if site has sufficient thickness, the natural vibration period of site(1D) would appears long periods character. Meanwhile, when earthquake propagated in sufficient thickness site,  the higher frequency(shorter periods) would be filter. so the frequency of earthquake would more close to the  natural vibration period of site. the soil amplification would greater. 

The natural period of vibration of a tall building is considerably lower than a 2 stories house. At the same time large and deep basins vibrate naturally at lower periods than fluvial valleys.  Larger structures allows that longer resonant wavelengths propagate within themselves.

But, in case of earthquakes, soil amplification is not only dependent by thickness or soil type, it depends even on magnitude, depth and distance of the specific earthquake.

To record long period ground motion you need that very low frequency wave have time to cycle within the basin, this means that you have to record at some distance the earthquakes (10 cycles at 5 seconds within a basin that have an average S-wave velocity of 1 km/s have to be recorded at least at 50 km or more)

Moreover, only strong earthquakes characterised by lower frequencies than medium size earthquakes, are able to excite longest periods and amplify deep sediments enhancing both duration and amplitude. Medium size earthquakes are unable to produce low frequencies (rupture length and width are small) and thus penetrate only the shallower part of the soil column (short periods).

The earthquake depth, at the same, takes some role. In particular where the rupture is efficient  in terms of depth is a key factor in generating surface waves that could be entrapped in a deep basin. Surface waves generally have longer periods than body waves and are geometrically less attenuated (attenuation works in a plane (2D) while body waves are attenuated in the volume (3D)).    

Other effects like directivity and radiation could have a strong influence on the periods that depending on distance from the fault could strongly influence your records.

Thanks you Dr. Chen Su and Dr. Alessandro Vuan for your answer

Natural period of the soil (assuming there is only one layer of soil over bedrock) is calculated as T=4H/V,  where V and H are shear velocity and thickness of the soil layer. As you can see, when H increases, T increases. (Also, note that T is inversely proportional to V, which means for softer soils V is smaller and T is higher.) So, if the earthquake time history at hand has this long period component in it, that period will be amplified while the other (higher) periods will be somewhat filtered out.

You could check this pdf http://users.ntua.gr/gbouck/downfiles/geot_earthquake_eng_Ch4-SITE-ADERS-10.pdf

Thanks you Rabia Sarica LeClerc and Dr. Alessandro Vuan

When the earthquake wave passes from a dense media to a looser one breaks in a greater angle which results in greater amplitudes. In this process all parts of wave will have higher amplitude, but the nature of media determine the amount of amplitude. As we can see the higher amplitude in looser media (loose soils) than firm one.

Naturally, the passing wave in a soil layer will filtered, but this filtering process affects the high frequency part of earthquake wave more deeply. This is because of nature of soil (a loos material) in which the energy of higher frequencies will dissipated since the soil particles damped this frequencies by moving in their place freely (this condition can not be met in rock).

As can be seen from previous results of researches also, the Looser soils have greater effects, on passing waves, than firm soils.

In other hand increasing the thickness of soil layer increases the pass of wave propagation and the filtering process will affect more deeply on dissipating the energy of high frequency part of earthquake wave.

thank you Dr. Reza Hossseini

in Case of soil site with Sufficient depth i.e there is greater depth of soil before the bedrock, it will obviously have higher natural period . So, during earthqauke, the soil will amplify the waves with higher natural period(lower frequency) and filter out those with lower period or higher frequency . It kind of follow the resonance effect.