Recent performance improvements and enhanced capabilities of the OpenQuake-engine now make it possible to run highly complex hazard and risk analysis. We are pleased to showcase a few key findings from GEM’s state-of-the-art risk assessment for California using the OpenQuake-engine. The hazard model used in this analysis is the 2014 update to the National Seismic Hazard Model for California, which itself is based on the Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3) published by the Working Group on California Earthquake Probabilities (WGCEP).

This article briefly describes the process involved in creating a residential exposure model for the United States and the derivation of analytical fragility models for the commonly observed building typologies in the country. We illustrate how these fragility models can be used to compare the collapse risk for these building typologies across different cities in California. Next, we highlight a few relevant risk results computed using the full logic-tree comprising 7,200 independent branches for the San Francisco Bay Area.

The penultimate section describes the sensitivity analysis conducted by GEM to investigate the relative contribution of the different components of the model to the overall uncertainty in the risk results. Finally, we present our methodology for trimming the logic-trees to obtain simplified models that can provide risk modelers with results that are close approximations of those obtained using the full model, but at a fraction of the computational cost.

### Exposure modeling

Starting with raw data on population and housing characteristics from the 2010—2014 American Community Survey, GEM has created a set of residential exposure models for the United States. Several other datasets have also been used to inform the model. For instance, the National Land Cover Database allows us to identify areas of high-intensity development, where we would expect to find a greater proportion of tall buildings, and undeveloped areas, which do not have any assets. Figure 2 shows the landcover map for the San Francisco Bay Area.

Datasets from the 2009 Residential Energy Consumption Survey (RECS) conducted by the Energy Information Administration (EIA) are used to improve our estimates of the average square footage of housing units across the United States. The exposure model classifies structures into 36 distinct typologies. For California, this classification is done by applying a set of “mapping schemes” defined for the Western U.S. in ATC-13. Finally, based on the age-profile of the buildings and the seismic design category assigned at the location of the buildings in the 2000 International Building Code, the assets were categorized into pre-code, low-code, moderate-code, and high-code classes. Figure 3 shows the seismic zonation for the San Francisco Bay Area, and Figure 4 shows the residential exposure for the same region.

### Seismic fragility modeling

Seismic fragility models for a large set of building typologies commonly observed in the United States were also derived using an analytical approach. These structural fragility models use spectral acceleration as the intensity measure, thus compatible with common probabilistic event-based risk analysis. To represent each building class, we created a set of single degree of freedom (SDOF) approximations. Next, we subjected each of these SDOF models to a nonlinear time-history analysis using the FEMA P695 set of far-field records scaled to increasing intensity levels. The building response statistics collected from these analyses were then used to derive the fragility models for each building class. Considerable effort has been taken to incorporate the various uncertainties in the fragility modeling process. The variability in the capacity curve representing each building class, the uncertainty in the damage state threshold, and also the record-to-record variability in the building response have been considered. Figure 5 shows the fragility curves derived for light-frame residential wood structures, with four distinct seismic provisions.

We used these fragility models with the OpenQuake probabilistic damage calculator to conduct a comparative collapse risk assessment for all common building typologies across several cities in California. Figure 6 shows the results from this assessment for two of these cities — Oakland and San Diego. San Diego has lower seismic hazard compared to Oakland, and this is reflected in the collapse risk: the same building typologies in Oakland can be seen to have significantly higher collapse risk compared to San Diego. Wooden structures, which comprise more than nine-tenths of all residential buildings in California, have the lowest collapse probabilities across all typologies. The building classes with the highest collapse probabilities include the low-code and pre-code versions of low-rise precast concrete frames, low-rise concrete frames with unreinforced masonry infill walls, and low- and mid-rise unreinforced masonry bearing walls.

Such studies for appraising the comparative collapse risk of different building types across different cities – and built in different eras according to different seismic design codes – can be quite useful for the development of policies for region-wide risk mitigation strategies for existing structures, or to assess the most adequate seismic design for the region of interest.

### Probabilistic risk assessment using UCERF3

In conjugation with the scientific staff, the software development team at GEM has built new hazard and risk calculators dedicated to run models based on the state-of-the-art Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3) published by the Working Groups on California Earthquake Probabilities. Both the time-independent version of the forecast (released in 2014) and the time-dependent version (released in 2015) have been implemented. The rest of this article, however, is based on analyses using the time-independent version of the rupture forecast, which has a simpler logic-tree structure.

The time-independent version of UCERF3 comprises a total of 1,440 alternate models to fully represent the uncertainties involved in modeling the complex system of faults and current tectonic deformation in California. The 2014 update to the National Seismic Hazard Model for California employs five different ground motion models (GMMs), making for a total of 7,200 individual hazard calculations. GEM has calculated economic losses for the residential exposure in California for all 7,200 of these branches. Using the newly implemented OpenQuake UCERF3 calculators, we compiled catalogs of simulated earthquakes spanning a period of 10,000 years for each of the 1,440 source model branches of the UCERF3 time-independent logic-tree. Figure 7 shows one such realisation of a catalog for the San Francisco Bay Area.

For each of the 7,200 branches, we computed various risk metrics, such as Average Annual Losses (AAL), and losses at 100-year and 250-year return periods. Figure 8 shows the loss exceedance curves generated by each of the 7,200 branches for the residential exposure in the San Francisco Bay Area. Figures 9 and 10 show the histograms of the AAL and 250-year loss for the same region. The topographic slope-based Vs30 values provided by the USGS Global Vs30 Server, based on the methodology described by Wald and Allen (2007) were used to model the site conditions for the above calculations.

These results demonstrate the computing capabilities of the OpenQuake-engine, particularly when faced with highly complex calculations such as the hazard and risk models for California.

### Sensitivity analysis

One of the advantages of having access to such a large number of solutions from OpenQuake is that we can subsequently use them to conduct a thorough sensitivity analysis. Such an exercise can provide the following information:

- Identify the full distribution of various risk metrics that can be considered feasible from a scientific point of view.
- Quantify the relative contribution of various branches to the overall uncertainty in the seismic risk results.
- Propose criteria to reduce the complexity of the model by trimming the logic-tree.

We proceeded to conduct such sensitivity analyses for portfolios of various sizes across California, studying the influence of the different components of the UCERF3 model on multiple risk metrics. The results from one such study, conducted for the 250-year loss metric for the San Francisco Bay Area are shown in Figures 11 and 12. Figure 11 is a tornado-diagram plot for this portfolio and metric, in which the two edges of each bar represent the minimum and maximum values of the range of 250-year loss values for each model component. The vertical line in the center of the chart represents the median 250-year loss across all branches.

Figure 12 shows the results from a marginal-means sensitivity analysis for the same portfolio. This type of analysis makes it simple to identify the model components that contribute most toward the overall uncertainty: if the marginal means within a particular component are nearly equal, we can conclude that that component has little influence on the results; on the other hand, if a component has a great influence on the results, then its marginal means would be expected to vary considerably.

From both the tornado diagram and the marginal means chart, we observe that the the assumptions concerning the total rate of M≥5 events in the region, the deformation model, and the choice of the ground motion model are the biggest contributors of uncertainty in the estimate of the 250-year loss for the San Francisco Bay Area residential portfolio.

The model components contributing most to the overall uncertainty can be quite different for different portfolios, and also for different risk metrics computed for the same portfolio. Figures 13 and 14 illustrate some additional findings considering different regions in California: The San Francisco Bay Area, Greater Sacramento, Napa County, and the San Diego Metropolitan region. Figure 13 considers the average annual loss metric while Figure 14 is based on the 250-year loss metric for the same building portfolios.

### Logic-tree trimming

Following the sensitivity studies, we gain an understanding about the low-sensitivity components of the full model. These components can potentially be excluded from the model without significantly affecting the distributions of the risk metrics. In this manner, the full logic-tree was selectively pruned for different portfolios across California, for three different risk metrics: the AAL, the 100-year loss, and the 250-year loss.

The resultant distributions from the trimmed logic-tree for the San Francisco Bay Area are shown below in Figure 15 for the AAL and Figure 16 for the 250-year loss. The trimmed logic-tree in both cases retains only the components of the deformation model, the total rate of M≥5 events in the region, and the ground motion model. We see in both cases that the results obtained using the simplified model comprising only 75 branches are very similar to the results obtained using the full logic tree.

All three of the steps described above serve important purposes in the risk modeling process. The computations involving uncertainty propagation through the full logic-tree allows understanding the range and distribution of different risk metrics. The sensitivity analysis can identify the parts of the model that contribute most toward the overall uncertainty. Finally, logic-tree trimming enables us to reduce the runtime for the model by at least two orders of magnitude while still managing to obtain results that are very close approximations of those obtained by running the full model.

[1] FM ≘ Fault Model, DM ≘ Deformation Model, SR ≘ Scaling Relationships, DSR ≘ Slip Along Rupture, M5 ≘ Total M≥5 Event Rate (yr^{-1}), MMAX ≘ Off-Fault M_{max}, SPATIALPDF ≘ Off-Fault Spatial Seismicity PDF, GMM ≘ Ground Motion Model, SM ≘ Site Conditions Model

For additional information about the datasets, methodologies, tools and models described herein, please contact us at **integrated_risk@globalquakemodel.org**.