Intensity measures: TSL2IM / getIntensity

Units

The function takes:

• units.source — source units for s ("mm", "cm", "m", "gal", "g"),
• units.target — target base-length units ("mm", "cm", "m"; default "mm").

A single factor SFU = .getSF(units.source, units.target) is applied to s for all rows, regardless of ID. This works if your AT, VT and DT series are already consistent in the same base-length unit (e.g. output of AT2TS / VT2TS / DT2TS in units.target).

Warning: if you mix incompatible units (e.g. units.source = "g" while also having VT / DT in the same table), the scaling will be wrong.

Internal unit conventions

After scaling:

• For AT: s is acceleration in units.target/s^2.
• For VT: s is velocity in units.target/s.
• For DT: s is displacement in units.target.

The acceleration of gravity in target units is \(g = .getG(\mathrm{units.target})\) (e.g. 9806.65 mm/s² for units.target = "mm").

imw <- TSL2IM(tsl, units.source = "mm", output = "IMW")
names(imw)[1:min(6, length(names(imw)))]
#> [1] "RSN"  "OCID" "AI"   "AIu"  "AId"  "PGA"

Acceleration (ID = “AT”)

Peak and RMS:

\[\mathrm{PGA} = \max_t |a(t)|, \qquad \mathrm{ARMS} = \sqrt{\frac{1}{N}\sum_{i=1}^{N} a_i^2}.\]

Zero crossings and edges:

• AZC — number of zero crossings (discrete count).
• ATo, ATn — first \(a(t_1)\) and last \(a(t_N)\) value.

Arias intensity (discretised with \(\Delta t = \mathrm{mean}(t_i - t_{i-1})\)):

\[\mathrm{AI} = \frac{\pi}{2g}\sum_{i=1}^{N} a_i^2\,\Delta t.\]

• AI — total Arias intensity.
• AIu — uses \(a_+(t) = \max(a, 0)\) only.
• AId — uses \(a_-(t) = \min(a, 0)\) only.

Units: units.target/s.

Significant duration (Husid): the code builds a cumulative curve proportional to energy,

\[H(t_k) = \pi\,\Delta t \sum_{i=1}^{k} a_i^2,\]

and measures the time interval between two fractions of the total.

• D0595 — 5 % → 95 %.
• D0575 — 5 % → 75 %.
• D2080 — 20 % → 80 %.

Units: s.

Mean period \(T_m\) (Rathje et al. 1998), from the Fourier amplitude spectrum over a frequency band:

\[T_m = \frac{\sum_{f \in [f_{\min}, f_{\max}]} C(f)^2 / f} {\sum_{f \in [f_{\min}, f_{\max}]} C(f)^2}.\]

TmA is computed on AT with \(f_{\min} = 0.1\) Hz, \(f_{\max} = 25\) Hz.

Duration / sampling:

• NP — number of samples.
• dt — mean \(\Delta t\).
• Fs — \(1/\Delta t\).
• Dmax — last time last(t).

Cumulative absolute velocity (CAV):

\[\mathrm{CAV} = \sum_{i=1}^{N} |a_i|\,\Delta t.\]

CAV5 applies the same sum but only over indices where \(|a_i| \ge 0.05\,g\). Units: units.target/s.

Derived indices (as implemented; not standardised):

\[\mathrm{EPI} = \frac{0.9}{\pi}\,\mathrm{AI}\,(2g)\,D_{05\text{–}95}, \qquad \mathrm{PDI} = \mathrm{AI}\,\left(\frac{D_{\max}}{\mathrm{AZC}}\right)^{\!2}.\]

Units: units.target^2/s^2 for EPI; units.target·s for PDI (with AZC treated as dimensionless).

Note: if AZC = 0, PDI becomes Inf/NaN.

Velocity (ID = “VT”)

• PGV — \(\max_t |v(t)|\).
• VRMS — RMS of \(v\).
• VZC — zero crossings.
• VTo, VTn — first / last value.
• TmV — mean period from the Fourier amplitude spectrum.

Units: units.target/s for PGV / VRMS / VTo / VTn; s for TmV.

Displacement (ID = “DT”)

• PGD — \(\max_t |d(t)|\).
• DRMS — RMS of \(d\).
• DZC — zero crossings.
• DTo, DTn — first / last value.
• TmD — mean period from the Fourier amplitude spectrum.

Units: units.target for PGD / DRMS / DTo / DTn; s for TmD.