This dissertation presents four studies that model site effects through seismological fundamentals. In the first study, the horizontal-to-vertical spectral ratios (HVSR) from microtremor data obtained in California are used to evaluate two alternative microtremor-based proxies for site amplification for use in ground-motion models: the period-dependent amplitude of the HVSR and the site predominant frequency f0. The evaluation is based on the correlation structure, which shows that the normalized HVSR amplitude can explain up to 54% of the site term variability at long periods (4 s). Given that a fraction of the site term variability is already explained by the VS30 and Z1.0 scaling, the normalized HVSR amplitude can explain 20% to 24% of the remaining variability for spectral periods above 0.5 s. For shorter periods, the scaling between the site term and the normalized HVSR amplitude is weaker. In the case of f0, this parameter was available only in 46% of the sample, so despite the fact that it shows promising potential for the scaling with the site term, a strong conclusion cannot be demonstrated given that the lack of data does not allow a wide predictor domain sampling. These models can be used directly in the ASK14 GMM to modify the median and aleatory standard deviation. Alternatively, they can be used to constrain the site term in the context of a partially non-ergodic GMM. Including the HVSR measurement can have a significant effect on estimates of the ground motion at a site: the 5-95% range on the observed HVSR(T) values corresponds to factors of 0.6 to 1.6 for the median spectral acceleration for periods between 0.5 to 4 sec.
The second study evaluates the performance of VS30 for explaining site-term variability in the subductive tectonic environment of South America, using the NGA-SUB dataset. The performance of VS30 was poor, resulting in a correlation coefficient below 0.2 in the scaling between VS30 and the site term. One issue considered was that 81% of the reported VS30 were estimated via proxies. In this study, new measured VS30 data were included in the adopted dataset, but this addition did not improve the scaling. The addition of measured data suggests that VS30 is not a good site-amplification predictor for this region. Nevertheless, the sparsity of the data available for the region (only 273 seismic stations for an area of 5500 km length) does not allow to categorically discard VS30 as an efficient site amplification predictor. In a subsequent study, HVSR amplitude was evaluated as an alternative site amplification predictor. HVSR amplitude shows a stronger scaling with the site terms than VS30, explaining approx 37% of the site term variance. Another parameter, the predominant frequency, f0, seems to also be a promising site predictor in South America, explaining up to a 37% of the variance by its own, but only 40 stations have a determined f0, following the SESAME procedure. The lack of f0 data prevent the formulation of a site-term model including f0.
The third study focused in the seismic hazard analysis of the San Francisco Bay Area through 3D seismological simulations. Given the exponential growth of the computational processing power in the last decade, it has allowed to solve the wave equation at shorter wavelengths, higher frequencies, and softer materials, pushing the seismological simulations into the frequency range of interest for engineering. Three of the most important sources of uncertainty are the rupture characterization, the velocity model and the constitutive model. This last factor exerts important influence on simulations when materials reach non-linear deformation regimes. This study assesses the epistemic uncertainty induced by the USGS detailed velocity model for the SFBA. To do this, seven small earthquakes were simulated considering events that occurred in the last 12 years, ranging magnitudes from 3.8 to 4.4. These earthquakes were selected because they have small rupture areas, and consequently point-source double-couple mechanisms simplify their modeling. Once the source is fixed, most of the remaining within-event variability is induced by the epistemic uncertainty from the velocity model. The wave equation was solved up to 4.5 Hz, truncating the minimum shear wave velocity to 250 m/s. Regarding the velocity model performance, the residuals between observed and simulated data in the Fourier domain are centered around zero up to 1 Hz for the horizontal component and 2 Hz for the vertical component. Above these frequencies, the USGS velocity model tends toward an average over-prediction of the ground-motion amplitude. The simulated ground-motion within-event residual variability increases with frequency, from 0.5~LN-units at 0.3 Hz to 0.8 LN-units at 4.5 Hz. The spatial distribution of the residuals shows areas in the simulated domain where there are systematic biases in terms of spectral amplification. To keep track of these biases, a random variable from a Gaussian Process Regression was used to map sub-regions where the velocity model systematically induces over- or under-prediction. This variable provides a tool to identify where the USGS velocity model for the San Francisco Bay Area needs to be better constrained.
Finally, in the fourth study, 3D seismological simulations using a finite-difference code (SW4) showed that an additive model for combining the source, path, and site terms performs better than a multiplicative model. Given these results, a ground-motion duration model for crustal earthquakes based on the normalized Arias intensity was developed. The source term magnitude scaling was constrained by stochastic finite source simulations, which shows a coupling between the magnitude and distance scaling that is stronger for larger magnitudes. Because the definition of duration based on the normalized Arias intensity includes amplitude information, the simple concept of summing the source duration and the path duration can break down for large-magnitude earthquakes at short distances. The simulation results show that there is a saturation of the source effects on the duration for large-magnitude earthquakes at short distances. The within-site residuals from the newly developed duration model follow a power-normal distribution, with a skewness smaller than that of a log-normal distribution. The standard deviation of the model is similar to that of models developed under the multiplicative assumption. However, given the physics-based constraints, the model can be extrapolated more confidently to regions lacking data.
