Marked spatio-temporal point patterns, periodicity analysis and earthquakes: an analytical extension including hypocenter depth

Abstract

The longitude, latitude and depth of the hypocenter in 3-D space and the date and time of rupture makes an earthquake a “point” in a spatio-temporal point pattern, observed over a region and months, years or decades. The magnitude of earthquakes marks the point pattern, as would hypocenter depth do if only the longitude and latitude of epicenters were used for location in 2-D space. Stochastic declustering, based on a space–time ETAS model (ETAS: epidemic-type aftershock sequence), is a procedure that can be applied in the preliminary stage of an earthquake catalog data analysis. Stochastic declustering procedures have underlying assumptions, such as the time independence of the background intensity function whether the spatial framework is 2-D or 3-D, and a separate treatment of hypocenter depth from longitude and latitude when the spatial framework is 3-D. Cyclical processes in the Earth, including tides and seasonal surface water loads, can introduce periodic behavior in earthquake occurrence and related variables. The effects of ETAS-based 2-D and 3-D declustering on the outcome of periodicity analyses performed from the resulting earthquake data catalogs are studied. The research objectives and statistical challenges include the detection of periodicities for hypocenter depth in addition to monthly earthquake number, and the risk of missing observations for hypocenter depth when the monthly earthquake number after declustering is zero. A version of the method of multi-frequential periodogram analysis (MFPA) that allows for missing observations in the input temporal series is presented in detail, and applied to hypocenter depth (monthly mean and median) for central and northern California from January 2006 to December 2014. The results obtained for the 2-D and 3-D declustered catalogs are compared with those for the original catalog for this region. A semiannual periodicity in hypocenter depth is detected for the original and 2-D declustered catalogs, and fitted with the goal of relating it to periodicities found in the time series of monthly earthquake numbers. Using these results for central and northern California earthquakes, some of the assumptions on the intensity function of the spatio-temporal point process in stochastic declustering are discussed and future research perspectives are proposed.