SPAR4DAS — early source-spectrum component

SPAR4DAS is developed by Mariano Supino for seismic source parameter estimation from distributed acoustic sensing (DAS) records. This small alpha release provides one usable component: the generalized Brune source-spectrum calculation used by SPAR. The full inversion software is still in development and is not included in this distribution.

Install and use

python -m pip install --pre spar4das

import numpy as np
from spar4das 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 convert raw strain or strain-rate measurements to moment, read waveform files, or estimate parameters. The alpha API may change as the complete SPAR4DAS package is developed.

License

GNU General Public License version 3 only; see LICENSE.