py-nfi 0.1.1

Normalized frequency index (nFI) computation for earthquake source spectra

py-nfi

Compute the normalized frequency index (nFI) from earthquake spectra. nFI is a data-driven measure of the relative high-frequency content of a seismic source, providing an observation-based alternative to stress-drop estimation for characterizing source behavior at high frequencies.

Installation

pip install py-nfi

or, with conda:

conda install -c conda-forge py-nfi

Quick start

import numpy as np
import pandas as pd
from nfi import nFIEstimator

# df_records: one row per event-station record (a single observed spectrum)
# spectra:    N x nf array of signal amplitude spectra, aligned row-for-row
#             with df_records (the signal windows; noise spectra are used
#             upstream for signal-to-noise screening, not passed here)
# f:          length-nf frequency array (0 to Nyquist)

est = nFIEstimator(df_records, spectra, f, save_dir="results/")
est.compute()

# per-event results, including the 'nfi' column, are written to results/
# and available as est.df_events

df_records must contain, at minimum, the columns event_name, channel_name, emag, elat, elon, edep, slat, slon, selev, and deldist, where e* fields describe the event and s* fields describe the recording station.

Method

nFI is computed from spectra in three stages.

1. Frequency index. For every observed spectrum, we take the log ratio of the median amplitude in a high-frequency band to that in a low-frequency band:

logbeta = log10(A_HF) - log10(A_LF)

This quantifies the richness of high frequencies relative to low frequencies for a single recording. The low band should sample the flat portion of the displacement spectrum below the corner frequency, and the high band should sample the decay above it.

2. Path and station correction. Observed spectra carry path and station effects that must be removed to isolate source variability. For each target event, we identify small nearby "calibration" earthquakes recorded at the same stations. Differencing logbeta between a target and a calibration event at a shared station cancels the common station and path terms. Taking the median of these differences across calibration events per station, then the median across stations, yields the corrected source term dlogbeta for each event. Calibration events are selected within a narrow magnitude range and a limited horizontal and vertical distance of the target.

3. Magnitude correction. Larger earthquakes radiate proportionally less high-frequency energy, so dlogbeta retains a magnitude dependence. We estimate this trend by taking the median dlogbeta in magnitude bins, smoothing it, and subtracting the interpolated trend from each event. The result is nFI: by construction it has approximately zero median at any magnitude, with positive values indicating high-frequency enrichment and negative values indicating depletion.

For full detail and validation of the method, see Vandevert et al. (2026) below.

Reproducing the Ridgecrest results

Where the spectra come from

Citation

If you use this software, please cite:

Vandevert, I., Shearer, P. M., & Fan, W. (2026). Using a High-to-Low-Frequency Spectral Ratio to Distinguish Variations in Earthquake Source Properties. Bulletin of the Seismological Society of America. https://doi.org/10.1785/0120250171

License

Released under the MIT License.