3.10. Significant Duration

imcalculator.get_significant_duration(start=0.05, end=0.95)[source]

Computes the significant duration of the ground-motion record.

Significant duration is defined as the elapsed time between specified fractions of the normalised Arias Intensity. The default thresholds correspond to the 5%-95% significant duration (t_5-95).

Parameters:

start (float, optional) – Lower fraction of normalised Arias Intensity. Default is 0.05 (5%).
end (float, optional) – Upper fraction of normalised Arias Intensity. Default is 0.95 (95%).

Returns:

sig_duration – Significant duration (s).

Return type:

float

References

Trifunac, M. D., and Brady, A. G., 1975. A study on the duration: of strong earthquake ground motion. Bulletin of the Seismological Society of America, 65(3), 581–626.

Notes

Because the Arias Intensity is normalised, the result is independent of the acceleration unit (g or m/s²).

Theoretical Background

Significant duration quantifies the time interval over which the most energetic portion of a ground-motion record occurs, defined by the accumulation of Arias Intensity between two threshold fractions (Trifunac & Brady, 1975).

Arias Intensity accumulation

The normalised cumulative Arias Intensity at time \(t\) is:

\[I_A^*(t) = \frac{1}{I_A} \cdot \frac{\pi}{2g} \int_0^{t} \bigl[\ddot{u}_g(\tau)\bigr]^2 d\tau\]

where \(I_A\) is the total Arias Intensity of the record.

Significant duration

The significant duration between fractions \(p_1\) and \(p_2\) is:

\[D_{p_1\text{–}p_2} = t(I_A^* = p_2) - t(I_A^* = p_1)\]

The default interval is 5%–95% (\(D_{5\text{–}95}\)), which captures the time between the onset and end of strong shaking while excluding the low-energy tails of the record.

Example

import numpy as np
from openquake.vmtk.imcalculator import imcalculator

acc = np.loadtxt("openquake/vmtk/tests/test_data/acceleration.txt")
im = imcalculator(acc, dt=0.005)

t595 = im.get_significant_duration()
print(f"D5-95 = {t595:.3f} s")