Dislocation Theory
Download as PPT, PDF1 like583 views
1) The document discusses different types of faults including strike-slip, dip-slip, and oblique-slip faults. It defines key parameters used to describe faults like length, width, dip angle, slip, and rake. 2) Equations are provided to calculate the geometry of faults using Green's functions which relate the dislocation field (displacement) to fault parameters. 3) The document gives an example of inverting GPS data using a single, two, and three dislocation models to model displacement from faults. Model parameters like length, width, depth and slip are estimated.
Dislocation Theory
- 1. Dislocation Theory Kutubuddin ANSARI kutubuddin.ansari@ikc.edu.tr GNSS Surveying, GE 205 Lecture 11, May 13, 2015
- 3. Length Width DIP Angle Slip Fault RakeFault is a planar fracture or discontinuity in a volume of rock, across which there has been significant displacement along the fractures as a result of rock mass movement. DIP Angle (δ ) Rake (ψ) Depth
- 4. Top Depth Length Width Bottom Depth Earth Surface ( ) Bottom Depth Top Depth Sin Dip Angle Width − =
- 5. Strike-Slip Fault • The movement of blocks along a fault is horizontal. •Rake zero (0o ) Fault plane solution of strike-slip Earthquake Slip
- 6. •If the block on the far side of the fault moves to the left, the fault is called Left-lateral (sinistral) Fault. •If the block on the far side moves to the right, the fault is called Right-lateral (dextral) Fault. Strike-Slip Fault
- 7. Dip-Slip Fault • The movement of blocks along a fault is vertical. •Rake zero (90o ) Slip
- 8. Dip-Slip Fault •If the hanging wall moves downward relative to the footwall, the fault is called Normal (extensional) Fault. •If the hanging wall moves upward relative to the footwall, the fault is called Reverse Fault. Reverse faults indicate compressive shortening of the crust. • Reverse fault having dip angle less than 450 is called Thrust Fault.
- 9. Dip-Slip Fault Normal Fault Thrust Fault Reverse Fault
- 10. Oblique-Slip Fault •A fault which has a component of dip-slip and a component of strike-slip is termed an oblique-slip fault. • Rake will be (0 < ψ >90) Slip
- 11. The Geometry of the fault having parameters (length, width, depth, dip angle) can be given by analytically by Green function (G): 2 2 1 1 AL AW AL AW G d dη ξ= ∫ ∫ (Okada, 1985 &1992) Length Width DIP Slip Length(AL) Width(AW) Length Width cos sin x AL y d AW ξ η δ δ = − = + − (δ) Dislocation Theory
- 12. 1 1 2 1 tan sin 2 ( ) 1 cos sin 2 ( ) x y q G I R R qR yq q G I R R R ξ ξη δ π η δ δ π η η − = − + + ÷ + = − + + + + % are arbitrary constants 1 2 3, , , , , ,R p y d I I I%% (Okada, 1985) 3 1 sin cos 2 x q G I R δ δ π =− − 1 1 1 cos tan sin cos 2 ( ) y yq G I R R qR ξη δ δ δ π ξ − = − + − + Strike Slip case Dip Slip case
- 13. (P. Cervelli et. al 2001) S is Slip For Oblique Slip S= s.cosα + s.sinα d= sG(m) Relationship between dislocation field (d) and the fault geometry G(m)
- 14. Consider the case we have observed data d1, d2, ……. dn and the Green function of each observation data are G1, G2, ……. Gn respectively, Then:
- 17. Results Single dislocation model
- 18. ' ' 1 11 11 ' ' 2 21 21 1 2 ' ' 1 1 ( ) ( ) ( ) ( ) . . . . . . . . . ( ) ( )n n n d G m G m d G m G m s s d G m G m = + Two dislocation model
- 21. Case Length (Km) Width (Km) Bottom Depth Top Depth Dip Angle Rever se Slip Strike Slip 1 73 (Fault 1) 115.18 25± 2 5±0.3 10± 1 15± 1 0 2 79 (Fault 1) 73 (Fault 2) 240.95 115.18 24± 3 25± 3 3± 0.2 5± 0.3 5± 0.5 10± 0.3 19±1 11 3 0 3 73 (Fault 1) 73 (Fault 2) 73 (Fault 3) 149.16 200.70 286.71 16± 0.2 16± 0.5 21± 4 3± 0.2 2± 0.3 1± 0.2 5± 0.1 4± 0.1 4± 0.5 20± 1 8 1 6 1 0
- 23. Richter magnitude scale The Richter magnitude scale (Richter scale) assigns a magnitude number to quantify the energy released by an earthquake. Seismic moment = μ* slip*rupture area MO= μ*s*A MO= μ*s*L*W μ = shear modulus of the crust (approx 3x1010 N/m2 ) L= Length of finite rectangular fault W= Width of finite rectangular fault s = slip
- 24. 10 0log ( ) 6.07 1.5 w M M Nm= − Moment Magnitude Moment magnitude Mw comes from seismic moment Mo
- 25. μ = 3x1010 N/m2 L=200 km W= 100 km s = 10 mm MO= μsLW Mo=(3x1010 )x(10 x10-3 )x (200 x 103 )x(100 x 103 ) Mo=(3x1010 )x(10-2 )x (2 x 105 )x(1x105 ) Mo=6x1018 Example 18 10log (6 10 ) 6.07 1.5 wM Nm × = −
- 26. 18 10 10 log (6 10 ) 6.07 1.5 log(6) 18log (10) 6.07 1.5 0.778+18 6.07 1.5 6.448 w w w w M M M M Nm × = − + = − = − =