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

Physical concept

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 !

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

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

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

Numerical modelling

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

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

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

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

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

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

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

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

West-Bohemian earthquake swarm in 2008

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

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

Examples of focal mechanisms Waveform inversion from P waves

Family of accurate focal mechanisms 101 most accurate focal mechanisms

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:

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

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

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 = -0.70 friction = 0.5 shape ratio = 0.75 cohesion = 0.2 σ3 σ2 σ1 principal fault planes 2008 principal focal mechanism 1997 pore pressure = -0.83 friction = 0.5 shape ratio = 0.75 cohesion = 0.2 2008 1997 σ3 σ2 σ1

Principal focal mechanisms versus friction shape = 0.60 Mohr’s diagram Nodal lines P/T axes friction = 1.20 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

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

Principal faults versus tectonics in West Bohemia

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

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