1. Václav Vavryčuk Institute of Geophysics, Prague
Principal earthquakes: Application to micro-earthquakes in West Bohemia
Václav Vavryčuk
Institute of Geophysics, Prague

2. Physical concept

3. Mohr-Coulomb failure criterion
c – critical shear traction
S – cohesion
k – friction
n – normal traction
p – pore pressure  
satisfied
not satisfied
s1, s1, s3 - principal stress values
s3-p
s2-p
s1-p 
 - shear traction
 - effective normal traction
The origin of  depends on p !

4. Tectonic stress & types of earthquakes
a) No earthquakes
b) Shear earthquakes
c) Shear & tensile earthquakes
Pore pressure:
low
high
very high

5. Shear & tensile faulting
Shear faulting
Tensile faulting u u   
Slip is along the fault
Slip is not along the fault
Moment tensor is DC
Moment tensor is non-DC
(DC+CLVD+ISO)
 – fault , u – slip,  – deviation of the slip from the fault

6. Orientations of activated faults
Types of faults:
favourably oriented faults (shear or tensile mechanisms)
misoriented faults

7. Numerical modelling

8. Procedure Assumptions: Modeled parameters:
Tectonic stress in the focal area (principal stress axes, shape ratio) is homgeneous
Pore pressure, cohesion and friction on faults is constant
Modeled parameters:
Orientation of faults satisfying the Mohr-Coulomb failure criterion
Statistical properties of focal mechanisms: nodal lines, P/T axes

9. Statistical distribution of focal mechanisms
Tectonic stress
Mohr’s diagram
orientation of principal axes
shape ratio = 0.5
friction = 0.6
cohesion = 0.2
pore pressure = 0.2 σ3 σ2 σ1
randomly distributed faults satisfying
the failure criterion
Focal mechanisms
slip is along the traction on the fault σ3
N = 250
o - P axis
+ - T axis σ2 σ1

10. Shape ratio dependence
friction = 0.8
Mohr’s diagram
Nodal lines
P/T axes
shape ratio = 0.25
friction = 0.8
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1
shape ratio = 0.50
friction = 0.8
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1
shape ratio = 0.75
friction = 0.8
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1

11. Shape ratio dependence
friction = 0.4
Mohr’s diagram
Nodal lines
P/T axes
shape ratio = 0.25
friction = 0.4
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1
shape ratio = 0.50
friction = 0.4
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1
shape ratio = 0.75
friction = 0.4
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1

12. Friction dependence shape = 0.5 σ3 σ2 σ1 σ3 σ2 σ1 σ3 σ2 σ1
Mohr’s diagram
Nodal lines
P/T axes
friction = 1.0
shape ratio = 0.5
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1
friction = 0.8
shape ratio = 0.5
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1
friction = 0.6
shape ratio = 0.5
cohesion = 0.2
pore pressure = 0.1 σ3 σ2 σ1

13. Pore pressure dependence
friction = 0.6
Mohr’s diagram
Nodal lines
P/T axes
pore pressure = 0.4
friction = 0.6
shape ratio = 0.5
cohesion = 0.2 σ3 σ2 σ1
pore pressure = 0.1
friction = 0.6
shape ratio = 0.5
cohesion = 0.2 σ3 σ2 σ1
pore pressure = -0.5
friction = 0.6
shape ratio = 0.5
cohesion = 0.2 σ3 σ2 σ1

14. Principal focal mechanisms
Principal focal mechanisms – the mechanisms which occur on the most unstable
fault planes
the most unstable fault plane
pore pressure = -0.61
shape ratio = 0.5
friction = 0.6
cohesion = 0.2
Principal nodal lines
Principal P/T aces
principal
fault planes σ3 σ1 σ2

15. Principal focal mechanisms
Principal focal mechanisms – the mechanisms which occur on the most unstable
fault planes
Principal nodal lines
principal
fault plane
principal
fault plane

16. West-Bohemian earthquake swarm in 2008

17. Seismicity in West Bohemia
active tectonics
geothermal area
mineral springs
emanations of CO2
earthquake swarms:
1985/86
1994
1997
2000
2008

18. Determination of focal mechanisms
Data
167 local micro-earthquakes from the 2008 swarm
Magnitudes between 0.5 – 3.7
Depth between 7 and 10 km
18-22 local short-period seismic stations
Sampling rate 250 Hz
Epicentral distance up to 40 km
Method
Waveform inversion from P waves in the frequency domain
1-D smooth model
Ray-theoretical Green functions
Good ray coverage

19. Examples of focal mechanisms
Waveform inversion from P waves

20. Family of accurate focal mechanisms
101 most accurate focal mechanisms

21. Inversion for stress: Angelier method (2002)
Misfit function
Mohr’s diagram σ2 x σ3 o σ1 + σ3 σ2 σ1
SSSC criterion is maximized
Optimum stress:

22. Forward modelling Real data Synthetic data N=101 N=250 σ3 σ2 σ1 σ3 σ2
Mohr’s diagram
Nodal lines
P/T axes
Real data
N=101 σ3 σ2 σ1
Synthetic data
N=250
pore pressure = -0.2
friction = 0.6
shape ratio = 0.6
cohesion = 0.2 σ3 σ2 σ1

23. Refining shape ratio friction = 0.6 σ3 σ2 σ1 σ3 σ2 σ1 σ3 σ2 σ1
Mohr’s diagram
Nodal lines
P/T axes
shape ratio = 0.85
friction = 0.6
cohesion = 0.2
pore pressure = -0.45 σ3 σ2 σ1
shape ratio = 0.75
friction = 0.6
cohesion = 0.2
pore pressure = -0.48 σ3 σ2 σ1
shape ratio = 0.60
friction = 0.6
cohesion = 0.2
pore pressure = -0.50 σ3 σ2 σ1

24. Principal focal mechanisms
shape = 0.75
Mohr’s diagram
Nodal lines
P/T axes
pore pressure = -0.48
friction = 0.5
shape ratio = 0.75
cohesion = 0.2 σ3 σ2 σ1
pore pressure =
friction = 0.5
shape ratio = 0.75
cohesion = 0.2 σ3 σ2 σ1
principal
fault planes
2008
principal
focal mechanism
1997
pore pressure =
friction = 0.5
shape ratio = 0.75
cohesion = 0.2
2008
1997 σ3 σ2 σ1

25. Principal focal mechanisms versus friction
shape = 0.60
Mohr’s diagram
Nodal lines
P/T axes
friction =
shape ratio = 0.6
cohesion = 0.2
pore pressure = -0.13 σ3 σ2 σ1
friction = 0.40
shape ratio = 0.6
cohesion = 0.2
pore pressure = -1.19 σ3 σ2 σ1

26. Optimum solution Real data Synthetic data Mohr’s diagram Nodal lines
P/T axes
Real data
Synthetic data
shape ratio = 0.75
friction = 0.5
pore pressure = -0.7
cohesion = 0.2

27. Principal faults versus tectonics in West Bohemia

28. Generic faults versus tectonics in West Bohemia
The most active faults
in recent seismic activity
Mariánské fault system:
one of the most pronounced
faults systems in the area

29. Conclusions
each stress regime: a specific distribution of focal mechanisms
the distribution is affected by pore pressure, friction and cohesion
for the stress inversion we need a large family of focal mechanisms (to study their statistical properties)
each stress tensor allows for two distinct characteristic mechanisms called principal focal mechanisms
principal focal mechanisms are connected with principal faults
existence of principal mechanisms explains a frequent observation of existence of two active fault systems in seismic regions
principal focal mechanisms can be used in the stress inversion