MODELING TEMPORAL VARIATIONS OF SEISMICITY PARAMETERS TO FORECAST

EARTHQUAKE RATES IN JAPAN

Christine Smyth and Jim Mori

Disaster Prevention Research Institute, Kyoto University

Talk Outline

Motivation behind and overview of the model

Overview of the theory

Results and validation of the model

Potential improvements

Motivation behind the Model Gutenberg-Richter distribution:

Parameters vary spatially [Schorlemmer et al., 2004; Wiemer and Wyss, 2002].

For short term studies, parameters vary temporally [Smyth and Mori, 2009].

Model temporal variations.

10log N a bM

Overview of the Model

For a small area:

1. Predict Gutenberg-Richter parameters for next year.

2. Overlay the distribution on a density of the area.

3. Adjust the rates of higher magnitude earthquakes based on their last occurrences.

MARFS

MARFSTA

Predicting Next Year’s N and B

Obtain N and b values for each year, using maximum likelihood (and counting!).

Apply a multivariate autoregressive model to these values.

Predict the next year’s values.

Predicting Next Year’s N and B

The autoregressive model is given by:

The matrix of predictor coefficients at lag k:

1

;p

T T k T

k

k

x A x ;t

t

t

b

N

x

1,...,t T

11 12

21 22

k kk

k k

A

Spatial Density Map

1

1

( , ) , ,

0 1, 1

G

g g gg

G

g gg

f

y y

1/2 1/2

1 1, , exp 22

T

g g g g g gd

y y y

Multivariate Normal Mixture Model

Spatial Density Map

135.0 135.5 136.0

34.4

34.6

34.8

35.0

35.2

35.4

35.6

Mixture Model of Tamba Region

LON

LAT

LON

LAT

0.2

1.2

1.6

1.8

135.0 135.5 136.0

34.4

34.6

34.8

35.0

35.2

35.4

35.6

Density Plot of Tamba Region given by Mixture Model

Simple Time Independent Formula MARFS

We obtain a prediction for each spatial bin (indexed by i) and each magnitude bin (indexed by j) by multiplying by the density of each bin and then scaling by .

1ˆ TijN

1ˆTb

1ˆ TN

1 1ˆ ˆ( , )T Ti iN f N y

Adjustment for Higher Magnitudes

Adjust the rates of earthquakes according to the last known time of a large earthquake.

Need the distribution of recurrence times for large earthquakes.

Use simulation approach.

Adjustment for Higher Magnitudes

1. Calculate the mean b, a and N over all years up to, but not including, the forecast year.

2. Obtain the Poisson probability for having greater than M5 earthquakes using “mean parameters”.

3. Simulate 1000 years of data using these probabilities, and thereby obtain simulated recurrence times of earthquakes.

4. Fit a logistic distribution to these times.

Simple Time Dependent Formula MARFSTA

1 1ˆ ˆT Tij ijN N AF

( *) ( * 1)

1 ( * 1)

P t P tAF

P t

Results

Results

Results

Validation of the Model

Points for Improvement Use more complicated time series

modeling.

Method to remove domination of the aftershock sequence (if necessary).

How much depth data to use?

Use a more complicated adjustment factor.

Conclusions

Future earthquakes are more likely in areas where they have already occurred.

Gradual slope along neighboring bins.

Pick up changes in rate and magnitude distribution.

Is temporal modeling important?

Acknowledgements

JSPS for financial support.

ERI for hosting the test centre.

Katao san for the Tamba dataset.

Nanjo san for answering a lot of questions.

Similar to Helmstetter et al., 2007. Differs wrt the derivation of the expected number of events in each bin, the spatial density estimation, and the magnitude distribution estimation.