Summary. We present an adaptive finite element (FE) solution for the marine controlled-source electromagnetic (CSEM) forward problem in 2-D dipping anisotropic

We present a finite volume (FV) algorithm for the magnetotelluric (MT) forward modeling in 3-D conductivity structures with general anisotropy. The electric and magnetic fields are discretized on a conventional staggered grid, which cannot directly address the full-tensor conductivity. To overcome this difficulty, an interpolation scheme is employed to average different components of the electric field to the same position. We formulate the algorithm in pure matrix form and implement it in a new language, Julia, making the programming process highly efficient and leading to a code with excellent readability, maintainability and extendability. The validity of the FV Julia code is demonstrated using a layered 1-D anisotropic model. For this model, the FV code provides accurate results, and the computational cost is reasonable. The iterative solvers QMR and BiCGStab preconditioned with the electromagnetic potential (A-ø) system exhibit good convergence rate for a wide range of periods. The direct solvers MUMPS and PARDISO are highly efficient for small model sizes. For a relatively large model size with 2.18 millions unknowns, the linear system of one period can be solved by MUMPS within 360 seconds with multiple threads involved in the computation, and the memory usage is only 11.6 GB in the “Out-of-Core” mode. We further calculate MT responses of a 3-D model with dipping and horizontal anisotropy, respectively. The results suggest that electrical anisotropy can have significant influence on the MT response.

In this article, we present a new method for the detection and localization of multiple dipole-like magnetic sources using magnetic gradient tensor data. We use the tilt angle that is the ratio of the vertical magnetic component to the horizontal field to determine the number of the magnetic sources and use the rotational-invariant normalized source strength (NSS) to estimate approximate horizontal coordinates of the magnetic sources. The differential evolution (DE) algorithm is used to estimate the locations and moments of the magnetic sources. Three synthetic examples, with and without random noise, are designed to validate the proposed method. The locations and magnetic moments of the magnetic sources can be well determined. The proposed method has also been applied to a field test with multiple magnetic sources and the result shows that the location of the magnetic source can be estimated well.

In this study, the complex frequency-shifted perfectly matched layer (CFS-PML) in stretching Cartesian coordinates is successfully applied to 3-D frequency-domain marine controlled-source electromagnetic (CSEM) field modelling. The Dirichlet boundary, which is usually used within the traditional framework of EM modelling algorithms, assumes that the electric or magnetic field values are zero at the boundaries. This requires the boundaries to be sufficiently far away from the area of interest. To mitigate the boundary artefacts, a large modelling area may be necessary even though cell sizes are allowed to grow toward the boundaries due to the diffusion of the electromagnetic wave propagation. Compared with the conventional Dirichlet boundary, the PML boundary is preferred as the modelling area of interest could be restricted to the target region and only a few absorbing layers surrounding can effectively depress the artificial boundary effect without losing the numerical accuracy. Furthermore, for joint inversion of seismic and marine CSEM data, if we use the PML for CSEM field simulation instead of the conventional Dirichlet, the modelling area for these two different geophysical data collected from the same survey area could be the same, which is convenient for joint inversion grid matching. We apply the CFS-PML boundary to 3-D marine CSEM modelling by using the staggered finite-difference discretization. Numerical test indicates that the modelling algorithm using the CFS-PML also shows good accuracy compared to the Dirichlet. Furthermore, the modelling algorithm using the CFS-PML shows advantages in computational time and memory saving than that using the Dirichlet boundary. For the 3-D example in this study, the memory saving using the PML is nearly 42 per cent and the time saving is around 48 per cent compared to using the Dirichlet.

In this paper, we present wavenumber domain (WD) electromagnetic field expressions at any depth in a layered conductivity earth due to both the horizontal and vertical electric dipoles, which can be buried anywhere within the layered earth. In modeling controlled-source electromagnetic (CSEM) responses for a 2D conductivity structure with a 3D source, it is very common to separate electromagnetic fields into a primary field and a secondary field to avoid the source singularity. This secondary field scheme requires WD background fields at any depth for a layered conductivity structure. To obtain primary electromagnetic fields in the WD, one can calculate quasi-analytical primary fields in the space domain (SD) and then transform them into the WD. However, this SD method is not a very efficient method of calculation. With the use of Schelkunoff potentials, we derive the quasi-analytic expressions for the electromagnetic fields in the WD, i.e. the WD method. Numerical tests indicate that the WD method can give results with the same accuracy as the SD method, and furthermore, the WD method is much faster than the SD method.