pykooh

Konno Ohmachi filter implemented in Numba.

This code implements Konno-Ohmachi spectral smoothing as defined in:

Konno, K. and Ohmachi, T., 1998. Ground-motion characteristics estimated
from spectral ratio between horizontal and vertical components of
microtremor. Bulletin of the Seismological Society of America, 88(1),
pp.228-241.

This code was originally written for smoothing submodule in gmprocess by Bruce Worden. Dave Boore has provided notes on this topic, which also may be of interest. Notes regarding the characteristics of the Konno-Ohmachi filter and the implementation are provided in the implementation Jupyter Notebook.

Installation

pykooh is available via pip and can be installed with:

pip install pykooh

pykooh uses numba for fast implementation of the filter.

Implementation Notes

Previous versions of pykooh supported both Numba and Cython implementations. Testing showed that both implementations provided similar calculation speeds, but Cython required significantly more effort for packaging and distribution. Therefore, Cython support has been removed in favor of the Numba-only implementation which provides excellent performance with much simpler packaging.

Usage

Two primary approaches for using this library. Smooth a signal using a bandwidth of 30.

import pykooh
signal_smooth = pykooh.smooth(freqs, freqs_raw, signal_raw, 30)

If you are okay with a little bit of inaccuracy, you can pass simplified=True and have a 10x increase in speed. In other instances, where the smoothing is repeated applied, it might make more sense to use the CachedSmoother. This pre-computes the weights and then applies them with np.dot.

import pykooh

smoother = CachedSmoother(freqs_raw, freqs, 30)

signal_smooth = smoother(signal_raw)

By default, all of the smoothing functions normalize that weights, which is different than the default behavior of obspy. By normalizing the weights, the amplitude of the FAS is perserved regardless of spacing of the frequency values. Comparison of the smoothing provided by pykooh is compared with that of obspy in the following figure. The simplified numba routine results in some minor reduction in accuracy.

Additional examples and comparison with obspy are provided in example.

Citation

Please cite this software using the following DOI.

Albert Kottke. (2025). arkottke/pykooh (v0.5.0). Zenodo. https://doi.org/10.5281/zenodo.15499453