About

RESTORE is a Python tool tackling the short-term aftershock incompleteness issue (STAI). It is based on a stochastic gap-filling procedure which reconstructs the missing events in the space-time-magnitude domain based on empirical earthquake properties. The subsets of the catalog affected by the STAI issue are automatically detected.

To run

Set the input parameters in the input_file.txt file:

• size: moving-window size (in number of events per window) --> 1000 by default (Mignan and Woessner, 2012).
• step: moving-window step (in number of events per step) --> 250 by default (Mignan and Woessner, 2012).
• st_dev_multiplier: multiplies the Mc standard deviation (Mc Sigma), controls the confidence level for STAI gaps identification; STAI gaps are windows where mc >= mc_ok + n*sigma, where n = st_dev_multiplier; increasing the value of st_dev_multiplier results in a more conservative approach in detecting temporary deviations of Mc.
• Sigma: smoothing distance of the Gaussian kernel, controls the spread of the smoothing; smaller values will result in sharper and more localized smoothing.
• sbin: bin in the latitude and longitude direction (degrees), controls the grid resolution
• fault_length_multiplier: multiplies the fault length rupture, controls the areal extent of the subcatalog where inferences about Mc trend with time are made; smaller values will result in higher resolution of STAI gaps detection, as local seismicity is less diluted.
• t_end_quiet: ending time of the seismically quiescent period.
• b: b-value of the Gutenberg-Richter law (alternatively, it can be estimated with the function provided in RESTORE).
• alpha: significance level for the Lilliefors test.
• mc: reference value for the magnitude of completeness, if set by the user (by default, it is estimated with the function provided in RESTORE).
• depth_distribution: [scipy.optimize.curve_fit] distribution to fit to hypocenter depths, available options are: normal, poisson, lognormal, beta, bimodal.
• p0: [scipy.optimize.curve_fit] initial guess for the parameters of the hypocenter depth distribution: 'mu', 'sigma' (normal), 'mu' (poisson), 'mu', 'sigma' (lognormal), 'a', 'b' (beta), 'mu1', 'sigma1', 'A1', 'mu2', 'sigma2', 'A2' (bimodal).

Run RESTORE using the following command:

python Run_RESTORE.py

Synthetic_Test [v 2.0.0 only]

Run_Synthetic_Test.py --> runs the synthetic test (uses ETAS_incomplete.txt as input dataset)

ETAS_complete.txt --> synthetic dataset (before STAI modeling)

ETAS_incomplete.txt --> the synthetic dataset (after STAI modeling)

Compare the replenished catalog with ETAS_complete.txt, to check how the missing events are reconstructed by RESTORE

Required external modules

mc_lilliefors (download it here)

How to cite

If you use RESTORE in your research, please cite using the following citation:

@software{Stallone_RESTORE,
author = {Stallone, Angela and Falcone, Giuseppe},
title = {{RESTORE}},
url = {https://github.com/INGV/RESTORE}
}

ZENODO

Linked article

Stallone, A., & Falcone, G. (2021). Missing earthquake data reconstruction in the space‐time‐magnitude domain. Earth and Space Science, 8(8), e2020EA001481. https://doi.org/10.1029/2020EA001481

For any comment, question or suggestion write to: angela.stallone@ingv.it

Acknowledgements

This project has been founded by the Seismic Hazard Center (Centro di Pericolosità Sismica, CPS, at the Istituto Nazionale di Geofisica e Vulcanologia, INGV)