Anisotropic Conductivity

MARE2DEM can model isotropic to triaxially anisotropic conductivity but tilted or generally anisotropic media is not supported. Switching between the various types of anisotropy is easily accomplished using the anisotropy menu in the Mamba2D model building assistant. For most modeling purposes, you will likely want to use simple isotropic conductivity, but for modeling a stack of interbedded marine sediments the transversely isotropic vertical (TIZ) option can be useful. The other options are for more specialized anisotropies. In general if you have no idea about anisotropy or which setting you should use, go for the isotropic default.

Here’s a guide to the five possible options:

  • isotropic - conductivity is the same in all direction of electric current flow. The conductivity tensor has the form:

\[\begin{split}{{ \bar{ \sigma}}}= \left[\begin{array}{ccc}\sigma & 0 & 0 \\0 & \sigma &0\\ 0 & 0 & \sigma \end{array}\right] .\end{split}\]

  • triaxial - conductivity varies in the direction of the three coordinate axes. The conductivity tensor has the form:

\[\begin{split}{\mathbf{ \bar{ \sigma}}} = \left[\begin{array}{ccc}\sigma_{x} & 0 & 0 \\0 & \sigma_{y} &0\\ 0 & 0 & \sigma_{z} \end{array}\right],\end{split}\]

where x,y,z are the 2D model axes.

There are three other possible anisotropies where the conductivity along one axis is different than the other two. This type of anisotropy is generally referred to as transverse isotropy, where conductivity is symmetric about an axis normal to the plane of isotropy. MARE2DEM uses the abbreviation TI for transverse isotropy and the third letter denotes the transverse axis. The three possible cases are:

  • TIX - transversely isotropic perpendicular to the x axis:

\[\begin{split}{\mathbf{ \bar{ \sigma}}} = \left[\begin{array}{ccc}\sigma_{\|} & 0 & 0 \\0 & \sigma_{\bot} &0\\ 0 & 0 & \sigma_{\bot} \end{array}\right],\end{split}\]

where \(\sigma_{\|}\) denotes conductivity along the x axis, and \(\sigma_{\bot}\) is conductivity in the transverse plane.

  • TIY - transversely isotropic perpendicular to the y axis:

\[\begin{split}{\mathbf{ \bar{ \sigma}}} = \left[\begin{array}{ccc}\sigma_{\bot} & 0 & 0 \\0 & \sigma_{\|} &0\\ 0 & 0 & \sigma_{\bot} \end{array}\right].\end{split}\]

  • TIZ - transversely isotropic perpendicular to the z axis:

\[\begin{split} {\mathbf{ \bar{ \sigma}}} = \left[\begin{array}{ccc}\sigma_{\bot} & 0 & 0 \\0 & \sigma_{\bot} &0\\ 0 & 0 & \sigma_{\|} \end{array}\right].\end{split}\]

This is also known in the exploration community as vertically transverse isotropy (VTI).