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The spectral ratio technique is a common useful way to estimate empirical transfer function to evaluates site effects in regions of moderate to high seismicity. The purpose of this paper is to show that it is possible to estimate empirical transfer function using spectral ratios between horizontal and vertical components of motion without a reference station. The technique, originally proposed by Nakamura to analyze Rayleigh waves in the microtremor records, is presented briefly and it is discussed why it may be applicable to study the intense S-wave part in earthquake records. Results are presented for three different cities in Mexico: Oaxaca, Oax., Acapulco, Gro., and Mexico City. These cities are very different by their geological and tectonic contexts and also by the very different epicentral distances to the main seismogenic zones affecting each city. Each time we compare the results of Nakamura's technique with standard spectral ratios. In all three cases the results are very encouraging. We conclude that, if site effects are caused by simple geology, a first estimate of dominant period and local amplification level can be obtained using records of only one station.

The linear, large-scale and small-scale amplification effects in the Mexico City valley, related to both the surficial clay layer and the underlying thick sediments, are investigated with two-dimensional (2D) models and compared with the results of simple one-dimensional (1D) models. The deep sediments are shown to be responsible, on their own, for an amplification ranging between 3 and 7, a part of which is due to the 2D effects in case of low damping and velocity gradient. This result is consistent with the observed relative amplification around 0.5 Hz at CU stations with respect to TACY station. The amplification due to the clay layer is much larger (above 10), and the corresponding 2D effects have very peculiar characteristics. On the one hand, the local surface waves generated on any lateral heterogeneity exhibit a strong spatial decay, even in case of low damping (2%), and the motion at a given site is therefore affected only by lateral heterogeneities lying within a radius smaller than 1 km. On the other hand, these local 2D effects may be extremely large, either on the very edges of the lake-bed zone, or over localized thicker areas, where they induce a duration increase and an overamplification. The main engineering consequences of these results are twofold: i) microzoning studies in Mexico City should take into account the effects of deep sediments, and ii) as the surface motion in the lake-bed zone is extremely sensitive to local heterogeneities, 1D models are probably inappropriate in many parts of Mexico City.

[1] We present results of the analysis of microtremor measurements using a small array. Our analysis is based on the computation of cross-correlation functions between stations in both frequency and time domains. We obtain similar results in both domains and link those results to the application of Aki's spatial autocorrelation method of using a single station pair and to recent studies that have shown that the Green's function between two stations can be retrieved from the temporal cross correlation of seismic noise. We show that the same simple subsoil structure allows interpretation of our correlation results in time and frequency. We observe both Love and Rayleigh waves; however, Love waves dominate the records in our lower-frequency range (between 3.6 and 6 Hz), while Rayleigh waves are prevalent in the records in our higher-frequency band (from 6 to 20 Hz). Frequency domain cross correlation yields better results in the lower-frequency range, while time domain cross correlation shows very clear results in the higher-frequency band. Thus both analyses are complementary. Our results show that ambient vibration recorded at the free surface includes different types of waves but that the correlation between any two stations is governed by the more stable propagation mode between them, surface waves in the case of a layered medium. Our results shed some light on the nature of microtremors and on the reasons why the spatial autocorrelation method or the horizontal-to-vertical spectral ratios are useful in geophysical and site response studies.

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