Anisotropy

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: 

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

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

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

    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.  The conductivity tensor has the form:  

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

    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.  The conductivity tensor has the form:  

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

  • TIZ - transversely isotropic  perpendicular to the z axis.  The conductivity tensor has the form:  

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

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

Note that when you specify the resistivity for anisotropic parameters using Mamba2D.m, the edit box expects a specific order for the components, as shown below for  the  TIZ anisotropy commonly used for marine sediments. In this case, the resistivity menu expects the resistivity for the transverse component (vertical resistivity  \rho_z) to be listed before the horizontal resistivity.  In the example below, the vertical to horizontal resistivity anisotropy factor is 3 since the vertical resistivity is 6 and the horizontal resistivity is 2.

TIZ

For triaxial resistivity, the edit menu expects resistivity in order of  \rho_x,\rho_y, \rho_z:

triaxial

 

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