ARIAS INTENSITY

The most commonly used measure of ground-shaking intensity is peak ground acceleration (PGA). Unfortunately, PGA measures only a single point in an acceleration-time history and is thus a rather crude measure of shaking intensity. A more comprehensive and quantitative measure of total shaking intensity developed by Arias (1970) is useful in seismic hazard analysis and correlates well with the distribution of earthquake-induced landslides. Arias intensity is the integral over time of the square of the acceleration, expressed as

where I_a is Arias intensity, in units of velocity, g is the acceleration of Earth's gravity, and a(t) is the ground acceleration as a function of time, and T is the total duration of strong shaking. An Arias intensity thus can be calculated for each directional component of a strong-motion record. Arias intensity is proportional to the RMS acceleration. Because Arias intensity is the integration of an acceleration record, it has units of velocity (meters per second).

Estimating the Arias intensity at a site can be done in more than one way. Wilson and Keefer (1983) developed a relationship between Arias intensity, earthquake magnitude, and source distance:

log I_a = M - 2logR - 4.1

where I_a is Arias intensity in meters per second, M is moment magnitude, and R is earthquake source distance in kilometers.

Arias intensity also correlates closely with the combination of PGA and duration. R.C. Wilson (U.S. Geological Survey, unpublished data) developed an empirical equation using 43 strong?motion records to predict Arias intensity from PGA and a specific measure of duration:

I_a = 0.9 (D_(5-95%)) (PGA)²

where I_a is Arias intensity in meters per second, PGA is in g's, and D_(5-95%) is the Dobry duration in seconds. Dobry duration is the time required to build up the central 90 percent of the Arias intensity (Dobry and others, 1978). Estimating Arias intensities using this method requires an estimate of the duration of strong shaking. Dobry and others (1978) proposed an empirical relation between duration and earthquake magnitude:

log D_(5-95%) = 0.432M - 1.83

where D_(5-95%) is Dobry duration in seconds and M is unspecified earthquake magnitude (probably local magnitude).