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Earth, Planets and Space

Table 1 Estimated parameters of models (1) and (2) and their respective AIC values

From: Measuring seismicity diversity and anomalies using point process models: case studies before and after the 2016 Kumamoto earthquakes in Kyushu, Japan

Mc

Model

Period

\(\mu\)

\(K_{0} \left( { \times \,10^{ - 2} } \right)\)

\(c\left( { \times \,10^{ - 3} } \right)\)

\(\alpha\)

\(p\)

\(K_{\tau } \left( { \times \,10^{ + 1} } \right)\)

\(c_{\tau } \left( { \times \,10^{ + 1} } \right)\)

\(p_{\tau }\)

ΔAIC

1.0

(1)

Total

0.895

2.951

1.226

0.872

1.005

–

–

–

0

P1

1.063

2.821

1.662

1.005

1.001

–

–

–

− 90.38

P2

0.552

3.320

0.504

0.625

0.971

–

–

–

(2)

Total

0.969

2.620

1.312

0.863

1.033

7.703

5.001

1.0*

− 18.26

P1

1.095

2.738

1.663

1.001

1.006

0.410

0.0168

1.0*

− 92.87

P2

0.552

3.320

0.504

0.625

0.971

0.000

0.0211

1.0*

1.5

(1)

Total

0.432

2.541

1.103

0.813

1.008

–

–

–

0

P1

0.457

2.600

0.106

0.922

0.963

–

–

–

− 29.54

P2

0.429

2.134

1.068

0.640

1.087

–

–

–

(2)

Total

0.450

2.166

1.308

0.772

1.055

4.079

5.302

1.0*

− 12.24

P1

0.469

2.508

1.063

0.910

0.969

0.168

0.0230

1.0*

− 31.15

P2

0.428

2.134

1.068

0.640

1.087

0.000

0.0223

1.0*

2.0

(1)

Total

0.183

1.685

0.941

1.099

0.966

–

–

–

0

P1

0.182

1.641

0.823

1.308

0.883

–

–

–

− 19.21

P2

0.204

0.696

2.209

0.742

1.322

–

–

–

(2)

Total

0.185

1.617

0.984

1.094

0.973

0.0782

0.00118

1.0*

− 5.02

P1

0.184

1.553

0.879

1.326

0.885

0.0623

0.00082

1.0*

− 17.32

P2

2.039

0.696

2.209

0.742

1.322

0.0000

0.0275

1.0*

  1. ΔAIC indicates differences from the AIC of baseline model (1) for the entire period. The smallest ΔAIC value for each dataset is indicated in italics. With each threshold magnitude M c , the first row (indicated “Total” in third column) shows the MLE of the parameters for the entire period (S = 0.01, T end = 2294.52) until the M6.5 event with AIC = AIC0. The second row (indicated “P1” in third column) represents the period prior to the change-point (S = 0.01, T c  = 1300) with AIC = AIC1. The third row (indicated “P2” in third column) represents the period after the change-point (T c  = 1300, T end = 2294.52) with AIC = AIC2. The last column shows ΔAIC = AIC1 + AIC2 − AIC0. The decay rate parameter \(p_{\tau }\) for model (2) is fixed to 1.0 in all cases, after Dieterich (1994)
  2. The asterisk symbols indicate that the values are fixed
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