Earthquake Forecasting under Short Term Aftershock Incompleteness

Forecasting earthquakes becomes problematic in the initial period after a massive earthquake. During this time, many earthquakes occur following the main event. These earthquakes are known as “aftershocks”. Seismic networks record information regarding earthquakes. Generally, a seismic network consists of several stations, which are set up in different locations. The energy released by the earthquakes travels to a seismic station in the form of a seismic wave. Each of the seismic stations in a seismic network measures the ground movement from the seismic wave signals arriving at the station. During the early hours after a large earthquake, seismic stations receive waves from many earthquakes. As a result, they can not capture the signals of many small aftershocks as their waveforms get overlapped or buried within the waveforms of stronger aftershocks. Instead, they detect only large events as their signals are easily distinguishable. Therefore, the earthquake data collected in the initial period remains incomplete. This incompleteness is known as Short Term Aftershock Incompleteness (STAI). This thesis focuses on developing statistical techniques for forecasting future earthquakes effectively in the presence of STAI. More specifically, we strive to provide short term earthquake forecasts under incompleteness. In this thesis, two methodologies have been developed to deal with the problem of earthquake forecasting under incompleteness. Earthquakes are broadly divided into three classes, namely- foreshocks, mainshocks, and aftershocks. Here the mainshock refers to the main event, whereas the foreshocks and aftershocks refer to the events preceding and following the main event, respectively. The first methodology uses the weighted foreshock data to construct a refined prior distribution for the parameters of the Epidemic Type Aftershock Sequence (ETAS) model. The ETAS model is a self-exciting point process and is widely used for modelling earthquake phenomena. The prior distribution of this ETAS model parameters, obtained from the foreshocks, is known in this thesis as- “Power prior”. We used this prior for estimating the forecasting model ( the Omi model ) from the aftershock data with high efficacy. This methodology was applied to four Southern Californian earthquake sequences, namely- Northridge, El-Mayor Cucapah, Hector Mine and the Landers earthquake sequences. From our analysis, we found that this approach is beneficial in the very initial period after the main event as it improves the earthquake forecasting at that time. The second methodology concentrates on simulating missing aftershocks in the initial period after the main event. For this, we developed a “Reversible Jump Markov Chain Monte Carlo (RJMCMC)” sampler to sample the events from their conditional posterior under the Epidemic Type Aftershock Sequence (ETAS) model framework. In other words, we can say that this methodology samples artificial aftershocks to fill up the missingness. Later these simulated missing aftershocks can be combined with the observed dataset for further analysis. We applied this methodology on both synthetic catalogs and on four Japanese earthquake catalogs, namely- the catalogs for Tohoku, Miyagi, Kuril and Chuetsu earthquake sequences. The result is striking. Both the synthetic and real seismic catalogs showed improved performance while using generated missing events for better earthquake forecasting