Tag Archives: geometry

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

 

Data geometry: rotation angles for receivers

Receiver rotations are described by three angles:   θ, α and β, as shown in the image below. These rotate from the model coordinates x,y,z to the fully rotated measurement coordinates x'',y'',z''. For the rotation matrices associated with these angles, see Key and Lockwood (2010).   The  θ angle describes the horizontal rotation of the receiver's x  axis from the 2D model strike direction x For a typical CSEM data set ,  the data should be rotated so that  θ = 0. Therefore, for an array of receivers inline to a horizontal electric dipole source (with transmitter azimuth of 90°), the inline electric field will be the E_y component.  There angles α and β describe tilts of the receiver.  α is the vertical tilt of the E_{x''} component. If  α =0, then β describes the vertical tilt of the E_{y''}, otherwise β  describes a slanted angle to E_{y''}.

Receiver rotations are described by three angles.  For horizontal receivers, alpha and beta will be zero.
Receiver rotations are described by three angles. \theta is the horizontal rotation from the model strike x. For horizontal receivers, \alpha and \beta will be zero.

 

For receivers rotated so that theta = 0, the \beta angle then describes the tilt of the E_y component, and is the angle positive clockwise down from the y axis.  For a receiver tilted  down to the right, \beta will be positive.

 

RxTilt2
For a receiver tilted up to the right, \beta will be negative.

 

 

References

Key, K., & Lockwood, A. (2010). Determining the orientation of marine CSEM receivers using orthogonal Procrustes rotation analysis. Geophysics, 75(3), F63–F70. doi:10.1190/1.3378765

Data geometry: rotation angles for transmitters

MARE2DEM allows for arbitrary orientations of  transmitter dipoles. The orientation of  electric and magnetic dipole transmitters are described by the two angles of the dipole axis: the horizontal azimuth and the vertical dip angle.

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Example sources including the horizontal electric dipole (HED), vertical electric dipole (VED), horizontal magnetic dipole (HMD) and vertical magnetic dipole (VMD).  Since MARE2DEM allows for arbitrary source transmitter orientations, you only need to specify the source type as electric or magnetic in the data file and list its location and two orientation angles.
The transmitter azimuth is the angle of the dipole measured clockwise from the 2D strike direction x.
The transmitter azimuth is the angle of the dipole measured clockwise from the 2D strike direction x.  Thus, typical inline electric dipole CSEM data have a transmitter azimuth of about 90° (or 270°), while broadside data have a transmitter azimuth of  0° (or 180°).
The transmitter dip angle
The transmitter dip angle is defined as the angle down, clockwise from the azimuth of the transmitter.  A normal horizontal  electric dipole transmitter  has a dip of 0°.

 

Data geometry: horizontal positions of transmitters and receivers

For MT receivers, the x coordinate of the receivers is ignored by MARE2DEM since the 2D MT fields are strike invariant. For controlled-source electromagnetic receivers, there are a few considerations you need to mind about the accuracy of MARE2DEM, which uses a total field implementation for the source and a wavenumber domain transformation to compute the spatially varying EM fields:

  • The receiver  component should be close the to  transmitter position. Receivers don't need to be perfectly inline, but  if they are more than 1-2 km down-strike from the transmitter (gray regions below), the default settings for the wavenumber domain transforms in MARE2DEM may break down due to highly oscillatory kernel functions.
  • Due to the source singularity in the 2.5D wavenumber domain, receivers located down strike from the transmitter (pink region below) may be inaccurate unless they are positioned much deeper than the source.
  • If modeling point dipoles, remember that receivers closer than a few real dipole lengths from the transmitter will be inaccurate due to finite length dipole effects (red region below). You can instead specify a finite length dipole in the data file, but this comes at an increased numerical effort for MARE2DEM (more on that in another tutorial).

 

EM (not MT) receivers should be positioned with an x coordinate in the green region. Receivers too close the transmitter will suffer from inaccuracy due to the source singularity (in the pink region). If a point dipole is being modeled, receivers should be located at least a few dipole lengths away (red region). Finally, while technically receivers can be given any x coordinate, the default setting used by MARE2DEM for the 2.5D wavenumber domain transforms may break down if the receivers are located too far down strike from the transmitter (gray regions); typically this may be 1 -2 km or more offline.
EM (not MT) receivers should be positioned with an x coordinate in the green region. Receivers too close to the transmitter will suffer from inaccuracy due to the source singularity (in the pink region). If a point dipole is being modeled, receivers should be located at least a few dipole lengths away (red region). Finally, while technically receivers can be given any x coordinate, the default setting used by MARE2DEM for the 2.5D wavenumber domain transforms may break down if the receivers are located too far down strike from the transmitter (gray regions); typically this may be 1 -2 km or more offline.

Geo-referencing to UTM coordinates

Note: UTM referencing is only used for plotting purposes. MARE2DEM completely ignores this for the 2D EM calculations.

To help with post-inversion plotting of well logs and SEG-Y seismic overlays on your 2D inversion models, the data file has a line for specifying the UTM zone, origin and rotation of the 2D model coordinates:

UTM0

The 2D strike angle is the geographic angle corresponding to the x direction of the 2D model, clockwise from north. The example below has a 2D strike of 20º.

UTMreferencing