Guralp Systems ART - Manual (Page 31)

User guide
calculated. The response spectra calculation must be
run again if the limits given in the ‘Options’ window
are changed after the response spectra calculation
was made);
20. Arias intensity (AI) in velocity units based on the
selected acceleration unit calculated from
where g is acceleration due to gravity in ms -2 (i.e.
g=9.80665ms -2 ) and a(t) is ground acceleration (Arias,
1970);
21. normalized energy density (ED) in units based on the
selected velocity unit calculated from
where v(t) is ground velocity [see Sarma (1971)] [note
that, to get the true energy density, the normalized
energy density should be multiplied by Vρ/4 where V
is wave velocity and ρ is mass density of the
recording site (Sarma, 1971)];
22. cumulative absolute velocity (CAV) in selected
velocity units calculated from
where a(t) is the ground acceleration, N is the number
of 1-second time windows in the time series, PGA
i
is
the PGA (in g) during time window i, t
i
is the start time
of time window i, a
min
is an acceleration threshold
(user-defined but commonly 0.025g) to exclude low
amplitude motions contributing to the sum and
H(x) is
the Heaviside step function (unity for x>0 and 0
otherwise) (EPRI, 2006);
23. number of absolute effective cycles (peak counting
including non-zero crossings) in acceleration time-
history (Hancock & Bommer, 2005);
24. number of equivalent effective cycles using user-
defined damage exponent (peak counting including
non-zero crossings) in acceleration time-history
(Hancock & Bommer, 2005);
May 2009 31
AI =

2 g
∫ a t 2 dt
ED= ∫ v t 2 dt
CAV = ∑
i=1
N
H  PGA
i
− a
min

∫
t=t
i
t
i1
∣ a  t ∣ dt