CNCHASH

Python implementation of HASH for earthquake focal mechanism determination from P-wave polarities.

Python uses Numba JIT compilation optimization and vectorization, achieving speed improvements while maintaining complete consistency with the core Fortran algorithm.

Performance

Metric	Python+Numba	Fortran	Speedup
24 events	0.068s	0.473s	6.9x
Per event	2.85ms	19.7ms	6.9x
5000 events	13.0s	98.5s	7.6x
10000 events	26.0s	197.0s	7.6x

Accuracy Verification

Key Results:

• Python dip error median: 5.6° (Fortran: 11.1°)
• Python rake error median: 24.1° (Fortran: 26.6°)
• Python synthetic trials: 300/300 successful solutions
• Fortran synthetic trials: 60/60 successful solutions (direct-runs)

Note: Strike differences (40-80°) are normal - focal mechanisms have two orthogonal nodal planes that both satisfy polarity data.

Quick Start

pip install cnchash

Basic Usage (P-wave polarities only)

from cnchash import run_hash
import numpy as np

# Azimuths, takeoff angles, polarities, quality
p_azi = np.array([45.0, 135.0, 225.0, 315.0])
p_the = np.array([30.0, 45.0, 60.0, 75.0])
p_pol = np.array([1, -1, 1, -1])  # 1=up, -1=down
p_qual = np.array([0, 0, 0, 0])

result = run_hash(p_azi, p_the, p_pol, p_qual)

print(f"Strike: {result['strike_avg']:.1f}")
print(f"Dip: {result['dip_avg']:.1f}")
print(f"Rake: {result['rake_avg']:.1f}")
print(f"Quality: {result['quality']}")

With S/P Amplitude Ratio

from cnchash import run_hash_with_amp
import numpy as np

# Same inputs as above, plus S/P amplitude ratios (log10 scale)
# sp_amp = 0.0 means no amplitude data for that station
sp_amp = np.array([0.3, -0.2, 0.5, 0.0])  # log10(S/P), 0.0 = no data

result = run_hash_with_amp(p_azi, p_the, p_pol, sp_amp)

print(f"Strike: {result['strike_avg']:.1f}")
print(f"Dip: {result['dip_avg']:.1f}")
print(f"Rake: {result['rake_avg']:.1f}")
print(f"Quality: {result['quality']}")
print(f"Polarity misfit: {result['mfrac']*100:.1f}%")
print(f"Amplitude misfit: {result['mavg']:.2f}")

Features

• Grid search for focal mechanism determination
• Monte Carlo uncertainty analysis
• S/P amplitude ratio constraint
• Quality rating (A-D, E, F)
• Multiple phase file formats
• Core algorithm matches Fortran exactly

Documentation

See https://cnchash.readthedocs.io/ for full documentation including:

• API reference
• Algorithm details
• File format specifications
• Performance optimization

Run Tests

jupyter notebook HASH_Tests.ipynb

Project Structure

cnchash/
├── core.py        # Grid search algorithm (focalmc)
├── amp_subs.py    # S/P amplitude ratio (focalamp_mc)
├── uncertainty.py # Uncertainty analysis (mech_prob)
├── driver.py      # Main driver (run_hash, run_hash_with_amp)
├── io.py          # File I/O
└── utils.py       # Utilities

HASH_complete/     # Complete Fortran code with examples

Author

He XingChen

License

BSD 3-Clause

References

Hardebeck, Jeanne L. and Peter M. Shearer, A new method for determining first-motion focal mechanisms, Bulletin of the Seismological Society of America, 92, 2264-2276, 2002.

Hardebeck, Jeanne L. and Peter M. Shearer, Using S/P Amplitude Ratios to Constrain the Focal Mechanisms of Small Earthquakes, Bulletin of the Seismological Society of America, 93, 2434-2444, 2003.