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In the chart below, change "Apx" to "Approx."
You need to refernce papers appropriately. Add the paper to the references section and provide a link to it. Refer to first author and provide a link.
There are too many figures, some of which are redundant or unnecessary, and some don't have captions. Let's discuss.
The "Effect of "Matching Method" and "Preserve H1/H2 ratio"" table does not apply to everything. For example, it doesn't apply to H1 + H2 or RotD100 and RotD00.
QuakeManager supports three matching types:
1.Component: Match all components in a suite, including H1, H2 or V components, to the target.
2.Bidirectional: Modify both H1 and H2 components of records such that their bidirectional resultant (SRSS, Geomean, RotD100, etc) matches the target.
3.3-Components: Same as Bidirectional, but also match the vertical component.
There are 7 possible bidirectional resultant types available, which can be used with matching types 2 & 3 above:
1.Geomean: Each record is modified such that Geometric mean of H1 and H2 matches the target.
2.SRSS: Each record is modified such that the SRSS of H1 and H2 matches the target.
3.H1 and H2: Each of the two horizontal components, H1 and H2, is matched to a different target (Tgt1 and Tgt2).
4.RotD50 (approximate): The H1 and H2 components are modified such that their RotD50 resultant approximately matches the target.
5.RotD100 (approximate): The H1 and H2 components are modified such that their RotD100 resultant approximately matches the target.
6.RotD100: The H1 and H2 components are modified such that their RotD100 resultant is directly matched the target.
7.RotD100 & RotD00: The H1 and H2 components are modified such that their RotD100 resultant and their RotD00 resultant are directly matched to the 1st target (Tgt1) the 2nd target (Tgt2).
Notes:
•The Geomean is calculated as Sqrt(Sa1 x Sa2) at each period T.
•The SRSS is calculated as Sqrt(Sa12 + Sa22) at each period T.
•RotD100 is This is the maximum possible Sa value along all orientations between 0 and 360 degrees
•RotD00 is This is the minimum possible Sa value along all orientations between 0 and 360 degrees. However, when matching RotD100 & RotD00, RotD00 is taken as Sa at an angle that 90-degrees from RotD100 orientation.
•In the above, Sa1 and Sa2 are the spectral values for the two horizontal components H1 and H2 respectively, at period T.
The chart below summarizes all available combinations "Bidir Type" options for each "Match" option.
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Figure: Spectral Matching "Match" and "Bidir Type" Options
The four available "Matching Methods" are:
1.Tight: Each record in the suite is individually spectrally matched to the target
2.Mean: Suite records are spectrally matched such that their average spectrum matches the target
3.Mean + Std. Dev: Suite records are spectrally matched such that their average and standard deviation match the target
4.Mean + LogSigma: Suite records are spectrally matched such that their average and lognormal standard deviation match the target
Mean Spectral Matching reduces the amount of spectral modification that is applied to each record which helps maintain the record characteristics such as velocity pulses and the general shape of the time history signature. It also preserves the dispersion and variability in the suite, and it is also possible to achieve a user-defined dispersion, all that while strictly meeting code requirements. Detailed information is provided in the research paper: "An Improved Approach for Ground Motion Suite Selection and Modification for Use in Response History Analysis".
The following table illustrates the pros and cons of tight and mean spectral matching compared to scaling:
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Feature
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Scaling
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Tight Spectral Matching
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Mean Spectral Matching
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Match suite Mean
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Yes*
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Yes
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Yes
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Meet code requirements (match or exceed target over period range)
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Yes
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Yes
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Yes
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Avoid amplification at short period/higher modes
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No
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Yes
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Yes
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Preserve Dispersion of GM Suite
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Yes
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No
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Yes
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Control Dispersion of GM Suite (to specified target)
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Yes*
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No
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Yes
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Preserve Pulse and other motion characteristics
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Yes
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No
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Yes
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* scaling usually cannot achieve a perfect match of the mean and dispersion. The goodness of fit for a particular suite can vary based on many factors.
As can be seen from the table above, each method has its pros and cons, but in general, the mean spectral matching method is seen as combining the benefits of scaling and tight matching, while avoiding their limitations.
The chart below shows the available "Matching Method" options including the selection one of the appropriate mathematical inequalities (Equals, Greater or Equal, Less or Equal).
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Figure: "Matching Method" Options
When Geomean or SRSS are selected as the bidirectional resultant type, the user is given the option to "Preserve H1/H2 ratio". GeoMean and SRSS matching works by setting the same target for components H1 and H2 such that the resultant GeoMean or SRSS is matched. With the "Preserve H1/H2 ratio" option selected, this is not true anymore.This option ensures that the ratio of the spectra of the two modified horizontal components (Sa1/Sa2) is the same as the ratio for the unmodified components. The targets for components H1 and H2 are modified such that the ratio of components H1 and H2 after matching stays similar to the ratio before it, while the resultant GeoMean or SRSS is still matched to the target. Effectively, the targets for components H1 and H2 would not be similar anymore, which preservers the original ratio between H1 and H2 and introduces some dispersion in the two horizontal component spectra. This means that the component spectra will not be smooth and equal, even when using tight spectral matching. However, the resultant spectra (SRSS or Geomean) will be smooth and equal with using tight spectral matching. In order to avoid that, it is recommended to use the mean spectral matching procedure which achieves dispersion in both the components and resultants, when combined with the " Preserve H1/H2 ratio" option).
The table below shows which "Bidir Types" support the "Preserve H1/H2 ratio" option.
Table: Cases in which the "Preserve H1/H2 Ratio" option can be used
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Bidir Type
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"Preserve H1/H2 Ratio" ?
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Geomean
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SRSS
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H1 & H2
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RotD100 (approximate)
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|
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RotD50 (approximate)
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RotD100
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RotD100 & RotD00
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The following tables shows different combinations of Bidirectional Type and the H1/H2 ratio option, and how the matching target for each individual component is calculated.
The first two columns represent input options, and the following columns describe how the calculation of the individual components (H1 & H2) are calculated.
Table: Calculation of Sa1 and Sa2 Target Spectra for different Matching Options
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Bidir Type
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Preserve H1/H2 Ratio
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Sa1 & Sa2 Calculation
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Resultant Target
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Geomean
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No
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Sa1= Sa2 at each T
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Geomean(Sa1,Sa2) = Tgt
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Geomean
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Yes
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Sa1/Sa2 = Sa1orig/Sa2orig at each T
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Geomean(Sa1,Sa2) = Tgt
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SRSS
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No
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Sa1= Sa2 at each T
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SRSS(Sa1,Sa2) = Tgt
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SRSS
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Yes
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Sa1/Sa2 = Sa1orig/Sa2orig at each T
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SRSS(Sa1,Sa2) = Tgt
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H1 & H2
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No
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Sa1=Tgt1 and Sa2= Tgt2 at each T
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Sa1=Tgt1 & Sa2=Tgt2
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RotD100 (approximate)
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No
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Sa1= Sa2 at each T
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SaRotD100 = Tgt
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RotD100 (approximate)
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Yes
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Sa1/Sa2 = Sa1orig/Sa2orig at each T
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SaRotD100 = Tgt
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RotD50 (approximate)
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No
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Sa1= Sa2 at each T
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SaRotD50 = Tgt
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RotD50 (approximate)
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Yes
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Sa1/Sa2 = Sa1orig/Sa2orig at each T
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SaRotD50 = Tgt
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RotD100
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No
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-
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SaRotD100 = Tgt
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RotD100 & RotD00
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No
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-
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SaRotD100 = Tgt1 & SaRotD00=Tgt2
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Depending on the options selected, the resulting spectrally matched component and triplet spectra may or may not be smooth/tight.
The different cases are illustrated in the table below, which illustrate the variety of spectral matching options offered by QuakeManager which allow the user to pick the preferred approach for a particular application. The table includes example figures that illustrate each case. The first two columns represent input options, and the following columns reflect the properties of the matched triplet and its components.
Table: Effect of "Matching Method" and "Preserve H1/H2 ratio" options on the matched component and triplet spectra
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Matching Method
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Preserve H1/H2 Ratio
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Sa1(T)=Sa2(T)?
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Component Spectra Smooth?
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Triplet Spectra Smooth?
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Component Spectra
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Triplet Spectra
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Tight
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No
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Yes
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Yes
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Yes
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Figure 1
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Figure 5
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Tight
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Yes
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No
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No
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Yes
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Figure 2
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Figure 6
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Mean
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No
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Yes
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No
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No
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Figure 3
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Figure 7
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Mean
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Yes
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No
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No
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No
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Figure 4
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Figure 8
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Figure 1: Tight Geomean Matching of Components without preserving H1/H2 Ratio
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Figure 2: Tight Geomean Matching of Components with preserving H1/H2 Ratio
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Figure 3: Mean Geomean Matching of Components without preserving H1/H2 Ratio
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Figure 4: Mean Geomean Matching of Components with preserving H1/H2 Ratio
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Figure 5: Tight Geomean Matching of Triplets without preserving H1/H2 Ratio
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Figure 6: Tight Geomean Matching of Triplets with preserving H1/H2 Ratio
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Figure 7: Mean Geomean Matching of Triplets without preserving H1/H2 Ratio
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Figure 8: Mean Geomean Matching of Triplets with preserving H1/H2 Ratio
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