Development Of Liquefaction Hazard Map Using A Geostatistical Method

Abstract

The liquefaction potential index (LPI) is currently used in practice to produce hazard maps in regions susceptible to liquefaction using traditional contouring methods. Limited studies exist using geostatistics as the contouring method (Baise et al. 2006); furthermore, data density has not been evaluated to determine what data is required to develop accurate maps. This study compares a liquefaction hazard map developed by kriging LPI values with observed liquefaction cases at very well documented sites to give further insight into the accuracy of these methods. Contour maps of LPI values in the Kaiapoi, New Zealand, and Oakland, California, areas were developed using both traditional contouring methods and more advanced geostatistical methods (i.e., kriging). These maps were then compared to liquefaction documented after the Darfield Earthquake in the Kaiapoi region (Cubrinovski et al., 2010) and the Loma Prieta earthquake in the Oakland region (Holzer 1989). Model calibration was completed by adjusting input parameters such as water elevation and the variogram model used in kriging. The goal was to begin with the most accurate predicted liquefaction hazard map (PLHM) possible and reduce the data and monitor the effects. The predicted liquefaction hazard map was compared to the observed liquefaction hazard map (OLHM) recorded after each of the actual earthquake events the match was quantified using kappa statistics. Input LPI data was reduced and the maps were compared to analyze for trends. Initial data density in the Kaiapoi region was significantly more favorable for this analysis approach and the resulting predicted map matched the observed liquefaction well, with a kappa value up to 0.43. Oakland data was significantly less dense and the resulting match yielded a kappa value up to 0.16. Trends showed that in all cases there was an inflection point in the plots of data density vs. kappa value. This change in slope indicated that data reduction below that point would significantly affect the match between the PLHM and the OLHM. Kappa value match was also found to be highly dependent on the data density. In Oakland the data density was nearly two orders of magnitude lower than in Kaiapoi, and the match between the PLHM and the OLHM reflected the reduced data density. Methods from this study can be used to develop more accurate maps in regions where traditional contouring methods are currently used with the available data. This research can also provide regions with the ability to forecast how many additional data points would be required to increase the accuracy of an existing PLHM. It would also allow users to focus efforts on areas that are the least defined in the existing maps—reducing costs for municipalities that want to develop more accurate maps.