Estimation of submarine mass failure probability from a sequence of deposits with age dates

The empirical probability of submarine mass failure is quantifi ed from a sequence of dated mass-transport deposits. Several different techniques are described to estimate the parameters for a suite of candidate probability models. The techniques, previously developed for analyzing paleoseismic data, include maximum likelihood and Type II (Bayesian) maximum likelihood methods derived from renewal process theory and Monte Carlo methods. The estimated mean return time from these methods, unlike estimates from a simple arithmetic mean of the center age dates and standard likelihood methods, includes the effects of age-dating uncertainty and of open time intervals before the fi rst and after the last event. The likelihood techniques are evaluated using Akaike’s Information Criterion (AIC) and Akaike’s Bayesian Information Criterion (ABIC) to select the optimal model. The techniques are applied to mass transport deposits recorded in two Integrated Ocean Drilling Program (IODP) drill sites located in the Ursa Basin, northern Gulf of Mexico. Dates of the deposits were constrained by regional bioand magnetostratigraphy from a previous study. Results of the analysis indicate that submarine mass failures in this location occur primarily according to a Poisson process in which failures are independent and return times follow an exponential distribution. However, some of the model results suggest that submarine mass failures may occur quasi peri odically at one of the sites (U1324). The suite of techniques described in this study provides quantitative probability estimates of submarine mass failure occurrence, for any number of deposits and age uncertainty distributions. INTRODUCTION Submarine mass failures present a signifi cant hazard for submarine infrastructure, for offshore energy development, and to coastal regions via the generation of tsunamis (Locat and Lee, 2002; Masson et al., 2006; Sawyer et al., 2009; ten Brink et al., 2009b; Jackson, 2012). One of the critical components of assessing natural hazards is determining the probability of occurrence. Empirically estimating the probability of submarine mass failures is particularly diffi cult, owing to the paucity of age dates for individual events. Typical problems in dating submarine mass failures and their deposits include lack of overlying strata, the inability to core underlying strata, and lack of datable material. William R. Normark, to whom the “Exploring the Deep Sea and Beyond” themed issue is dedicated, was heavily involved in several studies dating submarine mass failures (Lipman et al., 1988; Normark, 1990; Laursen and Normark, 2002; Lee et al., 2004; Fisher et al., 2005; Normark and Gutmacher, 1988). In particular, for the Palos Verdes debris avalanche in southern California, Normark et al. (2004) presented an ideal case where radiocarbon ages from piston cores of distal strata above and below an acoustically transparent layer continuous with the debris avalanche were used to constrain the age of the failure. This and similar studies (e.g., Hafl idason et al., 2005) provide the necessary data with which to determine the probability of submarine mass failures. For an empirical determination of failure probability, there are very few places in the world where repeated submarine mass failures have been individually dated. Cores from two Integrated Ocean Drilling Program (IODP) sites in the Ursa Basin, northern Gulf of Mexico (Fig. 1), penetrated a sequence of mass transport deposits (MTDs) (Expedition 308 Scientists, 2006a, 2006b). These deposits are interpreted to have been emplaced during episodes of retrogressive submarine mass failures upslope from the drill sites (Sawyer et al., 2009). As many as 14 MTDs have been identifi ed in both drill holes and have been assigned ages based on microfossils and magnetostratigraphy (Urgeles et al., 2007). The objective of this study is to develop a methodology to estimate the probability of submarine mass failures from a sequence of dated MTDs, such as found in the Ursa Basin. A previous study (Geist and Parsons, 2010) focused on the more common situation in which a sequence of MTDs are identifi ed in seismic refl ection records, but only a basal horizon beneath the oldest event is dated (e.g., Fisher et al., 2005). This previous method assumes that submarine mass failures occur as a stationary Poisson process . A gamma distribution is used as a conjugate prior to the Poisson distribution in a Bayesian framework, in order to estimate the Poisson intensity or rate parameter and its uncertainty. In contrast, it is not assumed from the outset of this study that submarine mass failures occur according to a Poisson process; several other time-dependent probability models that include clustering and quasiperiodic behavior are also examined. Other Bayesian techniques that have been adapted for small data sets have been proposed by, for example, Nomura et al. (2011). Paleoseismic records represent an analogous situation where a sequence of earthquake events has been dated. While similar in many respects, the stratigraphic record of paleoseismic and mass transport deposits differ in terms of the scale of their stratigraphic footprint and the effects of erosion and deposition processes on the retention of the event record. Individual paleoseismic events are generally marked by the presence of distinct colluvial wedges, angular unconformities, fi ssures, sand blows, upward termination of fault displacements, and abrupt lateral changes in bed thickness (McCalpin, 1996). Often, these stratigraphic indicators are present within close proximity to one another and over*[email protected] Exploring the Deep Sea and Beyond themed issue