SPARspec — early source-spectrum component

SPAR is developed by Mariano Supino to estimate earthquake source parameters from seismic amplitude spectra. SPARspec is an early distribution of a small component of this project: its generalized Brune source-spectrum calculation. The full SPAR inversion software is still in development and is not included in this distribution.

This alpha provides the same source-spectrum calculation as the initial spar4das alpha, under the sparspec Python namespace. The model is relevant to the moment-equivalent spectra used for both conventional instruments and distributed acoustic sensing (DAS).

Install and use

python -m pip install --pre sparspec

import numpy as np
from sparspec import log_moment_spectrum

frequencies_hz = np.array([0.0, 1.0, 4.0, 10.0])
log_amplitude = log_moment_spectrum(
    frequencies_hz, log_m0=12.7, fc_hz=4.0, gamma=2.0, t_star_s=0.02
)
amplitude_nm = 10.0 ** log_amplitude

The model returns

log10 A(f) = log10 M0 - log10[1 + (f/fc)^gamma] - pi*f*t_star*log10(e)

Here M0 is seismic moment in N m, fc is corner frequency in Hz, gamma is the high-frequency decay exponent, and t_star is effective attenuation time in seconds. For fixed Q it may be specified as travel time divided by Q, plus any separately justified kappa term. All parameters except frequency are scalars. Frequencies must be finite and nonnegative; corner frequency and gamma must be positive; attenuation time must be nonnegative.

This is a moment-equivalent spectral model. It does not read waveform files, convert raw instrument or DAS measurements to moment, or estimate parameters. The alpha API may change as the complete SPAR package is developed.

License

GNU General Public License version 3 only; see LICENSE.