Tag Archives: rotation

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°.