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Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA 90095-1567, [email protected], http://scec.ess.ucla.edu/ykagan.html. TIME DEPENDENT EARTHQUAKE PROBABILITIES. http://moho.ess.ucla.edu/~kagan/Arrowhead.ppt. Lake Arrowhead, WGCEP, March 6-8, 2007. (1).

Yan Y. Kagan

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Yan Y. Kagan

Dept. Earth and Space Sciences, UCLA, Los Angeles, CA 90095-1567, [email protected], http://scec.ess.ucla.edu/ykagan.html

TIME DEPENDENT EARTHQUAKE PROBABILITIES

Lake Arrowhead, WGCEP, March 6-8, 2007

### (1)

Kagan, Y. Y. and D. D. Jackson, 1999. Worldwide doublets of large shallow earthquakes, Bull. Seismol. Soc. Amer., 89, 1147-1155.

Kagan, Y. Y., and H. Houston, 2005. Relation between mainshock rupture process

and Omori's law for aftershock moment release rate, Geophys. J. Int., 163(3), 1039-1048

### Another view (WPGM Meeting 2000, S42B-01)

• HR: 1400hAN: S42B-01TI: The 1978 Kurile Islands Earthquake Doublet: No Conflict With Quasi-Periodic Recurrence ModelsAU: * Hurukawa, N EM: [email protected]: U. S. Geological Survey, 345 Middlefield Road, Menlo Park, CA 94025 United States AU: Ellsworth, W LEM: [email protected]: U. S. Geological Survey, 345 Middlefield Road, Menlo Park, CA 94025 United States AB: The M$_{w}$ 7.5 and 7.6 1978 Kurile Islands earthquakes of March 23 and 24, 1978 and their M$_{w}$ 7.0 foreshock are low-angle thrust events that occurred on the boundary between the Pacific and North American plates. Kagan and Jackson (BSSA, 1999) proposed that the rupture areas of the two main shocks have significant overlap because the Harvard catalog centroids for the main shocks are only 25 km apart, and the one day aftershocks listed in the PDE bulletin have significant overlap. Based on this and similar earthquake pairings in the Harvard catalog, they concluded that a power-law recurrence model is much better than quasi-periodic recurrence models on which the seismic gap model is based. We test the hypothesis that the Kurile Islands earthquakes ruptured the same area by re-determining the centroid locations using cross correlation methods, and relocating the foreshocks, main shocks and aftershocks using joint hypocenter determination methods. Differential travel times of long period body waves (f $<=$ 0.05 Hz) show that the centroids of the two main shocks are separated by 57 $\pm$ 5 km along the strike direction of the trench. A centroid separation of this amount implies little or no overlap of the rupture areas if the stress drop is about 3 MPa or greater. Hypocenters for the sequence were determined using P-wave arrival times reported by the International Seismological Center. Although the aftershock areas of the two main shocks overlap, the overlap area is where the intense foreshock activity, including the M$_{w}$ 7.0, occurred. If we exclude earthquakes that occurred in the foreshock area, there is no overlap of the one day aftershock areas of the two main shocks. The centroids of the three large events are located within their respective aftershock zones. We further test the relation between the two main shocks and the largest foreshock by locating correlative peaks in the broad band (f $<=$ 0.5 Hz) velocity P waveforms. These presumed areas of moment release for the three events are clearly separated from each other and coincide with their respective aftershock areas. Therefore, we can conclude that the source areas of the M$_{w}$ 7.5 and 7.6 events that form this doublet do not have significant overlap. The occurrence of this doublet does not conflict with the basic tenets of the elastic rebound model of earthquake occurrence or seismic gap theory as applied to the Kurile trench.

### Another view (WPGM Meeting 2000, S42B-01)

• Hurukawa, N. and W. L. Ellsworth, 2000. The 1978 Kurile Islands Earthquake Doublet: No Conflict With Quasi-Periodic Recurrence Models, abstract at 2000 Western Pacific Geophysics Meeting, S42B-01

… Therefore, we can conclude that the source areas of the Mw 7.5 and 7.6 events that form this doublet do not have significant overlap. The occurrence of this doublet does not conflict with the basic tenets of the elastic rebound model of earthquake occurrence or seismic gap theory as applied to the Kurile trench.

### Rules of the game

• ALL pairs ofshallow earthquakes M>=10^20.25 Nm (Mw>=7.5) with centroid distance less than 100 km from the CMT catalog have been processed (no pre-selection).

• CMT solutions for earthquakes are obtained using uniform assumptions and interpretation methods. The solutions are independent from our analysis.

• The results are easily reproducible.

Kagan, Y. Y. and D. D. Jackson, 1999. Worldwide doublets of large shallow earthquakes, Bull. Seismol. Soc. Amer., 89, 1147-1155.

First earthquake Second earthquake Difference 1st mechan. 2nd mechan. (L1+L2)

N Year Mo Da Lat Long De Mag Year Mo Da Lat Long De Mag Dist DM Angle Time_Diff Dip Str Dp Str Dip Str Dp Str /Dist

T-axis P-axis T-axis P-axis (2-3)

1* 1978 3 23 44.1 149.3 28 7.6 1978 3 24 44.2 149.0 31 7.6 24.9 0 7.2 1.6892 56 312 34 132 63 309 27 131 2.33

2* 1980 7 8 -12.9 166.2 44 7.5 1980 7 17 -12.4 165.9 34 7.8 61.7 -2 18.4 8.8496 81 320 4 75 74 49 14 253 1.07

3* 1980 7 8 -12.9 166.2 44 7.5 1997 4 21 -13.2 166.2 51 7.8 33.0 -1 42.5 6130.5302 81 320 4 75 57 131 15 245 1.95

4* 1980 7 17 -12.4 165.9 34 7.8 1997 4 21 -13.2 166.2 51 7.8 91.7 0 35.1 6121.6806 74 49 14 253 57 131 15 245 0.86

5* 1983 3 18 -4.9 153.3 70 7.8 1995 8 16 -5.5 153.6 46 7.8 83.0 0 26.3 4534.0569 68 150 0 59 86 259 3 48 0.96

6 1983 3 18 -4.9 153.3 70 7.8 2000 11 16 -4.6 152.8 24 8.1 83.3 -2 71.9 6452.8260 68 150 0 59 33 181 29 292 1.26

7 1983 3 18 -4.9 153.3 70 7.8 2000 11 16 -5.0 153.2 31 7.9 47.2 0 91.4 6452.9421 68 150 0 59 60 339 30 160 1.84

8* 1984 2 7 -9.8 160.4 22 7.6 1988 8 10 -10.5 160.8 16 7.6 84.9 0 50.2 1645.2952 51 130 20 247 61 35 28 235 0.69

9* 1985 9 19 17.9 -102.0 21 8.0 1985 9 21 17.6 -101.4 21 7.6 71.2 4 14.3 1.5133 62 9 28 199 62 33 28 209 1.27

10* 1987 3 5 -24.4 -70.9 42 7.6 1995 7 30 -24.2 -70.7 29 8.1 32.9 -4 7.4 3068.8296 66 73 23 270 67 90 23 267 2.82

11* 1990 4 18 1.3 123.3 33 7.7 1991 6 20 1.0 123.2 15 7.6 37.4 1 28.7 427.6524 66 135 17 0 52 185 38 8 1.64

12 1995 8 16 -5.5 153.6 46 7.8 2000 11 16 -5.0 153.2 31 7.9 76.0 0 74.5 1918.8852 86 259 3 48 60 339 30 160 1.14

13 2000 11 16 -4.6 152.8 24 8.1 2000 11 16 -5.0 153.2 31 7.9 67.4 2 88.5 0.1161 33 181 29 292 60 339 30 160 1.66

14 2000 11 16 -4.6 152.8 24 8.1 2000 11 17 -5.3 152.3 17 7.8 92.6 2 88.5 1.6713 33 181 29 292 65 7 22 160 1.17

15 2000 11 16 -5.0 153.2 31 7.9 2000 11 17 -5.3 152.3 17 7.8 96.4 0 13.9 1.5553 60 339 30 160 65 7 22 160 0.94

16 2001 6 23 -17.3 -72.7 30 8.5 2001 7 7 -17.5 -72.4 25 7.7 33.8 8 8.0 13.5449 60 80 29 242 55 86 33 248 4.72

17 2006 11 15 46.8 154.3 13 8.4 2007 1 13 46.2 154.8 12 8.2 73.2 2 80.1 58.7143 60 302 30 123 10 150 67 264 2.50

* -- this pair is included in Table 1 by Kagan and Jackson, BSSA, 89(5), 1999.

The last column is the ratio of earthquake focal zone sizes to twice their distance, see equations (2-3) in Kagan and Jackson, 1999.

7 pairs with zero magnitude difference, 4 pairs -- foreshocks, 6 pairs – aftershocks.

Kagan, Y. Y. and D. D. Jackson, 1999. Worldwide doublets of large shallow earthquakes, Bull. Seismol. Soc. Amer., 89, 1147-1155.

### CMT catalog (Peru 2001 M8.4 eq.)

M062301E 06/23/01 20:33:14.1 -16.26 -73.64 33.06.78.2NEAR COAST OF PERU

PDE BW: 0 0 0 MW:68170 135 DT= 69.2 0.1 -17.28 0.01 -72.71 0.01 29.6 0.4

DUR43.2 EX 28 2.24 0.01 -0.55 0.01 -1.70 0.01 1.34 0.05 -3.73 0.07 1.44 0.01

4.53 60 80 0.29 8 336 -4.82 29 242 4.67 310 18 63 159 74 98

C070701F 07/07/01 09:38:43.5 -17.54 -72.08 33.06.67.3NEAR COAST OF PERU

PDE BW:63158 45 MW:60136 135 DT= 18.3 0.1 -17.45 0.01 -72.45 0.01 25.0 0.4

DUR14.0 EX 27 1.14 0.01 -0.21 0.01 -0.93 0.01 0.68 0.03 -2.85 0.05 0.77 0.00

3.14 55 86 0.13 9 344 -3.26 33 248 3.20 306 14 52 165 79 99

-16

-17

-18

-74

-73

-72

Bilek, S. L., and L. J. Ruff, 2002. Analysis of the 23 June 2001 Mw = 8.4 Peru underthrusting

earthquake and its aftershocks, Geophys. Res. Lett., 29(20), 1960,

doi:10.1029/2002GL015543.

Robinson, D.P., S. Das, and A.B. Watts, 2006.

Earthquake rupture stalled by a subducting fracture zone,

Science, 312,

1203-1205.

Fig. S1. Aftershocks, relocated for this study, are shown for the 24 hours following the main earthquake. The main shock (red star), together with the centroid-moment tensor solution recalculated for this study (see below), is shown. The ISC reports 249 aftershocks in this time period. We relocated 233 of these successfully, with 155 having 90% confidence ellipse < 30 km (shown in grey). Relocated epicenters are shown as circles, the size of the circle scaling with magnitude and color coded in depth (< 50 km in red, between 50 to 150 km in green).

Fig. S2. Same as Fig. S1 but for the 6 month period following the main shock with the addition of earthquakes > 150 km depth colored blue. The ISC reports 967 aftershocks in this time period, 28 of which were large enough to have CMT solutions. We relocated all earthquakes with CMT solutions and 891 of the smaller earthquakes successfully, 551 of which had 90% confidence error ellipses < 30 km.

Robinson, D.P., S. Das, and A.B. Watts, 2006.

Earthquake rupture stalled by a subducting fracture zone, Science, 312,

1203-1205.

### (2)

Kagan, Y. Y., 2000. Temporal correlations of earthquake focal mechanisms, Geophys. J. Int., 143, 881-897.

### Best Available Science?

• What is the SCIENTIFIC approach? Karl Popper’s answer (1980): a hypothesis (model) which is falsifiable, testable.

• Almost all models employed in earthquake seismology do not satisfy this criterion – their predictions are not testable, at least in reasonable time, thus they are not yet science.

### Earthquake Scaling: M ~ L3

• It is commonly believed that the earthquake focal size scaling (i.e., dependence of the size on seismic moment) is different for events of various focal mechanisms.

• In particular, strike-slip earthquakes which occur on vertical faults are considered to have two power-law dependencies: break occurring around 15-20 km (corresponding to M6 event).

• Long debate between Scholz and Romanowicz.

### Kagan, Y. Y., 2002. Aftershock zone scaling, Bull. Seismol. Soc. Amer., 92, 641-655.

• Update for 1977-2006 (CMT catalog – focal mechanisms; PDE catalog – aftershock zones, approximated by two-dimensional Gaussian distribution).

• We obtain for all earthquakes (disregarding their focal mechanism) the same scaling relation: scalar moment proportional to the cube of aftershock zone length

### Characteristic Earthquakes, Seismic Gaps, Quasi-periodicity

• Schwartz and Coppersmith (1984) proposed the characteristic model. McCann et al. (1979) and Nishenko (1991) formulated testable hypothesis -- about 100 zones in circum-Pacific belt. Kagan & Jackson (JGR, 1991, 1995), and Rong et al. (JGR, 2003) tested these predictions and found that earthquakes after 1979 or 1989, respectively, do not support the model.

McCann et al. (1979) The map of seismic gap zones -- compare Sumatra 2004 rupture.

Kagan & Jackson (1991) tested the map – the result is negative.

### Characteristic Earthquakes, Seismic gaps, Quasi-periodicity

Bakun & Lindh (Science, 1985) -- Parkfield prediction, 95% probability of M6 event in 1985-1993. No earthquake occurred. In 2004 M6 event in the Parkfield area. Only few of the predicted features were observed. Bakun et al. (Nature, 2005) review the experiment results -- no new prediction is issued. See Jackson & Kagan (2006) http://scec.ess.ucla.edu/ ~ykagan/parkf2004_index.html.

### Characteristic Earthquakes, Seismic Gaps, Quasi-periodicity

• Chris Scholz in the 1999 Nature Debate:

In their [Kagan & Jackson] more recent study, they found, in contrast, less events than predicted by Nishenko [1991]. But here the failure was in a different part of the physics: the assumptions of recurrence times made by Nishenko. These recurrence times are based on very little data, no theory, and are unquestionably suspect.

### Characteristic Earthquakes, Seismic Gaps, Quasi-periodicity

• Bakun et al., Nature, 2005:

(The characteristic earthquake model can also

be tested using global data sets. Kagan and Jackson [1995] concluded that too few of Nishenko’s [1991] predicted gap-filling circum-Pacific earthquakes occurred in the first 5 yr.)

### Characteristic Earthquakes, Seismic Gaps, Quasi-periodicity

• Despite the failure of these predictions, this model was employed in San Francisco Bay area (Working Group, 2003) -- "there is a 0.62 [0.38--0.85] probability of a major, damaging [M > 6.7] earthquake striking the greater San Francisco Bay Region over the next 30 years (2002--2031)."

### Characteristic Earthquakes, Seismic Gaps, Quasi-periodicity

• Stark and Freedman (2003) argue that the probabilities defined in such a prediction are meaningless because they cannot be validated. They suggest that the reader "should largely ignore the USGS probability forecast."

• See more detail in Jackson & Kagan (2006) http://scec.ess.ucla.edu/~ykagan/parkf2004_index.html

### Characteristic Earthquakes, Seismic Gaps, Quasi-periodicity

• Thomas Kuhn (1965) questioned how one can distinguish scientific and non-scientific predictions. As an example, he used astronomy versus astrology -- both issue predictions that sometimes fail. However, astronomers learn from these mistakes, modify and update their models, whereas astrologers do not.

### What needs to be done?

• Bill Ellsworth (2007, January Swiss RE meeting): HEROIC effort to quantitatively test quasi-periodic, characteristic earthquake model (following McCann et al., 1979; Nishenko, 1989).

### Seismicity Model

Most of earthquake fault models use planar block boundary geometry. Incompatibility problem is circumvented because of flat plate boundaries. Real earthquake faults always contain triple junctions; further deformation is impossible without creating new fractures and rotational defects (disclinations).

Y. Kagan (GJRAS, 1982), G. King (PAGEOPH, 1983; 1986).

Example of geometric incompatibility near fault junction. Corners A and C are either converging and would overlap or are diverging; this indicates that the movement cannot be realized without the change of the fault geometry (Gabrielov, A., Keilis-Borok, V., and Jackson, D. D., 1996. Geometric incompatibility in a fault system, P. Natl. Acad. Sci. USA, 93, 3838-3842).

### Kagan, Y. Y. and D. D. Jackson, 1999. Worldwide doublets of large shallowearthquakes, Bull. Seismol. Soc. Amer., 89, 1147-1155.

• First earthquake Second earthquake Difference 1st mechanism 2nd mechanism E-ln/ N Year Mo Da Lat Long De Mag Year Mo Da Lat Long De Mag Dist DM Angle Time_Diff Dip Str Dp Str Dip Str Dp Str Dist T-axis P-axis T-axis P-axis 1* 1978 3 23 44.1 149.3 28 7.6 1978 3 24 44.2 149.0 31 7.6 24.9 0 7.2 1.6892 56 312 34 132 63 309 27 131 2.33 2* 1980 7 8 -12.9 166.2 44 7.5 1980 7 17 -12.4 165.9 34 7.8 61.7 -2 18.4 8.8496 81 320 4 75 74 49 14 253 1.07 3* 1980 7 8 -12.9 166.2 44 7.5 1997 4 21 -13.2 166.2 51 7.8 33.0 -1 42.5 6130.5302 81 320 4 75 57 131 15 245 1.95 4* 1980 7 17 -12.4 165.9 34 7.8 1997 4 21 -13.2 166.2 51 7.8 91.7 0 35.1 6121.6806 74 49 14 253 57 131 15 245 0.86 5* 1983 3 18 -4.9 153.3 70 7.8 1995 8 16 -5.5 153.6 46 7.8 83.0 0 26.3 4534.0569 68 150 0 59 86 259 3 48 0.96 6 1983 3 18 -4.9 153.3 70 7.8 2000 11 16 -4.6 152.8 24 8.1 83.3 -2 71.9 6452.8260 68 150 0 59 33 181 29 292 1.26 7 1983 3 18 -4.9 153.3 70 7.8 2000 11 16 -5.0 153.2 31 7.9 47.2 0 91.4 6452.9421 68 150 0 59 60 339 30 160 1.848* 1984 2 7 -9.8 160.4 22 7.6 1988 8 10 -10.5 160.8 16 7.6 84.9 0 50.2 1645.2952 51 130 20 247 61 35 28 235 0.69 9* 1985 9 19 17.9 -102.0 21 8.0 1985 9 21 17.6 -101.4 21 7.6 71.2 4 14.3 1.5133 62 9 28 199 62 33 28 209 1.27 10* 1987 3 5 -24.4 -70.9 42 7.6 1995 7 30 -24.2 -70.7 29 8.1 32.9 -4 7.4 3068.8296 66 73 23 270 67 90 23 267 2.82 11* 1990 4 18 1.3 123.3 33 7.7 1991 6 20 1.0 123.2 15 7.6 37.4 1 28.7 427.6524 66 135 17 0 52 185 38 8 1.64 12 1995 8 16 -5.5 153.6 46 7.8 2000 11 16 -5.0 153.2 31 7.9 76.0 0 74.5 1918.8852 86 259 3 48 60 339 30 160 1.14 13 2000 11 16 -4.6 152.8 24 8.1 2000 11 16 -5.0 153.2 31 7.9 67.4 2 88.5 0.1161 33 181 29 292 60 339 30 160 1.66 14 2000 11 16 -4.6 152.8 24 8.1 2000 11 17 -5.3 152.3 17 7.8 92.6 2 88.5 1.6713 33 181 29 292 65 7 22 160 1.17 15 2000 11 16 -5.0 153.2 31 7.9 2000 11 17 -5.3 152.3 17 7.8 96.4 0 13.9 1.5553 60 339 30 160 65 7 22 160 0.9416 2001 6 23 -17.3 -72.7 30 8.5 2001 7 7 -17.5 -72.4 25 7.7 33.8 8 8.0 13.5449 60 80 29 242 55 86 33 248 4.72 17 2006 11 15 46.8 154.3 13 8.4 2007 1 13 46.2 154.8 12 8.2 73.2 2 80.1 58.7143 60 302 30 123 10 150 67 264 2.50

First earthquake Second earthquake Difference 1st mechanism 2nd mechanism E-ln/ N Year Mo Da Lat Long De Mag Year Mo Da Lat Long De Mag Dist DM Angle Time_Diff Dip Str Dp Str Dip Str Dp Str Dist T-axis P-axis T-axis P-axis 1* 1978 3 23 44.1 149.3 28 7.6 1978 3 24 44.2 149.0 31 7.6 24.9 0 7.2 1.6892 56 312 34 132 63 309 27 131 2.33 2* 1980 7 8 -12.9 166.2 44 7.5 1980 7 17 -12.4 165.9 34 7.8 61.7 -2 18.4 8.8496 81 320 4 75 74 49 14 253 1.07 3* 1980 7 8 -12.9 166.2 44 7.5 1997 4 21 -13.2 166.2 51 7.8 33.0 -1 42.5 6130.5302 81 320 4 75 57 131 15 245 1.95 4* 1980 7 17 -12.4 165.9 34 7.8 1997 4 21 -13.2 166.2 51 7.8 91.7 0 35.1 6121.6806 74 49 14 253 57 131 15 245 0.86 5* 1983 3 18 -4.9 153.3 70 7.8 1995 8 16 -5.5 153.6 46 7.8 83.0 0 26.3 4534.0569 68 150 0 59 86 259 3 48 0.96 6 1983 3 18 -4.9 153.3 70 7.8 2000 11 16 -4.6 152.8 24 8.1 83.3 -2 71.9 6452.8260 68 150 0 59 33 181 29 292 1.26 7 1983 3 18 -4.9 153.3 70 7.8 2000 11 16 -5.0 153.2 31 7.9 47.2 0 91.4 6452.9421 68 150 0 59 60 339 30 160 1.84 8* 1984 2 7 -9.8 160.4 22 7.6 1988 8 10 -10.5 160.8 16 7.6 84.9 0 50.2 1645.2952 51 130 20 247 61 35 28 235 0.69 9* 1985 9 19 17.9 -102.0 21 8.0 1985 9 21 17.6 -101.4 21 7.6 71.2 4 14.3 1.5133 62 9 28 199 62 33 28 209 1.27 10* 1987 3 5 -24.4 -70.9 42 7.6 1995 7 30 -24.2 -70.7 29 8.1 32.9 -4 7.4 3068.8296 66 73 23 270 67 90 23 267 2.82 11* 1990 4 18 1.3 123.3 33 7.7 1991 6 20 1.0 123.2 15 7.6 37.4 1 28.7 427.6524 66 135 17 0 52 185 38 8 1.64 12 1995 8 16 -5.5 153.6 46 7.8 2000 11 16 -5.0 153.2 31 7.9 76.0 0 74.5 1918.8852 86 259 3 48 60 339 30 160 1.14 13 2000 11 16 -4.6 152.8 24 8.1 2000 11 16 -5.0 153.2 31 7.9 67.4 2 88.5 0.1161 33 181 29 292 60 339 30 160 1.66 14 2000 11 16 -4.6 152.8 24 8.1 2000 11 17 -5.3 152.3 17 7.8 92.6 2 88.5 1.6713 33 181 29 292 65 7 22 160 1.17 15 2000 11 16 -5.0 153.2 31 7.9 2000 11 17 -5.3 152.3 17 7.8 96.4 0 13.9 1.5553 60 339 30 160 65 7 22 160 0.94 16 2001 6 23 -17.3 -72.7 30 8.5 2001 7 7 -17.5 -72.4 25 7.7 33.8 8 8.0 13.5449 60 80 29 242 55 86 33 248 4.72 17 2006 11 15 46.8 154.3 13 8.4 2007 1 13 46.2 154.8 12 8.2 73.2 2 80.1 58.7143 60 302 30 123 10 150 67 264 2.50