Physical interpretation of DC and non-DC components of moment tensors Václav Vavryčuk Institute of Geophysics, Prague

MT for simple types of seismic sources

Explosive (implosive) source Source process Force equivalent Moment tensor explosion three linear dipoles implosion

Shear faulting Source process Force equivalent Moment tensor no torque double-couple (quadrupole)

Pure tensile faulting Source process Force equivalent Moment tensor opening fault opening closing

Shear-tensile faulting Source process Force equivalent Moment tensor DC + fault opening fault opening closing

Decomposition of MT

Decomposition of MT + + ISO DC CLVD non-shear shear non-shear

Double-couple component of the moment tensor Force equivalent Seismic moment tensor DC part double couple (DC) (shear faulting) rotated double-couple (DC)

Non-double couple components: ISO and CLVD Force equivalent Seismic moment tensor ISO part (explosion) CLVD part (tensile crack) compensated linear vector dipole

Decomposition of the moment tensor M – moment tensor MISO – trace of M M* – deviatoric part of M Percentage of ISO, CLVD and DC : |ISO|+|CLVD|+DC = 100%

Physical interpretation of MT

Parameters of shear faulting DC components Parameters of shear faulting orientation of active faults, fault mapping type of fracturing (strike-slip, normal/reverse faulting) Determination of present-day tectonic stress orientation of principal stress axes ratio between principal stresses

Numerical errors of the MT inversion insufficient number of stations presence of noise in the data unfavourable station coverage of the focal sphere inaccurate knowledge of the structure model approximate location and Green’s functions approximate moment tensor

Presence of single forces no dipole forces Examples: impact of meteorites, landslides, volcanic eruptions, fluid flow in volcanic channels the process is not described by the moment tensor!

Complex shear faulting DC1 DC2 DC + CLVD ISO = 0 fault Sum of two DCs of different orientations produces DC and CLVD

Combined shear-tensile faulting I DC + CLVD + ISO fault Example: hydrofracturing High pore pressure can cause opening faults during the rupture process (CLVD and ISO are then positive).

Combined shear-tensile faulting II CLVD and ISO are correlated! ISO/CLVD -> vP/vS

Correlation between ISO and CLVD shear-tensile faulting linear dependence different vP/vS ratios CLVD [%]

Shear faulting in anisotropic media DC + CLVD + ISO fault The relation between fracture geometry and acting forces is more complicated in anisotropic media than in isotropic media.

Moment tensors in isotropy Shear earthquakes in isotropy (Aki & Richards 2002, Eq. 3.22): n S un u – slip S – fault area  – shear modulus  – slip direction n – fault normal cijkl – elastic parameters double-couple (DC) mechanism

Moment tensors in anisotropy Shear earthquakes in anisotropy (Aki & Richards 2002, Eq. 3.19): n S un u – slip S – fault area  – shear modulus  – slip direction n – fault normal cijkl – elastic parameters general (non-DC) mechanism

Examples

1997 West-Bohemian earthquake swarm

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

Swarm 97: Basic characteristics Duration: 2 weeks Number of earthquakes: 1800 Strongest event: M=3.0 Depth of events: 8.5-9.5 km Focal area: 700x700x1000 m Faults activated: 2 different faults N P wave S wave Z E 1 s

Swarm 97: epicentres and mechanisms Nový Kostel focal area Fischer & Horálek (2000) Horálek et al. (2000)

DC & non-DC mechanisms Type A Type B

Correlation between ISO and CLVD corr. coeff = 0.91 + vP/vS = 1.48 strong indication for tensile faulting!

Shear & tensile faulting A events B events 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

Deviation of the slip from the fault A events: -5 <  < 5 B events: 10 <  <20

Induced microseismicity during the 2000 fluid injection experiment in KTB, Germany

KTB superdeep drilling hole location: northern Bavaria, Germany holes: pilot hole - 4 km, main borehole - 9.1 km (October 1994), distance – 185 m geology: crystalline unit, steeply inclined layers of gneisses, amphibolites borehole geometry: vertical to 7.5 km, then inclined bottom hole temperature: 265ºC N P wave S wave Z E 1 s

Injection experiment 2000 experiment: 60 days amount of fluid: 4000 m3 of fresh water entire 9.1 km borehole was pressurized well head pressure was between 20 to 30 MPa flow rate ranged between 30 to 70 l/min several sharp pressure drops during shut-in phases N P wave S wave Z E 1 s

Focal mechanisms of 37 events Nodal lines P/T axes P T Nodal lines and P/T axes are well clustered

Non-DC components ISO percentage CLVD percentage Mean value of ISO = 1.5% Mean value of CLVD = -5.7% Positive values - tensile components, negative values - compressive components

Correlation between ISO and CLVD corr. coeff. = 0.01 no correlation! strong indication for other origins than tensile faulting!

Anisotropy models at KTB P-wave velocity S-wave velocity P anisotropy: 2 - 18%, S1 anisotropy: 3 - 18%, S2 anisotropy: 8 - 26% anisotropic models of gneiss inferred from: VSP, sonic logs, lab measurements References: Jahns et al. (1996), Rabbel (1994), Rabbel et al. (2004)

Inversion for anisotropy: method Input: moment tensors of 37 events anisotropy at the focal area Output: fault normals and slip directions theoretical DC, CLVD and ISO components The misfit function: misfit between the theoretical and observed non-DC components Result: optimum orientation of anisotropy

Inversion for anisotropy: results Misfit for TI Misfit for ORT The misfit function is normalized so it equals 1 for an isotropic medium.

Optimum anisotropy orientation Triangles: optimum orientation from moment tensors Squares: orientation from MSP Rabbel et al. (2004) Anisotropy axes (plunge/azimuth): Axis 1: 5º/65º, Axis 2: 50º/160º, Axis 3: 40º/330º

Summary

Significance of the DC components Parameters of shear faulting orientation of active faults, fault mapping type of fracturing (strike-slip, normal/reverse faulting) Determination of present-day tectonic stress orientation of principal stress axes ratio between principal stresses

Significance of the non-DC components Discrimination explosions versus earthquakes Analysis of tensile faulting detection of overpressure regime temporal variation of pore pressure the vP/vS ratio in a focal area Estimation of anisotropy in a focal area orientation of anisotropy axes anisotropy strength