Conclusions

Chapter 5 Chapter 5 Static Stress Change Triggering of Earthquakes

5.5 Conclusions

The Coulomb stress change triggering model was tested for the aftershock sequences of the 1992 Landers and 1994 Northridge earthquakes. The model is generally successful, since the number of aftershocks consistent with the model is larger than would be expected to appear consistent purely by chance. The model works best for events at intermediate distances from the mainshock, where the stress changes are between 0.1 bar and 100 bar. Stress changes very near the rupture plane are difficult to model because they depend on the small-scale features of slip which generally cannot be resolved, and they are affected by slip discontinuities due to the discretization of the fault. Far from the mainshock, the stress changes are presumably too small to trigger a detectable number of events.

Although the model performs better than it should by chance, at least 40% of the events appear not to have been triggered by static stress changes. This, along with the failure of the model to explain the apparent triggering of the Mw7.1 Hector Mine earthquake by Landers, implies that static stress change is not the only impor- tant mechanism in aftershock triggering. Dynamic stress changes and pore pressure changes may also play a role.

(a) 0.1 (b) (c)

~ 0.1 0.2 ^r-_)>

:0 z

(0 0.05 ⁰

.g ^{0.05 0.1 m}

n nnn.

a.

:IJ

J1l ltl

^en

0 0

5 10 15 -50 0 50 100 150

0.2 -60-30 0 30 60 0.08

(e) (f) z

~0.06 0.04 0

:IJ

:0 ^-I

~ 0.04 0.1 ^I

0.02 ^:IJ

0 0

a.

^0.02 (j)

m

0 0

0 5 10 15 20 25 -10 0 10 20 -20 -10 0 10 20

depth (km) strike distance (km) normal distance (km)

.

~0.15 (g) 0.15 (h)

0.15 (i)

r-)>

:0 0.1 0.1 0.1 z

(0 0

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Ko.o5 0.05 ^:IJ en

0 0

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a.

^{0.05 0.05}

A ~

^{(j) m}

-45 0 45 90 0 -90 -45 0 45 90 -45 0 45 90

P-axis trend (deg) P-axis plunge (deg) T-axis plunge (deg)

Figure 5.1: Probability distributions used to choose the spatial coordinates and fo- cal mechanism parameters for the synthetic sequences. (a)-(f) Spatial coordinates.

The "strike distance" is the along-strike distance measured from the center of the Northridge mainshock or the southern end of the Landers mainshock. The "normal distance" is the distance in the direction normal to the fault, measured from the nearest mainshock fault segment or its extension. (g)-(1) Focal mechanism parame- ters. The P-axis trend is measured clockwise from north; and the plunge, down from horizontal. The T-axis plunge is positive for a clockwise rotation around the P-axis.

100.-~---~----~---~-, 100.-~---~---~---,

(a)

80

J.

T

.0

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~ =··===·=-~--:-

..

~.-:-

..

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.. ...

::I 40 - - - -

() 0

20

oL-~---~----~---~_J

2 3 4 5

magnitude

100~---~---~---,

(c)

20

oL-~---~---~--_J

10¹ distance (km)

100.---~---~---,

(d)

80

-t+

80

~ + ---

-g 60 - - - - - -

+-+

~ 60~~--~---~~----~ ^X

~ ~ - ~- ~- ~-~- :_::-: . -:-. ~:-: . -:- . t:-: ^. .1 .. - .:- ~ --

s 40 - - - - - .. - I. - - -

() 0

20

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1 0-²

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~ 40 ~ _- - - - - - - - - - - - - - -

() 0

20

OL---~---~---_J

0 10 20 30

time (days)

Figure 5.2: The Coulomb Index (CI), the percentage of events consistent with the Coulomb stress triggering model, for the Landers sequence. The asterisks indicate the CI for a bin versus the average parameter value in that bin. The vertical error bars indicate the 2u error estimates; and the horizontal bars, the bins. The dotted and dashed lines indicate the mean CI for the synthetic sequences and the 2u level of their distribution, respectively. (a) CI versus aftershock magnitude. (b) CI versus distance from the nearest point on the mainshock fault plane. (c) CI versus the magnitude of the stress change, represented by ..6.rmax, the maximum shear stress change on any plane. (d) CI versus time after the mainshock.

100r---~----~---~----~

(a) 80

X

~ 60~._---1 ~ ~---t- 1

^{________ -l}

.0 - - - . . ... T..

.Q E

::I 40

() 0

20

o~--~----~---~----~

2 3 4 5

magnitude

100

80

X Q)

"0

£ 60

.0 .Q E

40

::I 0

. ₁

(c)

- -~ _~ ~1!-+- _{- __ .J,-1 --}

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·r

()

20

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100r---~---~---,

(e) 80

20

o~---~---~---~

0 10 20 30

depth (km)

100r-~---~---~

(b) 80

~

^{60 - _!}

_=+f-_- -

.0 E f - - -T.... * - - -·... - - - - - . - - ..... .

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20

oL-~---~---~

10¹ distance (km)

100.---~---~---,

(d) 80

20

0~---~---~---~

0 10 20 30

time (days)

Figure 5.3: The Coulomb Index for the Northridge sequence, symbols as in Figure 5.2. (a) CI versus aftershock magnitude. (b) CI versus distance from the mainshock.

(c) CI versus the magnitude of the stress change. (d) CI versus time. (e) CI versus aftershock hypocentral depth.

A A'

.., ^.

0

36"

• .

^{f •}

^., ..

^-10

-···

,.. ... . .

0 • • :$

-10 0 10

. ^{· ·.}

⁰

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.

_E

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.

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0 0

~·A" -10 0 10

" ^c

^C'

0

_,: [!]

^{~ o,}

34" ⁸

-10 0 10

distance (km)

·118" -117" -116"

A A'

• M=2

o M=3 0

o M=4

~ -

36" •

.

^{0 M=5 0}

·

^{... •}

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.

35"

.

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<Po

A' -10 0 10

c

^C'

34"

10

' [!]

.,

·10 0 10

• distance (km)

-118" -117" -116"

Figure 5.4: Earthquakes occurring within one month after the Landers mainshock.

Events in the top panel have at least one nodal plane consistent with Coulomb stress triggering. Events with both planes inconsistent with triggering are shown in the bottom panel. Major faults shown in gray. The aftershocks clearly delineate the mainshock fault plane.

A A'

34' 30'

0

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·5 c-. ~ ....

A' E ^{q,. ,.·}

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km -20

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...

^,....,

0 0 5 10 -25

0 0 5 10 15 20 25 30

241'10' 241' 20' 241' 30' 241' 40' distance (km)

A A'

34' 30'

M=2 0 ⁰

-5

...

A' ⁰ ₀ ^{M=3 ... : .o.o}

M=4 E

..

_{0 M=5} 6 .s= ·10 •

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•

g.

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0 5 10 15 20 25 30

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^,....,

0 5 10 -25

0 5 10 15 20 25 30

241' 10' 241' 20' 241' 30' 241' 40' distance (km)

Figure 5.5: Earthquakes occurring within one month after the Northridge mainshock.

Events in the top panel have at least one nodal plane consistent with Coulomb stress triggering. Events with both planes inconsistent with triggering are shown in the bottom paneL Major faults shown in gray. The black rectangle indicates the surface projection of the mainshock fault plane.

(a) consistent LANDERS

(b) inconsistent

P-axis T-axis P-axis T-axis

(c) consistent NORTHRIDGE

(d) inconsistent

P-axis T-axis P-axis T-axis

Figure 5.6: Stereographic plots of the P and T axes of the first month of aftershocks.

(a) Landers aftershocks with at least one nodal plane consistent with triggering. (b) Landers aftershocks with both nodal planes inconsistent. (c) Northridge aftershocks with at least one plane consistent. (d) Northridge aftershocks with both planes inconsistent.

LANDERS 100

:I

80 ^{(a) :I}

X :I

:~

Q) ~

"0

*i + * * ⁺

c 60 +~

+ +

.D :I

E ---+-- ---1- ~--+----;I

!

.2 ^{::I 0} 40

* +

^{---+-- ~}

^:1

(.) :I

20 _:I

:I

0 -12 -10 -8 -6 -4 -2 0 2 4 6 8

time (yrs) NORTHRIDGE 100

80 ^(b)

+- + +L++++++-t

X Q)

"0

60 E

.D

t t

.2 E ::I 40

(.) 0

I 20

0 -12 -10 -8 -6 -4 -2 0 2 4 6

time (yrs)

Figure 5.7: Coulomb Index (CI) versus time, for all events within one fault length of the mainshock {80 km for Landers, 20 km for Northridge). The asterisks indicate the CI for a bin versus the average event time in that bin. The vertical error bars indicate the 20' error estimates; and the horizontal bars, the bins. (a) CI versus time for Landers. The vertical dashed line indicates the time of the mainshock.

The vertical dotted lines indicate the times of the Joshua Tree foreshock and the Hector Mine earthquake. (b) CI versus time for Northridge. The vertical dashed line indicates the time of the mainshock.

depth= 3 km depth= 5 km

0 0

-1

-10 -10

en en

Q) Q)

~ -20 -1.2 ^~ -20

Cl Cl

Q) Q)

~-30 ~-30

Q) Q)

.:.:: .:.::

·;:: ·;::

iii -40 iii -40

-0.4 -0.2

-50 -50

60 70 80 90 60 70 80 90

dip (degrees) dip (degrees)

depth= 7 km depth= 9 km

0 0

-10 -10

en _Q) en

~ -20 ^Q) ~ -20

Cl Cl

Q) Q)

~-30 ~-30

Q) Q)

.:.::

=E

·;::

iii -40 iii -40

-50 0.2

60 70 80 90 60 70 80 90

dip (degrees) dip (degrees)

Figure 5.8: Contours of Coulomb stress change due to the Landers mainshock on the Hector Mine hypocenter for various fault plane orientations and hypocentral depths.

The open triangle indicates the preferred fault plane orientation [Scientists from the USGS, SCEC, and CDMG, 2000]; the preferred depth is 5±3 km. The contours are in bars. The coefficient of friction, J.L, is assumed to be 0.6.

depth= 3 km depth= 5 km

0 0

-10 -10

Ui' Ui'

~ -20 ~ -20

0, 0,

Q) Q)

~-30 ~-30

Q) Q)

~ ~

·.::: ·.:::

ii5 -40 -0.2 ⁱⁱ⁵ -40

-50 0.4 0.2 -50 0.4

60 70 80 90 60 70 80 90

dip (degrees) dip {degrees)

depth= 7 km depth= 9 km

0 -10

Ui' Ui'

~ -20 ^Q) _~ -20

0, Cl

Q) Q)

~-30 ~-30

Q) Q)

~ ~

·.:::

ii5 -40 ⁱⁱ⁵ -40

0.2 0.4

-50 0.6

0.6

60 70 80 90 60 70 80 90

dip (degrees) dip {degrees)

Figure 5.9: The same as Figure 5.8, except with J.L=0.85.

Data Set or Number of Observed Synthetic Confidence Parameter Value Events CI (±2a) CI (±2a) Level

all 3204 63 ±2 45 ±2 99%

M ~2.5 1980 62 ±2 45 ±2 99%

2.5< M ~3 754 63 ±3 45 ±4 99%

3< M ~4 407 64 ±4 45 ±5 99%

M>4 63 72 ±10 44 ±11 99%

D ~5 krn 1843 54 ±2 45 ±3 99%

5< D ~10 549 77 ±3 47 ±4 99%

10< D ~15 128 78 ±7 45 ±4 99%

15< D ~20 131 79 ±6 44 ±5 99%

20< D ~35 130 63 ±8 44 ±5 99%

35< D ~50 146 80 ±6 46 ±6 99%

50< D ~115 75 66 ±9 47 ±7 98%

115< D ~175 116 72 ±7 49 ±12 99%

D >175 86 63 ±9 49 ±15 90%

I:::.Tmax ~0.1 bar 228 67 ±5 52 ±8 98%

0.1< ^f:::.Tmax ~0.5 74 77 ±8 53 ±8 99%

0.5< ^f:::.Tmax ~1 218 78 ±5 51 ±7 99%

1< ^f:::.Tmax ~5 1069 69 ±2 46 ±4 99%

5< ^f:::.Tmax ~10 369 60 ±4 44 ±5 99%

10< f:::.Tmax ~50 685 57 ±3 43 ±4 99%

50< ^I:::.Tmax ~100 304 52 ±5 41 ±6 98%

/:::. T max > 100 257 43 ±5 44 ±7 35%

t ~2 days 294 64 ±5 45 ±6 99%

2< t ~7 780 63 ±3 45 ±3 99%

7< t ~14 847 61 ±3 45 ±3 99%

7< t ~30 1283 63 ±3 45 ±3 99%

Table 5.1: The Coulomb Index (CI), the percent of events consistent with triggering, for the first month of Landers aftershocks. M indicates the aftershock magnitude, D the distance from the mainshock fault, ^I:::.Tmax the magnitude of stress change (the maximum shear stress change on a plane of any orientation), and t the time since the mainshock. Also shown is the mean and standard deviation of the distribution of CI values for a suite of random, synthetic sequences, and the confidence level at which one can reject the null hypothesis that the observed CI came from this distribution.

Data Set or Number of Observed Synthetic Confidence Parameter Value Events CI (±2a) CI (±2a) Level

all 2737 57 ±2 51 ±2 99%

M 5:2 1507 56 ±2 51 ±2 98%

2< M 5:3 1008 58 ±3 51 ±3 99%

M>3 222 58 ±6 52 ±6 90%

D 5:2 km 1219 52 ±3 49 ±3 91%

2< D 5:5 835 62 ±3 54 ±3 98%

5< D 5:10 415 64 ±4 55 ±4 98%

10< D 5:20 98 64 ±8 43 ±6 99%

D >20 27 41 ±17 49 ±8 19%

6.Tmax 5:0.1 bar 158 47 ±8 57 ±12 6%

0.1< ^6.Tmax '5:1 23 67 ±20 49 ±8 93%

1< ^6.Tmax '5:5 330 68 ±4 57 ±4 98%

5< 6.Tmax '5:10 603 65 ±4 55 ±4 98%

10< 6.Tmax '5:50 1265 55 ±3 46 ±3 99%

50< ^6.Tmax '5:100 234 47 ±6 42 ±7 81%

6.Tmax >100 124 43 ±6 42 ±9 58%

t 5:2 days 459 56 ±4 51 ±4 92%

2< t 5:7 761 57 ±3 51 ±3 98%

7< t 5:14 653 57 ±4 51 ±3 97%

t >14 864 57 ±3 51 ±3 98%

z 5:5 km 487 63 ±4 52 ±8 95%

5< z 5:8 635 63 ±3 52 ±4 99%

8< z 5:10 730 57 ±3 51 ±5 95%

10< z 5:15 693 49 ±3 50 ±5 25%

15< z 5:20 168 44 ±7 50 ±6 7%

z >20 24 62 ±18 51 ±9 84%

Table 5.2: The Coulomb Index (CI), the percent of events consistent with triggering, for the first month of Northridge aftershocks. M indicates the aftershock magnitude, D the distance from the mainshock fault, ^6.Tmax the magnitude of stress change (the maximum shear stress change on a plane of any orientation), t the time since the mainshock, and z the aftershock hypocentral depth. Also shown is the mean and standard deviation of the distribution of CI values for a suite of random, synthetic sequences, and the confidence level at which one can reject the null hypothesis that the observed CI came from this distribution.

Time (yy/mm/dd) Number of

Begining End Events CI (±2a) notes

81/02/13 82/11/27 1851 38 ±2 pre-Landers 82/11/27 84/04/11 739 39 ±3

84/04/11 85/08/23 1526 44 ±2 85/08/23 87/01/04 1857 38 ±2 87/01/04 88/05/19 956 46 ±3 88/05/19 89/10/01 996 38 ±3 89/10/01 91/02/15 796 41 ±3 91/02/15 92/04/23 516 44 ±3

92/04/23 92/06/28 2225 62 ±2 Joshua Tree sequence 92/06/28 92/07/28 2982 68 ±2 Landers sequence 92/07/28 92/10/06 2102 69 ±2

92/10/06 93/01/14 980 62 ±3 93/01/14 93/08/02 1310 62 ±2 93/08/02 94/02/18 1173 62 ±2 94/02/18 94/09/06 927 62 ±3 94/09/06 95/03/25 824 54 ±3 95/03/25 96/04/28 1146 58 ±2 96/04/28 97/06/02 677 56 ±3 97/06/02 98/07/07 599 56 ±4 98/07/07 99/10/16 447 64 ±4

99/10/16 99/12/26 225 46 ±6 Hector Mine sequence

Table 5.3: The Coulomb Index (CI) for earthquakes occurring within 80 krn of the Landers mainshock, versus time.

Time (yy/mm/dd) Number of

Begining End Events CI (±2a) notes

81/03/02 83/02/06 53 43 ±11 pre-Northridge 83/02/06 85/11/01 56 43 ±11

85/11/01 88/07/27 58 46 ±11 88/07/27 91/04/22 54 53 ±12 91/04/22 94/01/17 48 41 ±13

94/01/17 94/02/16 2535 58 ±2 post-Northridge 94/02/16 94/04/27 1048 55 ±3

94/04/27 94/08/05 494 57 ±4 94/08/05 95/02/21 519 55 ±4 95/02/21 95/09/09 270 60 ±5 95/09/09 96/03/27 193 53 ±6 96/03/27 96/10/13 103 56 ±8 96/10/13 97/11/17 228 50 ±5 97/11/17 98/12/22 60 55 ±10 98/12/22 99/09/25 20 60 ±22

Table 5.4: The Coulomb Index (CI) for earthquakes occurring within 20 km of the Northridge mainshock, versus time.

Appendix A An Evaluation of Stress