Development of magnitude-bound relations for paleoliquefaction analyses: New Zealand case study

Magnitude-bound relations are often used to estimate paleoearthquake magnitudes from paleoliquefaction data. This study proposes New Zealand-based magnitude-bound curves that are developed using (a) liquefaction field observations and (b) a newly proposed back-calculation approach that combines the simplified liquefaction evaluation procedure with a regionally appropriate ground motion prediction equation. For (b) both deterministic and probabilistic frameworks are proposed. The magnitude bound curves back-calculated using either the deterministic or probabilistic frameworks are advantageous in that they can be used to predict the spatial distribution of liquefaction in regions where historical liquefaction field observations are limited or poorly documented, and because soil- and site-specific conditions can be incorporated into magnitude-bound analyses. Moreover, curves developed using the probabilistic framework allow for the range of possible causative earthquake magnitudes to be better understood and quantified. To demonstrate the use of the proposed relations, paleoliquefaction features discovered in eastern Christchurch (NZ) are analyzed. The 1869 ~ Mw4.8 Christchurch earthquake and/or 1717 ~ Mw8.1 Alpine Fault earthquake are found to be the most likely candidates amongst known historical and paleoearthquakes for triggering liquefaction over the permissible time range (ca. 1660 to 1905 A.D.). This study demonstrates the potential of the proposed magnitude-bound curves to provide insight in to past, present, and future hazards, proving their utility even in cases of limited evidence. The approach of developing and applying magnitude bound curves proposed herein is not limited to parts of New Zealand, but rather, can be applied worldwide.