High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Wide-Band Numerical Solution and Examples

Avdeev, Dmitry B.; Kuvshinov, A. V.; Pankratov, Oleg V.; Newman, Gregory A.

doi:10.5636/jgg.49.1519

Cited by 82 publications

(51 citation statements)

References 22 publications

(28 reference statements)

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“…Further work will be concentrated on adapting various types of regularization techniques, and introducing the static shift into the penalty function (1). It is also planned to apply our inversion scheme to an experimental data set.…”

Section: Resultsmentioning

confidence: 99%

“…, N) of the prisms need to be recovered. The x3d forward modeling code described in [1,2] was exploited as an engine for inversion to solve the forward and adjoint problems given in Eq. (4) and (5).…”

Section: Model Examplementioning

confidence: 99%

“…The inversion also involves all four entries of the MT impedance matrix. The integral equation forward modelling code x3d by Avdeev et al [1,2] is employed as an engine for this inversion. Convergence, performance and accuracy of the inversion are demonstrated on a 3D MT synthetic, but realistic, example.…”

mentioning

confidence: 99%

See 2 more Smart Citations

A Rigorous Three-Dimensional Magnetotelluric Inversion

Avdeev¹,

Avdeeva²

2006

PIER

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Abstract-The limited-memory quasi-Newton optimization method with simple bounds has been applied to develop a novel fully threedimensional (3-D) magnetotelluric (MT) inversion technique. This nonlinear inversion is based on iterative minimization of a classical Tikhonov-type regularized penalty functional. But instead of the usual model space of log resistivities, the approach iterates in a model space with simple bounds imposed on the conductivities of the 3-D target. The method requires storage that is proportional to n cp ×N , where the N is the number of conductivities to be recovered and n cp is the number of the correction pairs (practically, only a few). This is much less than requirements imposed by other Newton type methods (that usually require storage proportional to N ×M , or N ×N , where M is the number of data to be inverted). Using an adjoint method to calculate the gradients of the misfit drastically accelerates the inversion. The inversion also involves all four entries of the MT impedance matrix. The integral equation forward modelling code x3d by Avdeev et al. [1,2] is employed as an engine for this inversion. Convergence, performance and accuracy of the inversion are demonstrated on a 3D MT synthetic, but realistic, example.

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Section: Resultsmentioning

confidence: 99%

Section: Model Examplementioning

confidence: 99%

See 1 more Smart Citation

A Rigorous Three-Dimensional Magnetotelluric Inversion

Avdeev¹,

Avdeeva²

2006

PIER

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“…In this paper we have developed a modified Neumann series (MNS) technique for a case when conductivity, dielectric permittivity and magnetic permeability are 3 x 3 matrices. Similar techniques to solve Maxwell's equations within arbitrary isotropic earth were presented in (Pankratov et al, 1995;Singer and Fainberg, 1995;Avdeev et al, 1997).…”

Section: Introductionmentioning

confidence: 99%

High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Anisotropic Earth

Pankratov

Kuvshinov

Avdeev

1997

J. geomagn. geoelec

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We have developed a modified Neumann series (MNS) technique to solve Maxwell's equations for three-dimensional anisotropic earth. We assume that both conductivity and dielectric permittivity are 3 x 3 matrices, elements of which are complex-valued functions of space coordinates and frequency, whereas the magnetic permeability is symmetric 3 x 3 matrix with elements being real-valued functions of depth. Both conduction and displacement currents are taken into account. In order to derive the MNS solution, we impose the positiveness condition of Joule losses inside anisotropic earth. The MNS solution so obtained is valid for any frequency range and for arbitrary three-dimensional anisotropic earth.

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“…For this study, we construct two synthetic models based on an existing salt dome in the North Sea, one with and one without overhang. Using the 3D frequency domain integral equation code x3D (Avdeev et al, 1997(Avdeev et al, , 2002, we compare the responses obtained for these two salt dome models. We then invert these two data sets and assess the inversion results.…”

Section: Introductionmentioning

confidence: 99%

Detecting a salt dome overhang with magnetotellurics: 3D inversion methodology and synthetic model studies

2012

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Detecting a salt dome overhang is known to be problematic by seismic methods alone. We used magnetotellurics (MT) as a complementary method to seismics to investigate the detectability of a salt dome overhang. A comparison of MT responses for 3D synthetic salt models with and without overhang shows that MT is very sensitive to shallow salt structures and suggests that it should be possible to detect an overhang. To further investigate the resolution capability of MT for a salt dome overhang, we performed a 3D MT inversion study and investigated the impact of model parametrization and regularization. We showed that using the logarithms of the conductivities as model parameters is crucial for inverting data from resistive salt structures because, in this case, commonly used Tikhonov-type stabilizers work more equally for smoothing the resistive and conductive structures. The use of a logarithmic parametrization also accelerated the convergence and produced better inversion results. When the Laplace operator was used as a regularization functional, we still observed that the inversion algorithm allows spatial resistivity gradients. These spatial gradients are reduced if a regularization based on first derivatives in contrast to the Laplace operator is introduced. To demonstrate the favorable performance when logarithmic parametrization and gradient-based regularization are employed, we first inverted a data set simulated for a simple model of two adjacent blocks. Subsequently, we applied the code to a more realistic salt dome overhang detectability study. The results from the detectability study are encouraging and suggest that 3D MT inversion can be applied to decide whether the overhang is present in the shallow salt structure even in the case when only profile data are available. However, to resolve the overhang, a dense MT site coverage above the flanks of the salt dome is required.

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High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Wide-Band Numerical Solution and Examples

Cited by 82 publications

References 22 publications

A Rigorous Three-Dimensional Magnetotelluric Inversion

A Rigorous Three-Dimensional Magnetotelluric Inversion

High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Anisotropic Earth

Detecting a salt dome overhang with magnetotellurics: 3D inversion methodology and synthetic model studies

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