INGV-RM approach Sample Clauses

INGV-RM approach. To assess to what extent each record is “different” from its statistical expectation and to judge if site behaviour or source is responsible for the “difference”, station-to-station and event-to- event variability are computed using the empirical attenuation relation discussed above in 2.3.2. We adopt the premixxx xxxx Xxxxxxxxxx and Xxxxxx (1992) described for their mixed model, assuming that, while deriving an empirical ground motion prediction equation, we can commit an error that can be a combination of fixed effects (i.e. whose estimate from all the dependencies can be considered) and a random effect (for which we do not estimate explicitly the dependency on all the data). According to them, the overall error can be partitioned into two parts: the inter-event and intra-event terms. An attenuation regression model has the form: ln yij = f(Mi, rij, θ) + εij + ηi (3.1) where yij is a ground motion parameter, f(Mi, rij, θ) is the attenuation equation, M is the earthquake magnitude, r is the distance, θ is a vector of model parameters, εij is the error term of the jth recording from the ith event and represent the intra-event variations, and ηi represent the inter-event variations. ηi and εij are assumed to be independent, normally-distributed variants with variances σ2 and τ2, respectively. For each period, to derive estimates of ηi and εij, we use a maximum likelihood formalism borroxxx xxxm Spudich et al. (1999), who in their turn adapted the maximum likelihood mxxxxx of Xxxxxx & Xxxxx (1993) to the problem of determining the mean value of the residuals (the bias) and its standard deviation. The residuals are evaluated with respect to the ad hoc computed regression (2.1) using the predominant period. Figure 3.2 shows the estimated values of the over-all standard deviation, as well as the inter- and intra-event variations as a function of period.