Fuzzy Clustering Analysis of HVSR Data for Seismic Microzonation at Lahore City

Table 1

SESAME criteria for HVSR data.

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Criteria for a reliable HVSR curve

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fo > 10/lw

nc (fo) > 200

ϭA(f) < 2 for 0.5fo < f < 2fo if fo > 0.5 Hz or ϭA(f) < 3 for 0.5fo < f < 2fo if fo < 0.5 Hz

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Criteria for a clear HVSR curve peak (at least 5 out of 6 criteria fulfilled)

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Exists f- in [fo/4, fo] | AH/V(f-) < Ao/2

Exists f+ in [fo, 4fo] | AH/V(f+) < Ao/2

Ao > 2 fpeak[AH/V(f) ± σA(f)] = fo ± 5%

σf < σ (fo)

σA (fo) < σ (fo)

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“nc =lwnw”; nw = number of windows selected for the average H/V curve; lw = window length; σf = standard deviation of H/V peak frequency; fo = number of significant cycles; f = current frequency; ε (fo) = threshold value for the stability condition σf < ε (fo); Ao = H/V peak amplitude at frequency; AH/V (f) = H/V curve amplitude at frequency; f+ = frequency between fo and 4fo for which AH/V(f+) < Ao/2; σA (f) = “standard deviation” of AH/V (f), σA (fo) is the factor by which the mean AH/V(f) curve should be multiplied or divided; f- = frequency between fo/4 and fo for which AH/V(f-) < Ao/2.