#!/usr/bin/env python
# -*- coding: utf-8 -*-
# ------------------------------------------------------------------
# Filename: invsim.py
# Purpose: Python Module for Instrument Correction (Seismology)
# Author: Moritz Beyreuther, Yannik Behr
# Email: moritz.beyreuther@geophysik.uni-muenchen.de
#
# Copyright (C) 2008-2012 Moritz Beyreuther, Yannik Behr
# --------------------------------------------------------------------
"""
Python Module for Instrument Correction (Seismology).
PAZ (Poles and zeros) information must be given in SEED convention, correction
to m/s.
:copyright:
The ObsPy Development Team (devs@obspy.org)
:license:
GNU Lesser General Public License, Version 3
(https://www.gnu.org/copyleft/lesser.html)
"""
import ctypes as C # NOQA
import math
import os
import warnings
import numpy as np
import scipy.signal
from obspy.core.util.attribdict import AttribDict
from obspy.core.util.base import NamedTemporaryFile
from obspy.core.inventory.response import Response
from obspy.signal import util
from obspy.signal.detrend import simple as simple_detrend
from obspy.signal.headers import clibevresp
from obspy.signal.util import _npts2nfft
# Sensitivity is 2080 according to:
# Bormann, P. (ed.) (2002). IASPEI New Manual of Seismological Observatory
# Practice (NMSOP), GeoForschungsZentrum Potsdam, ISBN: 3-9808780-0-7,
# IASPEI Chapter 3, page 24
# (PITSA has 2800)
WOODANDERSON = {'poles': [-6.283 + 4.7124j, -6.283 - 4.7124j],
'zeros': [0 + 0j], 'gain': 1.0, 'sensitivity': 2080}
[docs]def cosine_taper(npts, p=0.1, freqs=None, flimit=None, halfcosine=True,
sactaper=False):
"""
Cosine Taper.
:type npts: int
:param npts: Number of points of cosine taper.
:type p: float
:param p: Decimal percentage of cosine taper (ranging from 0 to 1). Default
is 0.1 (10%) which tapers 5% from the beginning and 5% form the end.
:rtype: float NumPy :class:`~numpy.ndarray`
:return: Cosine taper array/vector of length npts.
:type freqs: NumPy :class:`~numpy.ndarray`
:param freqs: Frequencies as, for example, returned by fftfreq
:type flimit: list(float, float, float, float) or
tuple(float, float, float, float)
:param flimit: The list or tuple defines the four corner frequencies
(f1, f2, f3, f4) of the cosine taper which is one between f2 and f3 and
tapers to zero for f1 < f < f2 and f3 < f < f4.
:type halfcosine: bool
:param halfcosine: If True the taper is a half cosine function. If False it
is a quarter cosine function.
:type sactaper: bool
:param sactaper: If set to True the cosine taper already tapers at the
corner frequency (SAC behavior). By default, the taper has a value
of 1.0 at the corner frequencies.
.. rubric:: Example
>>> tap = cosine_taper(100, 1.0)
>>> tap2 = 0.5 * (1 + np.cos(np.linspace(np.pi, 2 * np.pi, 50)))
>>> np.allclose(tap[0:50], tap2)
True
>>> npts = 100
>>> p = 0.1
>>> tap3 = cosine_taper(npts, p)
>>> (tap3[int(npts*p/2):int(npts*(1-p/2))]==np.ones(int(npts*(1-p)))).all()
True
"""
if p < 0 or p > 1:
msg = "Decimal taper percentage must be between 0 and 1."
raise ValueError(msg)
if p == 0.0 or p == 1.0:
frac = int(npts * p / 2.0)
else:
frac = int(npts * p / 2.0 + 0.5)
if freqs is not None and flimit is not None:
fl1, fl2, fl3, fl4 = flimit
idx1 = np.argmin(abs(freqs - fl1))
idx2 = np.argmin(abs(freqs - fl2))
idx3 = np.argmin(abs(freqs - fl3))
idx4 = np.argmin(abs(freqs - fl4))
else:
idx1 = 0
idx2 = frac - 1
idx3 = npts - frac
idx4 = npts - 1
if sactaper:
# in SAC the second and third
# index are already tapered
idx2 += 1
idx3 -= 1
# Very small data lengths or small decimal taper percentages can result in
# idx1 == idx2 and idx3 == idx4. This breaks the following calculations.
if idx1 == idx2:
idx2 += 1
if idx3 == idx4:
idx3 -= 1
# the taper at idx1 and idx4 equals zero and
# at idx2 and idx3 equals one
cos_win = np.zeros(npts)
if halfcosine:
# cos_win[idx1:idx2+1] = 0.5 * (1.0 + np.cos((np.pi * \
# (idx2 - np.arange(idx1, idx2+1)) / (idx2 - idx1))))
cos_win[idx1:idx2 + 1] = 0.5 * (
1.0 - np.cos((np.pi * (np.arange(idx1, idx2 + 1) - float(idx1)) /
(idx2 - idx1))))
cos_win[idx2 + 1:idx3] = 1.0
cos_win[idx3:idx4 + 1] = 0.5 * (
1.0 + np.cos((np.pi * (float(idx3) - np.arange(idx3, idx4 + 1)) /
(idx4 - idx3))))
else:
cos_win[idx1:idx2 + 1] = np.cos(-(
np.pi / 2.0 * (float(idx2) -
np.arange(idx1, idx2 + 1)) / (idx2 - idx1)))
cos_win[idx2 + 1:idx3] = 1.0
cos_win[idx3:idx4 + 1] = np.cos((
np.pi / 2.0 * (float(idx3) -
np.arange(idx3, idx4 + 1)) / (idx4 - idx3)))
# if indices are identical division by zero
# causes NaN values in cos_win
if idx1 == idx2:
cos_win[idx1] = 0.0
if idx3 == idx4:
cos_win[idx3] = 0.0
return cos_win
[docs]def cosine_sac_taper(freqs, flimit):
"""
Create a cosine taper similar to SAC.
Generate a cosine flank frequency domain taper similar to the one SAC
applies before instrument response deconvolution. This acts as a bandpass
filter when applied to the data in frequency space.
:param freqs: frequency vector to use
:type freqs: :class:`numpy.ndarray`
:param flimit: sequence containing the 4 frequency limits
:type flimit: tuple(float, float, float, float)
:returns: taper
:rtype: :class:`numpy.ndarray`
The `flimit` parameter is a tuple of four frequency values `(f1, f2,
f3, f4)`, the following plots illustrates the concept:
.. plot::
import matplotlib.pylab as plt
import numpy as np
from obspy.signal.invsim import cosine_sac_taper
plt.figure(figsize=(10, 3))
freqs = np.logspace(-2.01, 0, 2000)
plt.vlines([0.015, 0.03, 0.2, 0.4], -0.1, 1.3, color="#89160F")
plt.semilogx(freqs, cosine_sac_taper(freqs, (0.015, 0.03, 0.2, 0.4)),
lw=2, color="#4C72B0")
props = {
"bbox": dict(facecolor='white', edgecolor="0.5",
boxstyle="square,pad=0.2"),
"va": "top", "ha": "center", "color": "#89160F",
"size": "large"}
plt.text(0.015, 1.25, "f1", **props)
plt.text(0.03, 1.25, "f2", **props)
plt.text(0.2, 1.25, "f3", **props)
plt.text(0.4, 1.25, "f4", **props)
plt.xlim(freqs[0], freqs[-1])
plt.ylim(-0.1, 1.3)
plt.ylabel("Taper Amplitude")
plt.xlabel("Frequency [Hz]")
plt.grid()
plt.tight_layout()
plt.show()
"""
fl1, fl2, fl3, fl4 = flimit
taper = np.zeros_like(freqs)
a = (fl1 <= freqs) & (freqs <= fl2)
taper[a] = 0.5 * (1.0 - np.cos(np.pi * (freqs[a] - fl1) / (fl2 - fl1)))
b = (fl2 < freqs) & (freqs < fl3)
taper[b] = 1.0
c = (fl3 <= freqs) & (freqs <= fl4)
taper[c] = 0.5 * (1.0 + np.cos(np.pi * (freqs[c] - fl3) / (fl4 - fl3)))
return taper
[docs]def evalresp_for_frequencies(t_samp, frequencies, filename, date, station='*',
channel='*', network='*', locid='*', units="VEL",
debug=False):
"""
Get the instrument response from a SEED RESP-file for select frequencies.
Uses the evalresp library.
:type t_samp: float
:param t_samp: Sampling interval in seconds
:type frequencies: list[float]
:param frequencies: Discrete frequencies to calculate response for.
:type filename: str or file
:param filename: SEED RESP-filename or open file like object with RESP
information. Any object that provides a read() method will be
considered to be a file like object.
:type date: :class:`~obspy.core.utcdatetime.UTCDateTime`
:param date: Date of interest
:type station: str
:param station: Station id
:type channel: str
:param channel: Channel id
:type network: str
:param network: Network id
:type locid: str
:param locid: Location id
:type units: str
:param units: Units to return response in. Can be either DIS, VEL or ACC
:type debug: bool
:param debug: Verbose output to stdout. Disabled by default.
:rtype: :class:`numpy.ndarray` complex128
:return: Frequency response from SEED RESP-file for given frequencies
"""
if isinstance(filename, str):
with open(filename, 'rb') as fh:
data = fh.read()
elif hasattr(filename, 'read'):
data = filename.read()
# evalresp needs files with correct line separators depending on OS
with NamedTemporaryFile() as fh:
tempfile = fh.name
fh.write(os.linesep.encode('ascii', 'strict').join(data.splitlines()))
fh.close()
# start at zero to get zero for offset/ DC of fft
start_stage = C.c_int(-1)
stop_stage = C.c_int(0)
stdio_flag = C.c_int(0)
sta = C.create_string_buffer(station.encode('ascii', 'strict'))
cha = C.create_string_buffer(channel.encode('ascii', 'strict'))
net = C.create_string_buffer(network.encode('ascii', 'strict'))
locid = C.create_string_buffer(locid.encode('ascii', 'strict'))
unts = C.create_string_buffer(units.encode('ascii', 'strict'))
if debug:
vbs = C.create_string_buffer(b"-v")
else:
vbs = C.create_string_buffer(b"")
rtyp = C.create_string_buffer(b"CS")
datime = C.create_string_buffer(
date.format_seed().encode('ascii', 'strict'))
fn = C.create_string_buffer(tempfile.encode('ascii', 'strict'))
frequencies = np.asarray(frequencies)
nfreqs = C.c_int(frequencies.shape[0])
res = clibevresp.evresp(sta, cha, net, locid, datime, unts, fn,
frequencies, nfreqs, rtyp, vbs, start_stage,
stop_stage, stdio_flag, C.c_int(0))
# optimizing performance, see
# https://wiki.python.org/moin/PythonSpeed/PerformanceTips
try:
nfreqs, rfreqs, rvec = \
res[0].nfreqs, res[0].freqs, res[0].rvec
except ValueError:
msg = "evalresp failed to calculate a response."
raise ValueError(msg)
h = np.empty(nfreqs, dtype=np.complex128)
for i in range(nfreqs):
h[i] = rvec[i].real + rvec[i].imag * 1j
clibevresp.free_response(res)
del nfreqs, rfreqs, rvec, res
return h
[docs]def evalresp(t_samp, nfft, filename, date, station='*', channel='*',
network='*', locid='*', units="VEL", freq=False,
debug=False):
"""
Get the instrument response from a SEED RESP-file.
Uses the evalresp library.
:type t_samp: float
:param t_samp: Sampling interval in seconds
:type nfft: int
:param nfft: Number of FFT points of signal which needs correction
:type filename: str or file
:param filename: SEED RESP-filename or open file like object with RESP
information. Any object that provides a read() method will be
considered to be a file like object.
:type date: :class:`~obspy.core.utcdatetime.UTCDateTime`
:param date: Date of interest
:type station: str
:param station: Station id
:type channel: str
:param channel: Channel id
:type network: str
:param network: Network id
:type locid: str
:param locid: Location id
:type units: str
:param units: Units to return response in. Can be either DIS, VEL or ACC
:type debug: bool
:param debug: Verbose output to stdout. Disabled by default.
:rtype: :class:`numpy.ndarray` complex128
:return: Frequency response from SEED RESP-file of length nfft
"""
fy = 1 / (t_samp * 2.0)
# start at zero to get zero for offset/ DC of fft
freqs = np.linspace(0, fy, nfft // 2 + 1)
h = evalresp_for_frequencies(t_samp, freqs, filename, date, station,
channel, network, locid, units, debug=debug)
if freq:
return h, freqs
return h
[docs]def corn_freq_2_paz(fc, damp=0.707):
"""
Convert corner frequency and damping to poles and zeros.
2 zeros at position (0j, 0j) are given as output (m/s).
:param fc: Corner frequency
:param damping: Corner frequency
:return: Dictionary containing poles, zeros and gain
"""
poles = [-(damp + math.sqrt(1 - damp ** 2) * 1j) * 2 * np.pi * fc,
-(damp - math.sqrt(1 - damp ** 2) * 1j) * 2 * np.pi * fc]
return {'poles': poles, 'zeros': [0j, 0j], 'gain': 1, 'sensitivity': 1.0}
[docs]def paz_to_freq_resp(poles, zeros, scale_fac, t_samp, nfft, freq=False):
"""
Convert Poles and Zeros (PAZ) to frequency response.
The output contains the frequency zero which is the offset of the trace.
:type poles: list[complex]
:param poles: The poles of the transfer function
:type zeros: list[complex]
:param zeros: The zeros of the transfer function
:type scale_fac: float
:param scale_fac: Gain factor
:type t_samp: float
:param t_samp: Sampling interval in seconds
:type nfft: int
:param nfft: Number of FFT points of signal which needs correction
:rtype: :class:`numpy.ndarray` complex128
:return: Frequency response of PAZ of length nfft
"""
n = nfft // 2
b, a = scipy.signal.zpk2tf(zeros, poles, scale_fac)
# a has to be a list for the scipy.signal.freqs() call later but zpk2tf()
# strangely returns it as an integer.
if not isinstance(a, np.ndarray) and a == 1.0:
a = [1.0]
fy = 1 / (t_samp * 2.0)
# start at zero to get zero for offset / DC of fft
f = np.linspace(0, fy, n + 1)
_w, h = scipy.signal.freqs(b, a, f * 2 * np.pi)
if freq:
return h, f
return h
[docs]def waterlevel(spec, wlev):
"""
Get the absolute spectral value corresponding to dB wlev in spectrum spec.
:param spec: The spectrum
:param wlev: The water level
"""
return np.abs(spec).max() * 10.0 ** (-wlev / 20.0)
[docs]def invert_spectrum(spec, wlev):
"""
Invert Spectrum and shrink values under water-level of max spec amplitude.
The water-level is given in db scale.
:note: In place operations on spec, translated from PITSA spr_sinv.c
:param spec: Spectrum as returned by :func:`numpy.fft.rfft`
:param wlev: Water level to use
"""
# Calculated water level in the scale of spec
swamp = waterlevel(spec, wlev)
# Find length in real fft frequency domain, spec is complex
sqrt_len = np.abs(spec)
# Set/scale length to swamp, but leave phase untouched
# 0 sqrt_len will transform in np.nans when dividing by it
idx = np.where((sqrt_len < swamp) & (sqrt_len > 0.0))
spec[idx] *= swamp / sqrt_len[idx]
found = len(idx[0])
# Now invert the spectrum for values where sqrt_len is greater than
# 0.0, see PITSA spr_sinv.c for details
sqrt_len = np.abs(spec) # Find length of new scaled spec
inn = np.where(sqrt_len > 0.0)
spec[inn] = 1.0 / spec[inn]
# For numerical stability, set all zero length to zero, do not invert
spec[sqrt_len == 0.0] = complex(0.0, 0.0)
return found
[docs]def simulate_seismometer(
data, samp_rate, paz_remove=None, paz_simulate=None,
remove_sensitivity=True, simulate_sensitivity=True, water_level=600.0,
zero_mean=True, taper=True, taper_fraction=0.05, pre_filt=None,
seedresp=None, nfft_pow2=False, pitsasim=True, sacsim=False,
shsim=False):
"""
Simulate/Correct seismometer.
:type data: NumPy :class:`~numpy.ndarray`
:param data: Seismogram, detrend before hand (e.g. zero mean)
:type samp_rate: float
:param samp_rate: Sample Rate of Seismogram
:type paz_remove: dict, None
:param paz_remove: Dictionary containing keys 'poles', 'zeros', 'gain'
(A0 normalization factor). poles and zeros must be a list of complex
floating point numbers, gain must be of type float. Poles and Zeros are
assumed to correct to m/s, SEED convention. Use None for no inverse
filtering.
:type paz_simulate: dict, None
:param paz_simulate: Dictionary containing keys 'poles', 'zeros', 'gain'.
Poles and zeros must be a list of complex floating point numbers, gain
must be of type float. Or None for no simulation.
:type remove_sensitivity: bool
:param remove_sensitivity: Determines if data is divided by
`paz_remove['sensitivity']` to correct for overall sensitivity of
recording instrument (seismometer/digitizer) during instrument
correction.
:type simulate_sensitivity: bool
:param simulate_sensitivity: Determines if data is multiplied with
`paz_simulate['sensitivity']` to simulate overall sensitivity of
new instrument (seismometer/digitizer) during instrument simulation.
:type water_level: float
:param water_level: Water_Level for spectrum to simulate
:type zero_mean: bool
:param zero_mean: If true the mean of the data is subtracted
:type taper: bool
:param taper: If true a cosine taper is applied.
:type taper_fraction: float
:param taper_fraction: Taper fraction of cosine taper to use
:type pre_filt: list(float, float, float, float) or
tuple(float, float, float, float)
:param pre_filt: Apply a bandpass filter to the data trace before
deconvolution. The list or tuple defines the four corner frequencies
(f1,f2,f3,f4) of a cosine taper which is one between f2 and f3 and
tapers to zero for f1 < f < f2 and f3 < f < f4.
:type seedresp: dict, None
:param seedresp: Dictionary contains keys 'filename', 'date', 'units'.
'filename' is the path to a RESP-file generated from a dataless SEED
volume (or a file like object with RESP information);
'date' is a :class:`~obspy.core.utcdatetime.UTCDateTime` object for the
date that the response function should be extracted for (can be omitted
when calling simulate() on Trace/Stream. the Trace's starttime will
then be used);
'units' defines the units of the response function.
Can be either 'DIS', 'VEL' or 'ACC'.
:type nfft_pow2: bool
:param nfft_pow2: Number of frequency points to use for FFT. If True,
the exact power of two is taken (default in PITSA). If False the
data are not zero-padded to the next power of two which makes a
slower FFT but is then much faster for e.g. evalresp which scales
with the FFT points.
:type pitsasim: bool
:param pitsasim: Choose parameters to match
instrument correction as done by PITSA.
:type sacsim: bool
:param sacsim: Choose parameters to match
instrument correction as done by SAC.
:type shsim: bool
:param shsim: Choose parameters to match
instrument correction as done by Seismic Handler.
:return: The corrected data are returned as :class:`numpy.ndarray` float64
array. float64 is chosen to avoid numerical instabilities.
This function works in the frequency domain, where nfft is the next power
of len(data) to avoid wrap around effects during convolution. The inverse
of the frequency response of the seismometer (``paz_remove``) is
convolved with the spectrum of the data and with the frequency response
of the seismometer to simulate (``paz_simulate``). A 5% cosine taper is
taken before simulation. The data must be detrended (e.g.) zero mean
beforehand. If paz_simulate=None only the instrument correction is done.
In the latter case, a broadband filter can be applied to the data trace
using pre_filt. This restricts the signal to the valid frequency band and
thereby avoids artifacts due to amplification of frequencies outside of the
instrument's passband (for a detailed discussion see
*Of Poles and Zeros*, F. Scherbaum, Kluwer Academic Publishers).
.. versionchanged:: 0.5.1
The default for `remove_sensitivity` and `simulate_sensitivity` has
been changed to ``True``. Old deprecated keyword arguments `paz`,
`inst_sim`, `no_inverse_filtering` have been removed.
"""
# Checking the types
if not paz_remove and not paz_simulate and not seedresp:
msg = "Neither inverse nor forward instrument simulation specified."
raise TypeError(msg)
for d in [paz_remove, paz_simulate]:
if d is None:
continue
for key in ['poles', 'zeros', 'gain']:
if key not in d:
raise KeyError("Missing key: %s" % key)
# Translated from PITSA: spr_resg.c
delta = 1.0 / samp_rate
#
ndat = len(data)
data = data.astype(np.float64)
if zero_mean:
data -= data.mean()
if taper:
if sacsim:
data *= cosine_taper(ndat, taper_fraction,
sactaper=sacsim, halfcosine=False)
else:
data *= cosine_taper(ndat, taper_fraction)
# The number of points for the FFT has to be at least 2 * ndat (in
# order to prohibit wrap around effects during convolution) cf.
# Numerical Recipes p. 429 calculate next power of 2.
if nfft_pow2:
nfft = util.next_pow_2(2 * ndat)
# evalresp scales directly with nfft, therefore taking the next power of
# two has a greater negative performance impact than the slow down of a
# not power of two in the FFT
else:
nfft = _npts2nfft(ndat)
# Transform data in Fourier domain
data = np.fft.rfft(data, n=nfft)
# Inverse filtering = Instrument correction
if paz_remove:
freq_response, freqs = paz_to_freq_resp(
paz_remove['poles'], paz_remove['zeros'], paz_remove['gain'],
delta, nfft, freq=True)
if seedresp:
freq_response, freqs = evalresp(delta, nfft, seedresp['filename'],
seedresp['date'],
units=seedresp['units'], freq=True,
network=seedresp['network'],
station=seedresp['station'],
locid=seedresp['location'],
channel=seedresp['channel'])
if not remove_sensitivity:
msg = "remove_sensitivity is set to False, but since seedresp " + \
"is selected the overall sensitivity will be corrected " + \
" for anyway!"
warnings.warn(msg)
if paz_remove or seedresp:
if pre_filt:
# make cosine taper
fl1, fl2, fl3, fl4 = pre_filt
if sacsim:
cos_win = cosine_sac_taper(freqs, flimit=(fl1, fl2, fl3, fl4))
else:
cos_win = cosine_taper(freqs.size, freqs=freqs,
flimit=(fl1, fl2, fl3, fl4))
data *= cos_win
invert_spectrum(freq_response, water_level)
data *= freq_response
del freq_response
# Forward filtering = Instrument simulation
if paz_simulate:
data *= paz_to_freq_resp(paz_simulate['poles'], paz_simulate['zeros'],
paz_simulate['gain'], delta, nfft)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:ndat]
if pitsasim:
# linear detrend
data = simple_detrend(data)
if shsim:
# detrend using least squares
data = scipy.signal.detrend(data, type="linear")
# correct for involved overall sensitivities
if paz_remove and remove_sensitivity and not seedresp:
data /= paz_remove['sensitivity']
if paz_simulate and simulate_sensitivity:
data *= paz_simulate['sensitivity']
return data
[docs]def paz_2_amplitude_value_of_freq_resp(paz, freq):
"""
Returns Amplitude at one frequency for the given poles and zeros.
:param paz: Given poles and zeros
:param freq: Given frequency
The amplitude of the freq is estimated according to "Of Poles and
Zeros", Frank Scherbaum, p 43.
.. rubric:: Example
>>> paz = {'poles': [-4.44 + 4.44j, -4.44 - 4.44j],
... 'zeros': [0 + 0j, 0 + 0j],
... 'gain': 0.4}
>>> amp = paz_2_amplitude_value_of_freq_resp(paz, 1)
>>> print(round(amp, 7))
0.2830262
"""
jw = complex(0, 2 * np.pi * freq) # angular frequency
fac = complex(1, 0)
for zero in paz['zeros']: # numerator
fac *= jw - zero
for pole in paz['poles']: # denominator
fac /= jw - pole
return abs(fac) * paz['gain']
[docs]def estimate_magnitude(paz, amplitude, timespan, h_dist):
"""
Estimate local magnitude.
Estimates local magnitude from poles and zeros or full response of given
instrument, the peak to peak amplitude and the time span from peak to peak.
Readings on two components can be used in magnitude estimation by providing
lists for ``paz``, ``amplitude`` and ``timespan``.
.. note::
The input poles and zeros for the actual instrument in use need to
convert input data units to velocity in ``m/s``. Metadata from
accelerometers and other instruments might have to be adjusted
accordingly. It is strongly recommended to supply
:class:`~obspy.core.inventory.response.Response` objects instead of
poles and zeros dictionaries, as these adjustment are then done
automatically.
:param paz: PAZ of the instrument [m/s] (as a dictionary) or response of
the instrument (as :class:`~obspy.core.inventory.response.Response`) or
list of the same
:param amplitude: Peak to peak amplitude [counts] or list of the same
:param timespan: Timespan of peak to peak amplitude [s] or list of the same
:param h_dist: Hypocentral distance [km]
:returns: Estimated local magnitude Ml
.. note::
Magnitude estimation according to Bakun & Joyner, 1984, Eq. (3) page
1835. Bakun, W. H. and W. B. Joyner: The Ml scale in central
California, Bull. Seismol. Soc. Am., 74, 1827-1843, 1984
.. rubric:: Example
>>> paz = {'poles': [-4.444+4.444j, -4.444-4.444j, -1.083+0j],
... 'zeros': [0+0j, 0+0j, 0+0j],
... 'gain': 1.0, 'sensitivity': 671140000.0}
>>> mag = estimate_magnitude(paz, 3.34e6, 0.065, 0.255)
>>> print(round(mag, 6))
2.132873
>>> mag = estimate_magnitude([paz, paz], [3.34e6, 5e6], [0.065, 0.1],
... 0.255)
>>> print(round(mag, 6))
2.347618
"""
# convert input to lists
if not isinstance(paz, list) and not isinstance(paz, tuple):
paz = [paz]
# check if PAZ or Response objects are given and set correct functions to
# calculate wood anderson amplitude(s)
wood_anderson_amplitude_functions = []
for i in paz:
# unfortunately AttribDict is not a subclass of dict so we have to
# explicitly include it here
if isinstance(i, (dict, AttribDict)):
wood_anderson_amplitude_functions.append(
estimate_wood_anderson_amplitude)
elif isinstance(i, Response):
wood_anderson_amplitude_functions.append(
estimate_wood_anderson_amplitude_using_response)
else:
msg = ("Unknown response specification (type '{}'). Use a "
"dictionary structure with poles and zeros information or "
"an obspy Response object.").format(type(i))
raise TypeError(msg)
if not isinstance(amplitude, list) and not isinstance(amplitude, tuple):
amplitude = [amplitude]
if not isinstance(timespan, list) and not isinstance(timespan, tuple):
timespan = [timespan]
# convert every input amplitude to Wood Anderson and calculate the mean
wa_ampl_mean = 0.0
count = 0
for func, paz, amplitude, timespan in zip(
wood_anderson_amplitude_functions, paz, amplitude, timespan):
wa_ampl_mean += func(paz, amplitude, timespan)
count += 1
wa_ampl_mean /= count
# mean of input amplitudes (if more than one) should be used in final
# magnitude estimation (usually N and E components)
magnitude = np.log10(wa_ampl_mean) + np.log10(h_dist / 100.0) + \
0.00301 * (h_dist - 100.0) + 3.0
return magnitude
[docs]def estimate_wood_anderson_amplitude(paz, amplitude, timespan):
"""
Calculate the Wood-Anderson amplitude equivalent.
Convert amplitude in counts measured of instrument with given Poles and
Zeros information for use in :func:`estimate_magnitude`.
Amplitude should be measured as full peak to peak amplitude, timespan as
difference of the two readings.
.. note::
It is recommended to use
:func:`estimate_wood_anderson_amplitude_using_response` with a
:class:`~obspy.core.inventory.response.Response` object instead
whenever possible as this prevents user errors with potentially
misaligned in between units when using poles and zeros from e.g.
accelerometers.
:param paz: PAZ of the instrument [m/s] or list of the same
:param amplitude: Peak to peak amplitude [counts] or list of the same
:param timespan: Timespan of peak to peak amplitude [s] or list of the same
:returns: Simulated zero to peak displacement amplitude on Wood Anderson
seismometer [mm] for use in local magnitude estimation.
"""
# analog to pitsa/plt/RCS/plt_wave.c,v, lines 4881-4891
freq = 1.0 / (2 * timespan)
wa_ampl = amplitude / 2.0 # half peak to peak amplitude
wa_ampl /= (paz_2_amplitude_value_of_freq_resp(paz, freq) *
paz['sensitivity'])
wa_ampl *= paz_2_amplitude_value_of_freq_resp(WOODANDERSON, freq) * \
WOODANDERSON['sensitivity']
wa_ampl *= 1000 # convert to mm
return wa_ampl
[docs]def estimate_wood_anderson_amplitude_using_response(response, amplitude,
timespan):
"""
Estimate the Wood-Anderson amplitude with a given instrument response.
Convert amplitude in counts measured of instrument with given response
information for use in :func:`estimate_magnitude`.
Amplitude should be measured as full peak to peak amplitude, timespan as
difference of the two readings.
:param response: response of the instrument
:type response: :class:`obspy.core.inventory.response.Response`
:param amplitude: Peak to peak amplitude [counts] or list of the same
:type amplitude: float
:param timespan: Timespan of peak to peak amplitude [s] or list of the same
:type timespan: float
:returns: Simulated zero to peak displacement amplitude on Wood Anderson
seismometer [mm] for use in local magnitude estimation.
"""
freq = 1.0 / (2 * timespan)
wa_ampl = amplitude / 2.0 # half peak to peak amplitude
response = response.get_evalresp_response_for_frequencies(
[freq], output="VEL", start_stage=None, end_stage=None)[0]
response_amplitude = np.absolute(response)
wa_ampl /= response_amplitude
wa_ampl *= paz_2_amplitude_value_of_freq_resp(WOODANDERSON, freq) * \
WOODANDERSON['sensitivity']
wa_ampl *= 1000 # convert to mm
return wa_ampl
if __name__ == '__main__':
import doctest
doctest.testmod(exclude_empty=True)