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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
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Ground Motion
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Intensity Measure
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Formula
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Database Field Name
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Status
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Peak Ground Acceleration
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Max (Abs(a(t)))
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PGA
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Implemented
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Peak Ground Velocity
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Max (Abs(v(t)))
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PGV
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Implemented
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Peak Ground Displacement
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Max (Abs(d(t)))
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PGD
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Implemented
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Effective Peak Acceleration [21]
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Avg. Sa [0.1≤T≤0.5] ÷ 2.5
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EPA
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Implemented
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Effective Peak Velocity [21]
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Avg. Sv [0.7≤T≤2.0] ÷ 2.5
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EPV
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Implemented
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Effective Peak Displacement [22]
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Avg. Sd [2.5≤T≤4.0] ÷ 2.5
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EPD
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Implemented
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Sustained Peak Acceleration [23]
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Third highest peak acceleration
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SPA
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Planned
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Sustained Peak Velocity [23]
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third highest peak velocity
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SPV
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Planned
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Root-Mean-Square Acceleration [23]
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RMSs = Integral of a(t)^2, divided by Td
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RMSa
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Planned
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Incremental Velocity
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Largest peak-to-peak incremental velocity
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IncVel
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Implemented
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Incremental Displacement
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Largest peak-to-peak incremental displacement
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IncDisp
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Implemented
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Cumulative Absolute Velocity [23]
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CAV = Integral(ABS(a(t)))
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CAV
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Implemented
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Cumulative Absolute Velocity
(for Acc < 5cm/s/s) [24] [31] a
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CAV5
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Implemented
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Standardized Cumulative
Absolute Velocity [25] [26] b
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CAVstd
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Implemented
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Maximum Standardized
Cumulative Absolute Velocity [29] c
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CAVs
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Implemented
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Cumulative Absolute Displacement
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CAV = Integral(ABS(v(t)))
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CAD
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Implemented
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Engineering Intensities
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Housner Spectrum Intensity
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Integral of PSV(zeta,T)dt over [0.1,2.5]
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SIh
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Planned
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Hidalgo Clough Spectrum Intensity [28]
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Integral of PSV(zeta,T)dt over [0.1,1]
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SIhc
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Planned
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Nau & Hall Spectrum Intensity [22]
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Integral of PSV(zeta,T)dt over [0.028,0.185]
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SInh
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Planned
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Characteristic Intensity [23]
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Ic = RMSa1.5*Db5PcG0.5
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Ic
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Planned
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Arias Intensity
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Io = (pi/2g) * Integral(a(t)2 dt)
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Io
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Implemented
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Observational MMI
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MMIobs
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Input by user
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Instrumental MMI
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MMIinst
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Input by user
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Period and Duration
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Total Recorded Duration
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Duration
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Implemented
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Bracketed Duration of Record over 5%G [23] c
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Db5PcG
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Implemented
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Uniform Duration of Record over 5%G [23] c
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Du5PcG
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Implemented
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Significant (Arias) Duration (D5-95)
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D5_95
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Implemented
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Significant (Arias) Duration (D5-75)
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D5_75
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Implemented
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Predominant Period [23]
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Tp
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Planned
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Corner Period [23]
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Tc
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Planned
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Mean Period [30]
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Tm
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Planned
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Statistics and Correlation
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Cross-Correlation of
Acceleration Components 1 & 2 d
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XCorr12 = Sum( (a1_i - m1)*(a2_i - m2) ) / (s1 * s2 * Npts)
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XCorr12
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Implemented
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Cross-Correlation of
Acceleration Components 1 & 3
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Similar to XCorr12, defined for components 1 & 3 (one horizontal and one vertical).
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XCorr13
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Implemented
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Cross-Correlation of
Acceleration Components 2 & 3
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Similar to XCorr12, defined for components 2 & 3 (one horizontal and one vertical)
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XCorr23
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Implemented
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Max Cross-Correlation of
Acceleration Components 1, 2 & 3
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XCorrMax = Max (XCorr12, XCorr13, XCorr23)
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XCorrMax
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Implemented
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References
a CAV5 is proposed by [31] 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 [22] 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 [22].
e Standard CAV as defined by [25], based on the original proposal by [26]
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 [31] as the intensity measure that best correlates with prediction of pore water pressure and liquefaction. It is also suggested by [22] 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 [22].
c Defined by [27]. 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. 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 ([27]):
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.
d 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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