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

Highlights

• New Zealand-specific magnitude-bound curve is developed from liquefaction observational data.

• Frameworks are proposed to back-calculate magnitude-bound curves for paleoliquefaction studies.

• Probabilistic and deterministic magnitude-bound curves are back-calculated for New Zealand.

• Probabilistic magnitude-bound curve is used to assess possible causative earthquakes of a paleoliquefaction feature.

Abstract

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 ~ M_w4.8 Christchurch earthquake and/or 1717 ~ M_w8.1 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.

Introduction

In regions experiencing infrequent moderate-to-large earthquakes, the historic record may be insufficient to provide accurate inputs for seismic hazard analyses because (1) some active faults may be historically seismically quiescent and not easily identifiable from surface evidence, thereby posing an unspecified potential earthquake source, and (2) seismic phenomena such as liquefaction and rockfall may pose a potential hazard but may not have occurred historically. The 2010–2011 Canterbury earthquake sequence (CES) in New Zealand provided a powerful demonstration of these limitations. The CES involved at least 7 damaging earthquakes sourced from at least 12 faults (Beavan et al., 2012) that were previously unidentified and historically seismically quiescent. As many as ten distinct episodes of liquefaction (Quigley et al., 2013) and five distinct episodes of rockfall (Mackey and Quigley, 2014) occurred at some sites in the mainshock (M_w 7.1 Darfield earthquake) and largest aftershocks (e.g., 2011 M_w 6.2 Christchurch earthquake, 185 fatalities). Approximately 75% of buildings within the central business district (CBD) of Christchurch required demolition or extensive repair (Kam et al., 2011). Due to extensive liquefaction-induced land and infrastructure damage, more than 6000 residential properties in eastern Christchurch were purchased by the central government (http://cera.govt.nz/residential-red-zone) at a post-insurance pay out loss exceeding $NZ 1 b ($US 800 m) (Parker and Steenkamp, 2012).

Pre-CES seismic hazard models for the region (e.g., Stirling et al., 2007) that combined regional active faults (source models) with ‘floating’ unidentified sources (distributed seismicity) indicated that (a) proximal, moderate M_w earthquakes from unidentified distributed sources (including blind faults) contributed the largest seismic shaking hazard to Christchurch, (b) earthquakes up to M_w 7.2 on unidentified sources beneath the Canterbury Plains west of Christchurch were possible, and (c) expected return times of potentially liquefaction-inducing peak ground accelerations (PGA ~ 0.1 to 0.2 g) for class C (shallow soil) site conditions ranged from ca. 50 to 200 yr. However, prior to the CES, none of this data had been seriously validated with rigorous paleoseismic investigations in Christchurch. The occurrence of a highly damaging series of earthquakes sourced from previously unknown and primarily blind faults highlighted the inherent incompleteness of source-based seismic hazard catalogs, demonstrating the necessity for geologic studies of prehistoric phenomena such as rockfalls (Mackey and Quigley, 2014) and liquefaction features (Bastin et al., 2015) to supplement seismic hazard models and predict the impacts of future earthquakes. Despite a wealth of recent paleoliquefaction studies in Christchurch (e.g., Almond et al., 2012, Quigley et al., 2013, Bastin et al., 2015, Bastin et al., 2015, Maurer et al., 2014, Villamor et al., 2014), a significant challenge remains in understanding the spatial distribution of earthquake sources and shaking intensities that induced paleo-liquefaction, and are thus capable of inducing future liquefaction, in this region.

Paleoliquefaction studies have two phases. The first phase entails the performance of field investigations, wherein paleoliquefaction features are located, mapped, and dated. The reader is referred to Obermeier et al., 2001, Obermeier et al., 2005 for broad overviews of paleoliquefaction field investigation, and to the intensive investigations by Obermeier and Dickenson (2000), Tuttle (2001), Talwani and Schaeffer (2001), Cox et al. (2004), and Tuttle et al., 2002a, Tuttle et al., 2002b, Tuttle et al., 2005 for specific case studies. The second phase, and the focus of this study, is back-analysis, wherein quantitative techniques are used to determine the magnitude of the causative paleoearthquake and better constrain its source location. Specifically, this study aims to advance the state of the art in back-analysis techniques so that the results of field investigation can be used to accurately assess the paleoseismic history of a region to the extent possible.

Back-analysis techniques have been increasingly applied in paleoliquefaction studies in many seismically active regions (e.g., Obermeier, 1998, Tuttle, 2001, Talwani and Schaeffer, 2001, Cox, 2004, Green et al., 2005, Bastin et al., 2015). While several techniques have been proposed for estimating earthquake magnitudes from paleoliquefaction data, one of the more credible and widely-used is the “magnitude-bound” procedure (e.g., Obermeier, 1998, Olson et al., 2005a, Olson et al., 2005b, Papathanassiou et al., 2005, Pirrotta et al., 2007, Tuttle and Hartleb, 2012). This approach uses correlations relating earthquake magnitude to the site-to-source distance of the most distal observation of liquefaction. Developed from observations in modern earthquakes, these correlations are commonly referred to as magnitude-bound curves. Fig. 1 presents several such correlations for a variety of geographic and tectonic settings (Kuribayahsi and Tatsuoka, 1975, Ambraseys, 1988, Papadopoulos and Lefkopoulos, 1993, Wakamatsu, 1993, Galli, 2000, Aydan et al., 2000, Papathanassiou et al., 2005, Pirrotta et al., 2007, Castilla and Audemard, 2007), where site-to-source distance is quantified in terms of epicentral distance (Fig. 1a) and the distance to most proximal fault rupture (Fig. 1b). The position of these curves, which bound the most distal liquefaction features, is inherently a function of earthquake source characteristics (e.g., rupture mechanism), transmission characteristics (e.g., ground motion attenuation and site effects), and liquefaction susceptibility (e.g., soil state and gradation, and ground water depth). Because these factors vary regionally, region-specific correlations provide more accurate estimates than those developed from global data (Obermeier et al., 2001, Olson et al., 2005a, Olson et al., 2005b).

In addition, inherent to these curves are differing criteria for data inclusion, including the quality and extent of field study, the certainty of earthquake source location and magnitude (e.g., instrumental vs. macroseismic), the style of faulting and focal depth, and the overall anomalousness of data. For example, in developing his curves, Ambraseys (1988) did not consider (1) deep-focus earthquakes, which produce more distal liquefaction than shallow crustal earthquakes; or (2) anomalous cases that would bias the maximum site-to-source distance of liquefaction, including those where conditions greatly enhanced liquefaction susceptibility, such as irrigated fields or sloping ground. Conversely, Castilla and Audemard (2007) included both deep-focus earthquakes and anomalous cases in developing their correlation from global data. For example, Castilla and Audemard (2007) include data from the 1977 M_w7.5 Bucharest, Romania earthquake, having a focal depth of 91–110 km (Ambraseys, 1988, Berg et al., 1980), as well as data from aftershocks following the 1989 M_w5.9 Bova del Tocuyo, Venezuela and M_w6.9 Loma Prieta, USA earthquakes. While further research is needed, it has been shown that surface manifestations of liquefaction may be observed at greater site-to-source distances during aftershocks than in equivalent-magnitude mainshocks, possibly due to increased liquefaction susceptibility from reduced aging-effects, or to the presence of existing liquefaction dikes, which act as conduits between liquefied strata and the ground surface (Green et al., 2013, Maurer et al., 2014). Due to the inclusion of this data, and as shown in Fig. 1a, the Castilla and Audemard (2007) correlation estimates a significantly lower magnitude at shorter site-to-source distances, as compared to using correlations proposed by other authors. Importantly, differing criteria for data selection can result in significant differences to magnitude-bound curves. Therefore, in addition to using regionally-appropriate correlations, familiarity with the provenance of a magnitude-bound curve is critical; to place derivative results in proper context, a user must be aware of a correlation's source data, development, and caveats for use.

While magnitude-bound curves specific to New Zealand have not yet been proposed, there is a clear and present need. In light of the prior inconspicuousness of local faults and the exceedance of design ground-motions during the CES, there is a need to reassess the magnitude-recurrence rates of earthquakes local to Christchurch. Preliminary evidence suggests liquefaction-inducing earthquakes occurred between A.D. 1000 and A.D. 1400 (Villamor et al., 2014) and between AD 1660 – 1803 and ca. 1905 (Bastin et al., 2015) in distinct parts of Christchurch, however the origins of these earthquakes are unknown. The penultimate earthquake on the source of the Darfield earthquake (Greendale Fault) occurred ca. 20–30 kyr ago (Hornblow et al., 2014) and rock fall evidence suggests that no large earthquakes have occurred on the local faults responsible for the 2011 February M_w6.2 and June M_w6.0 Christchurch earthquakes within the last 6000 to 8000 years (Mackey and Quigley, 2014), indicating that the CES sources were not responsible for the paleoliquefaction. Region-specific magnitude-bound curves could thus assist in the interpretation of such evidence and help to elucidate the region's paleoseismic history. As such, the objectives of this study are to: (1) develop a NZ-based magnitude-bound curve using the traditional approach of using modern liquefaction field observations; (2) develop NZ-based magnitude-bound curves using a newly proposed back-calculation approach using the simplified liquefaction evaluation procedure in conjunction with a regionally appropriate ground motion prediction equation (GMPE); and (3) demonstrate the use of these curves by analyzing paleoliquefaction features recently discovered in Christchurch. It is hoped that these correlations ultimately aid in more accurately assessing the regional seismic hazard.