Tag Archives: alpha

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.


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




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