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mopad.py
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mopad.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
#######################################################################
######################### MoPaD ####################################
######### Moment tensor Plotting and Decomposition tool #############
#######################################################################
Multi method tool for:
- Plotting and saving of focal sphere diagrams ('Beachballs').
- Decomposition and Conversion of seismic moment tensors.
- Generating coordinates, describing a focal sphere diagram, to be
piped into GMT's psxy (Useful where psmeca or pscoupe fail.)
#######################################################################
Version 0.9b
THIS IS AN ALPHA VERSION -- FOR TESTING PURPOSES ONLY
THIS SOFTWARE COMES WITH NO WARRANTY
#######################################################################
Copyright (C) 2010
Lars Krieger & Sebastian Heimann
Contact
#######################################################################
License:
GNU Lesser General Public License, Version 3
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public License
as published by the Free Software Foundation; either version 3
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.
"""
#############################################################
mopad_version = 0.9
#standard libraries:
import sys, optparse, re, math
from cStringIO import StringIO
#additional library:
import numpy as N
#constants:
dynecm = 1e-7
pi = N.pi
epsilon = 1e-13
rad2deg = 180./pi
def wrap(text, line_length=80):
'''Paragraph and list-aware wrapping of text.'''
text = text.strip('\n')
at_lineend = re.compile(r' *\n')
at_para = re.compile(r'((^|(\n\s*)?\n)(\s+[*] )|\n\s*\n)')
paragraphs = at_para.split(text)[::5]
listindents = at_para.split(text)[4::5]
newlist = at_para.split(text)[3::5]
listindents[0:0] = [None]
listindents.append(True)
newlist.append(None)
det_indent = re.compile(r'^ *')
iso_latin_1_enc_failed = False
outlines = []
for ip, p in enumerate(paragraphs):
if not p:
continue
if listindents[ip] is None:
_indent = det_indent.findall(p)[0]
findent = _indent
else:
findent = listindents[ip]
_indent = ' '* len(findent)
ll = line_length - len(_indent)
llf = ll
oldlines = [ s.strip() for s in at_lineend.split(p.rstrip()) ]
p1 = ' '.join( oldlines )
possible = re.compile(r'(^.{1,%i}|.{1,%i})( |$)' % (llf, ll))
for imatch, match in enumerate(possible.finditer(p1)):
parout = match.group(1)
if imatch == 0:
outlines.append(findent + parout)
else:
outlines.append(_indent + parout)
if ip != len(paragraphs)-1 and (listindents[ip] is None or newlist[ip] is not None or listindents[ip+1] is None):
outlines.append('')
return outlines
def basis_switcher(in_system, out_system):
from_ned = {
'NED': N.matrix( [[1.,0.,0.],[0.,1.,0.],[0.,0.,1.]], dtype=N.float ),
'USE': N.matrix( [[0.,-1.,0.],[0.,0.,1.],[-1.,0.,0.]], dtype=N.float ).I,
'XYZ': N.matrix( [[0.,1.,0.],[1.,0.,0.],[0.,0.,-1.]], dtype=N.float ).I,
'NWU': N.matrix( [[1.,0.,0.],[0.,-1.,0.],[0.,0.,-1.]], dtype=N.float ).I }
return from_ned[in_system].I * from_ned[out_system]
def basis_transform_matrix(m, in_system, out_system):
r = basis_switcher(in_system, out_system)
return N.dot(r, N.dot(m, r.I))
def basis_transform_vector(v, in_system, out_system):
r = basis_switcher(in_system, out_system)
return N.dot(r, v)
class MopadHelpFormatter(optparse.IndentedHelpFormatter):
def format_option(self, option):
'''From IndentedHelpFormatter but using a different wrap method.'''
result = []
opts = self.option_strings[option]
opt_width = self.help_position - self.current_indent - 2
if len(opts) > opt_width:
opts = "%*s%s\n" % (self.current_indent, "", opts)
indent_first = self.help_position
else: # start help on same line as opts
opts = "%*s%-*s " % (self.current_indent, "", opt_width, opts)
indent_first = 0
result.append(opts)
if option.help:
help_text = self.expand_default(option)
help_lines = wrap(help_text, self.help_width)
if len(help_lines) > 1:
help_lines.append('')
result.append("%*s%s\n" % (indent_first, "", help_lines[0]))
result.extend(["%*s%s\n" % (self.help_position, "", line)
for line in help_lines[1:]])
elif opts[-1] != "\n":
result.append("\n")
return "".join(result)
def format_description(self, description):
if not description:
return ""
desc_width = self.width - self.current_indent
indent = " "*self.current_indent
return '\n'.join(wrap(description, desc_width)) + "\n"
#------------------------------------------
class MTError(Exception):
pass
#------------------------------------------
def euler_to_matrix( alpha, beta, gamma ):
'''Given the euler angles alpha,beta,gamma, create rotation matrix
Given coordinate system (x,y,z) and rotated system (xs,ys,zs)
the line of nodes is the intersection between the x-y and the xs-ys
planes.
alpha is the angle between the z-axis and the zs-axis.
beta is the angle between the x-axis and the line of nodes.
gamma is the angle between the line of nodes and the xs-axis.
Usage for moment tensors:
m_unrot = numpy.matrix([[0,0,-1],[0,0,0],[-1,0,0]])
rotmat = euler_to_matrix(dip,strike,-rake)
m = rotmat.T * m_unrot * rotmat'''
ca = math.cos(alpha)
cb = math.cos(beta)
cg = math.cos(gamma)
sa = math.sin(alpha)
sb = math.sin(beta)
sg = math.sin(gamma)
mat = N.matrix( [[cb*cg-ca*sb*sg, sb*cg+ca*cb*sg, sa*sg],
[-cb*sg-ca*sb*cg, -sb*sg+ca*cb*cg, sa*cg],
[sa*sb, -sa*cb, ca]], dtype=N.float )
return mat
class MomentTensor:
_m_unrot = N.matrix( [[0.,0.,-1.],[0.,0.,0.],[-1.,0.,0.]], dtype=N.float )
def __init__(self, M=None, in_system='NED', out_system='NED', debug=0):
"""
Creates a moment tensor object on the basis of a provided mechanism M.
If M is a non symmetric 3x3-matrix, the upper right triangle
of the matrix is taken as reference. M is symmetrisised
w.r.t. these entries. If M is provided as a 3-,4-,6-,7-tuple
or array, it is converted into a matrix internally according
to standard conventions (Aki & Richards).
'system' may be chosen as 'NED','USE','NWU', or 'XYZ'.
'debug' enables output on the shell at the intermediate steps.
"""
self._original_M = M[:]
self._input_basis = in_system.upper()
self._output_basis = out_system.upper()
# bring M to symmetric matrix form
self._M = self._setup_M(M, self._input_basis)
#decomposition:
self._decomposition_key = 1
#eigenvector / principal-axes system:
self._eigenvalues = None
self._eigenvectors = None
self._null_axis = None
self._t_axis = None
self._p_axis = None
self._rotation_matrix = None
# optional - maybe set afterwards by external application - for later plotting:
self._best_faultplane = None
self._auxiliary_plane = None
#initialise decomposition components
self._DC = None
self._DC_percentage = None
self._DC2 = None
self._DC2_percentage = None
self._DC3 = None
self._DC3_percentage = None
self._iso = None
self._iso_percentage = None
self._devi = None
self._devi_percentage = None
self._CLVD = None
self._CLVD_percentage = None
self._isotropic = None
self._deviatoric = None
self._seismic_moment = None
self._moment_magnitude = None
self._decomp_attrib_map_keys = ('in','out','type',
'full',
'iso','iso_perc',
'dev','devi','devi_perc',
'dc','dc_perc',
'dc2','dc2_perc',
'dc3','dc3_perc',
'clvd','clvd_perc',
'mom','mag',
'eigvals','eigvecs',
't','n','p')
self._decomp_attrib_map = dict(zip( self._decomp_attrib_map_keys,
('input_system','output_system','decomp_type',
'M',
'iso','iso_percentage',
'devi','devi','devi_percentage',
'DC','DC_percentage',
'DC2','DC2_percentage',
'DC3','DC3_percentage',
'CLVD','CLVD_percentage',
'moment','mag',
'eigvals','eigvecs',
't_axis','null_axis','p_axis')
))
#carry out the MT decomposition - results are in basis NED
self._decompose_M()
#set the appropriate principal axis system:
self._M_to_principal_axis_system()
#---------------------------------------------------------------
def _setup_M(self,mech, input_basis):
"""
Brings the provided mechanism into symmetric 3x3 matrix form.
The source mechanism may be provided in different forms:
-- as 3x3 matrix - symmetry is checked - one basis system has to be chosen, or NED as default is taken
-- as 3-element tuple or array - interpreted as strike, dip, slip-rake angles in degree
-- as 4-element tuple or array - interpreted as strike, dip, slip-rake angles in degree + seismic scalar moment in Nm
-- as 6-element tuple or array - interpreted as the 6 independent entries of the moment tensor
-- as 7-element tuple or array - interpreted as the 6 independent entries of the moment tensor + seismic scalar moment in Nm
-- as 9-element tuple or array - interpreted as the 9 entries of the moment tensor - checked for symmetry
-- as a nesting of one of the upper types (e.g. a list of n-tuples) - first element of outer nesting is taken
"""
#set source mechanism to matrix form
if mech==None:
raise MTError('Please provide a mechanism')
# if some stupid nesting occurs
if len(mech) == 1:
mech = mech[0]
# all 9 elements are given
if N.prod(N.shape(mech)) == 9:
if N.shape(mech)[0] == 3:
#assure symmetry:
mech[1,0] = mech[0,1]
mech[2,0] = mech[0,2]
mech[2,1] = mech[1,2]
new_M = mech
else:
new_M = N.array(mech).reshape(3,3).copy()
new_M[1,0]= new_M[0,1]
new_M[2,0]= new_M[0,2]
new_M[2,1]= new_M[1,2]
# mechanism given as 6- or 7-tuple, list or array
elif len(mech) == 6 or len(mech) == 7:
M = mech
new_M = N.matrix( N.array([M[0],M[3],M[4],M[3],M[1],M[5],M[4], M[5],M[2] ]).reshape(3,3) )
if len(mech) == 7 :
new_M = M[6] * new_M
# if given as strike, dip, rake, conventions from Jost & Herrmann hold - resulting matrix is in NED-basis:
elif len(mech) == 3 or len(mech) == 4 :
strike, dip, rake = mech[:3]
scalar_moment = 1.0
if len(mech) == 4:
scalar_moment = mech[3]
rotmat1 = euler_to_matrix( dip/rad2deg, strike/rad2deg, -rake/rad2deg )
new_M = rotmat1.T * MomentTensor._m_unrot * rotmat1 * scalar_moment
#to assure right basis system - others are meaningless, provided these angles
input_basis = 'NED'
return basis_transform_matrix(N.matrix(new_M), input_basis, 'NED')
#---------------------------------------------------------------
def _decompose_M(self):
"""
Running the decomposition of the moment tensor object.
the standard decompositions M = Isotropic + DC + (CLVD or 2nd DC) are supported (C.f. Jost & Herrmann, Aki & Richards)
"""
k = self._decomposition_key
d = MomentTensor.decomp_dict
if k in d:
d[k][1](self)
else:
raise MTError('Invalid decomposition key: %i' % k)
#---------------------------------------------------------------
def print_decomposition(self):
for arg in self._decomp_attrib_map_keys:
print getattr(self,'get_'+self._decomp_attrib_map[arg])(style='y',system=self._output_basis)
#---------------------------------------------------------------
def _standard_decomposition(self):
"""
Decomposition according Aki & Richards and Jost & Herrmann into
- isotropic
- deviatoric
- DC
- CLVD
parts of the input moment tensor.
results are given as attributes, which can be returned via 'get_<name of attribute>' functions:
DC
CLVD
DC_percentage
seismic_moment
moment_magnitude
"""
M = self._M
#isotropic part
M_iso = N.diag( N.array([1./3*N.trace(M),1./3*N.trace(M),1./3*N.trace(M)] ) )
M0_iso = abs(1./3*N.trace(M))
#deviatoric part
M_devi = M - M_iso
self._isotropic = M_iso
self._deviatoric = M_devi
#eigenvalues and -vectors
eigenwtot,eigenvtot = N.linalg.eig(M_devi)
#eigenvalues and -vectors of the deviatoric part
eigenw1,eigenv1 = N.linalg.eig(M_devi)
#eigenvalues in ascending order:
eigenw = N.real( N.take( eigenw1,N.argsort(abs(eigenwtot)) ) )
eigenv = N.real( N.take( eigenv1,N.argsort(abs(eigenwtot)) ,1 ) )
#eigenvalues in ascending order in absolute value!!:
eigenw_devi = N.real( N.take( eigenw1,N.argsort(abs(eigenw1)) ) )
eigenv_devi = N.real( N.take( eigenv1,N.argsort(abs(eigenw1)) ,1 ) )
M0_devi = max(abs(eigenw_devi))
#named according to Jost & Herrmann:
a1 = eigenv[:,0]#/N.linalg.norm(eigenv[:,0])
a2 = eigenv[:,1]#/N.linalg.norm(eigenv[:,1])
a3 = eigenv[:,2]#/N.linalg.norm(eigenv[:,2])
# if only isotropic part exists:
if M0_devi < epsilon:
F = 0.5
else:
F = -eigenw_devi[0]/eigenw_devi[2]
M_DC = N.matrix(N.zeros((9),float)).reshape(3,3)
M_CLVD = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC = eigenw[2]*(1-2*F)*( N.outer(a3,a3) - N.outer(a2,a2) )
M_CLVD = M_devi - M_DC #eigenw[2]*F*( 2*N.outer(a3,a3) - N.outer(a2,a2) - N.outer(a1,a1))
#according to Bowers & Hudson:
M0 = M0_iso + M0_devi
M_iso_percentage = int(round(M0_iso/M0 *100,6))
self._iso_percentage = M_iso_percentage
M_DC_percentage = int(round(( 1 - 2 * abs(F) )* ( 1 - M_iso_percentage/100.) * 100,6))
self._DC = M_DC
self._CLVD = M_CLVD
self._DC_percentage = M_DC_percentage
#self._seismic_moment = N.sqrt(1./2*N.sum(eigenw**2) )
self._seismic_moment = M0
self._moment_magnitude = N.log10(self._seismic_moment*1.0e7)/1.5 - 10.7
#---------------------------------------------------------------
def _decomposition_w_2DC(self):
"""
Decomposition according Aki & Richards and Jost & Herrmann into
- isotropic
- deviatoric
- 2 DC
parts of the input moment tensor.
results are given as attributes, which can be returned via 'get_<name of attribute>' functions:
DC1
DC2
DC_percentage
seismic_moment
moment_magnitude
"""
M = self._M
#isotropic part
M_iso = N.diag( N.array([1./3*N.trace(M),1./3*N.trace(M),1./3*N.trace(M)] ) )
M0_iso = abs(1./3*N.trace(M))
#deviatoric part
M_devi = M - M_iso
self._isotropic = M_iso
self._deviatoric = M_devi
#eigenvalues and -vectors of the deviatoric part
eigenw1,eigenv1 = N.linalg.eig(M_devi)
#eigenvalues in ascending order of their absolute values:
eigenw = N.real( N.take( eigenw1,N.argsort(abs(eigenw1)) ) )
eigenv = N.real( N.take( eigenv1,N.argsort(abs(eigenw1)) ,1 ) )
M0_devi = max(abs(eigenw))
#named according to Jost & Herrmann:
a1 = eigenv[:,0]
a2 = eigenv[:,1]
a3 = eigenv[:,2]
M_DC = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC2 = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC = eigenw[2]*( N.outer(a3,a3) - N.outer(a2,a2) )
M_DC2 = eigenw[0]*( N.outer(a1,a1) - N.outer(a2,a2) )
M_DC_percentage = abs(eigenw[2]/(abs(eigenw[2])+abs(eigenw[0]) ) )
self._DC = M_DC
self._DC2 = M_DC2
self._DC_percentage = M_DC_percentage
#according to Bowers & Hudson:
M0 = M0_iso + M0_devi
M_iso_percentage = int(M0_iso/M0 *100)
self._iso_percentage = M_iso_percentage
#self._seismic_moment = N.sqrt(1./2*N.sum(eigenw**2) )
self._seismic_moment = M0
self._moment_magnitude = N.log10(self._seismic_moment*1.0e7)/1.5 - 10.7
#---------------------------------------------------------------
def _decomposition_w_CLVD_2DC(self):
"""
Decomposition according to Dahm (1993) into
- isotropic
- CLVD
- strike-slip
- dip-slip
parts of the input moment tensor.
results are given as attributes, which can be returned via 'get_<name of attribute>' functions:
iso
CLVD
DC1
DC2
iso_percentage
DC_percentage
DC1_percentage
DC2_percentage
CLVD_percentage
seismic_moment
moment_magnitude
"""
M = self._M
#isotropic part
M_iso = N.diag( N.array([1./3*N.trace(M),1./3*N.trace(M),1./3*N.trace(M)] ) )
M0_iso = abs(1./3*N.trace(M))
#deviatoric part
M_devi = M - M_iso
self._isotropic = M_iso
self._deviatoric = M_devi
M_DC1 = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC2 = N.matrix(N.zeros((9),float)).reshape(3,3)
M_CLVD = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC1[0,0] = -0.5*(M[1,1]-M[0,0])
M_DC1[1,1] = 0.5*(M[1,1]-M[0,0])
M_DC1[0,1] = M_DC1[1,0] = M[0,1]
M_DC2[0,2] = M_DC2[2,0] = M[0,2]
M_DC2[1,2] = M_DC2[2,1] = M[1,2]
M_CLVD = 1./3.*(0.5*(M[1,1]+M[0,0])-M[2,2])*N.diag( N.array([1.,1.,-2.] ) )
M_DC = M_DC1 + M_DC2
self._DC = M_DC
self._DC1 = M_DC1
self._DC2 = M_DC2
self._DC_percentage = M_DC1_perc
self._DC2_percentage= M_DC2_perc
#according to Bowers & Hudson:
eigvals_M, dummy_vecs = N.linalg.eig(M)
eigvals_M_devi, dummy_vecs = N.linalg.eig(M_devi)
eigvals_M_iso, dummy_iso = N.linalg.eig(M_iso)
eigvals_M_clvd, dummy_vecs = N.linalg.eig(M_CLVD)
eigvals_M_dc1, dummy_vecs = N.linalg.eig(M_DC1)
eigvals_M_dc2, dummy_vecs = N.linalg.eig(M_DC2)
#M0_M = N.max(N.abs(eigvals_M - 1./3*N.sum(eigvals_M) ))
M0_M_iso = N.max(N.abs(eigvals_M_iso - 1./3*N.sum(eigvals_M) ))
M0_M_clvd = N.max(N.abs(eigvals_M_clvd - 1./3*N.sum(eigvals_M) ))
M0_M_dc1 = N.max(N.abs(eigvals_M_dc1 - 1./3*N.sum(eigvals_M) ))
M0_M_dc2 = N.max(N.abs(eigvals_M_dc2 - 1./3*N.sum(eigvals_M) ))
M0_M_dc = M0_M_dc1 + M0_M_dc2
M0_M_devi = M0_M_clvd + M0_M_dc
M0_M = M0_M_iso + M0_M_devi
M_iso_percentage = int(M0_M_iso/M0_M *100)
self._iso_percentage = M_iso_percentage
M_DC_percentage = int(M0_M_dc/M0_M *100)
self._dc_percentage = M_dc_percentage
M_DC1_percentage = int(M0_M_dc1/M0_M *100)
self._dc1_percentage = M_dc_percentage
M_DC2_percentage = int(M0_M_dc2/M0_M *100)
self._dc2_percentage = M_dc_percentage
#self._seismic_moment = N.sqrt(1./2*N.sum(eigenw**2) )
self._seismic_moment = M0_M
self._moment_magnitude = N.log10(self._seismic_moment*1.0e7)/1.5 - 10.7
#---------------------------------------------------------------
def _decomposition_w_3DC(self):
"""
Decomposition according Aki & Richards and Jost & Herrmann into
- isotropic
- deviatoric
- 3 DC
parts of the input moment tensor.
results are given as attributes, which can be returned via 'get_<name of attribute>' functions:
DC1
DC2
DC3
DC_percentage
seismic_moment
moment_magnitude
"""
M = self._M
#isotropic part
M_iso = N.diag( N.array([1./3*N.trace(M),1./3*N.trace(M),1./3*N.trace(M)] ) )
M0_iso = abs(1./3*N.trace(M))
#deviatoric part
M_devi = M - M_iso
self._isotropic = M_iso
self._deviatoric = M_devi
#eigenvalues and -vectors of the deviatoric part
eigenw1,eigenv1 = N.linalg.eig(M_devi)
M0_devi = max(abs(eigenw1))
#eigenvalues and -vectors of the full M !!!!!!!!
eigenw1,eigenv1 = N.linalg.eig(M)
#eigenvalues in ascending order of their absolute values:
eigenw = N.real( N.take( eigenw1,N.argsort(abs(eigenw1)) ) )
eigenv = N.real( N.take( eigenv1,N.argsort(abs(eigenw1)) ,1 ) )
#named according to Jost & Herrmann:
a1 = eigenv[:,0]
a2 = eigenv[:,1]
a3 = eigenv[:,2]
M_DC1 = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC2 = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC3 = N.matrix(N.zeros((9),float)).reshape(3,3)
M_DC1 = 1./3.*(eigenw[0] - eigenw[1]) *( N.outer(a1,a1) - N.outer(a2,a2) )
M_DC2 = 1./3.*(eigenw[1] - eigenw[2]) *( N.outer(a2,a2) - N.outer(a3,a3) )
M_DC3 = 1./3.*(eigenw[2] - eigenw[0]) *( N.outer(a3,a3) - N.outer(a1,a1) )
M_DC1_perc = int(100*abs((eigenw[0]-eigenw[1]))/ (abs((eigenw[1]-eigenw[2]))+abs((eigenw[1]-eigenw[2]))+abs((eigenw[2]-eigenw[0]))))
M_DC2_perc = int(100*abs((eigenw[1]-eigenw[2]))/ (abs((eigenw[1]-eigenw[2]))+abs((eigenw[1]-eigenw[2]))+abs((eigenw[2]-eigenw[0]))))
self._DC = M_DC1
self._DC2 = M_DC2
self._DC3 = M_DC3
self._DC_percentage = M_DC1_perc
self._DC2_percentage= M_DC2_perc
#according to Bowers & Hudson:
M0 = M0_iso + M0_devi
M_iso_percentage = int(M0_iso/M0 *100)
self._iso_percentage = M_iso_percentage
#self._seismic_moment = N.sqrt(1./2*N.sum(eigenw**2) )
self._seismic_moment = M0
self._moment_magnitude = N.log10(self._seismic_moment*1.0e7)/1.5 - 10.7
#---------------------------------------------------------------
def _M_to_principal_axis_system(self):
"""
Read in Matrix M and set up eigenvalues (EW) and eigenvectors
(EV) for setting up the principal axis system.
The internal convention is the 'HNS'-system: H is the
eigenvector for the smallest absolute eigenvalue, S is the
eigenvector for the largest absolute eigenvalue, N is the null
axis.
Naming due to the geometry: a CLVD is
Symmetric to the S-axis,
Null-axis is common sense, and the third (auxiliary) axis
Helps to construct the R³.
Additionally builds matrix for basis transformation back to NED system.
The eigensystem setup defines the colouring order for a later
plotting in the BeachBall class. This order is set by the
'_plot_clr_order' attribute.
"""
M = self._M
M_devi = self._deviatoric
# working in framework of 3 principal axes:
# eigenvalues (EW) are in order from high to low
# - neutral axis N, belongs to middle EW
# - symmetry axis S ('sigma') belongs to EW with largest absolute value (P- or T-axis)
# - auxiliary axis H ('help') belongs to remaining EW (T- or P-axis)
#EW sorting from lowest to highest value
EW_devi, EV_devi = N.linalg.eigh( M_devi )
EW_order = N.argsort(EW_devi)
#print 'order',EW_order
if 1:#self._plot_isotropic_part:
trace_M = N.trace(M)
if abs(trace_M) < epsilon:
trace_M = 0
EW, EV = N.linalg.eigh( M )
for i,ew in enumerate(EW):
if abs(EW[i]) < epsilon:
EW[i] = 0
else:
trace_M = N.trace(M_devi)
if abs(trace_M) < epsilon:
trace_M = 0
EW, EV = N.linalg.eigh( M_devi )
for i,ew in enumerate(EW):
if abs(EW[i]) < epsilon:
EW[i] = 0
trace_M_devi = N.trace(M_devi)
EW1_devi = EW_devi[EW_order[0]]
EW2_devi = EW_devi[EW_order[1]]
EW3_devi = EW_devi[EW_order[2]]
EV1_devi = EV_devi[:,EW_order[0]]
EV2_devi = EV_devi[:,EW_order[1]]
EV3_devi = EV_devi[:,EW_order[2]]
EW1 = EW[EW_order[0]]
EW2 = EW[EW_order[1]]
EW3 = EW[EW_order[2]]
EV1 = EV[:,EW_order[0]]
EV2 = EV[:,EW_order[1]]
EV3 = EV[:,EW_order[2]]
chng_basis_tmp = N.matrix(N.zeros((3,3)))
chng_basis_tmp[:,0] = EV1_devi
chng_basis_tmp[:,1] = EV2_devi
chng_basis_tmp[:,2] = EV3_devi
det_mat = N.linalg.det(chng_basis_tmp)
symmetry_around_tension = 1
clr = 1
if abs(EW2_devi) < epsilon:
EW2_devi = 0
#implosion
if EW1 < 0 and EW2 < 0 and EW3 < 0:
symmetry_around_tension = 0
#logger.debug( 'IMPLOSION - symmetry around pressure axis \n\n')
clr = 1
#explosion
elif EW1 > 0 and EW2 > 0 and EW3 > 0:
symmetry_around_tension = 1
if abs(EW1_devi) > abs(EW3_devi):
symmetry_around_tension = 0
#logger.debug( 'EXPLOSION - symmetry around tension axis \n\n')
clr = -1
#net-implosion
elif EW2 < 0 and sum([EW1,EW2,EW3]) < 0 :
if abs(EW1_devi) < abs(EW3_devi):
symmetry_around_tension = 1
clr = 1
else:
symmetry_around_tension = 1
clr = 1
#net-implosion
elif EW2_devi >= 0 and sum([EW1,EW2,EW3]) < 0 :
symmetry_around_tension = 0
clr = -1
if abs(EW1_devi) < abs(EW3_devi):
symmetry_around_tension = 1
clr = 1
#net-explosion
elif EW2_devi < 0 and sum([EW1,EW2,EW3]) > 0 :
symmetry_around_tension = 1
clr = 1
if abs(EW1_devi) > abs(EW3_devi):
symmetry_around_tension = 0
clr = -1
#net-explosion
elif EW2_devi >= 0 and sum([EW1,EW2,EW3]) > 0 :
symmetry_around_tension = 0
clr = -1
else:
#TODO check: this point should never be reached !!
pass
#test 26.9.2010:
if abs(EW1_devi) < abs(EW3_devi):
symmetry_around_tension = 1
clr = 1
if 0:#EW2 > 0 :#or (EW2 > 0 and EW2_devi > 0) :
symmetry_around_tension = 0
clr = -1
if abs(EW1_devi) >= abs(EW3_devi):
symmetry_around_tension = 0
clr = -1
if 0:#EW2 < 0 :
symmetry_around_tension = 1
clr = 1
if (EW3 < 0 and N.trace(self._M) >= 0):
#reaching this point means, we have a serious problem, likely of numerical nature
print 'Houston, we have had a problem - check M !!!!!! \n ( Trace(M) > 0, but largest eigenvalue is still negative)'
raise MTError(' !! ')
if trace_M == 0:
#print 'pure deviatoric'
if EW2 == 0:
#print 'pure shear'
symmetry_around_tension = 1
clr = 1
elif 2*abs(EW2) == abs(EW1) or 2*abs(EW2) == abs(EW3):
#print 'pure clvd'
if abs(EW1) < EW3:
#print 'CLVD: symmetry around tension'
symmetry_around_tension = 1
clr = 1
else:
#print 'CLVD: symmetry around pressure'
symmetry_around_tension = 0
clr = -1
else:
#print 'mix of DC and CLVD'
if abs(EW1) < EW3:
#print 'symmetry around tension'
symmetry_around_tension = 1
clr = 1
else:
#print 'symmetry around pressure'
symmetry_around_tension = 0
clr = -1
#define order of eigenvectors and values according to symmetry axis
if symmetry_around_tension == 1:
EWs = EW3.copy()
EVs = EV3.copy()
EWh = EW1.copy()
EVh = EV1.copy()
else:
EWs = EW1.copy()
EVs = EV1.copy()
EWh = EW3.copy()
EVh = EV3.copy()
EWn = EW2
EVn = EV2
# build the basis system change matrix:
chng_basis = N.matrix(N.zeros((3,3)))
chng_fp_basis = N.matrix(N.zeros((3,3)))
#order of eigenvector's basis: (H,N,S)
chng_basis[:,0] = EVh
chng_basis[:,1] = EVn
chng_basis[:,2] = EVs
# matrix for basis transformation
self._rotation_matrix = chng_basis
#collections of eigenvectors and eigenvalues
self._eigenvectors = [EVh,EVn,EVs]
self._eigenvalues = [EWh,EWn,EWs]
#principal axes
self._null_axis = EVn
self._t_axis = EV1
self._p_axis = EV3
#plotting order flag - important for plot in BeachBall class
self._plot_clr_order = clr
#print clr
#collection of the faultplanes, given in strike, dip, slip-rake
self._faultplanes = self._find_faultplanes()
#---------------------------------------------------------------
def _find_faultplanes(self):
"""
Sets the two angle-triples, describing the faultplanes of the
Double Couple, defined by the eigenvectors P and T of the
moment tensor object.
Define a reference Double Couple with strike = dip =
slip-rake = 0, the moment tensor object's DC is transformed
(rotated) w.r.t. this orientation. The respective rotation
matrix yields the first fault plane angles as the Euler
angles. After flipping the first reference plane by
multiplying the appropriate flip-matrix, one gets the second fault
plane's geometry.
All output angles are in degree