# 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 $E_{y''}$.

##### 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