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Tensile earthquakes: definition and observations

Tensile earthquakes: mathematical description and graphical representation Václav Vavryčuk Institute of Geophysics, Prague. Tensile earthquakes: definition and observations. Definition: slip does not lie in the fault fault is opening or closing during a rupture process. Observations:

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Tensile earthquakes: definition and observations

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  1. Tensile earthquakes: mathematical description and graphical representationVáclav VavryčukInstitute of Geophysics, Prague

  2. Tensile earthquakes: definition and observations • Definition: • slip does not lie in the fault • fault is opening or closing during a rupture process • Observations: • geothermal and volcanic areas (injection of fluids/magma) • hydro-fracturing in oil/gas fields • collapses in mines • complex fault geometry – tensile wing cracks • tensile vibrations of a fault

  3. Tensile faulting due to fluid injection DC + CLVD + ISO fault • high pore pressure can cause opening faults during the rupture process (CLVD and ISO are then positive).

  4. Tensile wing cracks DC + CLVD + ISO shear faulting on a main fault tensile wing crack tensile wing crack • wing cracks are induced by shear faulting • predominant frequency of shear and tensile motions can be significantly different

  5. Tensile vibrations of a fault DC + CLVD + ISO shear faulting on a main fault tensile vibrations • vibrations can be induced by small scale irregularities on a fault • predominant frequency of shear and tensile motions can be significantly different

  6. Mathematical model

  7. Source tensor & moment tensor Area with a continuous displacement Hooke’s law Strain tensor Stress tensor Area with a discontinuous displacement Hooke’s law Source tensor Moment tensor

  8. Shear earthquakes in isotropy Source tensor (potency) n S fault u double-couple Moment tensor u – slip vector S – fault area  – Lamé coefficient n– fault normal cijkl– elastic parameters double-couple

  9. Tensile earthquakes in isotropy Source tensor (potency) n u S fault non-double-couple Moment tensor u – slip vector S – fault area λ,  – Lamé coefficients n– fault normal cijkl– elastic parameters non-double-couple

  10. Eigenvectors of the source and moment tensors Shear earthquakes P/T axes form angle of 45 ° with the fault normal and slip P/T axes bisect the angle between the fault normal and slip

  11. Eigenvectors of the source and moment tensors Tensile earthquakes P/T axes form a general angle with the fault normal and slip P/T axes bisect the angle between the fault normal and slip

  12. Radiation pattern

  13. Shear and tensile radiation patterns I Shear earthquakes Tensile earthquakes pure extensive source

  14. Shear and tensile radiation patterns II Shear earthquakes Tensile earthquakes α= 0° α= 5° α= 10°

  15. Shear and tensile radiation patterns III Tensile earthquakes α= 10° α= 30° α= 90° no nodal lines no nodal lines

  16. Graphical representation of tensile sources

  17. Focal spheres and nodal lines Tensile earthquakes Shear earthquakes α= 0° α= 20° fault fault P P T T slip plane slip plane Φ = 45°, δ = 50°, λ = -45°

  18. Nodal lines and source lines Source lines Nodal lines α= 20° α= 20° fault fault P P P T T T slip plane slip plane Φ = 45°, δ = 50°, λ = -45°

  19. Nodal lines and source lines Source lines Nodal lines α= 30° α= 30° fault fault P P P T T T slip plane slip plane Φ = 45°, δ = 50°, λ = -45°

  20. Decomposition ofsource and moment tensors

  21. DC and non-DC components • Source and moment tensors: • tensile earthquakes generate DC, CLVD and ISO • CLVD and ISO have the same sign • CLVD and ISO are positive (negative) for extensive (compressive) sources • CLVD and ISO are linearly dependent • Moment tensors: • direction of the CLVD-ISO line depends on the P to S velocity ratio of the focal zone

  22. ISO versus CLVD Decomposition of source and moment tensors for tensile sources with slope ranging from -90° to 90° Source tensors Moment tensors 2.0 1.7 1.5 Direction of the ISO-CLVD line is independent of the vP / vS ratio Direction of the ISO-CLVD line is dependent on the vP / vS ratio

  23. Errors of ISO and CLVD Decomposition of noisy source and moment tensors for 1000 realizations of random noise Source tensors Moment tensors CLVD is about 2-3 times less accurate than ISO!

  24. Conclusions • tensile faulting is a frequently observed mechanism • source tensors and moment tensors are non-DC • nodal lines of the DC part have no physical meaning • new lines called ‘source lines’ are introduced for representing the tensile source on the focal sphere • CLVD is 2-3 times more sensitive to errors than ISO • the P to S velocity ratio can be retrieved from the ISO- CLVD function

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