#!/usr/bin/env python
# -*- coding: utf-8 -*-
# ------------------------------------------------------------------
# Filename: tf_misfit.py
# Purpose: Various Time Frequency Misfit Functions
# Author: Martin van Driel
# Email: vandriel@sed.ethz.ch
#
# Copyright (C) 2012 Martin van Driel
# --------------------------------------------------------------------
"""
Various Time Frequency Misfit Functions based on [Kristekova2006]_ and
[Kristekova2009]_.
:copyright:
The ObsPy Development Team (devs@obspy.org)
:license:
GNU Lesser General Public License, Version 3
(https://www.gnu.org/copyleft/lesser.html)
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
from future.builtins import * # NOQA
import numpy as np
from obspy.imaging.cm import obspy_sequential, obspy_divergent
from obspy.signal import util
[docs]def cwt(st, dt, w0, fmin, fmax, nf=100, wl='morlet'):
"""
Continuous Wavelet Transformation in the Frequency Domain.
.. seealso:: [Kristekova2006]_, eq. (4)
:param st: time dependent signal.
:param dt: time step between two samples in st (in seconds)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param fmin: minimum frequency (in Hz)
:param fmax: maximum frequency (in Hz)
:param nf: number of logarithmically spaced frequencies between fmin and
fmax
:param wl: wavelet to use, for now only 'morlet' is implemented
:return: time frequency representation of st, type numpy.ndarray of complex
values, shape = (nf, len(st)).
"""
npts = len(st) * 2
tmax = (npts - 1) * dt
t = np.linspace(0., tmax, npts)
f = np.logspace(np.log10(fmin), np.log10(fmax), nf)
cwt = np.zeros((npts // 2, nf), dtype=np.complex)
if wl == 'morlet':
def psi(t):
return np.pi ** (-.25) * np.exp(1j * w0 * t) * \
np.exp(-t ** 2 / 2.)
def scale(f):
return w0 / (2 * np.pi * f)
else:
raise ValueError('wavelet type "' + wl + '" not defined!')
nfft = util.next_pow_2(npts) * 2
sf = np.fft.fft(st, n=nfft)
# Ignore underflows.
with np.errstate(under="ignore"):
for n, _f in enumerate(f):
a = scale(_f)
# time shift necessary, because wavelet is defined around t = 0
psih = psi(-1 * (t - t[-1] / 2.) / a).conjugate() / np.abs(a) ** .5
psihf = np.fft.fft(psih, n=nfft)
tminin = int(t[-1] / 2. / (t[1] - t[0]))
cwt[:, n] = np.fft.ifft(psihf * sf)[tminin:tminin + npts // 2] * \
(t[1] - t[0])
return cwt.T
[docs]def tfem(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Time Frequency Envelope Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: time frequency representation of Envelope Misfit,
type numpy.ndarray with shape (nf, len(st1)) for single component data
and (number of components, nf, len(st1)) for multicomponent data
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
ar = np.abs(w_1)
else:
ar = np.abs(w_2)
_tfem = (np.abs(w_1) - np.abs(w_2))
if norm == 'global':
if len(st1.shape) == 1:
return _tfem[0] / np.max(ar)
else:
return _tfem / np.max(ar)
elif norm == 'local':
if len(st1.shape) == 1:
return _tfem[0] / ar[0]
else:
return _tfem / ar
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def tfpm(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Time Frequency Phase Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: time frequency representation of Phase Misfit,
type numpy.ndarray with shape (nf, len(st1)) for single component data
and (number of components, nf, len(st1)) for multicomponent data
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
_ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
_ar = np.abs(w_1)
else:
_ar = np.abs(w_2)
_tfpm = np.angle(w_1 / w_2) / np.pi
if norm == 'global':
if len(st1.shape) == 1:
return _ar[0] * _tfpm[0] / np.max(_ar)
else:
return _ar * _tfpm / np.max(_ar)
elif norm == 'local':
if len(st1.shape) == 1:
return _tfpm[0]
else:
return _tfpm
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def tem(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Time-dependent Envelope Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: Time-dependent Envelope Misfit, type numpy.ndarray with shape
(len(st1),) for single component data and (number of components,
len(st1)) for multicomponent data
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
_ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
_ar = np.abs(w_1)
else:
_ar = np.abs(w_2)
_tem = np.sum((np.abs(w_1) - np.abs(w_2)), axis=1)
if norm == 'global':
if len(st1.shape) == 1:
return _tem[0] / np.max(np.sum(_ar, axis=1))
else:
return _tem / np.max(np.sum(_ar, axis=1))
elif norm == 'local':
if len(st1.shape) == 1:
return _tem[0] / np.sum(_ar, axis=1)[0]
else:
return _tem / np.sum(_ar, axis=1)
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def tpm(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Time-dependent Phase Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: Time-dependent Phase Misfit, type numpy.ndarray with shape
(len(st1),) for single component data and (number of components,
len(st1)) for multicomponent data
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
_ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
_ar = np.abs(w_2)
else:
_ar = np.abs(w_1)
_tpm = np.angle(w_1 / w_2) / np.pi
_tpm = np.sum(_ar * _tpm, axis=1)
if norm == 'global':
if len(st1.shape) == 1:
return _tpm[0] / np.max(np.sum(_ar, axis=1))
else:
return _tpm / np.max(np.sum(_ar, axis=1))
elif norm == 'local':
if len(st1.shape) == 1:
return _tpm[0] / np.sum(_ar, axis=1)[0]
else:
return _tpm / np.sum(_ar, axis=1)
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def fem(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Frequency-dependent Envelope Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: Frequency-dependent Envelope Misfit, type numpy.ndarray with shape
(nf,) for single component data and (number of components, nf) for
multicomponent data
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
_ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
_ar = np.abs(w_1)
else:
_ar = np.abs(w_2)
_tem = np.abs(w_1) - np.abs(w_2)
_tem = np.sum(_tem, axis=2)
if norm == 'global':
if len(st1.shape) == 1:
return _tem[0] / np.max(np.sum(_ar, axis=2))
else:
return _tem / np.max(np.sum(_ar, axis=2))
elif norm == 'local':
if len(st1.shape) == 1:
return _tem[0] / np.sum(_ar, axis=2)[0]
else:
return _tem / np.sum(_ar, axis=2)
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def fpm(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Frequency-dependent Phase Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: Frequency-dependent Phase Misfit, type numpy.ndarray with shape
(nf,) for single component data and (number of components, nf) for
multicomponent data
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
_ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
_ar = np.abs(w_1)
else:
_ar = np.abs(w_2)
_tpm = np.angle(w_1 / w_2) / np.pi
_tpm = np.sum(_ar * _tpm, axis=2)
if norm == 'global':
if len(st1.shape) == 1:
return _tpm[0] / np.max(np.sum(_ar, axis=2))
else:
return _tpm / np.max(np.sum(_ar, axis=2))
elif norm == 'local':
if len(st1.shape) == 1:
return _tpm[0] / np.sum(_ar, axis=2)[0]
else:
return _tpm / np.sum(_ar, axis=2)
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def em(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Single Valued Envelope Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: Single Valued Envelope Misfit
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
_ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
_ar = np.abs(w_1)
else:
_ar = np.abs(w_2)
_em = (np.sum(np.sum((np.abs(w_1) - np.abs(w_2)) ** 2, axis=2),
axis=1)) ** .5
if norm == 'global':
if len(st1.shape) == 1:
return _em[0] / (np.sum(_ar ** 2)) ** .5
else:
return _em / ((np.sum(np.sum(_ar ** 2, axis=2),
axis=1)) ** .5).max()
elif norm == 'local':
if len(st1.shape) == 1:
return _em[0] / (np.sum(_ar ** 2)) ** .5
else:
return _em / (np.sum(np.sum(_ar ** 2, axis=2), axis=1)) ** .5
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def pm(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True):
"""
Single Valued Phase Misfit
.. seealso:: [Kristekova2009]_, Table 1. and 2.
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:return: Single Valued Phase Misfit
"""
if len(st1.shape) == 1:
w_1 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_2 = np.zeros((1, nf, st1.shape[0]), dtype=np.complex)
w_1[0] = cwt(st1, dt, w0, fmin, fmax, nf)
w_2[0] = cwt(st2, dt, w0, fmin, fmax, nf)
else:
w_1 = np.zeros((st1.shape[0], nf, st1.shape[1]), dtype=np.complex)
w_2 = np.zeros((st2.shape[0], nf, st2.shape[1]), dtype=np.complex)
for i in np.arange(st1.shape[0]):
w_1[i] = cwt(st1[i], dt, w0, fmin, fmax, nf)
w_2[i] = cwt(st2[i], dt, w0, fmin, fmax, nf)
if st2_isref:
_ar = np.abs(w_2)
else:
if np.abs(w_1).max() > np.abs(w_2).max():
_ar = np.abs(w_1)
else:
_ar = np.abs(w_2)
_pm = np.angle(w_1 / w_2) / np.pi
_pm = (np.sum(np.sum((_ar * _pm) ** 2, axis=2), axis=1)) ** .5
if norm == 'global':
if len(st1.shape) == 1:
return _pm[0] / (np.sum(_ar ** 2)) ** .5
else:
return _pm / ((np.sum(np.sum(_ar ** 2, axis=2),
axis=1)) ** .5).max()
elif norm == 'local':
if len(st1.shape) == 1:
return _pm[0] / (np.sum(_ar ** 2)) ** .5
else:
return _pm / (np.sum(np.sum(_ar ** 2, axis=2), axis=1)) ** .5
else:
raise ValueError('norm "' + norm + '" not defined!')
[docs]def tfeg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Time Frequency Envelope Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(15)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: time frequency representation of Envelope Goodness-of-Fit,
type numpy.ndarray with shape (nf, len(st1)) for single component data
and (number of components, nf, len(st1)) for multicomponent data
"""
_tfem = tfem(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0,
norm=norm, st2_isref=st2_isref)
return a * np.exp(-np.abs(_tfem) ** k)
[docs]def tfpg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Time Frequency Phase Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(16)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: time frequency representation of Phase Goodness-of-Fit,
type numpy.ndarray with shape (nf, len(st1)) for single component data
and (number of components, nf, len(st1)) for multicomponent data
"""
_tfpm = tfpm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0,
norm=norm, st2_isref=st2_isref)
return a * (1 - np.abs(_tfpm) ** k)
[docs]def teg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Time-dependent Envelope Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(15)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: time dependent Envelope Goodness-of-Fit, type numpy.ndarray with
shape (len(st1),) for single component data and (number of components,
len(st1)) for multicomponent data
"""
_tem = tem(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
return a * np.exp(-np.abs(_tem) ** k)
[docs]def tpg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Time-dependent Phase Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(16)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: time dependent Phase Goodness-of-Fit, type numpy.ndarray with
shape (len(st1),) for single component data and (number of components,
len(st1)) for multicomponent data
"""
_tpm = tpm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
return a * (1 - np.abs(_tpm) ** k)
[docs]def feg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Frequency-dependent Envelope Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(15)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: frequency dependent Envelope Goodness-of-Fit, type numpy.ndarray
with shape (nf,) for single component data and (number of components,
nf) for multicomponent data
"""
_fem = fem(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
return a * np.exp(-np.abs(_fem) ** k)
[docs]def fpg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Frequency-dependent Phase Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(16)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: frequency dependent Phase Goodness-of-Fit, type numpy.ndarray
with shape (nf,) for single component data and (number of components,
nf) for multicomponent data
"""
_fpm = fpm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
return a * (1 - np.abs(_fpm) ** k)
[docs]def eg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Single Valued Envelope Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(15)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: Single Valued Envelope Goodness-of-Fit
"""
_em = em(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
return a * np.exp(-np.abs(_em) ** k)
[docs]def pg(st1, st2, dt=0.01, fmin=1., fmax=10., nf=100, w0=6, norm='global',
st2_isref=True, a=10., k=1.):
"""
Single Valued Phase Goodness-of-Fit
.. seealso:: [Kristekova2009]_, Eq.(16)
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param a: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:return: Single Valued Phase Goodness-of-Fit
"""
_pm = pm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
return a * (1 - np.abs(_pm) ** k)
[docs]def plot_tf_misfits(st1, st2, dt=0.01, t0=0., fmin=1., fmax=10., nf=100, w0=6,
norm='global', st2_isref=True, left=0.1, bottom=0.1,
h_1=0.2, h_2=0.125, h_3=0.2, w_1=0.2, w_2=0.6, w_cb=0.01,
d_cb=0.0, show=True, plot_args=['k', 'r', 'b'], ylim=0.,
clim=0., cmap=obspy_divergent):
"""
Plot all time frequency misfits and the time series in one plot (per
component).
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param t0: starting time for plotting
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param left: plot distance from the left of the figure
:param bottom: plot distance from the bottom of the figure
:param h_1: height of the signal axes
:param h_2: height of the TEM and TPM axes
:param h_3: height of the TFEM and TFPM axes
:param w_1: width of the FEM and FPM axes
:param w_2: width of the TFEM, TFPM, signal etc. axes
:param w_cb: width of the colorbar axes
:param d_cb: distance of the colorbar axes to the other axes
:param show: show figure or return
:param plot_args: list of plot arguments passed to the signal 1/2 and
TEM/TPM/FEM/FPM plots
:param ylim: limits in misfit for TEM/TPM/FEM/FPM
:param clim: limits of the colorbars
:param cmap: colormap for TFEM/TFPM, either a string or
matplotlib.cm.Colormap instance
:return: If show is False, returns a matplotlib.pyplot.figure object
(single component data) or a list of figure objects (multi component
data)
.. rubric:: Example
For a signal with pure phase error
.. seealso:: [Kristekova2006]_, Fig.(4)
>>> import numpy as np
>>> from scipy.signal import hilbert
>>> tmax = 6.
>>> dt = 0.01
>>> npts = int(tmax / dt + 1)
>>> t = np.linspace(0., tmax, npts)
>>> A1 = 4.
>>> t1 = 2.
>>> f1 = 2.
>>> phi1 = 0.
>>> phase_shift = 0.1
>>> H1 = (np.sign(t - t1) + 1)/ 2
>>> st1 = (A1 * (t - t1) * np.exp(-2*(t - t1)) *
... np.cos(2. * np.pi * f1 * (t - t1) + phi1 * np.pi) * H1)
>>> # Reference signal
>>> st2 = st1.copy()
>>> # Distorted signal:
>>> # generate analytical signal (hilbert transform) and add phase shift
>>> st1 = hilbert(st1)
>>> st1 = np.real(np.abs(st1) * np.exp((np.angle(st1) +
... phase_shift * np.pi) * 1j))
>>> plot_tf_misfits(st1, st2, dt=dt, fmin=1., fmax=10.) # doctest: +SKIP
.. plot::
import numpy as np
from scipy.signal import hilbert
from obspy.signal.tf_misfit import plot_tf_misfits
tmax = 6.
dt = 0.01
npts = int(tmax / dt + 1)
t = np.linspace(0., tmax, npts)
A1 = 4.
t1 = 2.
f1 = 2.
phi1 = 0.
phase_shift = 0.1
H1 = (np.sign(t - t1) + 1)/ 2
st1 = (A1 * (t - t1) * np.exp(-2*(t - t1)) *
np.cos(2. * np.pi * f1 * (t - t1) + phi1 * np.pi) * H1)
# Reference signal
st2 = st1.copy()
# Distorted signal:
# generate analytical signal (hilbert transform) and add phase shift
st1 = hilbert(st1)
st1 = np.real(np.abs(st1) * np.exp((np.angle(st1) +
phase_shift * np.pi) * 1j))
plot_tf_misfits(st1, st2, dt=dt, fmin=1., fmax=10.)
"""
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
npts = st1.shape[-1]
tmax = (npts - 1) * dt
t = np.linspace(0., tmax, npts) + t0
f = np.logspace(np.log10(fmin), np.log10(fmax), nf)
# compute time frequency misfits
_tfem = tfem(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0,
norm=norm, st2_isref=st2_isref)
_tem = tem(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
_fem = fem(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
_em = em(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
_tfpm = tfpm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0,
norm=norm, st2_isref=st2_isref)
_tpm = tpm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
_fpm = fpm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
_pm = pm(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref)
if len(st1.shape) == 1:
_tfem = _tfem.reshape((1, nf, npts))
_tem = _tem.reshape((1, npts))
_fem = _fem.reshape((1, nf))
_em = _em.reshape((1, 1))
_tfpm = _tfpm.reshape((1, nf, npts))
_tpm = _tpm.reshape((1, npts))
_fpm = _fpm.reshape((1, nf))
_pm = _pm.reshape((1, 1))
st1 = st1.reshape((1, npts))
st2 = st2.reshape((1, npts))
ntr = 1
else:
ntr = st1.shape[0]
figs = []
for itr in np.arange(ntr):
fig = plt.figure()
# plot signals
ax_sig = fig.add_axes([left + w_1, bottom + h_2 + h_3, w_2, h_1])
ax_sig.plot(t, st1[itr], plot_args[0])
ax_sig.plot(t, st2[itr], plot_args[1])
# plot TEM
ax_tem = fig.add_axes([left + w_1, bottom + h_1 + h_2 + h_3, w_2, h_2])
ax_tem.plot(t, _tem[itr], plot_args[2])
# plot TFEM
ax_tfem = fig.add_axes([left + w_1, bottom + h_1 + 2 * h_2 + h_3, w_2,
h_3])
x, y = np.meshgrid(
t, np.logspace(np.log10(fmin), np.log10(fmax),
_tfem[itr].shape[0]))
img_tfem = ax_tfem.pcolormesh(x, y, _tfem[itr], cmap=cmap)
img_tfem.set_rasterized(True)
ax_tfem.set_yscale("log")
ax_tfem.set_ylim(fmin, fmax)
# plot FEM
ax_fem = fig.add_axes([left, bottom + h_1 + 2 * h_2 + h_3, w_1, h_3])
ax_fem.semilogy(_fem[itr], f, plot_args[2])
ax_fem.set_ylim(fmin, fmax)
# plot TPM
ax_tpm = fig.add_axes([left + w_1, bottom, w_2, h_2])
ax_tpm.plot(t, _tpm[itr], plot_args[2])
# plot TFPM
ax_tfpm = fig.add_axes([left + w_1, bottom + h_2, w_2, h_3])
x, y = np.meshgrid(t, f)
img_tfpm = ax_tfpm.pcolormesh(x, y, _tfpm[itr], cmap=cmap)
img_tfpm.set_rasterized(True)
ax_tfpm.set_yscale("log")
ax_tfpm.set_ylim(f[0], f[-1])
# add colorbars
ax_cb_tfpm = fig.add_axes([left + w_1 + w_2 + d_cb + w_cb, bottom,
w_cb, h_2 + h_3])
fig.colorbar(img_tfpm, cax=ax_cb_tfpm)
# plot FPM
ax_fpm = fig.add_axes([left, bottom + h_2, w_1, h_3])
ax_fpm.semilogy(_fpm[itr], f, plot_args[2])
ax_fpm.set_ylim(fmin, fmax)
# set limits
ylim_sig = np.max([np.abs(st1).max(), np.abs(st2).max()]) * 1.1
ax_sig.set_ylim(-ylim_sig, ylim_sig)
if ylim == 0.:
ylim = np.max([np.abs(_tem).max(), np.abs(_tpm).max(),
np.abs(_fem).max(), np.abs(_fpm).max()]) * 1.1
ax_tem.set_ylim(-ylim, ylim)
ax_fem.set_xlim(-ylim, ylim)
ax_tpm.set_ylim(-ylim, ylim)
ax_fpm.set_xlim(-ylim, ylim)
ax_sig.set_xlim(t[0], t[-1])
ax_tem.set_xlim(t[0], t[-1])
ax_tpm.set_xlim(t[0], t[-1])
if clim == 0.:
clim = np.max([np.abs(_tfem).max(), np.abs(_tfpm).max()])
img_tfpm.set_clim(-clim, clim)
img_tfem.set_clim(-clim, clim)
# add text box for EM + PM
textstr = 'EM = %.2f\nPM = %.2f' % (_em[itr], _pm[itr])
props = dict(boxstyle='round', facecolor='white')
ax_sig.text(-0.3, 0.5, textstr, transform=ax_sig.transAxes,
verticalalignment='center', horizontalalignment='left',
bbox=props)
ax_tpm.set_xlabel('time')
ax_fem.set_ylabel('frequency')
ax_fpm.set_ylabel('frequency')
# add text boxes
props = dict(boxstyle='round', facecolor='white', alpha=0.5)
ax_tfem.text(0.95, 0.85, 'TFEM', transform=ax_tfem.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_tfpm.text(0.95, 0.85, 'TFPM', transform=ax_tfpm.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_tem.text(0.95, 0.75, 'TEM', transform=ax_tem.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_tpm.text(0.95, 0.75, 'TPM', transform=ax_tpm.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_fem.text(0.9, 0.85, 'FEM', transform=ax_fem.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_fpm.text(0.9, 0.85, 'FPM', transform=ax_fpm.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
# remove axis labels
ax_tfpm.xaxis.set_major_formatter(NullFormatter())
ax_tfem.xaxis.set_major_formatter(NullFormatter())
ax_tem.xaxis.set_major_formatter(NullFormatter())
ax_sig.xaxis.set_major_formatter(NullFormatter())
ax_tfpm.yaxis.set_major_formatter(NullFormatter())
ax_tfem.yaxis.set_major_formatter(NullFormatter())
figs.append(fig)
if show:
plt.show()
else:
if ntr == 1:
return figs[0]
else:
return figs
[docs]def plot_tf_gofs(st1, st2, dt=0.01, t0=0., fmin=1., fmax=10., nf=100, w0=6,
norm='global', st2_isref=True, a=10., k=1., left=0.1,
bottom=0.1, h_1=0.2, h_2=0.125, h_3=0.2, w_1=0.2, w_2=0.6,
w_cb=0.01, d_cb=0.0, show=True, plot_args=['k', 'r', 'b'],
ylim=0., clim=0., cmap=obspy_sequential):
"""
Plot all time frequency Goodness-of-Fits and the time series in one plot
(per component).
:param st1: signal 1 of two signals to compare, type numpy.ndarray with
shape (number of components, number of time samples) or (number of
timesamples, ) for single component data
:param st2: signal 2 of two signals to compare, type and shape as st1
:param dt: time step between two samples in st1 and st2
:param t0: starting time for plotting
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param norm: 'global' or 'local' normalization of the misfit
:type st2_isref: bool
:param st2_isref: True if st2 is a reference signal, False if none is a
reference
:param A: Maximum value of Goodness-of-Fit for perfect agreement
:param k: sensitivity of Goodness-of-Fit to the misfit
:param left: plot distance from the left of the figure
:param bottom: plot distance from the bottom of the figure
:param h_1: height of the signal axes
:param h_2: height of the TEM and TPM axes
:param h_3: height of the TFEM and TFPM axes
:param w_1: width of the FEM and FPM axes
:param w_2: width of the TFEM, TFPM, signal etc. axes
:param w_cb: width of the colorbar axes
:param d_cb: distance of the colorbar axes to the other axes
:param show: show figure or return
:param plot_args: list of plot arguments passed to the signal 1/2 and
TEM/TPM/FEM/FPM plots
:param ylim: limits in misfit for TEM/TPM/FEM/FPM
:param clim: limits of the colorbars
:param cmap: colormap for TFEM/TFPM, either a string or
matplotlib.cm.Colormap instance
:return: If show is False, returns a matplotlib.pyplot.figure object
(single component data) or a list of figure objects (multi component
data)
.. rubric:: Example
For a signal with pure amplitude error
>>> import numpy as np
>>> tmax = 6.
>>> dt = 0.01
>>> npts = int(tmax / dt + 1)
>>> t = np.linspace(0., tmax, npts)
>>> A1 = 4.
>>> t1 = 2.
>>> f1 = 2.
>>> phi1 = 0.
>>> phase_shift = 0.1
>>> H1 = (np.sign(t - t1) + 1)/ 2
>>> st1 = (A1 * (t - t1) * np.exp(-2*(t - t1)) *
... np.cos(2. * np.pi * f1 * (t - t1) + phi1 * np.pi) * H1)
>>> # Reference signal
>>> st2 = st1.copy()
>>> # Distorted signal:
>>> st1 = st1 * 3.
>>> plot_tf_gofs(st1, st2, dt=dt, fmin=1., fmax=10.) # doctest: +SKIP
.. plot::
import numpy as np
from obspy.signal.tf_misfit import plot_tf_gofs
tmax = 6.
dt = 0.01
npts = int(tmax / dt + 1)
t = np.linspace(0., tmax, npts)
A1 = 4.
t1 = 2.
f1 = 2.
phi1 = 0.
phase_shift = 0.1
H1 = (np.sign(t - t1) + 1)/ 2
st1 = (A1 * (t - t1) * np.exp(-2*(t - t1)) *
np.cos(2. * np.pi * f1 * (t - t1) + phi1 * np.pi) * H1)
# Reference signal
st2 = st1.copy()
# Distorted signal:
st1 = st1 * 3.
plot_tf_gofs(st1, st2, dt=dt, fmin=1., fmax=10.)
"""
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
npts = st1.shape[-1]
tmax = (npts - 1) * dt
t = np.linspace(0., tmax, npts) + t0
f = np.logspace(np.log10(fmin), np.log10(fmax), nf)
# compute time frequency misfits
_tfeg = tfeg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0,
norm=norm, st2_isref=st2_isref, a=a, k=k)
_teg = teg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref, a=a, k=k)
_feg = feg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref, a=a, k=k)
_eg = eg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref, a=a, k=k)
_tfpg = tfpg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0,
norm=norm, st2_isref=st2_isref, a=a, k=k)
_tpg = tpg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref, a=a, k=k)
_fpg = fpg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref, a=a, k=k)
_pg = pg(st1, st2, dt=dt, fmin=fmin, fmax=fmax, nf=nf, w0=w0, norm=norm,
st2_isref=st2_isref, a=a, k=k)
if len(st1.shape) == 1:
_tfeg = _tfeg.reshape((1, nf, npts))
_teg = _teg.reshape((1, npts))
_feg = _feg.reshape((1, nf))
_eg = _eg.reshape((1, 1))
_tfpg = _tfpg.reshape((1, nf, npts))
_tpg = _tpg.reshape((1, npts))
_fpg = _fpg.reshape((1, nf))
_pg = _pg.reshape((1, 1))
st1 = st1.reshape((1, npts))
st2 = st2.reshape((1, npts))
ntr = 1
else:
ntr = st1.shape[0]
figs = []
for itr in np.arange(ntr):
fig = plt.figure()
# plot signals
ax_sig = fig.add_axes([left + w_1, bottom + h_2 + h_3, w_2, h_1])
ax_sig.plot(t, st1[itr], plot_args[0])
ax_sig.plot(t, st2[itr], plot_args[1])
# plot TEG
ax_teg = fig.add_axes([left + w_1, bottom + h_1 + h_2 + h_3, w_2, h_2])
ax_teg.plot(t, _teg[itr], plot_args[2])
# plot TFEG
ax_tfeg = fig.add_axes([left + w_1, bottom + h_1 + 2 * h_2 + h_3, w_2,
h_3])
x, y = np.meshgrid(
t, np.logspace(np.log10(fmin), np.log10(fmax),
_tfeg[itr].shape[0]))
img_tfeg = ax_tfeg.pcolormesh(x, y, _tfeg[itr], cmap=cmap)
img_tfeg.set_rasterized(True)
ax_tfeg.set_yscale("log")
ax_tfeg.set_ylim(fmin, fmax)
# plot FEG
ax_feg = fig.add_axes([left, bottom + h_1 + 2 * h_2 + h_3, w_1, h_3])
ax_feg.semilogy(_feg[itr], f, plot_args[2])
ax_feg.set_ylim(fmin, fmax)
# plot TPG
ax_tpg = fig.add_axes([left + w_1, bottom, w_2, h_2])
ax_tpg.plot(t, _tpg[itr], plot_args[2])
# plot TFPG
ax_tfpg = fig.add_axes([left + w_1, bottom + h_2, w_2, h_3])
x, y = np.meshgrid(t, f)
img_tfpg = ax_tfpg.pcolormesh(x, y, _tfpg[itr], cmap=cmap)
img_tfpg.set_rasterized(True)
ax_tfpg.set_yscale("log")
ax_tfpg.set_ylim(f[0], f[-1])
# add colorbars
ax_cb_tfpg = fig.add_axes([left + w_1 + w_2 + d_cb + w_cb, bottom,
w_cb, h_2 + h_3])
fig.colorbar(img_tfpg, cax=ax_cb_tfpg)
# plot FPG
ax_fpg = fig.add_axes([left, bottom + h_2, w_1, h_3])
ax_fpg.semilogy(_fpg[itr], f, plot_args[2])
ax_fpg.set_ylim(fmin, fmax)
# set limits
ylim_sig = np.max([np.abs(st1).max(), np.abs(st2).max()]) * 1.1
ax_sig.set_ylim(-ylim_sig, ylim_sig)
if ylim == 0.:
ylim = np.max([np.abs(_teg).max(), np.abs(_tpg).max(),
np.abs(_feg).max(), np.abs(_fpg).max()]) * 1.1
ax_teg.set_ylim(0., ylim)
ax_feg.set_xlim(0., ylim)
ax_tpg.set_ylim(0., ylim)
ax_fpg.set_xlim(0., ylim)
ax_sig.set_xlim(t[0], t[-1])
ax_teg.set_xlim(t[0], t[-1])
ax_tpg.set_xlim(t[0], t[-1])
if clim == 0.:
clim = np.max([np.abs(_tfeg).max(), np.abs(_tfpg).max()])
img_tfpg.set_clim(0., clim)
img_tfeg.set_clim(0., clim)
# add text box for EG + PG
textstr = 'EG = %2.2f\nPG = %2.2f' % (_eg[itr], _pg[itr])
props = dict(boxstyle='round', facecolor='white')
ax_sig.text(-0.3, 0.5, textstr, transform=ax_sig.transAxes,
verticalalignment='center', horizontalalignment='left',
bbox=props)
ax_tpg.set_xlabel('time')
ax_feg.set_ylabel('frequency')
ax_fpg.set_ylabel('frequency')
# add text boxes
props = dict(boxstyle='round', facecolor='white', alpha=0.5)
ax_tfeg.text(0.95, 0.85, 'TFEG', transform=ax_tfeg.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_tfpg.text(0.95, 0.85, 'TFPG', transform=ax_tfpg.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_teg.text(0.95, 0.75, 'TEG', transform=ax_teg.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_tpg.text(0.95, 0.75, 'TPG', transform=ax_tpg.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_feg.text(0.9, 0.85, 'FEG', transform=ax_feg.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
ax_fpg.text(0.9, 0.85, 'FPG', transform=ax_fpg.transAxes,
verticalalignment='top', horizontalalignment='right',
bbox=props)
# remove axis labels
ax_tfpg.xaxis.set_major_formatter(NullFormatter())
ax_tfeg.xaxis.set_major_formatter(NullFormatter())
ax_teg.xaxis.set_major_formatter(NullFormatter())
ax_sig.xaxis.set_major_formatter(NullFormatter())
ax_tfpg.yaxis.set_major_formatter(NullFormatter())
ax_tfeg.yaxis.set_major_formatter(NullFormatter())
figs.append(fig)
if show:
plt.show()
else:
if ntr == 1:
return figs[0]
else:
return figs
[docs]def plot_tfr(st, dt=0.01, t0=0., fmin=1., fmax=10., nf=100, w0=6, left=0.1,
bottom=0.1, h_1=0.2, h_2=0.6, w_1=0.2, w_2=0.6, w_cb=0.01,
d_cb=0.0, show=True, plot_args=['k', 'k'], clim=0.0,
cmap=obspy_sequential, mode='absolute', fft_zero_pad_fac=0):
"""
Plot time frequency representation, spectrum and time series of the signal.
:param st: signal, type numpy.ndarray with shape (number of components,
number of time samples) or (number of timesamples, ) for single
component data
:param dt: time step between two samples in st
:param t0: starting time for plotting
:param fmin: minimal frequency to be analyzed
:param fmax: maximal frequency to be analyzed
:param nf: number of frequencies (will be chosen with logarithmic spacing)
:param w0: parameter for the wavelet, tradeoff between time and frequency
resolution
:param left: plot distance from the left of the figure
:param bottom: plot distance from the bottom of the figure
:param h_1: height of the signal axis
:param h_2: height of the TFR/spectrum axis
:param w_1: width of the spectrum axis
:param w_2: width of the TFR/signal axes
:param w_cb: width of the colorbar axes
:param d_cb: distance of the colorbar axes to the other axes
:param show: show figure or return
:param plot_args: list of plot arguments passed to the signal and spectrum
plots
:param clim: limits of the colorbars
:param cmap: colormap for TFEM/TFPM, either a string or
matplotlib.cm.Colormap instance
:param mode: 'absolute' for absolute value of TFR, 'power' for ``|TFR|^2``
:param fft_zero_pad_fac: integer, if > 0, the signal is zero padded to
``nfft = next_pow_2(len(st)) * fft_zero_pad_fac`` to get smoother
spectrum in the low frequencies (has no effect on the TFR and might
make demeaning/tapering necessary to avoid artifacts)
:return: If show is False, returns a matplotlib.pyplot.figure object
(single component data) or a list of figure objects (multi component
data)
.. rubric:: Example
>>> from obspy import read
>>> tr = read("https://examples.obspy.org/a02i.2008.240.mseed")[0]
>>> plot_tfr(tr.data, dt=tr.stats.delta, fmin=.01, # doctest: +SKIP
... fmax=50., w0=8., nf=64, fft_zero_pad_fac=4)
.. plot::
from obspy.signal.tf_misfit import plot_tfr
from obspy import read
tr = read("https://examples.obspy.org/a02i.2008.240.mseed")[0]
plot_tfr(tr.data, dt=tr.stats.delta, fmin=.01,
fmax=50., w0=8., nf=64, fft_zero_pad_fac=4)
"""
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
npts = st.shape[-1]
tmax = (npts - 1) * dt
t = np.linspace(0., tmax, npts) + t0
if fft_zero_pad_fac == 0:
nfft = npts
else:
nfft = util.next_pow_2(npts) * fft_zero_pad_fac
f_lin = np.linspace(0, 0.5 / dt, nfft // 2 + 1)
if len(st.shape) == 1:
_w = np.zeros((1, nf, npts), dtype=np.complex)
_w[0] = cwt(st, dt, w0, fmin, fmax, nf)
ntr = 1
spec = np.zeros((1, nfft // 2 + 1), dtype=np.complex)
spec[0] = np.fft.rfft(st, n=nfft) * dt
st = st.reshape((1, npts))
else:
_w = np.zeros((st.shape[0], nf, npts), dtype=np.complex)
spec = np.zeros((st.shape[0], nfft // 2 + 1), dtype=np.complex)
for i in np.arange(st.shape[0]):
_w[i] = cwt(st[i], dt, w0, fmin, fmax, nf)
spec[i] = np.fft.rfft(st[i], n=nfft) * dt
ntr = st.shape[0]
if mode == 'absolute':
_tfr = np.abs(_w)
spec = np.abs(spec)
elif mode == 'power':
_tfr = np.abs(_w) ** 2
spec = np.abs(spec) ** 2
else:
raise ValueError('mode "' + mode + '" not defined!')
figs = []
for itr in np.arange(ntr):
fig = plt.figure()
# plot signals
ax_sig = fig.add_axes([left + w_1, bottom, w_2, h_1])
ax_sig.plot(t, st[itr], plot_args[0])
# plot TFR
ax_tfr = fig.add_axes([left + w_1, bottom + h_1, w_2, h_2])
x, y = np.meshgrid(
t, np.logspace(np.log10(fmin), np.log10(fmax),
_tfr[itr].shape[0]))
img_tfr = ax_tfr.pcolormesh(x, y, _tfr[itr], cmap=cmap)
img_tfr.set_rasterized(True)
ax_tfr.set_yscale("log")
ax_tfr.set_ylim(fmin, fmax)
ax_tfr.set_xlim(t[0], t[-1])
# plot spectrum
ax_spec = fig.add_axes([left, bottom + h_1, w_1, h_2])
ax_spec.semilogy(spec[itr], f_lin, plot_args[1])
# add colorbars
ax_cb_tfr = fig.add_axes([left + w_1 + w_2 + d_cb + w_cb, bottom +
h_1, w_cb, h_2])
fig.colorbar(img_tfr, cax=ax_cb_tfr)
# set limits
ax_sig.set_ylim(st.min() * 1.1, st.max() * 1.1)
ax_sig.set_xlim(t[0], t[-1])
xlim = spec.max() * 1.1
ax_spec.set_xlim(xlim, 0.)
ax_spec.set_ylim(fmin, fmax)
if clim == 0.:
clim = _tfr.max()
img_tfr.set_clim(0., clim)
ax_sig.set_xlabel('time')
ax_spec.set_ylabel('frequency')
# remove axis labels
ax_tfr.xaxis.set_major_formatter(NullFormatter())
ax_tfr.yaxis.set_major_formatter(NullFormatter())
figs.append(fig)
if show:
plt.show()
else:
if ntr == 1:
return figs[0]
else:
return figs
if __name__ == '__main__':
import doctest
doctest.testmod(exclude_empty=True)