A New Strategy for Developing Vs30 Maps

Despite obvious limitations as a proxy for site amplification, the use of time-averaged shear-wave velocity over the top 30 m (Vs30) is useful and widely practiced, most notably through its use as an explanatory variable in ground motion prediction equations (and thus hazard maps and ShakeMaps, among other applications). Local, regional, and global Vs30 maps thus have diverse and fundamental uses in earthquake and engineering seismology. An additional advantage of Vs30 measurements (rather than more complex frequency-dependent, site amplification characterizations), and perhaps one of the reasons it is so widely in use, is the ability to extrapolate Vs30 point observations to maps and thus to apply the limited existing data to important regional hazard mapping applications. It is this advantage upon which we expand in this study. Two common existing Vs30 mapping approaches, geology- and topographic-slope-based proxies, are attractive in that both are available in many areas of the world and can thus be applied over wide regions. Yet, although derived from or aimed to be consistent with observed Vs30 values, a limiting aspect of these current state-of-the-art Vs30 mapping strategies is that these approaches fail to directly incorporate the Vs30 observations back into the map. Likewise, predictive models typically fail to accommodate significant new Vs30 data as they become available even if they show trends that deviate from the default trend models. As such, we have developed a strategy for developing Vs30 maps that uses a hierarchical approach, where the baseline model is derived from topographic slope because it is available globally, yet geological maps and Vs30 observations contribute where available. Using the abundant measured Vs30 values in Taiwan as an example, we analyze Vs30 versus slope per geologic unit and observe minor trends that indicate potential interaction of geologic and slope terms. We then regress Vs30 for the geologic Vs30 medians, topographic-slope, and interaction (cross-term) coefficients for a hybrid model. The residuals of this hybrid model still exhibit a strong spatial correlation structure, so we use the kriging-with-a-trend method (the trend is the hybrid model) to further refine the Vs30 map so as to honor the Vs30 observations. Unlike the geology or slope models alone, this strategy takes advantage of the predictive capabilities of the two models, yet effectively defaults to ordinary kriging in the vicinity of the observed data, thereby achieving consistency with the observed data. Finally, we generalize this approach, outlining an overall "recipe" for hierarchical Vs30 map-making, dependent on the available data sources in a particular region. This new mapping strategy provides motivation for collecting Vs30 data at any spatial scale, because any new data can be used explicitly in refining Vs30 maps: geostatistically, both local point constraints and regional trend removal are extremely beneficial.