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The 3D forward model


The 3D forward model consist of 3 different blocks in a homogeneous 100 Ωm half-space. The figure below shows sketches of the construction in section and plan view, and the table summarizes the dimensions and resistivity values of the bodies.

The origin of the coordinate system (COSY) will be in lateral direction at the center of body 1, but of course on the surface - with z positive downwards. Looking at the plane view x is positive upwards and y to the right.

The sites are located on 3 profiles parallel to the y-direction: one at x = -15 km, the second at x = 0 km and the third at x = 15 km. Each profile has 16, equally distributed sites with a station spacing of 5 km (from y = -37.5 km to y = 37.5 km). And additional 11 sites are located on a fourth profile at y = 0 km with a site spacing of 5 km (from x = -25 km to x = 25 km).


  1. I.Please calculate the forward responses at all sites for the period range of 0.1 s to 10 000 s (0.1 s, 0.18 s, 0.32 s, 0.56 s, 1 s, 1.8 s, 3.2 s, ...., 5600 s, 10000 s).

  2. Please email (marion@cp.dias.ie) the results as a plain ASCII format file: x-coordinate, y-coordinate, period (in s - not frequency in Hz), Re Zxx, Im Zxx, Re Zxy, Im Zxy, Re Zyx, Im Zyx, Re Zyy, Im Zyy. The kind of code (FD, integral equation,...) you used and the computing time together with some properties (CPU speed, memory,...) of the used computer/cluster might also be interesting for comparison. It would be great if you could include a few words about that in your email.


  3. II. Run an inversion of the 3D forward responses you calculated yourself (in I.)



Forward modelling results from different person using different codes


At the moment only ascii format impedance or resistivity and phase files are available. The first line is a header line - the used sign convention for the time dependency is eiωt.

looking from

positive to negative x               negative to positive x

  1. Nuree Han & Tae Jong Lee: Myung Jin Nam’s code ( Nam, M. J., Kim, H. J., Song, Y., Lee, T. J., Son, J. S., and Suh, J. H., 2007, 3D magnetotelluric modelling including surface topography, Geophysical Prospecting, 55, 277-287) - impedances or resistivities & phases.

  2. Randy Mackie: Randy Mackie’s code  - impedances or resistivities & phases.

  3. Marion Miensopust: 

  4. i.Winglink ( Mackie, R. L., Smith, J. T., & Madden, T. R. (1994). Three-dimensional electromagnetic modeling using finite difference equations: The magnetotelluric example. Radio Science, 29, 923–935 ) - impedances or resistivities & phases.

  5. ii.wsinv3dmt (Siripunvaraporn W., G. Egbert and Y. Lenbury, 2002, Numerical Accuracy of      Magnetotelluric Modeling: A Comparison of Finite Difference Approximation, /Earth Planets Space/, 54, 721-725) - impedances or resistivities & phases. (Please note, due to the conflict of sites being located on top of the body edges and this code requiring the sites to be in the centre of the cells, boundaries had to be moved slightly -> not 100% identical to all other responses.)

  6. iii. UBC GIF code mt3dinv (Farquharson, C. G., Oldenburg, D. W., Haber, E., & Shekhtman, R. (2002, October). An algorithm for the three-dimensional inversion of magnetotelluric data. SEG Int’l Exposition and 72nd Annual Meeting, Salt Lake City, Utah) - impedances or resistivities & phases.