statseis package

Submodules

statseis.cartopy_maps module

statseis.geopandas_maps module

statseis.mc module

statseis.mc_lilliefors module

Routines for performing the Lilliefors test for exponentiality.

The Lilliefors test is performed as a function of lower magnitude cutoff. The provided p-value is eventually used to estimate a Mc-Lilliefors, which complies with the exponential Gutenberg–Richter relation to obtain a meaningful b-value.

The accompanied Jupyter notebook demonstrates the use of the class below.

Associated publication:

Herrmann, M. and W. Marzocchi (2020). “Inconsistencies and Lurking Pitfalls in the

Magnitude–Frequency Distribution of High-Resolution Earthquake Catalogs”. Seismological Research Letters 92(2A). doi: 10.1785/0220200337

copyright:

2020 Marcus Herrmann, Università degli Studi di Napoli ‘Federico II’

license:

European Union Public Licence (EUPL-1.2-or-later) (https://joinup.ec.europa.eu/collection/eupl/eupl-text-eupl-12)

class statseis.mc_lilliefors.McLilliefors(mags, signif_lev=0.1, log_level=20)

Bases: object

Class to perform the Lilliefors test for exponentiality (as function of Mc).

Note: this class is related and compatible to the FMD class in https://gitlab.seismo.ethz.ch/microEQ/TM/blob/master/TM/analysis.py#L910 , which also supports b-value estimation.

calc_testdistr_mcutoff(n_repeats=100, Mstart=None, log=True)

Get test distribution (e.g., p-value) as function of magnitude cutoff.

Parameters:

• n_repeats (int, optional) – Number of random initializations of noise added to mangitudes (which make the discrete magnitudes continuous), by default 100.

• Mstart (float, optional) – Overwrite minimum magnitude from where to start, by default starts at smallest magnitude present in the set.

• log (bool, optional) – Whether to log or not to log, by default True.

estimate_Mc_expon_test(mbin=None)

Get the magnitude of completeness using Lilliefors test of exponentiality.

This means: the Mc is determined as the lowest magnitude where the p-value is above

the significance level, i.e. where the exponential assumption is not rejected.

Here we will generally use the average p-value among several realizations of the random noise. For robustness, this average p-value must exceed the significance level for at least 0.05 magnitude units, in which case the first exceedance, i.e., the smallest magnitude bin, yields the eventual Mc-Lilliefors.

Parameters:

mbin (float, optional) – Overwrite the “binning”. Defaults to the magnitude binning.

Returns:

The estimated magnitude of completeness

Return type:

float

get_test_distribution(mags=None, Mc=None, n_repeats=100)

Perform a test several times and return its distribution.

Every repetition is performed with a newly sampled random noise that is added to the magnitudes.

lilliefors_test(mags=None, log=True)

Perform a Lilliefors hypothesis test for exponentiality.

Parameters:

• mags (1-D array_like, optional) – The magnitude set. Defaults to the magnitude set of this FMD object.

• log (bool, optional) – Whether to output the test results to stdout, by default True. Only useful to switch off for batch-processing tests.

Returns:

p-value of the hypothesis test.

Return type:

float

plot_testdist_expon_mcutoff(color='#000000', name=None, legendgroup=None, asfig=True)

Plot test distribution (e.g., p-value) as function of magnitude cutoff.

Plots the mean, min/max, and +/- std curves.

Parameters:

• color (str, optional) – The color to use, by default ‘#000000’ (black).

• name (str, optional) – The name in the legend entry, by default None.

• legendgroup (bool, int, or string, optional) – Whether to group all curves into one group, by default None. And if yes, in which (needs to be specified as an integer, i.e. the group id).

• asfig (bool, optional) – Whether to return a plotly Figure instance (True), or only a dict (False). Defaults to True.

Returns:

plotly Figure instance or a dictionary to be converted into a plotly Figure.

Return type:

plotly.graph_objs._figure.Figure or dict

update_mags(mags)

Update the magnitude vector.

Also recalculates n_ev property.

statseis.statseis module

statseis.utils module

Utility funcitons

statseis.utils.add_distance_to_position_haversine(lon, lat, distance_km_horizontal, distance_km_vertical)

Returns the a point shifted in km by the value of its arguments using the haversine method

statseis.utils.add_distance_to_position_pyproj(lon, lat, distance_km_horizontal, distance_km_vertical)

Returns the a point shifted in km by the value of its arguments using the Pyproj module

statseis.utils.calculate_distance_pyproj_vectorized(lon1, lat1, lon2_array, lat2_array, ellipsoid='WGS84')

Returns the distance (km) from a point to an array of points using the Pyproj module

statseis.utils.convert_extent_to_epsg3857(extent)

statseis.utils.datetime_to_decimal_days(DATETIMES)

Durn datetime objects to decimal days

statseis.utils.datetime_to_decimal_year(timestamps)

Turn datetime objects to decimal years

statseis.utils.estimate_axis_labels(array, n_labels=5)

Failed attempt to automaticallly generate better axis labels than matplotlib

statseis.utils.find_event_in_catalog(ID, catalog)

statseis.utils.find_nearest(array, value, index=False)

Returns the nearest value in an array to its argument.

statseis.utils.get_CDF(data)

statseis.utils.get_bins(numbers, nearest=10)

Returns optimal bins for plotting a histogram.

statseis.utils.get_catalogue_extent(catalogue, buffer=None)

Returns the min/max of the Lon/Lat of an earthquake catalogue

statseis.utils.haversine(lon1, lat1, lon2, lat2)

Calculate the great circle distance in kilometers between two points on the earth (specified in decimal degrees)

statseis.utils.haversine_vectorised(lon1, lat1, lon2, lat2)

Returns the distance (km) from a point to an array of points using the haversine method

statseis.utils.magnitude_to_moment(magnitude)

Covert moment magnitude to seismic moment

statseis.utils.min_max_median_mean(numbers)

Returns the min, max, median, and mean of a list of numbers

statseis.utils.no_nans_or_infs(res_file, metric=None)

statseis.utils.read_in_convert_datetime(path)

Read in a CSV of source parameters with datetimes (not strings).

statseis.utils.reformat_catalogue(df)

standardise column names, must feed in dataframe with columns: [‘ID’, ‘MAGNITUDE’, ‘DATETIME’, ‘DEPTH’, ‘LON’, ‘LAT’]

statseis.utils.restrict_catalogue_geographically(df, region)

Returns catalogue within LON/LAT region of interest

statseis.utils.select_within_box(LON, LAT, df, r)

statseis.utils.string_to_datetime(list_of_datetimes, format='%Y-%m-%d %H:%M:%S')

Turn datetimes from string into datetime objects

statseis.utils.string_to_datetime_df(dataframe, format='%Y-%m-%d %H:%M:%S.%f')

Find DATETIME column in df and change to datetime objects

statseis.utils.string_to_datetime_return(dataframe, format='%Y-%m-%d %H:%M:%S')

Find DATETIME column in df and change to datetime objects Returns dataframe so function can be mapped

Module contents