# pyacs.lib.euler module¶

Euler poles manipulation

`pyacs.lib.euler.``rot2euler`(Wx, Wy, Wz)[source]

Converts a rotation rate vector Wx Wy Wz in radians/yr into an Euler pole (long. lat. deg/Myr) into geographical (spherical) coordinates and angular velocity

Parameters

Wx,Wy,Wz – rotation rate vector in geocentric cartesian coordinates with units of radians/yr

Returns longitude,latitude,omega

longitude and latitude of the Euler pole in radians and the

angular velocity in decimal degrees per Myr.

Note

longitude and latitude are relative to the sphere, not the ellipsoid. This is because

Euler pole and rigid rotations only have sense on a sphere.

`pyacs.lib.euler.``euler2rot`(lon, lat, omega)[source]
Converts Euler poles (long., lat., deg/Myr) into cartesian geocentric

rotation rate vector Wx Wy Wz in radians/yr

Parameters longitude,latitude,omega

longitude and latitude of the Euler pole in decimal degrees and the

angular velocity in decimal degrees per Myr. :returns Wx Wy Wz: in radians/yr

Note

longitude and latitude are relative to the sphere, not the ellipsoid.

`pyacs.lib.euler.``euler_uncertainty`(w, vcv)[source]

Calculates Euler pole parameters uncertainty

Parameters
• w – rotation vector in XYZ coordinates as numpy 1D array

• vcv – covariance of w as numpy 2D array

Returns

vcv_euler as numpy 2D array

`pyacs.lib.euler.``vel_from_euler`(lonp, latp, lon_euler, lat_euler, omega_euler)[source]

Return the horizontal velocity predicted at lonp,latp from an Euler pole

Parameters
• lonp,latp – longitude,latitude in decimal degrees where velocity will be predicted

• lon_euler,lat_euler_omega_euler – longitude and latitude of the Euler pole in decimal degrees and the

angular velocity in decimal degrees per Myr.

Returns

ve,vn in mm/yr

`pyacs.lib.euler.``pole_matrix`(coor)[source]

Calculates the matrix relating the horizontal velocity to a rotation rate vector. Given a 2D-numpy array of n positions [lonp , latp] in decimal degrees the return matrix is W so that np.dot( W , w ) gives a 2D-numpy array of [ve1,vn1,ve2,vn2,….] expressed in m/yr for a rotation rate vector in rad/yr

Parameters

coor – 2D numpy array of [lon, lat] in decimal degrees

Returns

the pole matrix as a 2D-numpy array

`pyacs.lib.euler.``pole_matrix_fault`(coor, strike, order=None)[source]

Calculates the matrix relating the along strike and normal slip components of a fault to a rotation rate vector. Given a 2D-numpy array of n positions [lonp , latp] in decimal degrees and strike counter-clockwise from north the return matrix is W so that np.dot( W , w ) gives a 2D-numpy array of [ss1,ns1,ss2,ns2,….] expressed in m/yr for a rotation rate vector in rad/yr

:param coor : 2D numpy array of [lon, lat] in decimal degrees :param strike: 1D numpy array of [strike] in decimal degrees

Returns

the pole matrix as a 2D-numpy array

Note

np.dot( W , w ).reshape(-1,2) gives the along strike,and normal components in two columns

Note

the value are given for the hanging-wall block (right-polygon)