controlled-source electromagnetic response in horizontally layered transversely isotropic formation by using improved transmission line method

In this paper, the two-dimensional Fourier transform and wave decomposition technique are used to transform Maxwell’s equation in transversely isotropic (TI) formation into two independent sets of transmission line equations about transverse magnetic (TM) wave and transverse electric (TE) wave. According to both transmission line theory and superposition principle, an improved transmission line method is advanced to simplify the computational process of TM wave and TE wave only by introducing the transmission line Green’s functions of the current source. Thus, the new algorithm and the new expressions of current source electromagnetic (EM) dyadic Green’s functions in frequency-wavenumber domain are established for realizing the efficient simulation of marine controlled-source electromagnetic (MCSEM) responses in the horizontally layered TI formation. On this base, the basic solutions of the transmission line Green’s functions and EM boundary conditions are utilized to derive the recursive formula of the generalized reflections and amplitudes of the TE and TM waves, and the analytic solutions of the Green’s functions in each bed are obtained. Then, by using Fourier inverse transform and Bessel integral formula, the MCSEM responses in frequency-spatial domain are expressed in the Sommerfeld integral form. A combination of the cubic spline interpolation with the Lommel integral is used to efficiently compute the MCSEM responses. Finally, we validate the modeling algorithm and investigate the influences of changes in operation frequency and anisotropic coefficient on the MCSEM response in the TI formation.

Finite element modelling of marine controlled-source electromagnetic responses in two-dimensional dipping anisotropic conductivity structures

SUMMARY We present an adaptive finite element (FE) solution for the marine controlled-source electromagnetic (CSEM) forward problem in 2-D dipping anisotropic conductivity structures. Our code is implemented on an unstructured triangular mesh, which allows for arbitrary model geometries including bathymetry and dipping layers. We have verified the FE code using a layered 1-D model with anisotropy. For this model, the FE algorithm provides accurate results. The relative amplitude error between the analytical solution and numerical results for all electromagnetic components except Hz for large offsets is less than 1 per cent and the error in phase is less than 0.5°. We simulate the marine CSEM responses of a 2-D anisotropic model, and the numerical results show that the CSEM fields are affected considerably by anisotropy in both the reservoir target and the surrounding sediment, but to different extent.

The transient electromagnetic response of a resistive sheet: an extension to three dimensions

SUMMARY Controlled-source electromagnetic prospecting systems which produce vertical current flow in the Earth are sensitive to horizontal, electrically resistive structures such as hydrocarbon deposits and fresh water lenses. The electromagnetic response of such 3-D targets can sometimes be approximated by the fields produced by an arrangement of thin resistive sheets buried in a conductive host medium. We have previously shown, through simplified 2-D modelling, that the resistive sheet problem is more subtle than the conductive case commonly used in mineral exploration. Not only does the resistive sheet require the continuity of the normal current density as opposed to the continuity of the tangential electric field, interaction terms within the coupling matrix must also be calculated in full rather than approximated by point dipole sources representing each element. The purpose of this paper is to extend these results to the more realistic and practical situation of a 3-D resistive sheet buried in a multilayered earth. The algorithm is validated against 1-D calculations for a very large sheet and 3-D finite difference modelling for a smaller sheet. A current deflection number characterizes the effect of a resistive sheet's transverse impedance and governs its response in the same way that the current channelling number does for a conductive target. The sheet can be represented to first order by a single point dipole located at its centre; at most receiver locations, arrival times are nearly identical to those found from the full solution although amplitudes show some deviation near the target. As an example of the use of the algorithm, the marine controlled-source electromagnetic response of a simple anticlinal hydrocarbon reservoir underlying near surface resistors such as shallow gas or gas hydrate deposits is modelled. Results show that such near surface anomalies, even those with low deflection numbers, significantly affect the response of the deeper target and must be included in modelling and interpretation.

Useful characteristics of shallow and deep marine CSEM responses inferred from 3D finite-difference modeling

Hydrocarbon reservoirs can be mapped if sufficient resistivity contrasts exist between them and their confining layers, but practical problems remain in target discrimination in deep and shallow waters, especially in the presence of heterogeneous overburden. We have developed an efficient 3D staggered-grid finite-difference controlled-source electromagnetic (CSEM) modeling code that enables study of the physics underlying some practical problems. We undertook a comparative analysis of reservoir detection in [Formula: see text]- and [Formula: see text]-deep waters using the simulated electric and magnetic field responses of a simple 3D reservoir. We examined the effect of two types of near-surface heterogeneity (mimicking disconnected gas clouds and/or patchy geochemical alteration halos) on the 3D reservoir response. We found that small-scale, shallow heterogeneities cause distortions that are almost independent of the source frequency. These persist at all source-receiver offsets in the electric amplitude response in deep and shallow waters and phase response in shallow water. They decrease in magnitude with increasing offset in deepwater phase response. Large-scale near-surface heterogeneities distort the horizontal electric field response more significantly than the small-scale ones, but the near-surface response gets smaller in amplitude as the offset increases. The distortions in shallow water are much smaller in magnitude than those for the deepwater case, so that the reservoir signatures still are visible on the response profiles. This might be considered as a positive feature for shallow-water inline electric field exploration. The magnetic field responses for the orthogonal direction provide diagnostic target signatures that are similar to the inline electric field responses in deep water but that are different in shallow water. The magnetic responses are affected by the airwave in a different manner from the electric field, suggesting that combined 3D electric and magnetic field analysis might be vital for handling the airwave problem.

Three-dimensional numerical modeling of marine controlled-source electromagnetic responses in a layered anisotropic seabed using integral equation method

We perform a numerical simulation of marine controlled-source electromagnetic （MCSEM） responses in a layered anisotropic seabed using integral equation method. Firstly, we use the operator theory to deduce the contraction integral equation, which is always convergent regardless of any parameters, for it satisfies the contraction mapping condition. Then we introduce the subdomain multigrid and quasi-linear approximation to improve the computation efficiency. We also validate the accuracy and efficiency of the algorithm by synthetic numerical modelings. Finally, we simulate the three-dimensional MCSEM responses in the layered anisotropic seabed, and investigate the effects of anisotropy.