During the M-w = 7.4 Izmit earthquake of 17 August 1999, the Ye, silyurt district of Istanbul underwent damage despite the epicentral distance of 90 km. At Avcilar ( 20 km west of Ye, silyurt), the ground motion was even stronger and has caused heavy damage and fatalities. We investigate whether the observed ground motions can be explained by theoretical site amplifications calculated from one-dimensional (1-D) shear-wave velocity models. For this purpose, microtremors recorded with sensor-arrays set up at two sites were analyzed to obtain phase velocity dispersion curves using both the conventional and the Capon frequency - wavenumber ( f - k) methods. At the Ye, silyurt site, the conventional f - k method offered reliable phase velocity estimations whereas the Capon method showed scatter in the estimations. At the Avcilar site, on the other hand, the Capon method provided a higher resolution than the conventional method and hence, allowed estimation of wavelengths up to seven times the array size. At the Ye, silyurt site, the shallow shear-wave velocity profile that is correlated with the lithology obtained from boreholes yields a ground motion amplification factor of about 3 at the frequency of 1 Hz. At the Avcilar site, the phase velocity dispersion curve is comparable with the one previously obtained using the spatial autocorrelation method. The site amplification factors calculated from the 1-D shear-wave velocity model are around 2 - 3 at the frequencies of 0.4, 1.2 and 2.3 Hz, which are about 2 - 3 times smaller than the amplifications obtained from reference-site techniques using weak/strong motion records of earthquakes. We suggest that the discrepancy may be caused by a 2- or 3-D effect introduced by surface and/or bedrock topography not accounted for by the horizontally stratified model considered here.