application of earthquake simulations to seismicity …...application of earthquake simulations to...

Application of earthquake simulations to seismicity induced by fluid injection

James H. Dieterich, Keith B. Richards-Dinger, and Kayla A. Kroll*University of California, Riverside

*Now at Lawrence Livermore National Laboratory

• Based on rate and state dependent friction

• Simulations avoid repeated solutions of a large system simultaneous

equations fast computation

• Event driven computations based on changes of fault sliding state. A fault

element may be at one of three sliding states

0 – Aging by log time of stationary contact

1 – Nucleating slip: Time- dependent accelerating slip to instability

Analytic solutions with rate-state friction

2 – Earthquake slip: quasi-dynamic – to a first approximatio. Slip speed set by

by shear impedance.

Earthquake simulator – RSQSim

t

s= m = m0 + aln

d

d*

æ

èç

ö

ø÷+ bln

qd*

Dc

æ

èç

ö

ø÷ dq = dt -

q

Dc

dd -aq

Bsds

RSQSim

(Rate-State Quake Simulator)

• Comprehensive simulation of fault slip phenomena:

➞earthquakes, continuous creep, slow slip events, afterslip

RSQSim




• Implement rate- and state-dependent friction effects

➞Earthquake clustering effects (aftershocks and foreshocks)

RSQSim





➞Earthquake clustering effects (aftershocks and foreshocks)All-California simulationAftershocks follow the Omori Lawfor aftershock decay with time

RSQSim






• High resolution models of geometrically complex fault systems

➞Up to 106 fault elements

➞Range of earthquake magnitudes M=3.5 to M=8

RSQSim








➞Range of earthquake magnitudes M=xx to M=yy

Oak Ridge F.

RSQSim









• Long simulations of >106 earthquakes

➞Statistical characterizations are consistent with observations

➞Repeated simulations to explore parameter space

RSQSim









• Long simulations of >106 earthquakes

➞Good statistical characterizations

➞Repeated simulations to explore parameter space

Wells and Coppersmith (1994)

WGCEP 02 Appendix D

Hanks and Bakun (2007)

Rupture area km2

102 103

Magnitude

6.0

6

.5

7.0

7

.5

8

.0

Wells and Coppersmith

RSQSim

Simulation (random 200-yr period)

Tectonic stressing with fluid injection

Fault 1

Fault 2

Fault 1 Fault 2

Earth Surface

M=7.0 Multi-fault earthquake rupture simulation

Red shows areas that are actively slipping in the earthquake

Earthquake rate modelBased on rate-state nucleation solutions

Approach

The formulation is based on the premise that earthquake nucleation controls

the time and place of initiation of earthquakes. Hence, processes that alter

earthquake nucleation times control changes of seismicity rates. Assumes a

steady-state seismicity rate that is proportional to stressing rate.

Implemented with a simple planar fault models with 400-1600 fault elements

R =r

g ˙ t rdg =

1

Asdt - g dt +

t

s- a

æ è

ö ø ds

é

ë ê ù

û ú Earthquake rate ,

Coulomb stress

Earthquake rate ,

dS = dt - mds

R =r

g ˙ S rdg =

1

Asdt - g dS[ ]

(Dieterich, 1994), Dieterich and others, Nature, (2000), Dieterich and others, USGS Prof - 1676 (2003)

“Reservoir” Model

We use a simple analytic expression (Wang, 2000) for the diffusion of pore-fluid pressure, P, into a homogeneous full- or half-space from a point source, and only the effects of Pon the effective normal stress (vs. more complete poroelastic effects).

porosity compressibility

Zero Tectonic Stressing Rate Models

• If the initial shear stress τ0 is greater than τmax:

then events will nucleate even in the absence of pore-fluid pressure perturbations.

• If the initial shear stress τ0 is less than τmin:

where P is the maximum pore-fluid pressure perturbation, then no events will ever nucleate.

The semi-infinite reservoir model used in this initial study results in a long-term steady-state maximum fluid pressure that is inversely proportional to the distance from the point of injection. The maximum fluid pressure sets the minimum and maximum initial shear stress that will result in induced earthquakes

CM2

Pressure andEarthquake rate profiles

Simple fault model with 1600 fault elements (100m x 100m)

s0.5,

Change of fluid pressures along profile closest to injection point

Change of fluid pressures along profile closest to injection pointEarthquake rates (black)

Initial stress is 0.5 Mpa below that forstress for steady state seismicity

Diffusivity=0.01, Porosity=0.07, Initial Stress=-0.1MPa

Earthquake rate model

Example of simulation of induced seismicity using RSQSim

Space-time plot of earthquake ruptures and fluid pressures (along upper edge of fault)

Model: Single fault with initial shear stress ~5MPa below critical stress (for failure without injection), no tectonic stressing, injection rate = 0.01M3/s, injection point is 200m out of the plane of the fault

Startinjection

Endinjection

The average initial stress t on the fault surface strongly affects the characteristics of induced seismicity.

With increasing t in the range tmin to tmax :

• The delay between the start of injection and onset of seismicity decreases,

• the magnitude of the first induced event increases,

• the magnitude of the largest event in the sequence increases,

• the cumulative number of induced earthquakes increases,

• the distance from the injection point to the most distance earthquake increases, and

• the seismicity following shut-in increases and persists for longer times.

Initial shear stress and fluid pressures to induce earthquakes

0

2e13

4e13

Cu

mu

lati

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m

om

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Mag

nit

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e

0

20

-5 0 5 10 15 20 25

40

60

Cu

mu

lati

ve

nu

mber

o

f ev

ents

Time (years)

50 1 2 3 4

5

10

15

Easting (km)

TIm

e (y

ears

)

2

4

6

8 1

0

12

14 1

6

18

2

0

22

24

6

2 82 03 23

43

63

83

40

24

44

64 84

05

25

45

65

Initial Tau = 36 MPa

1.0

2.0

3.0

4.0

0

2e14

4e14

6e14

0

50

100

150

200

250

-5 0 5 10 15 20 25Time (years)

Initial Tau = 48 MPa

0 1 2 3 4 5

0

5

10

15

20

Easting (km)

Tim

e (y

ears

)

2

4

6 8

10

12 14

16

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56 58

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tive

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ber

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agnit

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1.0

2.0

3.0

4.0Initial Tau = 56 MPa

0 1 2 3 4 5

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20

25

30

Easting (km)

Tim

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300

500

700

1

2

3

4

0 10 20 30 40

Time (years)

τ0 = 48 MPaτ0

= 36 MPa

τ0 = 56 MPa • At lower τ0: events confined to

area near injection point

• At higher τ0: – events can rupture into areas of

lower pore-fluid pressure

– Post shut-in seismicity is enriched and continues for a longer time

Effect of Initial Shear Stress

Effect of Initial Shear Stress

Effect of injection pulses

The volume of the crust that contains an earthquake rupture scales by 10M1.5

Dieterich, Richards-Dinger, Kroll (2015, SRL)

For isolated fracture permeabilty: M ~1.0log10(V)

The maximum possible earthquake magnitude is set by the fault dimensions. However, for faults with sub-critical initial stresses, , induced earthquake ruptures affect only a sufficiently pressured portion of the fault, and the maximum magnitude of the induced events increases with injected volume, in general agreement with observations.

Figure. The volume of injected fluid needed to pressurize (by some fixed amount) the volume of crust that embeds an induced earthquake rupture, scales by 101.5M , which has a slope of 2/3 on this plot (dashed line). Results from simulations are indicated by data points in color (see legend). All models have a normal stress of 100MPa. Additional parameters that affect maximum magnitude include reservoir storage capacity, and normal stress s which controls earthquake stress drop.

t 0 < tmax

Maximum magnitude and injected volume

Dieterich, Richards-Dinger, Kroll (2015, SRL)

Effect of as on decay following shut-in

R =r

g ˙ S rdg =

1

asdt -gdS[ ]

Effect of diffusivity k on decay followingShut-in

Many factors affect the rate of earthquake decay following shut-in

Diffusivity and as

Duration of seismicity following shut-in

Continuing earthquakes following shut-in

Two effects may cause delayed earthquakes following shut-in:

1) Continuing increase of pressure until the shut-in pulse reaches progressively distant points from the injection well.

2) Delayed nucleation in the form of aftershocks to earlier induced events and the stress perturbation from injection.

Prevention by shut-in: Test of traffic light procedures

We first ran this simulation with injection for 20 years to establish base-line induced seismicity

Then we re-ran the simulation with different shut-in times to determine the latest shut-in times that prevented events A, B and C.

Maximum magnitude following shut-in Extent of rupture

Effect of shut-in times on maximum magnitude

1.0

2.0

3.0

4.0

Mag

nit

ude

Event A:

M3.8; 2.92 yrs

Event A:

M3.8; 2.92 yrs

Event B:

M3.2; 9.4 yrs

Event C:

M4.1; 15.5 yrs

1050 15 20 25 30

Time (years)

1.0

2.0

3.0

4.0

Mag

nit

ud

e

1050 15 20 25 30

Time (years)

Shut-In at

2.82 years;

36.5 days

before Event A

Shut-In at

2.82 years

●

●

● ● ●●

● ● ●

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● ● ●

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2.80 2.85 2.90 2.95

1.5

2.5

3.5

Shut●In Tim e (years)

Mag

nit

ud

e

●

●

● ● ●●

● ●

Shut-in following the first M>3.1 event would have prevented subsequent M>3earthquakes,

Rake Angles From Region Stressing Rate Field

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Easting (km)●2 ●1 0 1 2

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6090

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ears

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Tim

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Without injection

With injection


Fault zone consists of 6 anastomosing faults with fractal roughness

Induced seismicity from injection into a fault zone

Induced seismicity from injection into a fault zoneAverage initial shear stress 54MPa

Kayla Kroll PhD thesis)

Injection point

Conclusions

1) Modeling• We have computational tools for quantitative virtual experiments• This includes models with highly complex fault systems – needed

for case studies

2) Rate-state friction – Earthquake clustering can result in continuing seismicity long after Pfluid effects have dissipated.

3) Initial stresses strongly affect characteristics of induced seismicity

4) With qualifications, maximum earthquake magnitude should scale by injected volume. Slope depends on bulk vs (fault) fracture diffusion

5) Traffic light procedures – real-time hazard assessment and risk mitigation may be problematic because of the increasing time lag for pressure signals to more distant points.

application of earthquake simulations to seismicity …...application of earthquake simulations to...

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