01 13 05 Andersonian

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The last of the CIRCULAR GRAPHS which will HAUNT YOU ALL QUARTER: 

The last of the CIRCULAR GRAPHS which will HAUNT YOU ALL QUARTER January 13, 2005 [Many thanks to H. Bob]

Stress - Real Time: 

Stress - Real Time

Slide6: 

Map of global seismicity

Definitions: FRICTION: 

Definitions: FRICTION Same as sliding blocks from physics class (kinetic friction) Determines slope of Coulomb failure envelope For unconsolidated materials, m = angle of internal friction = angle of repose. For rocks, m = coefficient of friction of sliding surfaces

Definitions: COHESION: 

Definitions: COHESION For whole rocks: C = breaking strength. For broken surfaces: C = static friction. For unconsolidated sediment: C = ZERO. Like “static friction” from physics class

No shear stress on a FREE SURFACE: 

No shear stress on a FREE SURFACE

If stresses were everywhere aligned with the earth’s surface…: 

If stresses were everywhere aligned with the earth’s surface…

But if stresses are angled at depth…: 

But if stresses are angled at depth… Then they rotate to alignment near the surface!

Andersonian Theory of Faulting:: 

Andersonian Theory of Faulting: The optimum shear fracture plane is always oriented at 60° to s1, 30° to s3, s2 is in the plane. Simple idea but VERY USEFUL - Provides link between faults and stresses - present and past.

Rules of Thumb: 

Rules of Thumb “Thinning Direction” parallel to s1 “Thickening Direction” parallel to s3 Simple model - no motion along s2 SIMPLIFICATION! For now anyway. Remember the sandbox model from last week’s lab…

s1 horizontal, s3 vertical: 

s1 horizontal, s3 vertical

s1 horizontal, s3 vertical: 

s1 horizontal, s3 vertical

s1 horizontal, s3 horizontal: 

s1 horizontal, s3 horizontal

s1 horizontal, s3 horizontal: 

s1 horizontal, s3 horizontal

s1 vertical, s3 horizontal: 

s1 vertical, s3 horizontal

s1 vertical, s3 horizontal: 

s1 vertical, s3 horizontal

The last of the CIRCULAR GRAPHS which will HAUNT YOU ALL QUARTER: 

The last of the CIRCULAR GRAPHS which will HAUNT YOU ALL QUARTER And Now, As Promised…

Plane intersects sphere = Arc!: 

Plane intersects sphere = Arc!

Convention: use the “Southern” Hemisphere of an imaginary sphere : 

Convention: use the “Southern” Hemisphere of an imaginary sphere

Let’s start with a vertical plane cutting the hemisphere. It intersects on an ARC.: 

Let’s start with a vertical plane cutting the hemisphere. It intersects on an ARC.

Now let’s look down from the North Star…: 

Now let’s look down from the North Star…

Assign a coordinate system to get us oriented…: 

Assign a coordinate system to get us oriented…

Reduce the clutter to a circle. : 

Reduce the clutter to a circle. Now let’s graph a plane onto it! Vertical plane - straight line through the pole Strike=45

How about a horizontal plane?: 

How about a horizontal plane? Strike=?? It sits through the equator - all lines are horizontal so there’s no unique strike line

How about plane 0/25W? : 

How about plane 0/25W? Strike=0 Or plane 0/55W?

How about plane 45/25NW? : 

How about plane 45/25NW? Strike=45

Template on which we can draw our circles: stereonet: 

Template on which we can draw our circles: stereonet