1. Geol 600 Notable Historical Earthquakes Source mechanisms and body wave radiation patterns http://www-rohan.sdsu.edu/~kbolsen/geol600_nhe_mechanism.ppt

2. Force Couples: Forces must occur in opposing directions to conserve momentum  D no net torque double couple: D net torque no net torque

3. 9 Force Couples M ij (the moment tensor), 6 different (M ij =M ji ). |M|=fd M 11 M 12 M 13 Good approximation for distant M= M 21 M 22 M 23 earthquakes due to a point source M 31 M 32 M 33 Larger earthquakes can be modeled as sum of point sources

5. Because of ambiguity M ij =M ji two fault planes are consistent with a double-couple model: the primary fault plane, and the auxillary fault plane (model for both generates same far-field displacements). Distinguishing between the two requires further (geological) information

6.  Description of earthquakes using mome Parameters: strike , dip , rake Vertical fault, right-lateral =180 o Vertical fault, right-lateral =0 o Strike, dip, rake, slip define the focal m 0 M 0 0 Example: vertical right-lateral along x M= M 0 0 0 M 0 =  DA scalar seismic moment (Nm) 0 0 0

7.  Description of earthquakes using moment tensors: Parameters: strike , dip , rake Right-lateral =180 o, left-lateral =0 o, =90 reverse, =-90 normal faulting Strike, dip, rake, slip define the focal mechanism

8.  Description of earthquakes using moment tensors: M 11 = -M 0 (sin  cos sin2  s + sin2  sin sin 2  s ), M 12 = M 0 (sin  cos cos2  s + 0.5 sin2  sin sin2  s ), M 13 = -M 0 (cos  cos cos  s + cos2  sin sin  s ), M 22 = M 0 (sin  cos sin2  s - sin2  sin cos 2  s ), M 23 = -M 0 (cos  cos sin  s - cos2  sin cos  s ), M 33 = M 0 sin2  sin 

10.  Determining an earthquake’s mechanism from first P motions

12. Take-off angle: sin i dT v d∆ ___ __ =

14. Strike of fault plane dip Strike of fault plane dip

17. Earthquake focal mechanism determination from first P motion (assuming double-couple model): Only vertical component instruments needed No amplitude calibration needed Initial P motion easily determined (up or down) Up: ray left the source in compressional quadrant Down: ray left source in dilatational quadrant Plotted on focal sphere (lower hemisphere) Allows division of focal sphere into compressional/dilatational quadrants Focal mechanism is then found from two orthogonal planes (projections on the focal sphere)

18. Earthquake focal mechanism determination from first P motion (assuming double-couple model): Focal sphere is shaded in compressional quadrants, generating ‘beach ball’ Tension axis in the middle of shaded region Pressure axis in the middle of unshaded region Only represents stress tensor if slip on plane of max shear Normal faulting: white with black edges Reverse faulting: black with white edges Strike-slip: cross pattern