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The 11 selected records in GM selection example will be spectrally matched using the two methods: Tight Matching and Mean Matching. For the Tight matching, the RotD100 Bidirectional type was defined as the we used the RotD100 in the selection example, and the same target spectrum was set. Regarding the Matching Criteria, it is recommended to widen the frequency/period range to obtain better solutions. For that purpose, 0.1 to 35 Hz was defined as a frequency range. As a first pass, 3 steps were defined. This is an iterative process in which number of steps may be decreased or increased to improve the results. For this example, Model 7, "Improved Tapered Cosine Function" was selected to be the wavelet model. All remaining parameters were kept as default.
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After running the analysis of Tight Matching, QuakeManager generates a report that includes statistics about the matching process including the misfit (error) for both the matching frequencies and other "unmatched" frequencies. The red numbers indicate that these records did not reach the convergence tolerance defined in the Matching Criteria. QuakeManager can show the matching results step by step or the last step only.The step by step report illustrates how the matching is improving with each step. For example, 55461EW record resulted in a maximum misfit error of 37.48% in the first step, however, this misfit decreased to 10.72% leading to an approximate of 71% decrease in the maximum misfit. Note that this is not always the case, the misfit of some records may increase with the increase of the number of steps.
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Figure 6: Spectral Matching Report (showing last step only)
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Figure 7: Spectral Matching Report (showing all steps)
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Figure: Tight Matching
The advantage of using the Model 7 wavelet model is that most of the times, it overcomes the drift problems in the velocity and displacement time histories. Example below shows the AVD (acceleration-velocity-displacement) and acceleration charts of two different records.
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Figure: AVD Chart of a spectrally matched record
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Figure: Acceleration time histories of scaled B-IVW090 record and tightly matched
Concerning the Mean Spectral Matching, the selected suite will be matched using the "Mean + Standard Deviation" match method and the suite dispersion was set to be equal to the standard deviation. The figure below show an almost perfect match between the suite mean and standard deviation and the target spectrum.
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Figure: Mean Matching
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