**State Space Approach to
**

Signal Extraction Problems

in Seismology

**Roles of Statistical Models**

**Outline**

**Change of Statistical
Problems**

**Smoothness Prior**

**Automatic Parameter
Determination **

via Bayesian Interpretation

**Time Series Interpretation
**

and State Space Modeling

**Applications of State Space
Model**

** State Space Models**

**Kalman Filter**

**Non-Gaussian Filter/Smoother**

**Recursive
Filter/Smoother**

for State Estimation

**Sequential Monte Carlo
Filter**

**Self-Tuned State Space Model**

**Tools for Time Series
Modeling**

**Examples**

**Extraction of Signal From
Noisy Data**

**State Space Model**

**Extraction of Micro
Earthquake**

**Extraction of Micro
Earthquake**

**Extraction of Earthquake
Signal**

**3D-Modeling**

**Slide 23**

**Detection of Coseismic
Effect **

in Groundwater Level

**Automatic Data Cleaning**

**Model for Outliers**

**Missing and Outlying
Observations**

**Slide 28**

**Slide 29**

**Extraction of Coseismic
Effect**

**State Space Representation**

**AIC Values**

**Slide 33**

**Extraction of Coseismic
Effect**

**State Space Model**

**Slide 36**

**Detected Coseismic Effect**

**Slide 38**

**Slide 39**

**Effect of Earthquake**

**Findings**

**Exploring Underground
Structure **

by OBS (Ocean Bottom Seismogram) Data

**Observations by an
Experiment**

**Slide 44**

**An Example of the
Observations**

**Direct wave, Reflection,
Refraction**

**Objectives**

**Time series at hypocenter (D=0)**

**Model for Decomposition**

**Decomposition of Ch-701 (D=4km)**

**Decomposition of Ch-721 (D=8km)**

**A Small Portion of Data**

**“Spatial” Filter/Smoother**

**Spatial Model **

(Ignoring
time series structure)

**Local Cross-Correlation
Function**

**Spatial-Temporal Model**

**Model of Propagation Path**

**Examples of Wave Path**

**Path Models and Arrival
Times**

**Path models and arrival
times(OBS4)**

**Local Time Lag**

**Path Models and the
Differences of the Arrival Times Between Adjacent Channels**

**Model for Decomposition**

**Spatial-Temporal Model**

**Spatial-Temporal Filtering**

**Spatial-Temporal
Decomposition**

**Mt. Usu Eruption Data**

**Volatility and component
models**

**Decomposition**

**Summary**

**Slide 71**

**Time-varying Spectrum**

**Estimation of Nonstationary
AR Model**

**State Space Representation**

**State Space Representation**

**Time-varying Coefficients**

**Time-varying Spectrum**

**Slide 78**

**Estimation of Arrival Time**

**Estimation of Arrival Time**

**Estimation of Arrival Time**

**Model & Implementations**

**State Space Representation
of AR Model**

**Lower Order Models**

**Arrival Times of P-waves**

**Arrival Times of S-waves**

**Posterior Probabilities of
Arrival Times**