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source.py
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source.py
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# -*- coding: utf-8 -*-
"""
source - Module for seismic sources modeling
______________________________________________________________________
This module provide class hierarchy for earthquake modeling and
representation.
The seismic wave displacement is computed using the theoritical
definitions of the seismic source.
"""
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from obspy.imaging.scripts.mopad import MomentTensor
# Functions and classes are ordered from general to specific
def sphere(r=1.,n=100.):
"""
Produce the polar coordinates of a sphere.
______________________________________________________________________
:type r, n: variables
:param r, n: radius and number of resolution points.
:rtype : list
:return : 3d list of azimuth, polar angle and radial distance.
.. seealso::
numpy.linspace : produces the resolution vectors.
numpy.meshgrid : produce the grid from the vectors.
.. rubric:: Example
# import the module
import source
# 100 coordinates on sphere or radius 5
points = source.sphere(r=5, n=100)
# Unit sphere of 50 points
points = source.sphere(n=50)
.. plot::
# run one of the example
points = source.spherical_to_cartesian(points)
# plot using matplotlib
import matplotlib.pyplot as plt
fig = plt.figure()
ax=fig.gca(projection='3d')
ax.set_aspect("equal")
ax.plot_wireframe(points[0], points[1], points[2], color="r")
plt.show()
______________________________________________________________________
"""
# Get the resolution (sorry this is ugly)
c = 0.038 ;
na = n**(.5+c)
nt = n**(.5-c)
[AZIMUTH,TAKEOFF] = np.meshgrid( np.linspace(0, 2*np.pi, int(na+1)), np.linspace(0, 1*np.pi, int(nt)) )
RADIUS = np.ones(AZIMUTH.shape)*r
return [ AZIMUTH, TAKEOFF, RADIUS ]
def cartesian_to_spherical(vector):
"""
Convert the Cartesian vector [x, y, z] to spherical coordinates
[azimuth, polar angle, radial distance].
______________________________________________________________________
:type vector : 3D array, list | np.array
:param vector : The vector of cartessian coordinates.
:rtype : 3D array, np.array
:return : The spherical coordinate vector.
.. note::
This file is extracted & modified from the program relax (Edward
d'Auvergne).
.. seealso::
http://svn.gna.org/svn/relax/1.3/maths_fns/coord_transform.py
______________________________________________________________________
"""
# Make sure we got np.array
if np.asarray(vector) is not vector:
vector = np.asarray(vector)
# The radial distance.
radius = np.sqrt((vector**2).sum(axis=0))
# The horizontal radial distance.
rh = np.sqrt(vector[0]**2 + vector[1]**2)
# The polar angle.
takeoff = np.arccos( vector[2] / radius )
takeoff[radius == 0.0] = np.pi / 2 * np.sign(vector[2][radius == 0.0])
#theta = np.arctan2(vector[2], rh)
# The azimuth.
azimuth_trig = np.arctan2(vector[1], vector[0])
# Return the spherical coordinate vector.
return [azimuth_trig, takeoff, radius]
def spherical_to_cartesian(vector):
"""
Convert the spherical coordinates [azimuth, polar angle
radial distance] to Cartesian coordinates [x, y, z].
______________________________________________________________________
:type vector : 3D array, list | np.array
:param vector : The spherical coordinate vector.
:rtype : 3D array, np.array
:return : The vector of cartesian coordinates.
.. note::
This file is extracted & modified from the program relax (Edward
d'Auvergne).
.. seealso::
http://svn.gna.org/svn/relax/1.3/maths_fns/coord_transform.py
______________________________________________________________________
"""
# Unit vector if r is missing
if len(vector) == 2 :
radius =1
else:
radius=vector[2]
# Trig alias.
sin_takeoff = np.sin(vector[1])
# The vector.
x = radius * sin_takeoff * np.cos(vector[0])
y = radius * sin_takeoff * np.sin(vector[0])
z = radius * np.cos(vector[1])
return [x, y, z]
def project_vectors(b, a):
"""
Project the vectors b on vectors a.
______________________________________________________________________
:type b : 3D np.array
:param b : The cartesian coordinates of vectors to be projected.
:type a : 3D np.array
:param a : The cartesian coordinates of vectors to project onto.
:rtype : 3D np.array
:return : The cartesian coordinates of b projected on a.
.. note::
There is maybe better (built in numpy) ways to do this.
.. seealso::
:func:`numpy.dot()`
:func:`numpy.dotv()`
______________________________________________________________________
"""
# Project
## ratio (norm of b on a / norm of a)
proj_norm = a[0]*b[0] + a[1]*b[1] + a[2]*b[2]
proj_norm /= (a[0]**2 + a[1]**2 + a[2]**2)+0.0000000001
## project on a
b_on_a = proj_norm * a
return b_on_a
def vector_normal(XYZ, v_or_h):
"""
Compute the vertical or horizontal normal vectors.
______________________________________________________________________
:type XYZ : 3D np.array
:param b : The cartesian coordinates of vectors.
:type v_or_h : string
:param v_or_h : The normal direction to pick.
:rtype : 3D np.array
:return : Requested normal on vertical or horizontal plane
('v|vert|vertical' or 'h|horiz|horizontal').
.. rubric:: _`Supported v_or_h`
``'v'``
Vertical.
``'h'``
horizontal.
``'r'``
Radial component.
``'m'``
The meridian component.
.. note::
There is maybe better (built in numpy) ways to do this.
.. seealso::
:func:`numpy.cross()`
______________________________________________________________________
"""
oneheightydeg = np.ones(XYZ.shape) * np.pi
ninetydeg = np.ones(XYZ.shape) * np.pi/2.
ATR = np.asarray(cartesian_to_spherical(XYZ))
if v_or_h in ('m', 'meridian', 'n', 'nhr', 'normal horizontal radial', 'norm horiz rad'):
ATR_n = np.array([ ATR[0] , ATR[1] - ninetydeg[0], ATR[2]])
XYZ_n = np.asarray(spherical_to_cartesian(ATR_n))
elif v_or_h in ('h', 'horizontal', 'horiz'):
ATR_n = np.array([ ATR[0] - ninetydeg[0], ATR[1]+(ninetydeg[0]-ATR[1]) , ATR[2]])
XYZ_n = np.asarray(spherical_to_cartesian(ATR_n))
elif v_or_h in ('v', 'vertical', 'vertical'):
ATR_n = np.array([ ATR[0], ATR[1]-ATR[1] , ATR[2]])
XYZ_n = np.asarray(spherical_to_cartesian(ATR_n))
elif v_or_h in ('r', 'radial', 'self'):
XYZ_n = XYZ
return XYZ_n
def mt_full(mt):
"""
Takes 6 components moment tensor and returns full 3x3 moment
tensor.
______________________________________________________________________
:type mt : list or np.array.
:param mt : moment tensor NM x 6 (Mxx, Myy, Mzz, Mxy, Mxz, Myz,
the six independent components).
:rtype : np.array 3x3.
:return : full 3x3 moment tensor.
.. note::
Use obspy.imaging.scripts.mopad to get correct input.
______________________________________________________________________
"""
# Make sure we got np.array
if np.asarray(mt) is not mt:
mt = np.asarray(mt)
if len(mt) == 6:
mt = np.array(([[mt[0], mt[3], mt[4]],
[mt[3], mt[1], mt[5]],
[mt[4], mt[5], mt[2]]]))
if mt.shape != (3,3) :
raise Exception('I/O dimensions: only 1x6 or 3x3 input supported.')
return mt
def mt_angles(mt):
"""
Takes 6 components and returns fps tri-angles in degrees, with
deviatoric, isotropic, DC and CLVD percentages.
______________________________________________________________________
:type mt : list or np.array.
:param mt : moment tensor NM x 6 (Mxx, Myy, Mzz,
Mxy, Mxz, Myz, the six independent
components).
:rtype : np.array [[1x3], [1x4]].
:return : full 3x3 moment tensor.
.. note::
Nan value are returned for unknown parameters.
The deviatoric percentage is the sum of DC and CLVD percentages.
Use obspy.imaging.scripts.mopad to get correct input.
______________________________________________________________________
"""
# Make sure we got np.array
if np.asarray(mt) is not mt:
mt = np.asarray(mt)
# Getting various formats
## if given strike, dip, rake
if mt.shape == (3,):
strike, dip, rake = mt
DC = 100
CLVD = 0
iso = 0
devi = 100
## if given [[strike, dip, rake], [strike, dip, rake]] (e.g. by MoPad)
elif mt.shape == (2,3) :
strike, dip, rake = mt[0]
DC = 100
CLVD = 0
iso = 0
devi = 100
## if given [strike, dip, rake, devi]
elif mt.shape == (4,):
strike, dip, rake, devi = mt
DC = np.nan
CLVD = np.nan
iso = 0
## if given [Mxx, Myy, Mzz, Mxy, Mxz, Myz]
elif mt.shape == (6,) :
mt = MomentTensor(mt,'XYZ')
DC = mt.get_DC_percentage()
CLVD = mt.get_CLVD_percentage()
iso = mt.get_iso_percentage()
devi = mt.get_devi_percentage()
mt = mt_angles(mt.get_fps())
strike, dip, rake = mt[0]
## if given full moment tensor
elif mt.shape == (3,3) :
mt = mt_angles([mt[0,0], mt[1,1], mt[2,2], mt[0,1], mt[0,2], mt[1,2]])
strike, dip, rake = mt[0]
DC, CLVD, iso, devi = mt[1]
else:
raise Exception('I/O dimensions: only [1|2]x3, 1x[4|6] and 3x3 inputs supported.')
return np.array([[strike, dip, rake], [DC, CLVD, iso, devi]])
def plot_seismicsourcemodel(disp, xyz, style='*', mt=None, comp=None, ax=None) :
"""
Plot the given seismic wave radiation pattern as a color-coded surface
or focal sphere (not exactly as a beach ball diagram).
______________________________________________________________________
:type G : 3D array, list | np.array
:param G : The vector of cartessian coordinates of the radiation
pattern.
:type xyz : 3D array, list | np.array
:param xyz : The cartessian coordinates of the origin points of the
radiation pattern.
:type style : string
:param style : type of plot.
:type mt : list | np.array
:param mt : moment tensor definition supported by MoPad, used in title.
:type comp : string
:param comp : component onto radiation pattern is projected to
infer amplitudes (norm and sign).
:rtype : graphical object
:return : The axe3d including plot.
.. rubric:: _`Supported style`
``'*'``
Plot options q, s and p together.
``'b'``
Plot a unit sphere, amplitude sign being coded with color.
(uses :func:`numpy.abs`).
``'q'``
This a comet plot, displacements magnitudes, directions and
final state are given, respectively by the colors, lines and
points (as if looking at comets).
``'s'``
Plot the amplitudes as surface coding absolute amplitude as
radial distance from origin and amplitude polarity with color.
(uses :func:`numpy.abs`).
``'f'``
Plot the amplitudes as a wireframe, coding absolute amplitude as
radial distance. The displacement polarities are not
represented.
``'p'``
Plot the polarities sectors using a colorcoded wireframe.
The magnitudes of displacements are not represented.
.. rubric:: _`Supported comp`
``'None'``
The radiation pattern is rendered as is if no comp option is
given (best for S wave).
``'v'``
Vertical component (best for S or Sv wave).
``'h'``
horizontal component (best for S or Sh waves, null for P).
``'r'``
Radial component (best for P waves, null for S).
``'m'``
The meridian component (best for S or Sn waves, null for P).
.. note::
The radiation pattern is rendered as is if no comp option is given.
In the title of the plot, SDR stand for strike, dip, rake angles
and IDC stand for isotropic, double couple, compensated linear
vector dipole percentages.
.. seealso::
For earthquake focal mechanism rendering, use
obspy.imaging.beachball.Beachball() :
https://docs.obspy.org/packages/obspy.imaging.html#beachballs
For more info see and obspy.imaging.mopad_wrapper.Beachball().
______________________________________________________________________
"""
# Component
## Get direction(s)
if comp == None:
amplitude_direction = disp
else :
amplitude_direction = vector_normal(xyz, comp)
## Project
disp_projected = project_vectors(disp, amplitude_direction)
## Norms
amplitudes = np.sqrt(disp_projected[0]**2 + disp_projected[1]**2 + disp_projected[2]**2)
## Amplitudes (norm with sign)
amplitudes *= np.sign(np.sum(disp * amplitude_direction, axis=0)+0.00001)
## Easiness
U, V, W = disp_projected
X, Y, Z = xyz
amplitudes_surf = np.abs(amplitudes)/np.max(np.abs(amplitudes))
# Initializing
## Initializing the colormap machinery
norm = matplotlib.colors.Normalize(vmin=np.min(amplitudes),vmax=np.max(amplitudes))
c_m = matplotlib.cm.Spectral
s_m = matplotlib.cm.ScalarMappable(cmap=c_m, norm=norm)
s_m.set_array([])
## Initializing the plot
if ax == None:
fig = plt.figure(figsize=plt.figaspect(1.2))
ax = fig.gca(projection='3d')
plt.xlabel('X')
plt.ylabel('Y')
## Initializing the colorbar
if style not in ('frame', 'wireframe') :
cbar = plt.colorbar(s_m,orientation="horizontal",fraction=0.07)
cbar.ax.set_xlabel('Raw amplitudes')
## Initializing figure keys
if mt is not None :
[strike, dip, rake], [DC, CLVD, iso, deviatoric] = mt_angles(mt)
plt.title('SDR [' + str(int(strike)) + ', ' + str(int(dip)) + ', ' + str(int(rake)) + '] IDC [' + str(int(iso)) + ', ' + str(int(DC)) + ', ' + str(int(CLVD)) +']%' )
## Force axis equal
arrow_scale = (np.max(xyz)-np.min(xyz))/10
if style in ('p', 'polarities','b', 'bb', 'beachball'):
max_range = np.array([X.max()-X.min(), Y.max()-Y.min(), Z.max()-Z.min()]).max() / 2.0
elif style in ('f', 'w', 'frame', 'wireframe', 's', 'surf', 'surface'):
max_range = np.array([(X*np.abs(amplitudes)).max()-(X*np.abs(amplitudes)).min(), (Y*np.abs(amplitudes)).max()-(Y*np.abs(amplitudes)).min(), (Z*np.abs(amplitudes)).max()-(Z*np.abs(amplitudes)).min()]).max() / 2.0
else :
max_range = np.array([(X+arrow_scale).max()-(X+arrow_scale).min(), (Y+arrow_scale).max()-(Y+arrow_scale).min(), (Z+arrow_scale).max()-(Z+arrow_scale).min()]).max() / 2.0
mean_x = X.mean()
mean_y = Y.mean()
mean_z = Z.mean()
ax.set_xlim(mean_x - max_range, mean_x + max_range)
ax.set_ylim(mean_y - max_range, mean_y + max_range)
ax.set_zlim(mean_z - max_range, mean_z + max_range)
# Simple styles
## For a wireframe surface representing amplitudes
if style in ('f', 'w', 'frame', 'wireframe') :
ax.plot_wireframe(X*amplitudes_surf, Y*amplitudes_surf, Z*amplitudes_surf, rstride=1, cstride=1, linewidth=0.5, alpha=0.5)
## For focal sphere, with amplitude sign (~not a beach ball diagram) on unit sphere
if style in ('*', 'p', 'polarities'):
polarity_area = amplitudes.copy()
polarity_area[amplitudes > 0] = np.nan
polarity_area[amplitudes <= 0] = 1
ax.plot_wireframe(X*polarity_area, Y*polarity_area, Z*polarity_area, color='r', rstride=1, cstride=1, linewidth=.5, alpha=0.5)
polarity_area[amplitudes <= 0] = np.nan
polarity_area[amplitudes > 0] = 1
ax.plot_wireframe(X*polarity_area, Y*polarity_area, Z*polarity_area, color='b', rstride=1, cstride=1, linewidth=.5, alpha=0.5)
## For ~ beach ball diagram
if style in ('b', 'bb', 'beachball'):
polarity_area = amplitudes.copy()
polarity_area[amplitudes >= 0] = 1
polarity_area[amplitudes < 0] = -1
ax.plot_surface(X, Y, Z, linewidth=0, rstride=1, cstride=1, facecolors=s_m.to_rgba(polarity_area))
# Complexe styles
## For arrow vectors on obs points
if style in ('*', 'q', 'a', 'v', 'quiver', 'arrow', 'vect', 'vector', 'vectors') :
cmap = plt.get_cmap()
# qs = ax.quiver(X.flatten(), Y.flatten(), Z.flatten(), U.flatten(), V.flatten(), W.flatten(), pivot='tail', length=arrow_scale )
# qs.set_color(s_m.to_rgba(amplitudes.flatten())) #set_array(np.transpose(amplitudes.flatten()))
Us, Vs, Ws = disp_projected * arrow_scale / disp_projected.max()
ax.scatter((X+Us).flatten(), (Y+Vs).flatten(), (Z+Ws).flatten(), c=s_m.to_rgba(amplitudes.flatten()), marker='.', linewidths=0)
for i, x_val in np.ndenumerate(X):
ax.plot([X[i], X[i]+Us[i]], [Y[i], Y[i]+Vs[i]], [Z[i], Z[i]+Ws[i]],'-', color=s_m.to_rgba(amplitudes[i]) , linewidth=1)
## For a color-coded surface representing amplitudes
if style in ('*', 's', 'surf', 'surface'):
ax.plot_surface(X*amplitudes_surf, Y*amplitudes_surf, Z*amplitudes_surf,linewidth=0.5, rstride=1, cstride=1, facecolors=s_m.to_rgba(amplitudes))
plt.show()
return ax
def energy_seismicsourcemodel(G, XYZ) :
"""
Evaluate statistical properties of the given seismic wave radiation
pattern.
______________________________________________________________________
:type G : 3D array, list | np.array
:param G : The vector of cartessian coordinates of the radiation
pattern.
:type XYZ : 3D array, list | np.array
:param XYZ : The cartessian coordinates of the origin points of the
radiation pattern.
:rtype : list
:return : The statistical properties of amplitudes [rms, euclidian norm, average].
.. todo::
Compute more properties, add request handling.
______________________________________________________________________
"""
#amplitudes_correction = np.sum(G * XYZ, axis=0)
#amplitudes_correction /= np.max(np.abs(amplitudes_correction))
amplitudes = np.sqrt( G[0]**2 + G[1]**2 + G[2]**2 ) #* amplitudes_correction
# Classic rms
rms = np.sum(amplitudes**2)/np.prod(amplitudes.shape)
# Euclidian norm
norm = np.sqrt(np.sum(amplitudes**2))
# Amplitude average
average = np.average(np.abs(amplitudes))
return [rms, norm, average]
class Aki_Richards(object):
"""
Set an instance of class Aki_Richards() that can be used for
earthquake modeling based on Aki and Richards (2002, eq. 4.29).
______________________________________________________________________
:type mt : list
:param mt : The focal mechanism NM x 6 (Mxx, Myy, Mzz, Mxy, Mxz, Myz -
the six independent components of the moment tensor).
.. note::
This object is composed of three methods : radpat, plot and
energy.
.. seealso::
:meth: `radpat`
:meth: `plot`
:meth: `energy`
______________________________________________________________________
"""
def __init__(self, mt):
self.mt = mt
def radpat(self, wave='P', obs_cart='None', obs_sph='None'):
"""
Returns the farfield radiation pattern (normalized displacement) based
on Aki and Richards (2002, eq. 4.29) and the cartesian coordinates of
the observation points.
______________________________________________________________________
:type self : object: Aki_Richards
:param self : This method use de self.mt attribute, i.e. the focal
mechanism NM x 6 (Mxx, Myy, Mzz, Mxy, Mxz, Myz - the six
independent components of the moment tensor)
:type wave: String
:param wave: type of wave to compute
:type obs_cart : list | np.array
:param obs_cart : 3D vector array specifying the observations points
in cartesian coordinates.
:type obs_sph : list | np.array
:param obs_sph : 3D vector array specifying the observations points
in spherical coordinates (radians). The default is a unit sphere.
:rtype : np.array
:return : 3D vector array with same shape than requested, that
contains the displacement vector for each observation point.
.. rubric:: _`Supported wave`
``'P'``
Bodywave P.
``'S' or 'S wave' or 'S-wave``
Bodywave S.
``'Sv'``
Projection of S on the vertical.
``'Sh'``
Projection of S on the parallels of the focal sphere.
``'Sm'``
Projection of S on the meridian of the focal sphere.
.. note::
This is based on MMesch, ObsPy, radpattern.py :
https://github.com/MMesch/obspy/blob/radpattern/obspy/core/event/radpattern.py
.. seealso::
Aki, K., & Richards, P. G. (2002). Quantitative Seismology. (J.
Ellis, Ed.) (2nd ed.). University Science Books
.. todo::
Implement Sv and Sh wave (see below)
______________________________________________________________________
"""
# Special cases ######################################################
if wave in ('Sv', 'Sv', 'S_v', 'Sv wave', 'Sv-wave'):
## Get S waves
disp, obs_cart = self.radpat(wave='S', obs_cart=obs_cart, obs_sph=obs_sph)
## Project on Sv component
disp = project_vectors(disp, vector_normal(obs_cart, 'v'))
return disp, obs_cart
elif wave in ('Sm', 'SM', 'SN', 'Sn', 'Snrh', 'Snrh wave', 'Snrh-wave'):
## Get S waves
disp, obs_cart = self.radpat(wave='S', obs_cart=obs_cart, obs_sph=obs_sph)
## Project on Sh component
disp = project_vectors(disp, vector_normal(obs_cart, 'm'))
return disp, obs_cart
elif wave in ('SH', 'Sh', 'S_h', 'Sh wave', 'Sh-wave'):
## Get S waves
disp, obs_cart = self.radpat(wave='S', obs_cart=obs_cart, obs_sph=obs_sph)
## Project on Sh component
disp = project_vectors(disp, vector_normal(obs_cart, 'h'))
return disp, obs_cart
######################################################################
# Get full mt
Mpq = mt_full(self.mt)
# Get observation points
if obs_sph == 'None':
obs_sph = sphere(r=1.,n=1000)
## Get unit sphere, or spherical coordinate if given
if obs_cart == 'None' :
obs_cart = spherical_to_cartesian(obs_sph)
## Make sure they are np.array
if np.asarray(obs_cart) is not obs_cart:
obs_cart = np.asarray(obs_cart)
## Keeping that in mind
requestdimension = obs_cart.shape
obs_cart = np.reshape(obs_cart, (3, int(np.prod(requestdimension)/3)))
# Displacement array
# precompute directional cosine array
dists = np.sqrt(obs_cart[0] * obs_cart[0] + obs_cart[1] * obs_cart[1] +
obs_cart[2] * obs_cart[2])
# In gamma, all points are taken to a unit distance, same angle:
gammas = obs_cart / dists
# initialize displacement array
ndim, npoints = obs_cart.shape
disp = np.empty(obs_cart.shape)
# loop through points
for ipoint in range(npoints):
gamma = gammas[:, ipoint]
if wave in ('S', 'S wave', 'S-wave'):
# loop through displacement component [n index]
Mp = np.dot(Mpq, gamma)
for n in range(ndim):
psum = 0.0
for p in range(ndim):
deltanp = int(n == p)
psum += (gamma[n] * gamma[p] - deltanp) * Mp[p]
disp[n, ipoint] = psum
elif wave in ('P', 'P wave', 'P-wave'):
gammapq = np.outer(gamma, gamma)
gammatimesmt = gammapq * Mpq
# loop through displacement component [n index]
for n in range(ndim):
disp[n, ipoint] = gamma[n] * np.sum(gammatimesmt.flatten())
# Reshape to request dimensions
obs_cart = np.reshape(obs_cart, requestdimension)
disp = np.reshape(disp, requestdimension)
return disp, obs_cart
def plot(self, wave='P',style='*', comp=None, ax=None) :
"""
Plot the radiation pattern.
______________________________________________________________________
:type self : object: Aki_Richards
:param self : This method use de self.mt attribute, i.e. the focal
mechanism NM x 6 (Mxx, Myy, Mzz, Mxy, Mxz, Myz - the six
independent components of the moment tensor)
:type wave: String
:param wave: type of wave to compute
:type style : string
:param style : type of plot.
:type comp : string
:param comp : component onto radiation pattern is projected to
infer amplitudes (norm and sign).
:rtype : graphical object
:return : The axe3d including plot.
.. rubric:: _`Supported wave`
``'P'``
Bodywave P.
``'S' or 'S wave' or 'S-wave``
Bodywave S.
``'Sv'``
Projection of S on the vertical.
``'Sh'``
Projection of S on the parallels of the focal sphere.
``'Sm'``
Projection of S on the meridian of the focal sphere.
.. rubric:: _`Supported style`
``'*'``
Plot options q, s and p together.
``'b'``
Plot a unit sphere, amplitude sign being coded with color.
(uses :func:`numpy.abs`).
``'q'``
This a comet plot, displacements magnitudes, directions and
final state are given, respectively by the colors, lines and
points (as if looking at comets).
``'s'``
Plot the amplitudes as surface coding absolute amplitude as
radial distance from origin and amplitude polarity with color.
(uses :func:`numpy.abs`).
``'f'``
Plot the amplitudes as a wireframe, coding absolute amplitude as
radial distance. The displacement polarities are not
represented.
``'p'``
Plot the polarities sectors using a colorcoded wireframe.
The magnitudes of displacements are not represented.
.. rubric:: _`Supported comp`
``'None'``
The radiation pattern is rendered as is if no comp option is
given (best for S wave).
``'v'``
Vertical component (best for S or Sv wave).
``'h'``
horizontal component (best for S or Sh waves, null for P).
``'r'``
Radial component (best for P waves, null for S).
``'n'``
The meridian component (best for S or Sn waves, null for P).
.. note::
The radiation pattern is rendered as is if no comp option is given.
In the title of the plot, SDR stand for strike, dip, rake angles
and IDC stand for isotropic, double couple, compensated linear
vector dipole percentages.
.. seealso::
:func: `plot_seismicsourcemodel`
:class: `Aki_Richards.radpat`
______________________________________________________________________
"""
# Get radiation pattern
G, XYZ = self.radpat(wave)
if comp == None :
if wave in ('Sv', 'Sv wave', 'Sv-wave'):
comp='v'
elif wave in ('Sm', 'Sn', 'Snrh','Snrh wave', 'Snrh-wave'):
comp='m'
elif wave in ('Sh', 'Sh wave', 'Sh-wave'):
comp='h'
elif wave in ('P', 'P wave', 'P-wave'):
comp='r'
plot_seismicsourcemodel(G, XYZ, style=style, mt=self.mt, comp=comp, ax=ax)
def energy(self, wave='P') :
"""
Get statistical properties of radiation pattern.
______________________________________________________________________
:type self : object: Aki_Richards
:param self : This method use de self.mt attribute, i.e. the focal
mechanism NM x 6 (Mxx, Myy, Mzz, Mxy, Mxz, Myz - the six
independent components of the moment tensor)
:type wave: string
:param wave: type of wave to compute
:rtype : list
:return : The statistical properties of amplitudes [rms, euclidian norm, average].
.. rubric:: _`Supported wave`
``'P'``
Bodywave P.
``'S' or 'S wave' or 'S-wave``
Bodywave S.
``'Sv'``
Projection of S on the vertical.
``'Sh'``
Projection of S on the parallels of the focal sphere.
``'Sm'``
Projection of S on the meridian of the focal sphere.
.. seealso::
:func: `energy_seismicsourcemodel`
:class: `Aki_Richards.radpat`
______________________________________________________________________
"""
# Get radiation pattern and estimate energy
G, XYZ = self.radpat(wave)
estimators = energy_seismicsourcemodel(G, XYZ)
return estimators
class Vavryeuk(object):
"""
Set an instance of class Vavryeuk() that can be used for
earthquake modeling based on Vavryèuk (2001).
______________________________________________________________________
:type mt : list
:param mt : The focal mechanism NM x 6 (Mxx, Myy, Mzz, Mxy, Mxz, Myz -
the six independent components of the moment tensor).
:type poisson: variable
:param poisson: Poisson coefficient (0.25 by default).
.. note::
This object is composed of three methods : radpat, plot and
energy.
.. seealso::
:meth: `radpat`
:meth: `plot`
:meth: `energy`
______________________________________________________________________
"""
def __init__(self, mt, poisson=0.25):
self.mt = mt
self.poisson = poisson
def radpat(self, wave='P', obs_cart='None', obs_sph='None'):
"""
Returns the farfield radiation pattern (normalized displacement) based
on Vavryèuk (2001) and the cartesian coordinates of the observation
points.
______________________________________________________________________
:type self : object: Vavryeuk
:param self : This method use de self.poisson and self.mt attributes,
i.e. the focal mechanism NM x 6 (Mxx, Myy, Mzz, Mxy, Mxz, Myz -
the six independent components of the moment tensor).
:type wave: String
:param wave: type of wave to compute
:type obs_cart : list | np.array
:param obs_cart : 3D vector array specifying the observations points
in cartesian coordinates.
:type obs_sph : list | np.array
:param obs_sph : 3D vector array specifying the observations points
in spherical coordinates (radians). The default is a unit sphere.
:rtype : np.array
:return : 3D vector array with same shape than requested, that
contains the displacement vector for each observation point.
.. rubric:: _`Supported wave`
``'P'``
Bodywave P.
``'S' or 'S wave' or 'S-wave``
Bodywave S.
``'Sv'``
Projection of S on the vertical.
``'Sh'``
Projection of S on the parallels of the focal sphere.
.. note::