State Space Approach to Signal Extraction Problems in Seismology

State space methods for extracting signal from noisy seismic data are shown. The method is based on the general state space model, recursive filtering and smoothing algorithms. The self-organizing state space model is used for the estimation of time-varying parameter of the model. In this paper, we show five specific examples of time series modeling for signal extraction problems related to seismology. Namely, we consider the estimation of the arrival time of a seismic signal, the extraction of small seismic signal from noisy data, the detection of the coseismic effect in groundwater level data contaminated by various effects from air pressure etc., the estimation of changing spectral characteristic of seismic record, and spatial-temporal smoothing of OBS data.