RMS is currently defined as divided by Total duration. We need to settle this issue.

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Tm missing from table

A number of intensity measures have been proposed by researchers over time with the intent of providing a simplified estimate of the damage potential of the ground motion.

This grew out of the realization that the earthquake magnitude alone was not a good predictor of damage, since damage depends on many factors including the distance to site, soil properties, frequency content of the record, and the structure's period among others. Other parameters that contribute to the variation of the Intensity Measures include rupture directivity and surface geology. QuakeManager has the capability of computing many of the commonly used ground motion parameters (also called "intensity measures" or "intensity indices"). These measures are usually computed from the acceleration, velocity or displacement history, but some are related to the ground motion spectrum (acceleration, velocity, displacement), or other related quantities such as the PSD (Power Spectral Density), etc. Some intensity measures are not calculated by QuakeManager (such as Observational and Instrumental MMI), but QuakeManager provides a data field and may input by the user.

Below is a list of intensity measures that are implemented or are being considered for implementation (and a few others that are not currently planned, but may be considered in the future).

The total number of currently implemented Intensity Measures is 22.

Table: Intensity Measures

1. EPA is defined by ATC 3-06 (1978) as the average spectral acceleration over the period range 0.1 to 0.5 sec, divided by 2.5. See Kramer [8] pp 83 and Danciu [2] page 32.

ATC 3-06 also defined the unitless coefficient Aa which is numerically equivalent to EPA when EPA is expressed in g's. See the following reference:

http://www.cflhd.gov/programs/techDevelopment/geotech/rockeries/documents/13_Appendix_A_Seismic_Design.pdf

Also see:

http://chl.erdc.usace.army.mil/library/publications/chetn/pdf/chetn-vi-41.pdf

http://earthquake.usgs.gov/hazards/about/technical.php

2. EPV is defined by ATC 3-06 (1978) as the average spectral velocity at a period of 1 sec (averaged between 0.7s and 2.0s), divided by 2.5. See Kramer [8] pp 83 and Danciu [2] page 32.

ATC 3-06 also defined the unitless coefficient Av. Av=1 is equivalent to 76.2 cm/s (30 in/s). See the following reference:

http://www.cflhd.gov/programs/techDevelopment/geotech/rockeries/documents/13_Appendix_A_Seismic_Design.pdf

3. EPD is defined as the average spectral displacement between 2.5s and 4s, divided by 2.5.

4. Can be defined as third highest peak acceleration (SPA3) or 5th highest acceleration peak (SPA5).

See Kramer [8] pp 69-70.

5. Defined similar to the SPA as 3rd (SPV3) or 5th (SPV5) highest velocity peak.

See Kramer [8] pp 69-70.

6. The Cumulative Absolute Velocity (CAV) is calculated as the integral of the absolute value of the acceleration time history over the full duration of the ground motion.

7. CAV5 is proposed by Kramer et al. (2005) as an intensity measure that correlates well with prediction of pore water pressure and liquefaction.

CAV5 is computed similar to CAV, except all values of acceleration smaller than 5 cm/s/s are discarded (assumed zero).

Other parameters can be similarly defined such as CAV5, CAV10, CAV15, CAV20, CAV25.

CAV5 is also suggested by Danciu [3] as a good measure of longer period components of the motion. Cabanas at al (1997) considered the five different measures and found CAV20 best correlates with local earthquake intensity (Danciu [4]).

8. Standard CAV as defined by Abrahamson & Watson-Lamprey (EPRI 2006), based on the original proposal by O’Hara and Jacobson (1991)

It is computed similar to CAV, however, it excludes any one-second interval of a recording in which the peak acceleration was less than 0.025G.

CAVstd is somewhat similar to CAV25, with some differences in the way the calculation is performed. CAV25 uses a similar limit of 25 cm/s/s, which approximately equal to 0.025G. However, the CAV25 does not subdivide the data into 1-second intervals, and hence the CAVstd measure is usually larger than CAV25 since CAV25 discards a large portion of the record (all acceleration points < 25 cm/s/s) before performing the integration, while CAVstd keeps some acceleration points that are < 0.025G.

Other parameters can be defined such as CAV5, CAV10, CAV15, CAV20, CAV25. CAV5 (defined above) is proposed by Kramer et al. (2005) as the intensity measure that best correlates with prediction of pore water pressure and liquefaction. It is also suggested by Danciu [3] as a good measure of longer period components of the motion. Cabanas at al (1997) considered the five different measures and found CAV20 best correlates with local earthquake intensity (Danciu [4]).

9. Defined by Campbell & Bozorgnia [9]. This is defined for each component of a record as a function of CAVstd, but the record is required to have three components for this measure to be defined. If a record has less than three components, or if the ground motion data file for any of the components is missing, a Null value is assigned to this measure. If three components are defined, then the measure is calculated according to the criteria in Campbell and Bozorgnia [9]. The measure is defined as the CAVstd for that direction when the three components satisfy the minimum criteria (see below), and zero otherwise.

The minimum criteria consist of satisfying the following criteria ([9]):

1. At least one of the following two criteria needs to be satisfied:

1.The maximum value of PSA in the period range 0.1–0.5 sec (2–10 Hz) for all three components is at least 0.2g, Or

2.The maximum value of PSV (5%-damped pseudo-relative response-spectral velocity) in the period range 0.5–1 sec (1–2 Hz) for all three components is at least 15.24 cm/sec.

2. The maximum value of the standardized CAV (i.e. CAVstd) for all three components is at least 0.16 g-sec

Since this intensity measure requires the presence of three components, it may be undefined for many record components that are not part of a triplet, or for triplets that are missing one or more records.

Additionally, if CAVstd in any of the three directions is less than 0.16 g-sec, then CAVs is zero in all directions.

10. The Cumulative Absolute Displacement (CAD) is defined similar to the Cumulative Absolute Velocity (CAV). It is calculated as the integral of the absolute value of the velocity time history over the full duration of the ground motion.

11. Linearly related to an index of structural damage due to maximum deformation and absorbed hysteretic energy. See Kramer [8].

12. The Arias intensity is defined (Arias 1970) [10] as being proportional to the integral of the square of the acceleration history over the duration of the record. It has units of velocity and is usually expressed in m/s [8].

13. This measures the duration of the record during which the acceleration exceeds 5%g. This can be computed by finding the first and last instance during the record at which the 5%g acceleration threshold is reached. The duration is then taken as the time between these two instances.

Also called "Bracketed Duration" or "Tb", as defined in Bold [3] (see pp 13 of Danciu [2]). 

14. Similar to bracketed duration, but only intervals with acceleration above the limit are counted.

15. Defined as "Significant Duration" or "Tsa" by Trifunac and Brady [1]. See pp 12-13 of Danciu [2]. "ts" can be defined for acceleration, velocity and displacement time-histories...

Also called [Dhusid] Husid Duration

Referenced by Sommerville [6] as being D5-90 using the husid plot (arias intensity).

Also Da5-75, Da5-95, Dv5-75, Dv5-95 are used (pp 70 of Stewart and Baturay [4]).

16. Reports the cross-correlation of the acceleration signals of the first two components (two horizontal componets).

The cross-correlation is computed according to the following equation:

XCorr12 = Sum( (a1_i - m1)*(a2_i - m2) ) / (s1 * s2 * Npts )

Where:

•a1_i = ith acceleration point in direction 1

•a2_i = ith acceleration point in direction 2

•m1 = mean acceleration in direction 1 (over full record duration)

•m2 = mean acceleration in direction 2 (over full record duration)

•s1 = standard deviation of acceleration in direction 1 (over full record duration)

•s2 = standard deviation of acceleration in direction 2 (over full record duration)

A high value of cross-correlation is usually interpreted as an indicator that the two components are not fully independent.

Some requirements (e.g. NRC, other) require that the cross-correlation value be less than a certain threshold (e.g. 0.16, 0.30, etc).

For example, The U.S.NRC's Standard Review Plan (SRP) Section 3.7.1 [11] requires that "Each pair of time histories are considered to be statistically independent if the absolute value of their correlation coefficient does not exceed 0.16"

Similarly, NUREG/CR-6728, Section 5.3(g) [12] states "it is recommended that the upper limit for the zero-lag cross-correlation coefficient between any two design ground motions be 0.3"

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