Magnitude

Magnitude estimation methods.

mag module

Magnitude calculation utilities for local magnitude (Ml) and moment magnitude (Mw) estimation.

This module provides tools for:

  • Selecting waveform streams according to channel/location preferences.

  • Calculating local magnitude (Ml).

  • Calculating moment magnitude (Mw).

  • Managing waveform retrieval and response selection.

The implementation is based partially on:

author:

Emmanuel Castillo

copyright:

Lion Krischer (2012)

license:

Original concepts adapted from ObsPy-based implementations.

Example

>>> from obspy.core.event import read_events
>>> catalog = read_events("catalog.xml")
>>> magnitude = Magnitude(providers, catalog, "./output")
class SeisMonitor.monitor.magnitude.mag.Magnitude(providers, catalog, out_dir)[source]

Bases: object

Magnitude calculator for seismic events.

Parameters:

  • providers (list) – List of waveform providers.

  • catalog (str or obspy.Catalog) – Catalog object or path to QuakeML file.

  • out_dir (str) – Output directory for generated magnitude files.

get_Ml(mag_type='RSNC', trimmedtime=50, padding=20, waterlevel=10, zone=None, out_format='QUAKEML')[source]

Calculate local magnitude (Ml) for all events.

Parameters:

  • mag_type (str, optional) – Magnitude relationship type.

  • trimmedtime (float, optional) – Signal trimming window in seconds.

  • padding (float, optional) – Waveform retrieval padding.

  • waterlevel (float, optional) – Water level for response correction.

  • zone (str, optional) – Regional magnitude zone.

  • out_format (str, optional) – Output catalog format.

Returns:

Updated catalog with Ml magnitudes.

Return type:

obspy.Catalog

get_Mw(physparams, procparams, out_format='QUAKEML')[source]

Calculate moment magnitude (Mw).

Parameters:
Returns:

Updated catalog with Mw magnitudes.

Return type:

obspy.Catalog

class SeisMonitor.monitor.magnitude.mag.MwPhysicalMagParams(vp=4800, vsp_factor=1.73, density=2650.0, waterlevel=10, p_radiation_pattern=0.52, s_radiation_pattern=0.63)[source]

Bases: object

Physical parameters used during Mw calculation.

Parameters:

  • vp (float, optional) – P-wave velocity in m/s.

  • vsp_factor (float, optional) – Vp/Vs ratio.

  • density (float, optional) – Density in kg/m³.

  • waterlevel (float, optional) – Water level for deconvolution stabilization.

  • p_radiation_pattern (float, optional) – Radiation pattern coefficient for P waves.

  • s_radiation_pattern (float, optional) – Radiation pattern coefficient for S waves.

class SeisMonitor.monitor.magnitude.mag.MwProcessingMagParams(time_before_pick=5, time_after_pick=30, padding=40, only_proc_p_pick=False, only_proc_s_pick=False)[source]

Bases: object

SeisMonitor.monitor.magnitude.mag.get_st_according2preference(st, location_list, channel_list)[source]

Select a preferred stream according to location and channel priorities.

The function filters streams first by location preference and then by channel preference.

Parameters:

  • st (obspy.Stream) – Input waveform stream.

  • location_list (list of str) – Preferred locations ordered by priority.

  • channel_list (list of str) – Preferred channel codes ordered by priority.

Returns:

Filtered stream according to preferences.

Return type:

obspy.Stream or None

Example

>>> new_st = get_st_according2preference(
...     st,
...     ["00", "20"],
...     ["HH", "BH"]
... )

utils module

Utilities for seismic magnitude estimation and ObsPy event object creation.

This module provides helper functions for:

  • Retrieving poles and zeros (PAZ) from ObsPy responses.

  • Computing local magnitudes (Ml).

  • Processing waveforms for magnitude estimation.

  • Fitting seismic source spectra.

  • Creating ObsPy magnitude and amplitude objects.

author:

Emmanuel Castillo

SeisMonitor.monitor.magnitude.utils.Mw_st_processing(st, response, waterlevel, datetime)[source]

Remove instrument response for moment magnitude estimation.

Parameters:

  • stream – ObsPy Stream object.

  • response – ObsPy response object.

  • water_level – Water level used during deconvolution.

  • datetime – Datetime associated with traces.

Returns:

Processed ObsPy Stream or None if failed.

SeisMonitor.monitor.magnitude.utils.calculate_source_spectrum(frequencies, omega_0, corner_frequency, Q, traveltime)[source]

After Abercrombie (1995) and Boatwright (1980).

Abercrombie, R. E. (1995). Earthquake locations using single-station deep borehole recordings: Implications for microseismicity on the San Andreas fault in southern California. Journal of Geophysical Research, 100, 24003–24013.

Boatwright, J. (1980). A spectral theory for circular seismic sources, simple estimates of source dimension, dynamic stress drop, and radiated energy. Bulletin of the Seismological Society of America, 70(1).

The used formula is:

Omega(f) = (Omege(0) * e^(-pi * f * T / Q)) / (1 + (f/f_c)^4) ^ 0.5

Parameters:

  • frequencies – Input array to perform the calculation on.

  • omega_0 – Low frequency amplitude in [meter x second].

  • corner_frequency – Corner frequency in [Hz].

  • Q – Quality factor.

  • traveltime – Traveltime in [s].

SeisMonitor.monitor.magnitude.utils.fit_spectrum(spectrum, frequencies, traveltime, initial_omega_0, initial_f_c, quality_factor=500)[source]

Fit a theoretical source spectrum to a measured source spectrum.

Uses a Levenburg-Marquardt algorithm.

Parameters:

  • spectrum – The measured source spectrum.

  • frequencies – The corresponding frequencies.

  • initial_omega_0 – Initial guess for Omega_0.

  • initial_f_c – Initial guess for the corner frequency.

Para traveltime:

Event traveltime in [s].

Returns:

Best fits and standard deviations. (Omega_0, f_c, Omega_0_std, f_c_std) Returns None, if the fit failed.

SeisMonitor.monitor.magnitude.utils.get_M0_magnitude_by_pick(st, picktime, traveltime, phasehint, physparams, procparams)[source]

Estimate seismic moment (M0) from waveform picks.

The function computes multitaper spectra for each component, fits a theoretical source spectrum, and estimates seismic moment.

Parameters:

  • stream – ObsPy Stream object containing three-component data.

  • pick_time – Pick time associated with the phase.

  • travel_time (float) – Seismic travel time in seconds.

  • phase_hint (str) – Seismic phase identifier (e.g. "P" or "S").

  • physical_parameters – Object containing physical properties such as: vp, vs, density, p_radiation_pattern, s_radiation_pattern.

  • processing_parameters – Object containing processing configuration such as: time_before_pick and time_after_pick.

Returns:

Tuple containing:

  • Seismic moment (M0)

  • List of estimated corner frequencies

Returns (None, None) if estimation fails.

Return type:

Tuple[Optional[float], Optional[List[float]]]

SeisMonitor.monitor.magnitude.utils.get_Ml(ampl, epi_dist, mag_type, zone=None)[source]

Compute local magnitude (Ml).

Supports predefined empirical relationships or custom functions.

Parameters:

  • amplitude (float) – Peak amplitude.

  • epicentral_distance (float) – Epicentral distance in kilometers.

  • magnitude_type (Union[str, Callable]) – Magnitude model name or callable.

  • zone (Optional[int]) – Regional zone identifier.

Returns:

Computed local magnitude.

Return type:

float

SeisMonitor.monitor.magnitude.utils.get_Ml_magparams_by_station(st, response, ev_params, trimmedtime=50, waterlevel=10)[source]

Compute local magnitude (Ml).

Supports predefined empirical relationships or custom functions.

Parameters:

  • amplitude (float) – Peak amplitude.

  • epicentral_distance (float) – Epicentral distance in kilometers.

  • magnitude_type (Union[str, Callable]) – Magnitude model name or callable.

  • zone (Optional[int]) – Regional zone identifier.

Returns:

Computed local magnitude.

Return type:

float

SeisMonitor.monitor.magnitude.utils.get_paz_from_response(seed_id, response, datetime=None)[source]

Retrieve poles and zeros (PAZ) from a response object.

Supports both ObsPy Parser and Inventory response types.

Parameters:

  • seed_id (str) – Full SEED identifier.

  • response (Union[Parser, Inventory]) – ObsPy response object.

  • datetime (Optional[UTCDateTime]) – Datetime associated with waveform trace.

Returns:

Dictionary containing PAZ information or None if unavailable.

Return type:

Optional[Dict]

Example

>>> paz = get_paz_from_response("IU.ANMO..BHZ", inventory)
SeisMonitor.monitor.magnitude.utils.write_amplitude_values(value, amp_type='A', category='duration', unit='m/s', method_id='https://docs.obspy.org/tutorial/advanced_exercise/advanced_exercise_solution_3b.html', time_window=obspy.core.event.base.TimeWindow, pick_id=obspy.core.event.resourceid.ResourceIdentifier, waveform_id=obspy.core.event.base.WaveformStreamID, magnitude_hint='M', evaluation_mode='automatic', evaluation_status='preliminary', agency=None)[source]

Create an ObsPy Amplitude object.

Parameters:

value (float) – Measured amplitude value.

Returns:

ObsPy Amplitude object.

Return type:

Amplitude

SeisMonitor.monitor.magnitude.utils.write_magnitude_values(value, uncertainty, station_count, mag_type, evaluation_mode='automatic', evaluation_status='preliminary', method_id=obspy.core.event.resourceid.ResourceIdentifier, agency=None, origin_id=obspy.core.event.resourceid.ResourceIdentifier, comments=None)[source]

Create an ObsPy Magnitude object.

Parameters:

  • value (float) – Magnitude value.

  • uncertainty (float) – Magnitude uncertainty.

  • station_count (int) – Number of stations used.

  • magnitude_type (str) – Magnitude type (e.g. "Mw", "Ml").

  • comments (Optional[str]) – Optional comments associated with the magnitude.

Returns:

ObsPy Magnitude object.

Return type:

Magnitude

SeisMonitor.monitor.magnitude.utils.write_magsta_values(value, uncertainty, mag_type, origin_id=obspy.core.event.resourceid.ResourceIdentifier, amplitude_id=obspy.core.event.resourceid.ResourceIdentifier, method_id=obspy.core.event.resourceid.ResourceIdentifier, waveform_id=obspy.core.event.base.WaveformStreamID, agency=None)[source]

Create an ObsPy StationMagnitude object.

Parameters:

  • value (float) – Station magnitude value.

  • uncertainty (float) – Magnitude uncertainty.

  • magnitude_type (str) – Magnitude type (e.g. "Ml").

Returns:

ObsPy StationMagnitude object.

Return type:

StationMagnitude