3D magnetotelluric modelling including surface topography

Abstract

A B S T R A C TAn edge finite-element method has been applied to compute magnetotelluric (MT) responses to three-dimensional (3D) earth topography. The finite-element algorithm uses a single edge shape function at each edge of hexahedral elements, guaranteeing the continuity of the tangential electric field while conserving the continuity of magnetic flux at boundaries. We solve the resulting system of equations using the biconjugate gradient method with a Jacobian preconditioner. The solution gives electric fields parallel to the slope of a surface relief that is often encountered in MT surveys. The algorithm is successfully verified by comparison with other numerical solutions for a 3D-2 model for comparison of modelling methods for EM induction and a ridge model. We use a 3D trapezoidal-hill model to investigate 3D topographic effects, which are caused mainly by galvanic effects, not only in the Zxy mode but also in the Zyx mode. If a 3D topography were approximated by a two-dimensional topography therefore errors occurring in the transverse electric mode would be more serious than those in the transverse magnetic mode.

Hydrothermal system beneath the crater of Tarumai volcano, Japan: 3-D resistivity structure revealed using audio-magnetotellurics and induction vector

“…The 2-D assumption, however, can be a problem when investigating volcanoes because of the effect of surface topography. The topographic effect on MT data is quite different between 2-D and 3-D topography (Nam et al, 2007); thus using a 2-D assumption for 3-D topography can provide misleading results in the resulting resistivity model. Another problem is determining the strike of a 2-D structure.…”

“…Topography has a measurable effect even on apparent resistivity and the impedance phase. Nam et al (2007) numerically calculated MT impedance from 3-D models that included topography consisting of a symmetrical hill. The assumed slope angle (31º) was as steep as the Tarumai dome (28 35º), and the calculated impedance change was significant (maximum 75 % for apparent resistivity and 13 % for phase at 2 Hz; Nam et al, 2007).…”

Three-dimensional resistivity structure of Asama Volcano revealed by data-space magnetotelluric inversion using unstructured tetrahedral elements

“…7b). Nam et al (2007) calculated the MT response functions along the centre line of a 3-D trapezoidal hill using a computational mesh with the 3-D topography, and compared them with those obtained by the 2-D forward calculation in which only the topography parallel to the profile was included in the mesh (Wannamaker et al 1986). They revealed that the TM-mode apparent resistivity obtained by the 2-D calculation was not much different from that obtained by the 3-D calculation while, in TE mode, the 2-D calculation did not reproduce the decrease of the TE-mode apparent resistivity on the hill obtained by the 3-D calculation.…”

3D MT Data Modelling using Multi-order Hexahedral Vector Finite Element Method, including Anisotropy and Complex Geometry

“…Therefore, the main target of these numerical implementations is to reduce the computational load and obtain accurate solutions including anisotropy and complex model geometry (Avdeev, 2005). 3D VFEM has been applied for MT modelling, with vector basis functions of linear order on a rectilinear mesh (Farquharson and Miensopust, 2011;Mitsuhata and Uchida, 2004;Shi et al, 2004) or on hexahedral elements (Nam et al, 2007). In this project, a VFEM algorithm is being developed with multi-order vector basis functions.…”

“…The main numerical techniques applied to 3D MT modelling are Finite Differences (Mackie, et al, 1993;Newman, 2002, 2003;Haber and Heldmann, 2007), Integral Equations (Wannamaker, 1991;Zhdanov, et al, 2006) and Finite Element (Farquharson and Miensopust, 2011;Mitsuhata and Uchida, 2004;Nam et al, 2007;Shi, et al, 2004) methods. The main problem of 3D EM modelling is the computational memory and time required to obtain the solutions.…”