L3 - Earthquake Scaling and Fault Stress

Question 1

How can fault length be estimated? (4)

Answer 1

Standard Time Function (STF)
Aftershock locations
Field observations
Geodetic data (GPS/InSAR)

Question 2

What is the relationship between the number of EQs and magnitude? (1)

Answer 2

log(N) = a -2/3 log(M0)

Question 3

What is the expression of there being different scaling between moment and fault dimensions for small and large EQs?

Answer 3

EQ have a circular rupture unless extending throughout the seismogenic layer
In this case they can’t get deeper so grow laterally

Question 4

How does seismogenic thickness affect earthquakes given the size of the rupture? (2)

Answer 4

EQ have a circular rupture unless extending throughout the seismogenic layer
In this case they can’t get deeper so grow laterally

Question 5

How is total EQ moment release related to EQ magnitude? (1)

Answer 5

> 95% of strain occurs in EQs big enough to (Mw >5.5)

Question 6

Why should one care about the magnitude and frequency of EQs?

Answer 6

1. Seismic hazard
   Building in EQ prone place, mag. to withstand?
2. Insight into underlying mechanics of faulting
   What controls fault behaviour?
   What are the forces on faults?
   How much stress is released in an EQ?

Question 7

What information must be known to try to understand the underlying mechanics of faulting?

Answer 7

Slip in EQs
Fault lengths
Depth extent of faults

Question 8

How can fault length be estimated? (4)

Answer 8

Standard Time Function (STF)
Aftershock locations
Field observations
Geodetic data (GPS/InSAR)

Question 9

How can fault width be estimated? (2)

Answer 9

Aftershocks/seismogenic thickness

Geodetic data

Question 10

How can fault slip be estimated? (2)

Answer 10

Field measurements

Geodetic data

Question 11

Define stress drop (1)

Stress drop equation (1)

Answer 11

Change in shear stress on the fault plane during the EQ
Δσ = Cμ(ū/Λ)
Δσ = stress drop
C = geometrical constant (~1)
ū = shear modulus (displacement)
Λ = rupture dimension (length)

Question 12

Define stress drop (1)

Stress drop equation (1)

Answer 12

Change in shear stress on the fault plane during the EQ
Δσ = Cμ(ū/Λ)
Δσ = stress drop
C = geometrical constant (~1)
ū = shear modulus (displacement)
Λ = rupture dimension (length)

Question 13

What is the difference in magnitude scaling between small and large EQs? (2)

Answer 13

Small: M0 ~ L^3
Large: M0 ~ L^2 W

Question 14

How do faults compare in interplate and intraplate settings compare (maybe)? (1)
Why is this relationship hard to define? (1)
What does it imply? (1)

Answer 14

Interplate (fast-moving) faults have lower ū/Λ so lower stress drops than intraplate (slow-moving) faults
Uncertainties in fault slip rates and stress drops
Implies slow-moving faults in plate interiors are stronger than those in rapidly-deforming regions

Question 15

What is the difference between “weak” and “strong” faulting? (2)

Answer 15

“Weak”: stress drop = total stress on fault

“Strong”: stress drop =/= total stress, only partial

Question 16

Why is there a change in scaling between ‘small’ and ‘large’ faults? (1)

Answer 16

Faults must grow in length as they accumulate displacement

Question 17

What are the main arguments used to estimate stress state on active faults? (5)

Answer 17

Fault orientations relative to the principal stress
Thermal effects of faulting
Places with independent estimates of total force
Lab experiments
Fault dip angles

Question 18

How can fault orientations relative to the principal stress be used to estimate stress on active faults? (4)
Are they trustworthy? (1)

Answer 18

San Andreas fault strikes perpendicular to estimated max horizontal compressive stress
Normal compressive stress on the fault is high
Shear stress is a small fraction of this
Fault has very low frictional resistance and can move at very low shear stresses

Unclear if the fold orientations used have been rotated

Question 19

How can the thermal effects of faulting be used to estimate stress on active faults? (4)
What is a problem for this method? (1)

Answer 19

Thermal anomalies at faults should give an estimate of a fault’s frictional properties
W/At = F/A * d/t
No observable heat flow anomaly on San Andreas
T_f limited to <20MPa ~ EQ stress drops

Doesn’t account for hydrothermal circulation (messes up heat flow)

Question 20

How can places with independent estimates of total force be used to estimate stress on active faults? (4)

Answer 20

Indian EQ: ruptured Indian Shield due to compressive force of India-Asia collision
Estimate force using Indian Plate motion and crustal thickness contrast
Stress drop large and faults account for all compressive force in the area
Stress drop in EQ was complete

Question 21

How can lab experiments be used to estimate stress on active faults? (2)

Answer 21

Byerlee suggested coefficient of friction was 0.6-0.85

Implies faults like San Andreas should support stresses over 200MPa

Question 22

What are the associated problems with Byerlee’s law? (4)

Answer 22

Unclear if these values should be used or those for clay minerals (much lower μ)
What is the pore fluid pressure?
Do I get the wrong answer by using sample sizes and strain rates in the lab very different from to natural faults?
How are results on shallow rocks applicable to depths of 10-15km (most EQs rupture here)?

Question 23

How can fault dip angles be used to estimate stress on active faults? (4)

Answer 23

New faults being formed in oceanic outer rises
Dip angles should provide constraints on μ, which controls the preferential angle of fault formation
New faults dominantly dip close to 45 degrees
Implies μ < 0.3, and fault shear stresses similar to EQ stress drops