11 State of Stress · GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD State of Stress in the Crust Lecture 11 Tectonics. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

State of Stress in the Crust

Lecture 11

Tectonics


Global distribution of tectonic deformationPlate boundaries and zones of distributed deformation (after Gordon, 1994)

Many plate boundaries are so indistinct that they occupy 15% of the Earth’s surface


Deformation of tectonic plates

• Strain rates inferred from summation of Quaternary fault slip rates (white axes), and spatial averages of predicted strain rates (black axes) given by fitted velocities• Fitted strain rate field is a self-consistent estimate in which both strain rates and GPS velocities are matched by model strain rates and velocity fields.


Deformation of tectonic platesGlobal strain rate model

For the global model ~1600 geodetic velocities are currently used. These velocities comprise mainly of GPS, but velocities from the SLR, VLBI and DORIS techniques are also used. Seismic moment tensors from the Harvard CMT catalogue are taken to infer a seismic strain rate field.


Diangxiong Fault, Tibet

UCL-Birkbeck China joint project:

InSAR edge-reflector and GPS network around theDangxiong Fault

and Quaternary geology slip rates


The Tectonic Cycle


Forces on Plates•Large meteoritic impacts

May explain sudden changes in rates or direction of plates (e.g.Scotia arc)

• Slab pull at ocean trenches

Argument against: Once a plate has reached terminal velocity slab pull is balanced by viscous and frictional forces

• Drag at the base of the plate through mantle convection

Implausible because plates not coupled to mantle. Strain rates at plate boundaries are up to 109 than in plate interiors.

•Ridge push at mid-ocean ridges from upwelling magma

10x less effective than slab pull but also have gravity slide


Ridge push / gravity slide

Gravity slide 0.28 kbar

Ridge push 0.3 kbar

Necessary Zagros fold force 0.145 kbar


Crustal stress map

Measurements of stress are usually derived from displacement. However there are some more direct methods such as measuring stress of borehole breakouts, and also methods derived from seismology, which we will discuss later.

The stress maps display the orientations of the maximum horizontal stress SH


State of stress in the crust

Near the surface1 vertical + 2 horizontal

principal stresses

Deeper in the crustthe overburden pressure or

lithostatic stress becomes increasingly significant

Earth’s surface

air/water – can’t support shear stress

rock – only shear stresses in this plane

free surface

atmospheric pressure neglected – but can be significant on VenusAt the surface

p = σZ

p =σz = ρ g z

depth z

lithostatic stress:

density ρ


Lithostatic stressp = σZ

p = σz = ρ g z

depth z

lithostatic stress:

Acceleration due to gravity g = 9.8 m/s2

Typical density ρ = 2.5 x 103kg.m-3 in the upper crust

The geobaric gradient is 25 MPa/km in the upper crustal. Density is pressure and temperature sensitive and so thegeobaric gradient varies according to tectonic environment.

Lithostatic stress or pressure: overburden pressure


Tectonic stress

Differential stress σd

Is the difference between the max & min stresses: σd = σmax - σminOften p = σ3 is called the pressure

• Deviatoric stress tensor = total stress tensor – hydrostatic pressure

• Deviatoric stress drives deformation of the crust

• Differential stress = max stress – pressure (-σ3)

• Differential stress also drives deformation of the crust

• Both can be considered to be the tectonic stress, σtect

Deviatoric stress σ’Is the amount the total stress deviates from the mean stress or hydrostatic pressureit is a tensor


Seismic / aseismic transition

Strength profileShear resistance

Depth

Brittle

Ductile

Overburden

40km 1 kbar 100MPa

Maximum shear strength, maximum stress drop → big earthquakes

Thermally activated creep: exp(-H/kT)

Higher strain rate Low geothermal gradientPore fluid pressure

Earthquake locations show the seismic zone is close to the uppersurface of the down-going plate


Measuring stresses in the crust

0-600 MPa0-25 kmUpper crust350 GPa5,100 kmCore

Pressures0.1 MPaSea levelAtmospheric pressure

Tectonic stresses

10-100 MPa15 MPa30 MPa

20-30 MPa

Stress

Strain 0.2-0.6 x10-6VariousActive regionsGeodynamicsZagrosContinental collisionGeodynamicsRed SeaRidge gravity slideGeodynamicsRed SeaRidge push

Comment


Water in the crustHydrostat

pf = ρw g z

pf – pore fluid pressure

ρw – density of water

lithostatic stress: p= σz = ρ g z

p = σZ

depth zhydrostat:

pf = ρw g z

The average bulk density of water is approximately 1.0 x 103kg.m-3 . This will vary depending on salinity, temperature and pressure

The hydrostat or pore fluid pressure gradient is 10 MPa/km in the crust. This is about 40% of the lithostatic pressure

The ratio of the pore fluid pressure to the lithostatic pressure is the pore fluid factor: λv = pf / pThe effective overburden pressure may then be written

peff = p - pf = ρ g z (1 - λv)


Water in the crust

Lithostatic stress vshydrostat

The hydrostat or pore fluid pressure gradient is 10 MPa/km in the crust. This is about 40% of the lithostatic pressureTypically the pore fluid factor: λv = pf / p = 0.4

Suprahydrostatic gradients are known to occur in tectonically controlled areas created by fault sealing or by impervious rock layers. Fluid pressures are commonly greater than hydrostatic during crustal deformation, particularly in compressional tectonic regions. For example, east of the San Andreas, fault fluid levels deviate from an initial hydrostatic gradient to λv values of 0.9 over the depth range of 2-5km .

This is just the weight of the water column to the rock column.

KTB borehole


2D stress field

Resolution of forces and areas both parallel and perpendicular to the fault leads to the following equations for normal and shear stress on the fault plate:

( ) ( )θσσσ

ϑσσσσσ2sin)(21

2cos2121

21

2121

−=−−+=

S

N

Note that: ½ (σ1 + σ2) = σm = mean stress

fault plane

Normal stress σN and shear stress σS

σ1

σ2 σ2

σ1

σN

σS

θnormal stress

shear stress

remote principal stressre

mot

e pr

inci

pal s

tress P

Local stresses on fault: σ1 > σ2 > σ3 compression positive


Construction of Mohr stress circle: shear stress vs. normal stress

σS axis

σN axisσ1σ2 σm

(σ1 + σ2)/2

2θ

σS

σN

σS max

(σ1 - σ2)/2

P

Maximum shear stress = ½ (σ1 - σ2) when θ = 45o

Any point on circle has coordinates (σN, σS) where:

( ) ( )θσσσ

ϑσσσσσ2sin)(21

2cos2121

21

2121

−=−−+=

S

N

Documents

11 State of Stress · GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD State of Stress in the Crust Lecture 11 Tectonics. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND