Source code for eqcorrscan.utils.mag_calc

"""Functions to calculate local magnitudes automatically, and to calcualte \
relative moments for near-repeating earthquakes using singular-value \
decomposition techniques.

:copyright:
    EQcorrscan developers.

:license:
    GNU Lesser General Public License, Version 3
    (https://www.gnu.org/copyleft/lesser.html)
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals

import numpy as np
import warnings
import os
import glob
import matplotlib.pyplot as plt
import datetime as dt
import itertools
import sys
import shutil
import copy
import random
import pickle

from scipy.signal import iirfilter
from collections import Counter
from obspy.signal.invsim import simulate_seismometer as seis_sim
from obspy.signal.invsim import evalresp, paz_2_amplitude_value_of_freq_resp
from obspy import UTCDateTime, read
from obspy.core.event import Amplitude, Pick, WaveformStreamID

from eqcorrscan.utils import sfile_util


[docs]def dist_calc(loc1, loc2): """ Function to calculate the distance in km between two points. Uses the flat Earth approximation. Better things are available for this, like `gdal <http://www.gdal.org/>`_. :type loc1: tuple :param loc1: Tuple of lat, lon, depth (in decimal degrees and km) :type loc2: tuple :param loc2: Tuple of lat, lon, depth (in decimal degrees and km) :returns: Distance between points in km. :rtype: float """ R = 6371.009 # Radius of the Earth in km dlat = np.radians(abs(loc1[0] - loc2[0])) dlong = np.radians(abs(loc1[1] - loc2[1])) ddepth = abs(loc1[2] - loc2[2]) mean_lat = np.radians((loc1[0] + loc2[0]) / 2) dist = R * np.sqrt(dlat ** 2 + (np.cos(mean_lat) * dlong) ** 2) dist = np.sqrt(dist ** 2 + ddepth ** 2) return dist
[docs]def calc_max_curv(magnitudes, plotvar=False): """ Calculate the magnitude of completeness using the maximum curvature method. :type magnitudes: list :param magnitudes: List of magnitudes from which to compute the maximum curvature which will give an estimate of the magnitude of completeness given the assumption of a power-law scaling. :type plotvar: bool :param plotvar: Turn plotting on and off :rtype: float :return: Magnitude at maximum curvature .. Note:: Should be used as a guide, often under-estimates Mc. .. rubric:: Example >>> from obspy.clients.fdsn import Client >>> from obspy import UTCDateTime >>> from eqcorrscan.utils.mag_calc import calc_max_curv >>> client = Client('IRIS') >>> t1 = UTCDateTime('2012-03-26T00:00:00') >>> t2 = t1 + (3 * 86400) >>> catalog = client.get_events(starttime=t1, endtime=t2, minmagnitude=3) >>> magnitudes = [event.magnitudes[0].mag for event in catalog] >>> calc_max_curv(magnitudes, plotvar=False) 3.1000000000000001 """ counts = Counter(magnitudes) df = np.zeros(len(counts)) mag_steps = np.zeros(len(counts)) grad = np.zeros(len(counts) - 1) grad_points = grad.copy() for i, magnitude in enumerate(sorted(counts.keys(), reverse=True)): mag_steps[i] = magnitude if i > 0: df[i] = counts[magnitude] + df[i - 1] else: df[i] = counts[magnitude] for i, val in enumerate(df): if i > 0: grad[i - 1] = (val - df[i - 1]) / (mag_steps[i] - mag_steps[i - 1]) grad_points[i - 1] = mag_steps[i] - ((mag_steps[i] - mag_steps[i - 1]) / 2.0) # Need to find the second order derivative curvature = np.zeros(len(grad) - 1) curvature_points = curvature.copy() for i, _grad in enumerate(grad): if i > 0: curvature[i - 1] = (_grad - grad[i - 1]) / (grad_points[i] - grad_points[i - 1]) curvature_points[i - 1] = grad_points[i] - ((grad_points[i] - grad_points[i - 1]) / 2.0) if plotvar: plt.scatter(mag_steps, df, c='k', label='Magnitude function') plt.plot(mag_steps, df, c='k') plt.scatter(grad_points, grad, c='r', label='Gradient') plt.plot(grad_points, grad, c='r') plt.scatter(curvature_points, curvature, c='g', label='Curvature') plt.plot(curvature_points, curvature, c='g') plt.legend() plt.show() return curvature_points[np.argmax(abs(curvature))]
[docs]def calc_b_value(magnitudes, completeness, max_mag=None, plotvar=True): """ Calculate the b-value for a range of completeness magnitudes. Calculates a power-law fit to given magnitudes for each completeness magnitude. Plots the b-values and residuals for the fitted catalogue against the completeness values. Computes fits using numpy.polyfit, which uses a least-squares technique. :type magnitudes: list :param magnitudes: Magnitudes to compute the b-value for. :type completeness: list :param completeness: list of completeness values to compute b-values for. :type max_mag: float :param max_mag: Maximum magnitude to attempt to fit in magnitudes. :type plotvar: bool :param plotvar: Turn plotting on or off. :rtype: list :return: List of tuples of (completeness, b-value, residual,\ number of magnitudes used) .. rubric:: Example >>> from obspy.clients.fdsn import Client >>> from obspy import UTCDateTime >>> from eqcorrscan.utils.mag_calc import calc_b_value >>> client = Client('IRIS') >>> t1 = UTCDateTime('2012-03-26T00:00:00') >>> t2 = t1 + (3 * 86400) >>> catalog = client.get_events(starttime=t1, endtime=t2, minmagnitude=3) >>> magnitudes = [event.magnitudes[0].mag for event in catalog] >>> b_values = calc_b_value(magnitudes, completeness=np.arange(3, 7, 0.2), ... plotvar=False) >>> round(b_values[4][1]) 1.0 """ b_values = [] # Calculate the cdf for all magnitudes counts = Counter(magnitudes) cdf = np.zeros(len(counts)) mag_steps = np.zeros(len(counts)) for i, magnitude in enumerate(sorted(counts.keys(), reverse=True)): mag_steps[i] = magnitude if i > 0: cdf[i] = cdf[i - 1] + counts[magnitude] else: cdf[i] = counts[magnitude] if not max_mag: max_mag = max(magnitudes) for m_c in completeness: if m_c >= max_mag or m_c >= max(magnitudes): warnings.warn('Not computing completeness at %s, above max_mag' % str(m_c)) break complete_mags = [] complete_freq = [] for i, mag in enumerate(mag_steps): if mag >= m_c <= max_mag: complete_mags.append(mag) complete_freq.append(np.log10(cdf[i])) if len(complete_mags) < 4: warnings.warn('Not computing completeness above ' + str(m_c) + ', fewer than 4 events') break fit = np.polyfit(complete_mags, complete_freq, 1, full=True) # Calculate the residuals according to the Wiemer & Wys 2000 definition predicted_freqs = [fit[0][1] - abs(fit[0][0] * M) for M in complete_mags] r = 100 - ((np.sum([abs(complete_freq[i] - predicted_freqs[i]) for i in range(len(complete_freq))]) * 100) / np.sum(complete_freq)) b_values.append((m_c, abs(fit[0][0]), r, str(len(complete_mags)))) if plotvar: fig, ax1 = plt.subplots() b_vals = ax1.scatter(zip(*b_values)[0], zip(*b_values)[1], c='k') resid = ax1.scatter(zip(*b_values)[0], [100 - b for b in zip(*b_values)[2]], c='r') ax1.set_ylabel('b-value and residual') plt.xlabel('Completeness magnitude') ax2 = ax1.twinx() ax2.set_ylabel('Number of events used in fit') n_ev = ax2.scatter(zip(*b_values)[0], zip(*b_values)[3], c='g') fig.legend((b_vals, resid, n_ev), ('b-values', 'residuals', 'number of events'), 'lower right') ax1.set_title('Possible completeness values') plt.show() return b_values
[docs]def _sim_WA(trace, PAZ, seedresp, water_level): """ Remove the instrument response from a trace and simulate a Wood-Anderson. Returns a de-meaned, de-trended, Wood Anderson simulated trace in it's place. Works in-place on data and will destroy your original data, copy the \ trace before giving it to this function! :type trace: obspy.core.trace.Trace :param trace: A standard obspy trace, generally should be given without pre-filtering, if given with pre-filtering for use with amplitude determiniation for magnitudes you will need to worry about how you cope with the response of this filter yourself. :type PAZ: dict :param PAZ: Dictionary containing lists of poles and zeros, the gain and the sensitivity. If unset will expect seedresp. :type seedresp: dict :param seedresp: Seed response information - if unset will expect PAZ. :type water_level: int :param water_level: Water level for the simulation. :returns: Trace of Wood-Anderson simulated data :rtype: :class:`obspy.core.trace.Trace` """ # Note Wood anderson sensitivity is 2080 as per Uhrhammer & Collins 1990 PAZ_WA = {'poles': [-6.283 + 4.7124j, -6.283 - 4.7124j], 'zeros': [0 + 0j], 'gain': 1.0, 'sensitivity': 2080} # De-trend data trace.detrend('simple') # Simulate Wood Anderson if PAZ: trace.data = seis_sim(trace.data, trace.stats.sampling_rate, paz_remove=PAZ, paz_simulate=PAZ_WA, water_level=water_level, remove_sensitivity=True) elif seedresp: trace.data = seis_sim(trace.data, trace.stats.sampling_rate, paz_remove=None, paz_simulate=PAZ_WA, water_level=water_level, seedresp=seedresp) else: UserWarning('No response given to remove, will just simulate WA') trace.data = seis_sim(trace.data, trace.stats.sampling_rate, paz_remove=None, paz_simulate=PAZ_WA, water_level=water_level) return trace
[docs]def _max_p2t(data, delta): """ Finds the maximum peak-to-trough amplitude and period. Originally designed to be used to calculate magnitudes (by \ taking half of the peak-to-trough amplitude as the peak amplitude). :type data: numpy.ndarray :param data: waveform trace to find the peak-to-trough in. :type delta: float :param delta: Sampling interval in seconds :returns: tuple of (amplitude, period, time) with amplitude in the same \ scale as given in the input data, and period in seconds, and time in \ seconds from the start of the data window. :rtype: tuple """ debug_plot = False turning_points = [] # A list of tuples of (amplitude, sample) for i in range(1, len(data) - 1): if (data[i] < data[i - 1] and data[i] < data[i + 1]) or\ (data[i] > data[i - 1] and data[i] > data[i + 1]): turning_points.append((data[i], i)) if len(turning_points) >= 1: amplitudes = np.empty([len(turning_points) - 1],) half_periods = np.empty([len(turning_points) - 1],) else: plt.plot(data) plt.show() print('Turning points has length: ' + str(len(turning_points)) + ' data have length: ' + str(len(data))) return 0.0, 0.0, 0.0 for i in range(1, len(turning_points)): half_periods[i - 1] = (delta * (turning_points[i][1] - turning_points[i - 1][1])) amplitudes[i - 1] = np.abs(turning_points[i][0] - turning_points[i - 1][0]) amplitude = np.max(amplitudes) period = 2 * half_periods[np.argmax(amplitudes)] if debug_plot: plt.plot(data, 'k') plt.plot([turning_points[np.argmax(amplitudes)][1], turning_points[np.argmax(amplitudes) - 1][1]], [turning_points[np.argmax(amplitudes)][0], turning_points[np.argmax(amplitudes) - 1][0]], 'r') plt.show() return amplitude, period, delta * turning_points[np.argmax(amplitudes)][1]
[docs]def _GSE2_PAZ_read(gsefile): """ Read the instrument response information from a GSE Poles and Zeros file. Formatted for files generated by the SEISAN program RESP. Format must be CAL2, not coded for any other format at the moment, contact the authors to add others in. :type gsefile: string :param gsefile: Path to GSE file :returns: Dictionary of poles, zeros, gain and sensitivity :rtype: dict """ with open(gsefile, 'r') as f: # First line should start with CAL2 header = f.readline() if not header[0:4] == 'CAL2': raise IOError('Unknown format for GSE file, only coded for CAL2') station = header.split()[1] channel = header.split()[2] sensor = header.split()[3] date = dt.datetime.strptime(header.split()[7], '%Y/%m/%d') header = f.readline() if not header[0:4] == 'PAZ2': raise IOError('Unknown format for GSE file, only coded for PAZ2') gain = float(header.split()[3]) # Measured in nm/counts kpoles = int(header.split()[4]) kzeros = int(header.split()[5]) poles = [] for i in range(kpoles): pole = f.readline() poles.append(complex(float(pole.split()[0]), float(pole.split()[1]))) zeros = [] for i in range(kzeros): zero = f.readline() zeros.append(complex(float(zero.split()[0]), float(zero.split()[1]))) # Have Poles and Zeros, but need Gain and Sensitivity # Gain should be in the DIG2 line: for line in f: if line[0:4] == 'DIG2': sensitivity = float(line.split()[2]) # measured in counts/muVolt PAZ = {'poles': poles, 'zeros': zeros, 'gain': gain, 'sensitivity': sensitivity} return PAZ, date, station, channel, sensor
[docs]def _find_resp(station, channel, network, time, delta, directory): """ Helper function to find the response information. Works for a given station and channel at a given time and return a dictionary of poles and zeros, gain and sensitivity. :type station: str :param station: Station name (as in the response files) :type channel: str :param channel: Channel name (as in the response files) :type network: str :param network: Network to scan for, can be a wildcard :type time: datetime.datetime :param time: Date-time to look for repsonse information :type delta: float :param delta: Sample interval in seconds :type directory: str :param directory: Directory to scan for response information :returns: dictionary of response information :rtype: dict """ possible_respfiles = glob.glob(directory + os.path.sep + 'RESP.' + network + '.' + station + '.*.' + channel) # GeoNet RESP naming possible_respfiles += glob.glob(directory + os.path.sep + 'RESP.' + network + '.' + channel + '.' + station) # RDseed RESP naming possible_respfiles += glob.glob(directory + os.path.sep + 'RESP.' + station + '.' + network) # WIZARD resp naming # GSE format, station needs to be 5 characters padded with _, channel is 4 # characters padded with _ station = str(station) channel = str(channel) possible_respfiles += glob.glob(directory + os.path.sep + station.ljust(5, str('_')) + channel[0:len(channel) - 1]. ljust(3, str('_')) + channel[-1] + '.*_GSE') PAZ = [] seedresp = [] for respfile in possible_respfiles: print('Reading response from: ' + respfile) if respfile.split(os.path.sep)[-1][0:4] == 'RESP': # Read from a resp file seedresp = {'filename': respfile, 'date': UTCDateTime(time), 'units': 'DIS', 'network': network, 'station': station, 'channel': channel, 'location': '*'} try: # Attempt to evaluate the response for this information, if not # then this is not the correct response info! freq_resp, freqs = evalresp(delta, 100, seedresp['filename'], seedresp['date'], units=seedresp['units'], freq=True, network=seedresp['network'], station=seedresp['station'], channel=seedresp['channel']) except: print('Issues with RESP file') seedresp = [] continue elif respfile[-3:] == 'GSE': PAZ, pazdate, pazstation, pazchannel, pazsensor =\ _GSE2_PAZ_read(respfile) # check that the date is good! if pazdate >= time and pazchannel != channel and\ pazstation != station: print('Issue with GSE file') print('date: ' + str(pazdate) + ' channel: ' + pazchannel + ' station: ' + pazstation) PAZ = [] else: continue # Check that PAZ are for the correct station, channel and date if PAZ or seedresp: break if PAZ: return PAZ elif seedresp: return seedresp
[docs]def _pairwise(iterable): """ Wrapper on itertools for SVD_magnitude. """ a, b = itertools.tee(iterable) next(b, None) if sys.version_info.major == 2: return itertools.izip(a, b) else: return zip(a, b)
[docs]def amp_pick_event(event, st, respdir, chans=['Z'], var_wintype=True, winlen=0.9, pre_pick=0.2, pre_filt=True, lowcut=1.0, highcut=20.0, corners=4, min_snr=1.0, plot=False, remove_old=False): """ Pick amplitudes for local magnitude for a single event. Looks for maximum peak-to-trough amplitude for a channel in a stream, and picks this amplitude and period. There are a few things it does internally to stabilise the result: 1. Applies a given filter to the data - very necessary for small magnitude earthquakes; 2. Keeps track of the poles and zeros of this filter and removes them from the picked amplitude; 3. Picks the peak-to-trough amplitude, but records half of this: the specification for the local magnitude is to use a peak amplitude on a horizontal, however, with modern digital seismometers, the peak amplitude often has an additional, DC-shift applied to it, to stabilise this, and to remove possible issues with de-meaning data recorded during the wave-train of an event (e.g. the mean may not be the same as it would be for longer durations), we use half the peak-to-trough amplitude; 4. Despite the original definition of local magnitude requiring the use of a horizontal channel, more recent work has shown that the vertical channels give more consistent magnitude estimations between stations, due to a reduction in site-amplification effects, we therefore use the vertical channels by default, but allow the user to chose which channels they deem appropriate; 5. We do not specify that the maximum amplitude should be the S-phase: The original definition holds that the maximum body-wave amplitude should be used - while this is often the S-phase, we do not discriminate against the P-phase. We do note that, unless the user takes care when assigning winlen and filters, they may end up with amplitude picks for surface waves; 6. We use a variable window-length by default that takes into account P-S times if available, this is in an effort to include only the body waves. When P-S times are not available we hard-wire a P-S at 0.34 x hypocentral distance. :type event: obspy.core.event.event.Event :param event: Event to pick :type st: obspy.core.stream.Stream :param st: Stream associated with event :type respdir: str :param respdir: Path to the response information directory :type chans: list :param chans: List of the channels to pick on, defaults to ['Z'] - should \ just be the orientations, e.g. Z,1,2,N,E :type var_wintype: bool :param var_wintype: If True, the winlen will be \ multiplied by the P-S time if both P and S picks are \ available, otherwise it will be multiplied by the \ hypocentral distance*0.34 - derived using a p-s ratio of \ 1.68 and S-velocity of 1.5km/s to give a large window, \ defaults to True :type winlen: float :param winlen: Length of window, see above parameter, if var_wintype is \ False then this will be in seconds, otherwise it is the \ multiplier to the p-s time, defaults to 0.5. :type pre_pick: float :param pre_pick: Time before the s-pick to start the cut window, defaults \ to 0.2 :type pre_filt: bool :param pre_filt: To apply a pre-filter or not, defaults to True :type lowcut: float :param lowcut: Lowcut in Hz for the pre-filter, defaults to 1.0 :type highcut: float :param highcut: Highcut in Hz for the pre-filter, defaults to 20.0 :type corners: int :param corners: Number of corners to use in the pre-filter :type min_snr: float :param min_snr: Minimum signal-to-noise ratio to allow a pick - see note \ below on signal-to-noise ratio calculation. :type plot: bool :param plot: Turn plotting on or off. :type remove_old: bool :param remove_old: If True, will remove old amplitude picks from event and overwrite with new picks. Defaults to False. :returns: Picked event :rtype: :class:`obspy.core.event.Event` .. Note:: Signal-to-noise ratio is calculated using the filtered data by \ dividing the maximum amplitude in the signal window (pick window) \ by the normalized noise amplitude (taken from the whole window \ supplied). """ # Hardwire a p-s multiplier of hypocentral distance based on p-s ratio of # 1.68 and an S-velocity 0f 1.5km/s, deliberately chosen to be quite slow ps_multiplier = 0.34 # Convert these picks into a lists stations = [] # List of stations channels = [] # List of channels picktimes = [] # List of pick times picktypes = [] # List of pick types distances = [] # List of hypocentral distances picks_out = [] if remove_old and event.amplitudes: for amp in event.amplitudes: # Find the pick and remove it too pick = [p for p in event.picks if p.resource_id == amp.pick_id][0] event.picks.remove(pick) event.amplitudes.remove(amp) for pick in event.picks: if pick.phase_hint in ['P', 'S']: picks_out.append(pick) # Need to be able to remove this if there # isn't data for a station! stations.append(pick.waveform_id.station_code) channels.append(pick.waveform_id.channel_code) picktimes.append(pick.time) picktypes.append(pick.phase_hint) arrival = [arrival for arrival in event.origins[0].arrivals if arrival.pick_id == pick.resource_id][0] distances.append(arrival.distance) st.merge() # merge the data, just in case! # For each station cut the window uniq_stas = list(set(stations)) del(arrival) for sta in uniq_stas: for chan in chans: print('Working on ' + sta + ' ' + chan) tr = st.select(station=sta, channel='*' + chan) if not tr: # Remove picks from file # picks_out=[picks_out[i] for i in range(len(picks))\ # if picks_out[i].station+picks_out[i].channel != \ # sta+chan] warnings.warn('There is no station and channel match in the ' 'wavefile!') continue else: tr = tr[0] # Apply the pre-filter if pre_filt: try: tr.split().detrend('simple').merge(fill_value=0) except: print('Some issue splitting this one') dummy = tr.split() dummy.detrend('simple') tr = dummy.merge(fill_value=0) try: tr.filter('bandpass', freqmin=lowcut, freqmax=highcut, corners=corners) except NotImplementedError: print('For some reason trace is not continuous:') print(tr) continue # Find the response information resp_info = _find_resp(tr.stats.station, tr.stats.channel, tr.stats.network, tr.stats.starttime, tr.stats.delta, respdir) PAZ = [] seedresp = [] if resp_info and 'gain' in resp_info: PAZ = resp_info elif resp_info: seedresp = resp_info # Simulate a Wood Anderson Seismograph if PAZ and len(tr.data) > 10: # Set ten data points to be the minimum to pass tr = _sim_WA(tr, PAZ, None, 10) elif seedresp and len(tr.data) > 10: tr = _sim_WA(tr, None, seedresp, 10) elif len(tr.data) > 10: warnings.warn('No PAZ for ' + tr.stats.station + ' ' + tr.stats.channel + ' at time: ' + str(tr.stats.starttime)) continue noise = tr.copy() # Copy the data to use for noise calculation sta_picks = [i for i in range(len(stations)) if stations[i] == sta] pick_id = event.picks[sta_picks[0]].resource_id arrival = [arrival for arrival in event.origins[0].arrivals if arrival.pick_id == pick_id][0] hypo_dist = arrival.distance if var_wintype and hypo_dist: if 'S' in [picktypes[i] for i in sta_picks] and\ 'P' in [picktypes[i] for i in sta_picks]: # If there is an S-pick we can use this :D S_pick = [picktimes[i] for i in sta_picks if picktypes[i] == 'S'] S_pick = min(S_pick) P_pick = [picktimes[i] for i in sta_picks if picktypes[i] == 'P'] P_pick = min(P_pick) try: tr.trim(starttime=S_pick - pre_pick, endtime=S_pick + (S_pick - P_pick) * winlen) except ValueError: continue elif 'S' in [picktypes[i] for i in sta_picks]: S_pick = [picktimes[i] for i in sta_picks if picktypes[i] == 'S'] S_pick = min(S_pick) P_modelled = S_pick - hypo_dist * ps_multiplier try: tr.trim(starttime=S_pick - pre_pick, endtime=S_pick + (S_pick - P_modelled) * winlen) except ValueError: continue else: # In this case we only have a P pick P_pick = [picktimes[i] for i in sta_picks if picktypes[i] == 'P'] P_pick = min(P_pick) S_modelled = P_pick + hypo_dist * ps_multiplier try: tr.trim(starttime=S_modelled - pre_pick, endtime=S_modelled + (S_modelled - P_pick) * winlen) except ValueError: continue # Work out the window length based on p-s time or distance elif 'S' in [picktypes[i] for i in sta_picks]: # If the window is fixed we still need to find the start time, # which can be based either on the S-pick (this elif), or # on the hypocentral distance and the P-pick # Take the minimum S-pick time if more than one S-pick is # available S_pick = [picktimes[i] for i in sta_picks if picktypes[i] == 'S'] S_pick = min(S_pick) try: tr.trim(starttime=S_pick - pre_pick, endtime=S_pick + winlen) except ValueError: continue else: # In this case, there is no S-pick and the window length is # fixed we need to calculate an expected S_pick based on the # hypocentral distance, this will be quite hand-wavey as we # are not using any kind of velocity model. P_pick = [picktimes[i] for i in sta_picks if picktypes[i] == 'P'] P_pick = min(P_pick) hypo_dist = [distances[i] for i in sta_picks if picktypes[i] == 'P'][0] S_modelled = P_pick + hypo_dist * ps_multiplier try: tr.trim(starttime=S_modelled - pre_pick, endtime=S_modelled + winlen) except ValueError: continue if len(tr.data) <= 10: # Should remove the P and S picks if len(tr.data)==0 warnings.warn('No data found for: ' + tr.stats.station) # print 'No data in miniseed file for '+tr.stats.station+\ # ' removing picks' # picks_out=[picks_out[i] for i in range(len(picks_out))\ # if i not in sta_picks] continue # Get the amplitude amplitude, period, delay = _max_p2t(tr.data, tr.stats.delta) # Calculate the normalized noise amplitude noise_amplitude = np.sqrt(np.mean(np.square(noise.data))) if amplitude == 0.0: continue if amplitude / noise_amplitude < min_snr: print('Signal to noise ratio of %s is below threshold.' % (amplitude / noise_amplitude)) continue if plot: plt.plot(np.arange(len(tr.data)), tr.data, 'k') plt.scatter(tr.stats.sampling_rate * delay, amplitude / 2) plt.scatter(tr.stats.sampling_rate * (delay + period), -amplitude / 2) plt.show() print('Amplitude picked: ' + str(amplitude)) print('Signal-to-noise ratio is: %s' % (amplitude / noise_amplitude)) # Note, amplitude should be in meters at the moment! # Remove the pre-filter response if pre_filt: # Generate poles and zeros for the filter we used earlier: this # is how the filter is designed in the convenience methods of # filtering in obspy. z, p, k = iirfilter(corners, [lowcut / (0.5 * tr.stats. sampling_rate), highcut / (0.5 * tr.stats. sampling_rate)], btype='band', ftype='butter', output='zpk') filt_paz = {'poles': list(p), 'zeros': list(z), 'gain': k, 'sensitivity': 1.0} amplitude /= (paz_2_amplitude_value_of_freq_resp(filt_paz, 1 / period) * filt_paz['sensitivity']) # Convert amplitude to mm if PAZ: # Divide by Gain to get to nm (returns pm? 10^-12) # amplitude *=PAZ['gain'] amplitude /= 1000 if seedresp: # Seedresp method returns mm amplitude *= 1000000 # Write out the half amplitude, approximately the peak amplitude as # used directly in magnitude calculations # Page 343 of Seisan manual: # Amplitude (Zero-Peak) in units of nm, nm/s, nm/s^2 or counts amplitude *= 0.5 # Append an amplitude reading to the event _waveform_id = WaveformStreamID(station_code=tr.stats.station, channel_code=tr.stats.channel, network_code=tr.stats.network) pick_ind = len(event.picks) event.picks.append(Pick(waveform_id=_waveform_id, phase_hint='IAML', polarity='undecidable', time=tr.stats.starttime + delay, evaluation_mode='automatic')) event.amplitudes.append(Amplitude(generic_amplitude=amplitude / 1e9, period=period, pick_id=event. picks[pick_ind].resource_id, waveform_id=event. picks[pick_ind].waveform_id, unit='m', magnitude_hint='ML', type='AML', category='point')) return event
[docs]def amp_pick_sfile(sfile, datapath, respdir, chans=['Z'], var_wintype=True, winlen=0.9, pre_pick=0.2, pre_filt=True, lowcut=1.0, highcut=20.0, corners=4, min_snr=1.0, plot=False, remove_old=False): """ Function to pick amplitudes for local magnitudes from NORDIC s-files. Reads information from a SEISAN s-file, load the data and the \ picks, cut the data for the channels given around the S-window, simulate \ a Wood Anderson seismometer, then pick the maximum peak-to-trough \ amplitude. Output will be put into a mag_calc.out file which will be in full S-file \ format and can be copied to a REA database. See docs for :func:`eqcorrscan.utils.mag_calc.amp_pick_event` for methods used here for stabilisation. :type sfile: str :param sfile: Path to NORDIC format s-file :type datapath: str :param datapath: Path to the waveform files - usually the path to the WAV \ directory :type respdir: str :param respdir: Path to the response information directory :type chans: list :param chans: List of the channels to pick on, defaults to ['Z'] - should \ just be the orientations, e.g. Z,1,2,N,E :type var_wintype: bool :param var_wintype: If True, the winlen will be \ multiplied by the P-S time if both P and S picks are \ available, otherwise it will be multiplied by the \ hypocentral distance*0.34 - derived using a p-s ratio of \ 1.68 and S-velocity of 1.5km/s to give a large window, \ defaults to True :type winlen: float :param winlen: Length of window, see above parameter, if var_wintype is \ False then this will be in seconds, otherwise it is the \ multiplier to the p-s time, defaults to 0.5. :type pre_pick: float :param pre_pick: Time before the s-pick to start the cut window, defaults \ to 0.2 :type pre_filt: bool :param pre_filt: To apply a pre-filter or not, defaults to True :type lowcut: float :param lowcut: Lowcut in Hz for the pre-filter, defaults to 1.0 :type highcut: float :param highcut: Highcut in Hz for the pre-filter, defaults to 20.0 :type corners: int :param corners: Number of corners to use in the pre-filter :type min_snr: float :param min_snr: Minimum signal-to-noise ratio to allow a pick - see note \ in amp_pick_event on signal-to-noise ratio calculation. :type plot: bool :param plot: Turn plotting on or off. :type remove_old: bool :param remove_old: If True, will remove old amplitude picks from event and overwrite with new picks. Defaults to False. :returns: Picked event :rtype: :class:`obspy.core.event.event.Event` """ # First we need to work out what stations have what picks event = sfile_util.readpicks(sfile) # Read in waveforms try: stream = read(os.path.join(datapath, sfile_util.readwavename(sfile)[0])) except IOError: stream = read(os.path.join(datapath, str(event.origins[0].time.year), str(event.origins[0].time.month).zfill(2), sfile_util.readwavename(sfile)[0])) if len(sfile_util.readwavename(sfile)) > 1: for wavfile in sfile_util.readwavename(sfile): try: stream += read(os.path.join(datapath, wavfile)) except IOError: stream += read(os.path.join(datapath, str(event.origins[0].time.year), str(event.origins[0].time.month). zfill(2), wavfile)) stream.merge() # merge the data, just in case! event_picked = amp_pick_event(event=event, st=stream, respdir=respdir, chans=chans, var_wintype=var_wintype, winlen=winlen, pre_pick=pre_pick, pre_filt=pre_filt, lowcut=lowcut, highcut=highcut, corners=corners, min_snr=min_snr, plot=plot, remove_old=remove_old) new_sfile = sfile_util.eventtosfile(event=event_picked, userID=str('EQCO'), evtype=str('L'), outdir=str('.'), wavefiles=sfile_util. readwavename(sfile)) shutil.move(new_sfile, 'mag_calc.out') return event_picked
[docs]def SVD_moments(U, s, V, stachans, event_list, n_SVs=4): """ Calculate relative moments/amplitudes using singular-value decomposition. Convert basis vectors calculated by singular value \ decomposition (see the SVD functions in clustering) into relative \ moments. For more information see the paper by \ `Rubinstein & Ellsworth (2010). <http://www.bssaonline.org/content/100/5A/1952.short>`_ :type U: list :param U: List of the :class:`numpy.ndarray` input basis vectors from the SVD, one array for each channel used. :type s: list :param s: List of the :class:`numpy.ndarray` of singular values, one array for each channel. :type V: list :param V: List of :class:`numpy.ndarray` of output basis vectors from SVD, one array per channel. :type stachans: list :param stachans: List of station.channel input :type event_list: list :param event_list: List of events for which you have data, such that \ event_list[i] corresponds to stachans[i], U[i] etc. and \ event_list[i][j] corresponds to event j in U[i]. These are a series \ of indexes that map the basis vectors to their relative events and \ channels - if you have every channel for every event generating these \ is trivial (see example). :type n_SVs: int :param n_SVs: Number of singular values to use, defaults to 4. :returns: M, array of relative moments :rtype: :class:`numpy.ndarray` :returns: events_out, list of events that relate to M (in order), \ does not include the magnitude information in the events, see note. :rtype: :class:`obspy.core.event.event.Event` .. note:: M is an array of relative moments (or amplitudes), these cannot be directly compared to true moments without calibration. .. rubric:: Example >>> from eqcorrscan.utils.mag_calc import SVD_moments >>> from obspy import read >>> import glob >>> import os >>> from eqcorrscan.utils.clustering import SVD >>> import numpy as np >>> # Do the set-up >>> testing_path = 'eqcorrscan/tests/test_data/similar_events' >>> stream_files = glob.glob(os.path.join(testing_path, '*')) >>> stream_list = [read(stream_file) for stream_file in stream_files] >>> event_list = [] >>> for i, stream in enumerate(stream_list): ... st_list = [] ... for tr in stream: ... if (tr.stats.station, tr.stats.channel) not in ... [('WHAT2', 'SH1'), ('WV04', 'SHZ'), ('GCSZ', 'EHZ')]: ... stream.remove(tr) ... continue ... tr.detrend('simple') ... tr.filter('bandpass', freqmin=5.0, freqmax=15.0) ... tr.trim(tr.stats.starttime + 40, tr.stats.endtime - 45) ... st_list.append(i) ... event_list.append(st_list) # doctest: +SKIP >>> event_list = np.asarray(event_list).T.tolist() >>> SVec, SVal, U, stachans = SVD(stream_list=stream_list) # doctest: +SKIP ['GCSZ.EHZ', 'WV04.SHZ', 'WHAT2.SH1'] >>> M, events_out = SVD_moments(U=U, s=SVal, V=SVec, stachans=stachans, ... event_list=event_list) # doctest: +SKIP """ # Define maximum number of events, will be the width of K K_width = max([max(ev_list) for ev_list in event_list]) + 1 # Sometimes the randomisation generates a singular matrix - rather than # attempting to regulerize this matrix I propose undertaking the # randomisation step a further time if len(stachans) == 1: print('Only provided data from one station-channel - ' 'will not try to invert') return U[0][:, 0], event_list[0] for i, stachan in enumerate(stachans): k = [] # Small kernel matrix for one station - channel # Copy the relevant vectors so as not to destroy them U_working = copy.deepcopy(U[i]) V_working = copy.deepcopy(V[i]) s_working = copy.deepcopy(s[i]) ev_list = event_list[i] if len(ev_list) > len(V_working): print('V is : ' + str(len(V_working))) f_dump = open('mag_calc_V_working.pkl', 'wb') pickle.dump(V_working, f_dump) f_dump.close() raise IOError('More events than represented in V') # Set all non-important singular values to zero s_working[n_SVs:len(s_working)] = 0 s_working = np.diag(s_working) # Convert to numpy matrices U_working = np.matrix(U_working) V_working = np.matrix(V_working) s_working = np.matrix(s_working) SVD_weights = U_working[:, 0] # If all the weights are negative take the abs if np.all(SVD_weights < 0): warnings.warn('All weights are negative - flipping them') SVD_weights = np.abs(SVD_weights) SVD_weights = np.array(SVD_weights).reshape(-1).tolist() # Shuffle the SVD_weights prior to pairing - will give one of multiple # pairwise options - see p1956 of Rubinstein & Ellsworth 2010 # We need to keep the real indexes though, otherwise, if there are # multiple events with the same weight we will end up with multiple # -1 values random_SVD_weights = np.copy(SVD_weights) # Tack on the indexes random_SVD_weights = random_SVD_weights.tolist() random_SVD_weights = [(random_SVD_weights[_i], _i) for _i in range(len(random_SVD_weights))] random.shuffle(random_SVD_weights) # Add the first element to the end so all elements will be paired twice random_SVD_weights.append(random_SVD_weights[0]) # Take pairs of all the SVD_weights (each weight appears in 2 pairs) pairs = [] for pair in _pairwise(random_SVD_weights): pairs.append(pair) # Deciding values for each place in kernel matrix using the pairs for pairsIndex in range(len(pairs)): # We will normalize by the minimum weight _weights = list(zip(*list(pairs[pairsIndex])))[0] _indeces = list(zip(*list(pairs[pairsIndex])))[1] min_weight = min(_weights) max_weight = max(_weights) min_index = _indeces[np.argmin(_weights)] max_index = _indeces[np.argmax(_weights)] row = [] # Working out values for each row of kernel matrix for j in range(len(SVD_weights)): if j == max_index: result = -1 elif j == min_index: normalised = max_weight / min_weight result = float(normalised) else: result = 0 row.append(result) # Add each row to the K matrix k.append(row) # k is now a square matrix, we need to flesh it out to be K_width k_filled = np.zeros([len(k), K_width]) for j in range(len(k)): for l, ev in enumerate(ev_list): k_filled[j, ev] = k[j][l] if 'K' not in locals(): K = k_filled else: K = np.concatenate([K, k_filled]) # Remove any empty rows K_nonempty = [] events_out = [] for i in range(0, K_width): if not np.all(K[:, i] == 0): K_nonempty.append(K[:, i]) events_out.append(i) K = np.array(K_nonempty).T K = K.tolist() K_width = len(K[0]) # Add an extra row to K, so average moment = 1 K.append(np.ones(K_width) * (1. / K_width)) print("\nCreated Kernel matrix: ") del row print('\n'.join([''.join([str(round(float(item), 3)).ljust(6) for item in row]) for row in K])) Krounded = np.around(K, decimals=4) # Create a weighting matrix to put emphasis on the final row. W = np.matrix(np.identity(len(K))) # the final element of W = the number of stations*number of events W[-1, -1] = len(K) - 1 # Make K into a matrix K = np.matrix(K) ############ # Solve using the weighted least squares equation, K.T is K transpose Kinv = np.array(np.linalg.inv(K.T * W * K) * K.T * W) # M are the relative moments of the events M = Kinv[:, -1] return M, events_out
[docs]def pick_db(indir, outdir, calpath, startdate, enddate, wavepath=None): """ Wrapper to loop through a SEISAN database and make a lot of magnitude \ picks. :type indir: str :param indir: Path to the seisan REA directory (not including yyyy/mm) :type outdir: str :param outdir: Path to output seisan REA directory (not including yyyy/mm) :type calpath: str :param calpath: Path to the directory containing the response files :type startdate: datetime.datetime :param startdate: Date to start looking for S-files :type enddate: datetime.datetime :param enddate: Date to stop looking for S-files :type wavepath: str :param wavepath: Path to the seisan WAV directory (not including yyyy/mm) """ kdays = ((enddate + dt.timedelta(1)) - startdate).days for i in range(kdays): day = startdate + dt.timedelta(i) print('Working on ' + str(day)) sfiles = glob.glob(os.path.join(indir, str(day.year), str(day.month).zfill(2), str(day.day).zfill(2) + '-*L.S' + str(day.year) + str(day.month).zfill(2))) datetimes = [dt.datetime.strptime(os.path.split(sfiles[i])[-1], '%d-%H%M-%SL.S%Y%m') for i in range(len(sfiles))] sfiles = [sfiles[i] for i in range(len(sfiles)) if startdate < datetimes[i] < enddate] if not wavepath: wavedir = os.path.join(os.path.split(indir), 'WAV', os.path.split(indir)[-1], str(day.year), str(day.month).zfill(2)) else: wavedir = os.path.join(wavepath, str(day.year), str(day.month).zfill(2)) sfiles.sort() for sfile in sfiles: # Make the picks! print('\tWorking on Sfile: ' + sfile) event = amp_pick_sfile(sfile, wavedir, calpath) del event # Copy the mag_calc.out file to the correct place shutil.copyfile('mag_calc.out', os.path.join(outdir, str(day.year), str(day.month).zfill(2), os.path.split(sfile)[-1]))
if __name__ == "__main__": import doctest doctest.testmod()