SUMMARY

Rotate a set of 3 perpendicular components either around the vertical (V) direction (TO VRT or TO VNE) or around the Transverse (T) direction (TO LQT)

SYNTAX

Rotations around the vertical (cmpinc = 0 degrees) direction:

ROTINC {TO VRT|VNE}

Rotations around the transverse (cmpaz = baz-90) direction:

ROTINC {TO LQT} {ANGLE angle}

or:

ROTINC {TO LQT} {iP | iS} {vP alpha} {vS beta} {RAY p} {VERBOSE}

INPUT

TO VRT:	rotate into vertical,radial, transverse coordinate system
TO VNE:	rotate into system aligned with vertical, north, and east
TO LQT:	rotate into P, SV, and SH coordinate system
ANGLE a:	Rotation through an angle a (V to L) around T. L cmpinc = a
iP:	incident P wave: calculated L cmpinc is the incident P apparent angle
iS:	Incident S wave: calculated Q cmpinc is the incident SV apparent angle
vP v:	v is P-wave velocity at the surface (default 5.8)
vS v:	v is S-wave velocity at the surface (default 3.36)
RAY p:	ray parameter, p in sec/km (no default value, so must be set)
VERBOSE:	prints information to the screen for iP or iS options (default off)

DESCRIPTION

Given three perpendicular components of a recorded time series, ROTINC rotates the set into the selected coordinate system. It works its way through all records in memory until it fails to find three consecutive perpendicular traces. It assumes vertical up (cmpinc = 0.0), cmpaz measured clockwise from N. T to the right from the vertical-radial plane facing towards the station (baz - 90). Hence, VNE, VRT, and LQT are all left-handed coordinate systems.

For TO LQT, the "TO LQT" can be left out because that is the only option for which there are additional arguments. For TO LQT, there are two choices:

1 ROTINC ANGLE a: rotation around the T axis (a=0.0 is up)

2.ROTINC iP or ROTINC iS: rotation around T, through a calculated angle that is calculated assuming the P or SV wave is incident on the free surface (top of a half space). For iP, the output cmpinc for L is often called the apparent angle: the arctangent of the radial (R) amplitude divided by the vertical (V) amplitude. For iS, the output cmpinc for Q is the incident SV apparent angle. For ROTINC iS, the incident SV angle must be less than the critical angle: vP * RAY < 1.0.

EXAMPLES

Rotations around the vertical are straightforward: either TO VNE or TO VRT with no arguments.

Here are examples for TO LQT. For a rotation around T through an angle 24.44:

SAC> ROTINC ANGLE 24.44 (or ROTINC TO LQT ANGLE 24.44)
   Input: rotation angle from V to L

For a free-surface correction (Note: one must specify RAY.) Here p = sin(21.32)/5.8) = 0.063, where 21.32 is the P incident angle:

SAC> ROTINC iP RAY 0.063 VERBOSE
  Incident P wave; free-surface response
  vP: 5.80 km/s vS: 3.36 km/s Ray Param: 0.063000 s/km
  Apparent angle: 24.44
SAC> message &1,cmpinc &1,kcmpnm
  24.4416
  L

Generally vP and vS are the velocities in the surface layer. If the wavelength of the dominant arrivals are larger than the thickness of that layer, one may have to average over two or more layers. This can be tested by plotting the vertical-radial particle motion (PLOTPM) as the output motion is along the apparent angle. The ray parameter will not be changed. Here is an example for the same ray but assuming the wavelengths are long enough to average over the whole crust:

SAC> ROTINC iP vp 8.04 vs 4.47 RAY 0.063 VERBOSE
  Incident P wave; free-surface response
  vP: 8.04 km/s vS: 4.47 km/s Ray Param: 0.063000 s/km
  Apparent angle: 32.71

Here is an example for iS (p = sin(23.12)/3.36) = 0.1169, where 23.12 is the SV incident angle:

SAC> ROTINC iS RAY 0.1169 VERBOSE
   Incident S wave; free surface response
   vP: 5.80 km/s vS: 3.36 km/s Ray Param: 0.116900 s/km
   Apparent angle: 115.82
SAC> message &2,cmpinc &2,kcmpnm
  115.817
  Q

There is often interference with other arrivals for SV on the vertical, so the SV on V and R are generally not that similar. Hence V-R particle motion is less useful for SV than it is for P.

EQUATIONS

The relevant cmpinc (apparent angle) is computed using the following equations:

• iP:

  L cmpinc = atan(2*Vs*p*sqrt(1-(Vs*p)**2)/(1-2*(Vs*p)**2) )
  

• iS:

  Q cmpinc = atan(Vp*(1-2*(Vs*p)**2))/(2*Vs**2*p*sqrt(1-(Vp*p)**2)) )
  

where p is the ray parameter. Equations are based on Problem 5.6 in Aki and Richards, 2002, pg. 184.

HEADER CHANGES

CMPINC, CMPAZ, KCMPNM, DEPMAX, DEPMIN, DEPMEN

AUTHOR

This command was originally contributed by Frederik Tilmann in 2015,

LATEST REVISION

May 2017 (Version 102.0)