This notebook contains:
Read a seismic catalogue and pre-defined seismic sources.
Explore basic methods for qualitative analysis of the catalogue.
Declustering: Aftershocks and foreshocks identification and removal.
Completeness
Estimation of the Gutenberg-Richter parameters.
Exploration of some methods to estimate the maximum magnitude (statistically from the catalogue)
To use the toolkit features we need to import at the start of the session those tools that we are planning to use.
In [1]:
%load_ext autoreload
%autoreload 2
import warnings; warnings.filterwarnings('ignore')
In [2]:
%matplotlib inline
# Python dependences
import os
import numpy as np # Numpy - Python's numerical library
import matplotlib.pyplot as plt # Matplotlib - Python's plotting library
from copy import deepcopy # Python module for copying objects
# Input and Output Tools
# Catalogue and sources
from openquake.hmtk.parsers.catalogue import CsvCatalogueParser # Reads an earthquake catalogue from CSV
from openquake.hmtk.parsers.catalogue.csv_catalogue_parser import CsvCatalogueWriter # Writes an earthquake catalogue to CSV
from openquake.hmtk.parsers.source_model.nrml04_parser import nrmlSourceModelParser # Imports a source model from XML
# Plotting tools
from openquake.hmtk.plotting.mapping import HMTKBaseMap
from openquake.hmtk.plotting.seismicity.completeness import plot_stepp_1972
from openquake.hmtk.plotting.seismicity.catalogue_plots import plot_magnitude_time_scatter
from openquake.hmtk.plotting.seismicity.catalogue_plots import plot_depth_histogram
from openquake.hmtk.plotting.seismicity.catalogue_plots import plot_magnitude_time_density
from openquake.hmtk.plotting.seismicity.max_magnitude.cumulative_moment import plot_cumulative_moment
from openquake.hmtk.plotting.seismicity.occurrence.recurrence_plot import plot_recurrence_model
from openquake.hmtk.plotting.seismicity.catalogue_plots import (plot_observed_recurrence,
get_completeness_adjusted_table,
_get_catalogue_bin_limits)
# Seismicity tools: Events and declustering methods
from openquake.hmtk.seismicity.selector import CatalogueSelector
from openquake.hmtk.seismicity.declusterer.dec_afteran import Afteran
from openquake.hmtk.seismicity.declusterer.dec_gardner_knopoff import GardnerKnopoffType1
from openquake.hmtk.seismicity.declusterer.distance_time_windows import (GardnerKnopoffWindow,
GruenthalWindow,
UhrhammerWindow)
# Completeness tools
from openquake.hmtk.seismicity.completeness.comp_stepp_1971 import Stepp1971
# Seismicity tools: Recurrence methods
from openquake.hazardlib.mfd import TruncatedGRMFD
from openquake.hmtk.seismicity.occurrence.aki_maximum_likelihood import AkiMaxLikelihood
from openquake.hmtk.seismicity.occurrence.b_maximum_likelihood import BMaxLikelihood
from openquake.hmtk.seismicity.occurrence.kijko_smit import KijkoSmit
from openquake.hmtk.seismicity.max_magnitude.kijko_sellevol_bayes import KijkoSellevolBayes
from openquake.hmtk.seismicity.occurrence.weichert import Weichert
# Seismicity tools: Recurrence methods
from openquake.hmtk.seismicity.max_magnitude.kijko_sellevol_fixed_b import KijkoSellevolFixedb
from openquake.hmtk.seismicity.max_magnitude.kijko_sellevol_bayes import KijkoSellevolBayes
from openquake.hmtk.seismicity.max_magnitude.kijko_nonparametric_gaussian import KijkoNonParametricGaussian
from openquake.hmtk.seismicity.max_magnitude.cumulative_moment_release import CumulativeMoment
# Seismicity tools: Smoothed seismicity
from openquake.hmtk.seismicity.smoothing.smoothed_seismicity import SmoothedSeismicity
from openquake.hmtk.seismicity.smoothing.kernels.isotropic_gaussian import IsotropicGaussian
print "Everything Imported OK!"
Everything Imported OK!
Seismic catalogue format
The hmtk is able to read a catalogue in .csv format (Windows comma separated values). There are a minimum number of fields that are required to import and use the catalogue information into hmtk. The fields require:
eventID* Agency year* month* day* hour* minute* second* longitude* latitude* depth* magnitude*
The fields marked with a star are mandatory.
In [3]:
#Importing catalogue
catalogue_filename = 'input_data/Aegean_ExtendedCat1.csv'
parser = CsvCatalogueParser(catalogue_filename) # From .csv to hmtk
# Read and process the catalogue content in a variable called "catalogue"
catalogue = parser.read_file(start_year=1900, end_year=2012)
# How many events in the catalogue?
print "The catalogue contains %g events" % catalogue.get_number_events()
# What is the geographical extent of the catalogue?
bbox = catalogue.get_bounding_box()
print "Catalogue ranges from %.4f E to %.4f E Longitude and %.4f N to %.4f N Latitude\n" % bbox
Catalogue Attribute Identifier is not a recognised catalogue key
The catalogue contains 16401 events
Catalogue ranges from 18.5739 E to 32.0796 E Longitude and 32.7480 N to 42.5912 N Latitude
It is generally a good idea for the catalogue to be input in chronological order.
If the catalogue is not in chronological order then the following re-sorts the catalogue in-place to ensure it is in order
In [4]:
catalogue.sort_catalogue_chronologically()
To see how the distribution of magnitudes changes with time we can simply plot magnitude against time:
In [5]:
plot_magnitude_time_scatter(catalogue, plot_error=True)
Or, more informatively, plot the density of events with time
In [6]:
magnitude_bin_width = 0.1 # In magnitude units
time_bin_width = 1.0 # In years
plot_magnitude_time_density(catalogue, magnitude_bin_width, time_bin_width)
In [7]:
# Shows depth histogram every 5 km
plot_depth_histogram(catalogue, 5., normalisation=True)
We can map the catalogue using the HMTK's mapping functions. A 'basemap' can support multiple layers:
In [8]:
# Map configuration
llon, ulon, llat, ulat = catalogue.get_bounding_box()
map_config = {'min_lon': np.floor(llon), 'max_lon': np.ceil(ulon),
'min_lat': np.floor(llat), 'max_lat': np.ceil(ulat), 'resolution':'i'}
# Creating a basemap - input a cconfiguration and (if desired) a title
basemap1 = HMTKBaseMap(map_config, 'Earthquake Catalogue')
# Adding the catalogue to the basemap
# In this case we will 'close' the figure after rendering, we do this by setting 'overlay=False'
# This is also the default option
# If we wanted to add another layer on top, we would set the overlay to True
basemap1.add_catalogue(catalogue, overlay=False)
The HMTK supports several methods for declustering the earthquake catalogue:
Gardner & Knopoff (1974)
AFTERAN (Musson, 1999)
Others will (eventually) be added in the future
We illustrate the use of the Gardner & Knopoff Algorithm
In [9]:
# Create an `instance' of the tool
declust_method = GardnerKnopoffType1()
# Create a configuration file
declust_config = {"time_distance_window": GardnerKnopoffWindow(), "fs_time_prop": 1.0}
All declustering algorithms produce two outputs:
In [10]:
cluster_index, cluster_flag = declust_method.decluster(catalogue, declust_config)
data = np.column_stack([catalogue.get_decimal_time(),
catalogue.data['magnitude'],
catalogue.data['longitude'],
catalogue.data['latitude'], cluster_index, cluster_flag])
print ' Time Magnitude Long. Lat. Cluster No. Index (-1 = foreshock, 0 = mainshock, 1 = afterschock)'
for row in data:
print '%14.8f %6.2f %8.3f %8.3f %6.0f %6.0f' %(row[0], row[1], row[2], row[3], row[4], row[5])
Time Magnitude Long. Lat. Cluster No. Index (-1 = foreshock, 0 = mainshock, 1 = afterschock)
1904.25801837 7.50 23.250 41.750 0 0
1905.85457799 7.36 23.974 39.114 0 0
1908.37574169 6.80 24.000 35.000 0 0
1910.13209532 7.00 24.500 36.000 0 0
1910.63746480 6.50 27.000 34.000 0 0
1911.25659037 7.00 25.500 36.500 0 0
1911.32839136 6.20 30.000 36.000 0 0
1912.06470685 6.80 20.500 38.000 0 0
1912.30360827 5.80 19.500 37.500 0 0
1912.60399416 7.12 27.023 40.638 0 0
1913.74606887 5.80 24.000 35.000 0 0
1914.75594966 7.02 30.021 37.629 0 0
1914.79250856 5.60 23.500 38.250 0 0
1918.53927657 6.50 25.500 35.500 0 0
1919.88195380 6.51 26.530 39.498 0 0
1922.60916992 6.32 27.176 34.989 18 -1
1922.61371753 6.73 27.547 35.324 18 0
1923.58176649 5.62 25.160 34.786 0 0
1923.92841867 6.24 23.597 39.802 0 0
1925.51098919 6.50 21.750 38.250 0 0
1925.59803390 5.80 30.500 38.000 0 0
1926.20982930 6.85 29.521 36.021 0 0
1926.48444933 6.92 26.795 36.681 8 0
1926.50791838 5.50 27.000 36.500 8 1
1926.66160215 6.27 22.995 36.570 10 -1
1926.71519016 6.20 22.000 36.000 0 0
1927.42561828 6.20 31.000 36.000 0 0
1927.49683993 6.90 22.750 36.750 10 0
1928.24595828 6.40 27.494 38.202 0 0
1929.23375526 5.80 26.500 36.750 0 0
1929.59007588 5.60 31.000 36.000 0 0
1930.12267567 6.80 24.750 35.750 0 0
1930.17629699 5.80 26.000 34.500 0 0
1930.17640512 6.00 24.500 35.000 0 0
1930.69459044 6.00 31.000 37.000 0 0
1930.88790034 6.00 19.500 40.500 0 0
1931.00822054 5.60 23.000 38.000 0 0
1931.17811396 6.00 22.500 41.000 23 -1
1931.18103192 6.63 22.659 41.340 23 0
1931.49433777 5.50 23.000 36.500 0 0
1931.52858517 5.60 26.000 39.500 0 0
1932.18696266 5.60 20.500 38.000 0 0
1932.31987661 5.60 23.500 34.000 0 0
1932.36654691 5.60 28.500 36.000 0 0
1932.49208792 5.60 27.500 35.500 150 0
1932.62073973 5.50 22.000 39.250 0 0
1932.73717512 6.93 23.743 40.269 7 0
1932.74361989 6.33 23.408 40.794 7 1
1932.74660775 5.60 22.750 36.000 0 0
1932.81029255 5.60 27.250 35.250 150 1
1932.83519170 5.60 23.250 40.500 7 1
1933.30752970 6.32 27.292 36.751 0 0
1933.32311393 5.60 27.000 35.250 0 0
1933.35835201 6.26 23.537 40.575 7 1
1933.54750216 6.00 29.750 38.250 0 0
1934.09424537 5.60 19.250 41.500 0 0
1934.14105254 5.60 22.500 34.500 0 0
1934.18115826 5.60 26.000 33.250 0 0
1934.46515078 5.60 31.000 39.000 0 0
1934.85635642 6.20 25.750 36.750 0 0
1934.89023253 5.60 26.000 34.000 0 0
1935.00989639 6.40 27.481 40.652 39 0
1935.01008398 6.26 27.500 40.667 39 1
1935.15101145 6.80 25.000 35.750 0 0
1935.20920982 6.20 27.000 35.500 0 0
1936.32505205 5.80 26.750 36.750 0 0
1936.60157240 5.60 26.000 34.000 0 0
1937.00434557 5.60 25.000 35.000 0 0
1937.95817256 6.50 23.500 35.000 0 0
1938.04265078 5.20 28.000 36.500 0 0
1938.42107696 5.80 26.500 34.500 0 0
1938.54799007 5.80 23.750 38.250 0 0
1938.71276757 6.50 22.500 38.000 0 0
1939.38191663 5.60 19.500 41.000 0 0
1939.70676636 5.60 30.250 39.750 0 0
1939.71784535 6.50 20.500 38.000 0 0
1939.72335753 6.31 27.164 39.209 0 0
1940.16303829 6.00 25.500 35.500 0 0
1941.16208676 6.20 22.000 39.500 0 0
1941.36536596 5.60 23.000 39.500 0 0
1941.39130876 6.00 28.000 37.250 78 0
1941.39161758 5.60 28.000 37.250 78 1
1941.47845542 5.60 20.500 41.000 0 0
1941.53055464 5.60 26.250 38.000 0 0
1941.94866074 6.00 28.000 37.000 78 1
1942.35121217 5.80 26.000 35.500 0 0
1942.38398532 5.50 20.500 37.500 0 0
1942.46902343 6.20 27.000 36.500 51 0
1942.65276671 5.60 21.000 42.000 0 0
1943.01772213 5.50 20.500 38.500 0 0
1943.12140100 5.60 20.000 38.000 0 0
1943.46752832 6.20 30.000 41.000 0 0
1943.48608375 5.80 26.000 35.000 0 0
1943.79054202 6.20 27.500 36.500 51 1
1944.40435735 6.20 27.500 36.000 54 0
1944.60582995 5.50 27.500 36.500 54 1
1944.76258883 6.79 26.596 39.502 0 0
1945.66985150 6.50 28.500 33.750 0 0
1946.25992025 6.00 23.500 35.250 0 0
1947.42197473 6.00 24.000 40.000 0 0
1947.51490836 5.50 20.500 38.000 29 -1
1947.76391865 7.30 21.897 36.728 0 0
1948.10803416 7.30 27.153 35.631 0 0
1948.30723059 6.50 20.425 38.532 29 0
1948.49594209 6.44 20.532 38.992 29 1
1949.55788359 6.53 26.447 38.712 0 0
1952.96164249 6.50 24.346 34.474 0 0
1953.21040014 7.30 27.648 40.175 0 0
1953.60862341 6.53 20.846 38.301 14 -1
1953.61203185 6.81 20.942 38.182 14 0
1954.32751650 6.66 22.162 39.228 0 0
1955.53779920 6.57 27.284 37.617 0 0
1956.51948954 7.70 25.957 36.664 0 0
1957.18221900 6.41 22.701 39.323 27 1
1957.18223229 6.55 22.596 39.310 27 0
1957.31177749 7.10 28.829 36.493 3 -1
1957.31260598 7.30 28.699 36.405 3 0
1957.39800923 7.09 31.090 40.730 0 0
1959.87319027 6.65 20.568 37.844 22 0
1960.14567133 5.59 20.587 38.841 81 -1
1960.19534394 5.82 20.977 41.805 0 0
1960.39949584 6.22 20.629 40.619 0 0
1960.84657882 5.98 20.668 39.081 81 0
1960.86128482 5.58 20.681 38.724 81 1
1961.38935566 6.40 28.594 36.693 0 0
1961.75152547 5.64 21.882 36.579 0 0
1962.06944007 5.96 22.769 35.191 0 0
1962.20998971 6.13 19.626 40.723 0 0
1962.27370094 6.21 20.132 37.780 22 1
1962.27520458 5.53 20.074 37.648 22 1
1962.32183993 5.81 26.860 36.021 0 0
1962.69150768 5.58 26.780 34.587 0 0
1963.56487311 6.00 21.306 41.976 0 0
1963.71426610 6.20 29.159 40.698 48 0
1963.95773967 5.70 21.001 36.898 0 0
1964.02499696 4.28 21.000 38.700 0 0
1964.07906196 4.70 28.900 36.400 631 -1
1964.08125754 5.52 29.931 37.401 176 0
1964.08126954 4.28 29.700 37.400 176 1
1964.08303593 4.28 22.510 37.680 65 -1
1964.13212517 4.42 23.700 37.800 52 -1
1964.13263946 4.14 23.300 38.100 52 -1
1964.14739132 4.97 23.712 39.177 68 -1
1964.15017251 4.01 23.700 39.180 68 -1
1964.15019964 4.56 24.000 38.100 52 -1
1964.15021719 4.97 23.800 39.090 68 -1
1964.15592337 4.14 21.400 40.540 0 0
1964.17458220 4.01 24.100 34.580 50 -1
1964.20698469 4.42 23.200 34.900 0 0
1964.24356259 4.42 23.944 34.882 50 -1
1964.24599416 4.01 21.600 39.300 0 0
1964.24698923 4.83 28.780 36.430 631 0
1964.26937704 5.25 24.290 35.040 50 -1
1964.27777903 5.25 24.921 40.190 0 0
1964.27959557 3.87 25.000 39.800 0 0
1964.28926544 4.56 23.710 39.040 68 -1
1964.29442103 4.01 20.300 38.200 0 0
1964.29757305 4.01 29.000 41.100 48 1
1964.29913040 4.01 19.800 41.800 0 0
1964.30266686 4.14 24.460 35.090 50 -1
1964.30421740 4.14 22.200 38.300 16 -1
1964.31191156 4.01 21.300 37.980 0 0
1964.31434381 4.56 29.800 37.800 88 -1
1964.31565773 4.83 27.700 35.460 0 0
1964.31711418 4.28 26.200 34.400 0 0
1964.32563199 5.52 23.719 39.087 68 -1
1964.32707208 4.97 23.591 39.077 68 -1
1964.32712756 4.01 23.970 39.020 68 -1
1964.32993989 4.28 23.800 39.170 68 -1
1964.36533517 4.42 28.210 36.280 881 -1
1964.36805643 4.28 20.440 38.520 0 0
1964.37933219 4.01 24.290 36.950 0 0
1964.39849615 4.14 20.700 37.700 0 0
1964.43634081 4.56 28.260 36.260 881 0
1964.44624004 4.42 29.930 37.340 176 1
1964.45365041 4.42 25.700 34.600 310 -1
1964.50407686 3.87 23.800 39.000 68 -1
1964.50673820 4.56 23.430 41.960 0 0
1964.50875335 4.28 21.100 37.400 0 0
1964.51656978 4.01 21.800 35.100 0 0
1964.54026265 4.70 30.780 36.140 0 0
1964.54127671 6.20 23.640 38.092 52 0
1964.54413393 5.11 26.035 36.094 0 0
1964.61596484 4.14 25.600 34.200 310 -1
1964.62123877 2.63 28.000 33.900 1167 -1
1964.62571693 4.83 25.816 35.307 0 0
1964.62824482 4.14 25.600 34.800 650 -1
1964.64051100 4.01 30.600 36.930 0 0
1964.64728060 4.42 19.200 40.510 0 0
1964.64835354 4.56 28.760 35.500 521 1
1964.64846127 4.56 28.670 35.280 757 -1
1964.64881580 4.97 28.851 35.668 521 0
1964.64887472 4.56 28.580 35.350 757 -1
1964.64920611 4.83 28.778 35.541 521 1
1964.64958190 4.28 28.600 34.600 0 0
1964.64974310 4.01 28.500 34.300 0 0
1964.65522923 4.83 28.761 35.522 521 1
1964.65711579 4.42 19.950 37.800 0 0
1964.66070492 4.70 28.720 35.290 757 0
1964.66300961 4.42 21.600 37.300 65 -1
1964.66616509 4.28 20.200 36.100 0 0
1964.70205939 3.73 20.600 41.710 0 0
1964.71313143 4.83 28.834 35.541 521 1
1964.71331379 4.56 22.000 38.100 16 -1
1964.71581030 4.28 28.200 33.800 1167 0
1964.72189239 4.28 22.680 39.650 0 0
1964.74282901 4.28 29.200 36.700 0 0
1964.74344006 4.14 20.100 37.000 0 0
1964.74510486 4.01 23.700 38.900 68 -1
1964.74643248 4.83 23.207 34.462 646 0
1964.74709159 4.01 20.200 37.400 0 0
1964.75454890 4.28 23.100 34.200 646 1
1964.75944329 4.01 20.670 37.780 0 0
1964.75972192 3.87 19.700 40.150 0 0
1964.76394581 5.66 28.153 40.186 17 1
1964.76394853 6.80 28.177 40.159 17 0
1964.76766071 4.28 28.360 40.190 17 1
1964.77185611 4.28 24.600 34.700 50 -1
1964.78031361 4.14 28.600 35.200 757 1
1964.78261641 4.42 28.290 36.940 0 0
1964.79347008 4.83 25.380 34.964 650 0
1964.79388583 4.14 22.000 38.200 16 -1
1964.84664497 4.56 24.130 35.110 50 -1
1964.88604150 4.28 28.060 40.200 17 1
1964.90175141 5.25 25.400 34.400 310 0
1964.91647893 4.42 22.450 38.530 16 -1
1964.93926223 4.14 20.920 41.570 0 0
1964.93933355 4.28 20.920 41.200 1173 0
1964.94685757 4.28 22.600 34.900 0 0
1964.95387745 4.28 26.060 34.870 0 0
1964.95450200 4.14 20.900 40.500 0 0
1964.95594881 4.70 28.790 40.020 17 1
1964.96264562 3.73 28.700 35.600 521 1
1964.97004054 4.56 27.500 40.500 0 0
1964.97780635 3.87 20.770 41.090 1173 1
1964.99912354 4.97 25.516 35.826 0 0
1965.01762239 5.11 26.844 36.531 423 0
1965.02239697 4.28 27.400 36.000 89 -1
1965.02557622 4.28 22.000 38.700 16 -1
1965.03212714 3.87 21.700 37.190 65 -1
1965.04006215 4.14 21.800 36.970 0 0
1965.04425331 4.56 27.830 34.580 0 0
1965.07661868 4.14 23.100 42.500 0 0
1965.07941218 4.56 27.600 34.910 0 0
1965.09906386 4.70 27.040 35.410 0 0
1965.10920604 4.70 20.250 37.920 773 0
1965.10953756 4.42 20.280 37.790 773 1
1965.13958741 4.28 22.100 38.400 16 -1
1965.16689517 5.81 28.226 38.399 101 0
1965.16730842 4.42 28.470 38.270 101 1
1965.18345307 4.14 21.000 37.850 0 0
1965.18561253 6.10 23.860 39.197 68 0
1965.18565380 4.28 24.100 38.940 68 1
1965.18568851 5.25 23.935 39.232 68 1
1965.18571540 4.01 24.300 38.900 68 1
1965.18572948 3.59 22.400 38.500 16 -1
1965.18581997 4.97 23.860 39.120 68 1
1965.18587237 3.73 23.300 38.500 52 1
1965.18599710 4.42 23.870 39.190 68 1
1965.18610941 4.28 23.960 39.170 68 1
1965.18611863 4.28 22.600 36.200 0 0
1965.18614014 4.70 23.840 39.260 68 1
1965.18631002 3.73 23.760 39.190 68 1
1965.18648427 5.11 23.756 39.045 68 1
1965.18879439 4.56 23.940 39.350 68 1
1965.19499368 4.70 23.970 39.110 68 1
1965.19499554 5.25 23.756 39.020 68 1
1965.19556600 3.73 24.100 39.100 68 1
1965.19583905 4.56 23.970 39.130 68 1
1965.19631331 4.56 23.900 39.140 68 1
1965.19795438 4.28 20.200 39.900 0 0
1965.20264177 4.70 24.000 39.160 68 1
1965.20708717 4.28 28.100 38.100 101 1
1965.21148356 4.01 23.100 41.500 1239 1
1965.21318714 3.59 22.900 41.500 1239 1
1965.21365588 4.14 22.880 41.390 1239 0
1965.21956311 4.42 23.840 39.130 68 1
1965.22385514 4.28 22.500 36.600 0 0
1965.23247604 4.97 30.891 36.888 0 0
1965.24495345 6.80 22.405 38.365 16 0
1965.24520775 4.42 22.230 38.470 16 1
1965.24613475 4.42 24.100 39.200 68 1
1965.25266229 4.14 23.800 37.700 52 1
1965.25371157 4.70 20.500 38.240 0 0
1965.25376950 3.73 20.300 37.400 0 0
1965.25790128 6.10 22.067 37.505 65 0
1965.26350202 4.28 22.300 37.100 65 1
1965.26379156 3.73 24.400 35.000 50 -1
1965.26570351 4.14 27.700 38.100 0 0
1965.27090658 4.70 26.500 36.800 0 0
1965.27122740 6.20 24.318 35.047 50 0
1965.27127092 4.83 24.370 34.900 50 1
1965.27164222 3.73 26.200 36.200 0 0
1965.29261070 4.01 22.300 38.200 16 1
1965.29666393 4.42 28.360 34.560 0 0
1965.31942387 6.10 23.425 35.626 66 0
1965.32440439 4.70 26.890 37.140 740 0
1965.32899492 4.56 26.910 37.180 740 1
1965.33408186 4.56 23.520 35.610 66 1
1965.33507658 4.14 21.600 36.900 0 0
1965.34688425 4.42 26.860 36.740 423 1
1965.36405875 4.14 20.700 39.220 0 0
1965.36867314 4.01 21.900 37.400 65 1
1965.36880082 3.87 20.700 37.100 0 0
1965.37004564 4.56 27.827 35.290 0 0
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2010.76671076 4.01 21.581 42.428 1098 -1
2010.76847383 4.21 21.004 38.009 0 0
2010.77073906 3.45 21.575 42.424 1098 -1
2010.77149859 3.73 20.328 37.268 98 1
2010.77191835 2.90 27.242 35.351 60 -1
2010.77204117 4.41 22.708 38.147 1097 0
2010.77220633 3.32 21.579 42.431 1098 -1
2010.77480589 4.47 22.348 35.459 993 0
2010.77540829 4.41 21.602 42.435 1098 0
2010.77545653 2.90 23.286 35.180 0 0
2010.78460503 4.68 29.592 36.160 58 -1
2010.78693528 4.14 30.396 35.954 0 0
2010.79224186 4.07 27.250 35.482 60 -1
2010.79236095 3.32 27.188 35.524 60 -1
2010.79382627 4.54 20.583 39.390 919 1
2010.79389855 3.32 20.544 39.386 919 1
2010.80385988 3.18 26.049 38.860 0 0
2010.80695404 4.21 27.419 35.428 0 0
2010.80744899 4.07 24.573 34.671 694 1
2010.80893782 4.81 21.379 39.986 696 0
2010.80942310 3.87 22.006 38.720 1408 0
2010.81028164 3.04 25.180 33.982 33 1
2010.81053814 3.18 21.822 37.985 0 0
2010.81318406 3.45 19.997 37.067 0 0
2010.81445525 3.59 26.956 35.198 60 -1
2010.81457522 4.88 23.546 34.825 616 0
2010.81613405 3.45 20.365 38.060 0 0
2010.82175549 3.45 24.185 34.980 694 1
2010.82507310 3.87 20.138 37.337 98 1
2010.82623051 4.01 30.746 37.124 1357 0
2010.82729257 3.45 20.412 37.451 98 1
2010.82772062 4.01 28.514 37.033 1358 0
2010.83467273 3.04 28.252 36.944 1358 1
2010.83562471 3.18 21.410 36.748 0 0
2010.83565807 2.90 19.767 37.748 0 0
2010.83764033 3.45 28.815 37.089 1358 1
2010.83868238 5.30 26.296 40.413 265 0
2010.84082146 3.59 21.470 39.406 0 0
2010.84099537 2.63 29.496 35.487 0 0
2010.84260214 3.32 28.181 36.194 0 0
2010.84303833 3.45 20.378 37.347 98 1
2010.84321613 3.73 25.678 34.943 123 -1
2010.85022171 4.41 20.197 41.913 0 0
2010.85055798 3.32 30.569 37.211 1357 1
2010.85128611 3.18 20.334 38.362 1612 0
2010.85308649 3.04 23.915 40.186 0 0
2010.85596551 3.59 30.656 34.884 0 0
2010.85770514 3.18 25.321 34.809 123 -1
2010.85783701 3.45 22.456 40.006 0 0
2010.85959523 3.59 25.586 34.568 33 1
2010.86009830 3.04 24.652 34.639 694 1
2010.86247319 3.59 27.327 37.850 500 1
2010.86257236 5.00 27.373 37.863 500 0
2010.86544392 3.32 23.800 35.817 0 0
2010.86825259 3.32 31.205 36.806 0 0
2010.86910532 4.27 27.360 37.840 500 1
2010.87224015 3.18 20.427 38.370 1612 1
2010.87379500 3.45 20.305 37.401 98 1
2010.87538042 4.27 23.907 34.765 616 1
2010.87626559 3.18 25.339 33.752 33 1
2010.87835053 3.18 26.770 34.902 264 1
2010.88142270 3.73 23.312 34.804 616 1
2010.88916440 3.18 22.053 38.120 0 0
2010.88931209 3.18 20.307 37.355 98 1
2010.89066676 3.18 22.049 38.958 1408 1
2010.89397334 4.01 25.002 33.919 33 1
2010.90181237 3.32 20.421 39.333 0 0
2010.90839545 3.32 26.095 34.228 33 1
2010.90900578 3.18 20.319 37.360 98 1
2010.91087877 3.18 19.972 40.125 1616 0
2010.91480935 3.45 23.175 35.095 0 0
2010.92312221 3.73 29.980 34.726 0 0
2010.92372366 4.70 26.393 36.458 0 0
2010.92443230 3.73 22.080 35.749 0 0
2010.92526544 3.04 25.029 35.666 0 0
2010.92701177 3.45 26.137 34.254 1060 1
2010.92846808 2.90 20.178 40.182 1616 1
2010.92869155 4.94 28.601 35.314 0 0
2010.93618212 4.27 23.499 34.429 1211 0
2010.93645030 3.32 20.273 37.330 494 -1
2010.93674067 4.01 27.363 37.829 500 1
2010.93680377 3.32 20.319 37.332 494 -1
2010.93863971 3.18 21.571 38.083 0 0
2010.94239180 3.32 30.730 36.272 0 0
2010.94302800 4.01 21.473 40.612 0 0
2010.94509573 4.54 25.587 38.481 0 0
2010.94520195 3.45 20.431 40.037 0 0
2010.95001111 2.49 29.564 35.397 0 0
2010.95179021 4.14 21.534 35.485 1296 0
2010.95228098 3.73 22.787 38.061 1097 1
2010.95290059 3.45 21.465 36.593 995 -1
2010.95331431 3.87 28.053 36.599 1406 0
2010.95494641 3.59 21.503 35.403 1296 1
2010.95916836 3.32 23.783 34.496 1211 1
2010.95974394 3.04 20.032 40.135 1638 0
2010.96000342 4.70 23.990 36.962 0 0
2010.96136570 3.87 20.372 38.098 1318 -1
2010.96233966 5.01 20.294 37.347 494 0
2010.96319084 3.04 21.463 37.519 0 0
2010.97027792 2.90 29.191 37.640 0 0
2010.97466894 3.45 27.300 36.544 290 -1
2010.97552478 4.47 24.794 40.090 994 0
2010.97553324 3.45 24.780 40.066 994 1
2010.97579414 3.59 19.743 37.525 0 0
2010.97626052 3.45 20.633 38.334 1318 -1
2010.97821830 3.32 21.638 36.454 995 -1
2010.97945330 3.45 25.537 34.692 123 -1
2010.97994119 3.59 24.389 34.977 0 0
2010.98050589 3.04 27.777 35.226 0 0
2010.98082796 2.90 20.242 40.262 1638 1
2010.98414829 4.54 25.882 40.322 265 1
2010.99040584 3.32 25.666 34.266 33 1
2010.99174433 3.04 20.579 38.269 1318 -1
2010.99245437 3.59 20.795 39.437 0 0
2010.99306359 3.45 21.786 35.561 1296 1
2010.99419217 3.18 23.372 36.165 0 0
2010.99465417 3.32 23.598 35.099 616 1
2010.99681035 3.32 24.223 34.366 0 0
2010.99965301 2.90 27.396 40.584 0 0
2011.00001136 3.45 22.382 34.732 0 0
2011.00323136 3.87 28.688 34.050 0 0
2011.00441436 4.01 20.674 38.211 1318 0
2011.00456690 3.45 25.490 33.886 33 1
2011.00591708 3.18 21.534 35.466 1296 1
2011.00640378 3.59 25.522 33.884 33 1
2011.00653309 3.18 25.723 34.241 33 1
2011.00656205 3.59 21.817 37.583 0 0
2011.00885901 3.32 21.750 35.733 1137 -1
2011.00923579 3.18 24.194 34.789 1622 0
2011.01540812 3.59 21.981 36.001 0 0
2011.01657919 3.73 27.550 36.095 0 0
2011.02045219 4.54 25.737 33.934 33 1
2011.02196776 3.73 21.607 36.190 1137 -1
2011.02283776 3.18 21.438 39.105 823 -1
2011.02919858 3.32 22.203 38.751 0 0
2011.03048720 3.45 28.091 36.853 1406 1
2011.03110939 2.90 24.041 34.803 1622 1
2011.03534804 3.32 22.710 35.451 1563 1
2011.03542515 3.45 22.803 35.543 1563 0
2011.03811087 3.45 19.729 37.740 824 -1
2011.03811372 3.18 19.735 37.647 824 -1
2011.03942850 4.34 21.531 35.938 1137 0
2011.04021036 3.32 23.164 34.882 616 1
2011.04509523 3.04 20.247 38.950 0 0
2011.04597888 3.73 21.062 37.836 1451 -1
2011.05148316 4.14 20.385 39.458 1297 0
2011.05150754 3.45 20.339 39.454 1297 1
2011.05188502 2.90 31.228 36.066 0 0
2011.05230141 4.07 29.773 40.734 0 0
2011.05338589 4.41 23.442 39.552 1099 0
2011.05461169 3.18 21.527 38.585 859 -1
2011.05564275 3.45 31.732 35.420 0 0
2011.05697952 3.32 20.669 38.278 1318 1
2011.05924357 3.18 25.089 34.758 123 -1
2011.06177053 4.27 23.486 39.545 1099 1
2011.06313319 3.18 21.151 37.826 1451 -1
2011.07158736 3.04 23.088 36.263 0 0
2011.07466410 3.04 20.241 41.531 0 0
2011.07762950 3.73 21.580 35.911 1137 1
2011.07792235 3.45 26.664 35.518 60 -1
2011.08350616 3.59 20.350 37.337 364 -1
2011.08417663 3.04 22.713 37.878 0 0
2011.08419706 3.18 21.310 37.743 0 0
2011.08581278 3.04 25.625 33.976 33 1
2011.08693616 3.18 19.842 40.662 0 0
2011.08720013 3.59 21.790 38.393 859 -1
2011.08755734 3.32 23.488 39.541 1099 1
2011.09034721 3.32 23.125 35.284 1571 0
2011.09089348 3.18 23.146 35.361 1571 1
2011.09419171 3.73 21.224 38.042 1451 0
2011.09470763 3.32 19.486 41.794 0 0
2011.09560036 3.04 30.397 35.955 0 0
2011.09579943 4.68 27.342 37.892 500 1
2011.09619080 3.73 27.244 37.869 500 1
2011.09621889 3.32 22.042 38.416 859 -1
2011.09887555 4.27 27.290 37.856 500 1
2011.09950631 3.32 21.645 36.432 995 -1
2011.10226979 3.18 20.807 37.444 0 0
2011.10341093 3.18 26.798 35.863 60 -1
2011.10348497 3.87 26.935 36.624 290 -1
2011.10431235 4.47 23.250 34.910 616 1
2011.10456001 3.04 20.263 41.207 0 0
2011.10778764 3.18 22.486 38.648 0 0
2011.10899543 3.45 21.489 36.597 995 -1
2011.10985784 3.32 21.125 38.928 823 1
2011.10989026 4.68 21.079 38.935 823 0
2011.11080741 4.61 21.183 39.684 696 1
2011.11430040 4.47 21.483 36.704 995 0
2011.11437776 4.61 21.798 38.387 859 0
2011.11609027 3.04 21.800 38.402 859 1
2011.11614849 3.45 21.785 38.403 859 1
2011.11639577 3.45 21.771 38.389 859 1
2011.11784130 3.04 22.829 38.722 0 0
2011.11831092 2.76 23.801 35.092 616 1
2011.12160905 4.01 19.431 40.485 0 0
2011.12640824 3.32 19.848 37.858 824 -1
2011.12831842 3.32 26.380 34.889 264 1
2011.13681057 2.76 21.666 38.513 859 1
2011.13872052 4.68 19.903 37.863 824 0
2011.13920119 3.32 21.670 38.507 859 1
2011.13949257 3.73 21.671 38.502 859 1
2011.13974967 3.18 21.652 38.504 859 1
2011.13981662 3.04 19.684 37.656 824 1
2011.14337360 3.18 26.435 35.113 60 -1
2011.14422315 3.04 27.292 37.864 500 1
2011.14436389 3.18 19.763 37.768 824 1
2011.14481933 4.54 24.926 38.847 0 0
2011.14583229 4.54 26.576 34.435 0 0
2011.14659179 3.59 26.363 35.034 264 1
2011.14756755 3.73 21.825 36.011 1137 1
2011.14762973 3.59 21.846 35.995 1137 1
2011.14838069 3.18 23.457 39.552 1099 1
2011.14990723 4.68 24.813 34.607 0 0
2011.15062743 3.59 21.786 38.389 859 1
2011.15314579 3.59 27.166 36.590 290 -1
2011.15647856 3.18 20.503 42.097 0 0
2011.15979664 5.70 25.453 34.867 123 0
2011.24811491 6.17 26.670 35.490 60 0
2011.34872604 5.27 27.360 36.570 290 0
2011.38039463 5.93 29.110 39.080 84 0
2011.38043967 5.27 23.660 34.320 236 -1
2011.40340053 5.09 29.040 39.090 84 1
2011.48735543 5.04 29.130 39.070 84 1
2011.54602994 5.15 20.120 37.310 364 0
2011.56369361 5.12 27.720 40.800 0 0
2011.56826152 4.86 31.820 38.320 0 0
2011.59892613 5.00 21.990 38.210 0 0
2011.61656217 4.98 21.810 37.390 501 0
2011.63310586 5.10 21.600 37.840 0 0
2011.70049375 5.24 23.650 34.360 236 -1
2011.73837211 5.37 23.690 34.360 236 0
2011.77478511 4.87 21.870 37.110 501 1
2011.84896666 4.81 25.640 35.750 0 0
2011.89455452 5.49 25.070 34.170 33 1
2011.92697386 4.80 26.350 38.810 0 0
2012.06880880 5.25 24.900 35.920 203 -1
2012.07121550 5.45 24.880 35.890 203 0
2012.07763192 4.77 24.930 35.920 203 1
2012.12039819 5.22 24.060 40.060 251 -1
2012.17253179 5.32 24.010 40.070 251 0
2012.29091485 5.86 21.410 36.400 0 0
2012.31945500 4.85 29.250 39.090 84 1
2012.33228691 4.87 27.000 38.550 0 0
2012.33781202 5.27 29.170 39.060 84 1
2012.38797921 5.64 23.050 42.510 134 0
2012.38815052 4.87 23.120 42.510 134 1
2012.43407423 5.03 27.950 40.900 0 0
2012.44134090 6.17 29.060 36.280 58 0
2012.48236478 5.07 28.950 36.420 58 1
2012.50817135 5.03 26.730 34.870 0 0
2012.52071002 5.77 28.960 35.360 0 0
2012.59924922 4.91 23.880 34.280 211 -1
2012.69711554 5.41 24.040 34.350 211 0
2012.72231273 5.00 22.510 35.290 495 0
2012.72309374 4.82 22.640 35.140 495 1
2012.72448480 5.04 22.680 38.020 0 0
2012.72475708 4.85 20.710 40.000 0 0
2012.81049013 4.87 20.560 38.850 0 0
2012.81959011 4.84 23.030 38.810 0 0
2012.90364247 4.82 27.940 36.610 0 0
Having run the declustering algorithm you may want to remove all of the 'non-Poissonian' events (i.e. foreshocks and aftershocks) from the catalogue
In [11]:
# Copying the catalogue and saving it under a new name "catalogue_dec"(declustered catalogue)
catalogue_dec = deepcopy(catalogue)
# Logical indexing: Chossing the outputs for the main events: Cluster_flag = 0
mainshock_flag = cluster_flag == 0
# Filtering the foreshocks and aftershocks in the copy of the catalogue
catalogue_dec.purge_catalogue(mainshock_flag)
# Printing the number of events considered main shocks
print 'Declustering: ok'
print "Number of events in original catalogue: %g" % catalogue.get_number_events()
print 'Number of mainshocks: %g' % catalogue_dec.get_number_events()
Declustering: ok
Number of events in original catalogue: 16401
Number of mainshocks: 5754
In [12]:
basemap1 = HMTKBaseMap(map_config, 'Declustered Earthquake Catalogue')
basemap1.add_catalogue(catalogue_dec, overlay=False)
In [13]:
# Selecting path and name for the output file
output_cat_dec = 'output_data/aegean_cat_dec.csv'
if os.path.exists(output_cat_dec):
os.remove(output_cat_dec)
# Call the method and save the output file under the name "cat_csv"
cat_csv = CsvCatalogueWriter(output_cat_dec)
# Write the purged catalogue
cat_csv.write_file(catalogue_dec)
print "Catalogue successfully written to %s" % output_cat_dec
Catalogue successfully written to output_data/aegean_cat_dec.csv
In [ ]:
# Set up the configuration parameters
comp_config = {'magnitude_bin': 0.5, 'time_bin': 5.0, 'increment_lock': True}
# Calling the method
completeness_algorithm = Stepp1971()
# Use the catalogue and completeness configuration
completeness_table = completeness_algorithm.completeness(catalogue_dec, comp_config)
print 'Completeness: ok'
# Print the completeness table
print '\n'
print 'Completeness table using Stepp method (1971)'
print completeness_table
print '\n'
# Setting configuration for the completeness plot
completeness_parameters = completeness_algorithm
output_file = "output_data/Stepp_aegean.png"
if os.path.exists(output_file):
os.remove(output_file)
plot_stepp_1972.create_stepp_plot(completeness_parameters, output_file)
Completeness: ok
Completeness table using Stepp method (1971)
[[ 1970. 2. ]
[ 1970. 2.5]
[ 1970. 3. ]
[ 1970. 3.5]
[ 1966. 4. ]
[ 1965. 4.5]
[ 1965. 5. ]
[ 1965. 5.5]
[ 1928. 6. ]
[ 1899. 6.5]
[ 1896. 7. ]]
The hmtk allows to use a completeness table proposed by the modeller.
In [15]:
# Table format
completeness_table_a = np.array([[2000., 4.5],
[1964., 5.0],
[1960., 5.5],
[1900., 6.5]])
plot_magnitude_time_density(catalogue_dec, 0.1, 1.0,
completeness=completeness_table_a)
(2012.0, 4.5)
(2000.0, 4.5)
(1964.0, 5.0)
(1960.0, 5.5)
(1900.0, 6.5)
(1904.0, 6.5)
Several methods are available for estimating recurrence taking into account time-dependent completeness
In [16]:
recurrence_estimator = Weichert()
recurrence_config = {"magnitude_interval": 0.1}
bval, sigma_b, aval, sigma_a = recurrence_estimator.calculate(catalogue_dec,
recurrence_config,
completeness_table_a)
print "a = %.3f (+/- %.3f), b = %.3f (+/-%.3f)" % (aval, sigma_a, bval, sigma_b)
a = 5.377 (+/- 0.015), b = 0.867 (+/-0.024)
In [17]:
mfd0 = TruncatedGRMFD(4.5, 7.8, 0.1, aval, bval)
plot_recurrence_model(mfd0, catalogue_dec, completeness_table_a, 0.1)
The toolkit contains several tools for making statistical inferences on the maximum magnitude using the earthquake catalogue.
Three of these are based on the methods proposed by Kijko (2004):
KijkoSellevolFixedb - Maximum likelihood estimator of $M_{MAX}$ assuming no uncertainty in the b-value
KijkoSellevolBayes - Maximum likelihood estimator of $M_{MAX}$ assuming an uncertain b-value
KijkoNonParametricGaussian -Maximum likelihood estimator of $M_{MAX}$ assuming no specific magnitude frequency distribution
More details are given in the HMTK manual.
An additional method - based on cumulative moment release (adaptation of Makropolous & Burton (1983)) is also included
In [18]:
# Create the configuration
mmax_config = {
"input_mmin": 5.0,
"input_mmax": None, # It will take the maximum observed in the catalogue
"input_mmax_uncertainty": None, # It will take the uncertainty of the maximum observed in the catalogue
"b-value": bval,
"sigma-b": sigma_b
}
# Instantiate the tool
mmax_estimator = KijkoSellevolBayes()
# Execute!
mmax, sigma_mmax = mmax_estimator.get_mmax(catalogue_dec, mmax_config)
print "Maximum Magnitude (Estimated - KSB): %.3f +/- %.3f" % (mmax, sigma_mmax)
Maximum Magnitude (Estimated - KSB): 7.870 +/- 0.263
In [19]:
mmax_estimator2 = KijkoSellevolFixedb()
mmax2, sigma_mmax2 = mmax_estimator2.get_mmax(catalogue_dec, mmax_config)
print "Maximum Magnitude (Estimated - K-S-fixed-b): %.3f +/- %.3f" % (mmax2, sigma_mmax2)
(5.0, array(7.7), 658.0, 1.9956322345932438)
Maximum Magnitude (Estimated - K-S-fixed-b): 7.872 +/- 0.263
In [20]:
mfd0 = TruncatedGRMFD(4.5, mmax, 0.1, aval, bval)
plot_recurrence_model(mfd0, catalogue_dec, completeness_table_a, 0.1)
In [21]:
mmax_cm_config = {"number_bootstraps": 100}
mmax_estimator3 = CumulativeMoment()
mmax3, sigma_mmax3 = mmax_estimator3.get_mmax(catalogue_dec, mmax_cm_config)
print "Maximum Magnitude (Cumulative Moment): %.3f +/- %.3f" % (mmax3, sigma_mmax3)
mfd0 = TruncatedGRMFD(4.5, mmax3, 0.1, aval, bval)
plot_recurrence_model(mfd0, catalogue_dec, completeness_table_a, 0.1)
Maximum Magnitude (Cumulative Moment): 8.203 +/- 0.351
In [22]:
plot_cumulative_moment(catalogue_dec.data["year"], catalogue_dec.data["magnitude"])
In [ ]:
Content source: GEMScienceTools/notebooks
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