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