Deterministic hazard assessment

Methodology

A Deterministic Seismic Hazard Assessment (DSHA) involves the development of a particular seismic scenario upon which a ground-motion hazard evaluation is based.84 The scenario involves the postulated occurrence of an earthquake of a specified size occurring at a specified location that produces a ground-motion estimated using a specified empirical model. The controlling scenario (from all possible seismic scenarios) defines a Maximum Credible Earthquake (MCE) in terms of magnitude, source-to-site distances, and ground-motion intensity.

For a given source, the ground-motion model and the hazard level selected defines an earthquake scenario. The source with the combination of magnitude, source-to-site distance and ground-motion models which gives the largest ground-motion intensity will be the controlling scenario. The controlling scenario from all possible seismic scenarios defines the maximum credible earthquake in terms of magnitude and source-to-site distances.

The ground-motion hazard level should be established based on the uncertainty of the seismic hazard characterisation, the critical nature of the project, and the consequences of underperformance.

The following steps will be required for a DSHA:

Step 1: Identify all seismic sources that can generate strong ground shaking at the site, and characterise each seismic source in terms of location, geometry, sense of slip, maximum size of rupture area, and earthquake occurrence rates for all magnitudes relevant to the site hazard.

Step 2: From historical and instrumental seismicity, identify the maximum probable earthquake (MPE) that occurred at the site and the maximum credible earthquakes (MCEs) for each source.

Step 3: Select ground-motion models appropriate for the seismic sources, seismotectonic setting and site conditions.

Step 4: Estimate the different source-to-site distances required for each ground-motion model. For finite fault type sources, estimate the source-to-site distances based on the MCEs.

Step 5: Identify the controlling scenario in terms of M-R pairs and define the ranges of representative magnitudes and distances for the records selection stage.

The above parameters determines a large number of different rupture plane combinations, which keep the size of the rupture area, the hypocentral depth and the epicentral distance to the project site invariant. Using a simple numerical simulation algorithm, the intensities \(S_a(T_n)\) can be obtained for all periods of interest and all ground-motion models. Assuming a log-normal distribution, the first and second order moments of the probability density function of the seismic intensity can be obtained and therefore, the hazard spectra for all periods.

Uncertainty Analysis

The estimation of the maximum credible earthquake (MCE) associated with a known finite rupture source postulates a scenario in which the magnitude and hypocentre of the fault are assumed and is equivalent in its basic form to a deterministic seismic hazard assessment. As GMPEs include other source parameters, such as fault plane rake angle, fault plane dip, faulting type (strike-slip, normal, reverse), the estimation of the maximum expected intensity of a given source requires a strategy to incorporate the uncertainty of these parameters.

To incorporate these epistemic uncertainties in the design values it is assumed that the seismic intensities reported by GMPE models are realizations of a random process, in which each set of parameters \(\theta\) determines a set (realization) of seismic intensities in rock for a given \(M_w,R\) scenario.

If the unknown fault parameters can be defined from discrete parameters (e.g. a hypocentral depth, or a single dip angle), the simplest approach to incorporate this uncertainty is to add a sub-level of new branches of the logic tree that now includes the possible deterministic scenarios that could be assumed for these parameters. The main limitation of this strategy is that in general the parameters that allow postulating a deterministic failure scenario are not known, but rather a continuous range of physically reasonable values, which makes it difficult to address using logic trees.

To overcome this limitation, a modified methodology of the classical DSHA approach is proposed that basically consists in performing a series of simulated realizations of possible scenarios resulting from the combination of discrete parameters of the rupture area. Then, for a given magnitude and epicentral distance, ranges of physically possible values of fault rupture parameters are selected, and all the seismic motion intensities associated with that rupture scenario are estimated.

For each intensity probability distribution function of each model, about 100,000 scenarios were simulated and then averaged by a weighted sum in log-normal space according to the weights assumed in the logic tree. Assuming that the logarithm of these intensities has an approximately normal distribution, the set of realizations allows direct estimation of the parameters of the weighted intensity probability density function for source and scenario. Then, the intensity of the maximum credible earthquake can be treated probabilistically as a random variable, in the same way as the intensity obtained by the PSHA model.

As in the PSHA methodology, the scenario-based methodology incorporates epistemic uncertainty through a logic tree, but intensities are not obtained as a direct sum of percentiles for all possible combinations of rupture parameters for a given scenario.

The fundamental difference between the classical DSHA methodology and the methodology implemented in this work is that in the deterministic approach the values of each seismic motion prediction model are obtained and the models are combined by means of a weighted sum for a selected target percentile (for example 84th). In the proposed methodology, random variables representing intensity are simulated and summed (by weighted averages) over a large number of realizations in log-normal space, and the density function parameters and the probability of exceedance at any given percentile are estimated.

Results

Controlling scenario

The scenario controlling of the seismic hazard is given by the Dorothy Hills fault. For this scenario, the finite-fault metrics were obtained assuming a hypocentre depth between 5 and 15 km and a dip angle of \(\delta=45\,^\circ\). Given the site position relative to the fault, the Joyner-Boore distance \(R_{JB}=4.1\,\mathrm{km}\) and the rupture distance ranges \(R_{RUP}=7.1-15.3\,\mathrm{km}\).

Peak Ground Acceleration (PGA)

Peak Ground Acceleration (PGA) is defined as the maximum ground acceleration that can occur during earthquake shaking at a particular location and represents the amplitude of the largest absolute acceleration recorded on an accelerogram during a particular earthquake. Mean PGA values in rock reported by the different ground-motion models selected for GGM, assuming a maximum credible event of \(M_w\approx\) 5 and different distances to the source are shown in Figure 17. The solid line represents the weighted-average model obtained from the logic-tree adopted before (Figure 16). The distribution percentiles are available in the project’s dashboard DSHA.

Mean PGA values in rock reported by the different ground-motion models

Figure: 17: Mean PGA values in rock reported by the different ground-motion models

Figure 18 shows percentile distribution of the weighted-average PGA values in rock for different source-to-site distances assuming a maximum credible event of \(M_w\approx\) 5.

Weighted-average PGA values in rock for different confidence levels. [g]

Figure: 18: Weighted-average PGA values in rock for different confidence levels. [g]

Table 9 and Table 10 summarise the unweighted peak-ground accelerations (PGA) of the different seismic motion prediction models used in this study and the resultant weighted-average obtained from the logic-tree adopted for the region. The maximum credible earthquake assumed for the controlling scenario results in \(PGA\approx\) 0.322 \(\mathrm{g}\)

Hazard Spectra

The seismic shaking intensities resulting from the linear response of an SDOF oscillator at different fundamental periods \(T_n\) define the response spectrum \(S_a(T_n)\) of each GM model in rock, for a scenario given by the source size \(M_w\), the closest distance to the source \(R\), source rupture area parameters and distance metrics. The weighted-average ground-motion model for \(M_w\approx\) 5 and \(R\approx\) 5 \(\mathrm{km}\) determines the design earthquakes \(S_a(T_n)\) for rock at the site. Figure 19 shows the mean spectral ordinates reported from different ground-motion models. Figure 20 shows the mean weighted-average spectral ordinates \(S_a(T_n)\) and different percentiles. Mean spectral ordinates for other site conditions than rock in terms of NEHRP classes are shown in Figure 21. The plots for other percentiles are available in the project’s dashboard DSHA.

Mean spectral Ordinates Sa(T) for different ground-motion models [g]

Figure: 19: Mean spectral Ordinates Sa(T) for different ground-motion models [g]

Spectral Ordinates Sa(T) distribution [g]

Figure: 20: Spectral Ordinates Sa(T) distribution [g]

Mean scenario-based spectral ordinates for different site conditions in  [g]

Figure: 21: Mean scenario-based spectral ordinates for different site conditions in [g]


  1. S. Kramer, Geotechnical Earthquake Engineering (Prentice Hall Upper Saddle River, NJ, 1998).↩︎