Statistical models for earthquakes incorporating ancillary data : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Palmerston North, New Zealand
This thesis consists of two parts. The first part proposes a new model – the Markov-modulated
Hawkes process with stepwise decay (MMHPSD) to investigate the seismicity rate. The MMHPSD
is a self-exciting process which switches among different states, in each of which the process has
distinguishable background seismicity and decay rates. Parameter estimation is developed via the
expectation maximization algorithm. The model is applied to data from the Landers earthquake
sequence, demonstrating that it is useful for modelling changes in the temporal patterns of seismicity.
The states in the model can capture the behavior of main shocks, large aftershocks, secondary
aftershocks and a period of quiescence with different background rates and decay rates. The state
transitions can then explain the seismicity rate changes and help indicate if there is any seismicity
shadow or relative quiescence.
The second part of this thesis develops statistical methods to examine earthquake sequences
possessing ancillary data, in this case groundwater level data or GPS measurements of deformation.
For the former, signals from groundwater level data at Tangshan Well, China, are extracted for the
period from 2002 to 2005 using a moving window method. A number of different statistical techniques
are used to detect and quantify coseismic responses to P, S, Love and Rayleigh wave arrivals.
The P phase arrivals appear to trigger identifiable oscillations in groundwater level, whereas the
Rayleigh waves amplify the water level movement. Identifiable coseismic responses are found for
approximately 40 percent of magnitude 6+ earthquakes worldwide. A threshold in the relationship
between earthquake magnitude and well–epicenter distance is also found, satisfied by 97% of the
identified coseismic responses, above which coseismic changes in groundwater level at Tangshan
Well are most likely.
A non-linear filter measuring short-term deformation rate changes is introduced to extract signals
from GPS data. For two case studies of a) deep earthquakes in central North Island, New
Zealand, and b) shallow earthquakes in Southern California, a hidden Markov model (HMM) is
fitted to the output from the filter. Mutual information analysis indicates that the state having the
largest variation of deformation rate contains precursory information that indicates an elevated probability
for earthquake occurrence.