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The solution with the maximum variance reduction is the optimal solution.
The centroid depth was constrained to 11 km, where the maximum variance reduction appeared and the PHS interface exists.
The inversion is performed for a set of trial depths, and the best solution is defined as the one with the maximum variance reduction.
Waveform fittings of the solution with maximum variance reduction (depth of 11 km) are also improved by introducing low-velocity layers, especially the accretionary prism, which contributes to the excitation of large-amplitude Love waves in the transverse component.
Since the animal effect cannot explain the environmental variance, the maximum variance reduction is (1 - ρ max ) = σ e 2 / V y), where σ e 2 is from Table 1, and V y) is the variance of the masked records.
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The reason for which we add these three and four SCPs cases is to obtain an estimate of the maximum possible variance reduction when many site parameters are known.
Overall, the largest reduction is observed for the "reference" model accounting simultaneously for the four SCPs, followed by the three best SCPs model combining the use of [V S30, f 0, H 800]; it is noteworthy, however, that such "maximum possible" variance reduction does not exceed 1.5% for PGA (Table 3) and 4% for short periods around 0.08 s, while it reaches 29% around 0.4 s.
The measurement that yields the maximum domain averaged variance reduction is selected.
For the short periods [0.1 0.6 s], the best is V S30 with a maximum of 25% variance reduction at 0.4 s while f 0 outperform in the [0.6, 4] s.
We take the variance reduction of the maximum value in the shifted time range as the estimated results.
Other senses of optimality include the metric for reduction defined by Seysen [40] and the minimization of the maximum variance of the integer-transformed real-valued solution proposed recently by Zhou and Ma [43].
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