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Home , Overburden pressure, Stress (mechanics)

Lecture 11

State of in the Crust

GNH7/GG09/GEOL4002 SEISMOLOGY AND EARTHQUAKE HAZARD Global distribution of tectonic ß Plate boundaries and zones of distributed deformation (after Gordon, 1994)

Many plate boundaries are so indistinct that they occupy 15% of the Earth’s surface GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Deformation of tectonic plates

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

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Global strain Deformation of tectonic plates 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 from the Harvard CMT catalogue are taken to infer a seismic strain rate field. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Diangxiong Fault, Tibet

UCL-Birkbeck China project: InSAR edge- reflector and GPS network around the Dangxiong Fault and Quaternary geology slip rates

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD The Tectonic Cycle

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD on Plates •Large meteoritic impacts May explain sudden changes in rates or direction of plates (e.g. Scotia arc) • Slab pull at ocean 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 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 slide

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Ridge push / gravity slide

Necessary Zagros 0.145 kbar

Gravity slide 0.28 kbar Ridge push 0.3 kbar

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Crustal stress map

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

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

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD State of stress in the crust ß At the surface atmospheric neglected – but can be significant on Venus free surface air/water – can’t support stress rock – only shear stresses in this plane Earth’s surface density ρ

ß Near the surface p = σZ 1 vertical + 2 horizontal principal stresses lithostatic stress:

p =σz = ρ g z ß Deeper in the crust the overburden pressure or lithostatic stress becomes increasingly significant depth z GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Lithostatic stress p = σ ß Lithostatic stress or pressure: Z ß overburden pressure lithostatic stress:

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

2 Acceleration due to gravity g = 9.8 m/s depth z

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

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Tectonic stress

ß Deviatoric stress σ’ a Is the amount the total stress deviates from the mean stress or hydrostatic pressure a it is a ß Differential stress σd a Is the difference between the max & min d stresses: σ = σmax - σmin

a Often 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

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic / aseismic transition

Strength profile Shear resistance

Overburden Brittle Maximum , maximum 40km 1 kbar stress drop → big 100MPa Thermally activated Ductile : exp(-H/kT)

Depth Higher strain rate Low geothermal gradient Pore pressure Earthquake locations show the seismic zone is close to the upper surface of the down-going plate

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Measuring stresses in the crust

Stress Comment

Pressures Atmospheric pressure Sea level 0.1 MPa Upper crust 0-25 km 0-600 MPa Core 5,100 km 350 GPa Tectonic stresses Ridge push Red Sea 20-30 MPa Ridge gravity slide Red Sea 30 MPa Geodynamics Zagros 15 MPa Geodynamics Active regions Various 10-100 MPa Strain 0.2-0.6 x10-6

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Water in the crust p = σZ ß Hydrostat lithostatic stress: pf = ρw g z p= σz = ρ g z pf – pore fluid pressure

ρw – density of water The average of water is 3 -3 approximately 1.0 x 10 kg.m . This hydrostat: will vary depending on salinity, depth z temperature and pressure pf = ρw g z 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 / p The effective overburden pressure may then be written eff p = p - pf = ρ g z (1 - λv) GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Water in the crust ß Lithostatic stress vs hydrostat The hydrostat or pore fluid pressure gradient is 10 MPa/km in the crust. This is about 40% of the lithostatic pressure Typically the pore fluid factor:

λv = pf / p = 0.4 This is just the of the water KTB borehole column to the rock column. Suprahydrostatic are known to occur in tectonically controlled areas created by fault sealing or by impervious rock layers. Fluid 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 .

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD 2D remote principal stress σ 1 Resolution of forces and areas both parallel and fault plane perpendicular to the fault normal stress P leads to the following σ N θ equations for normal and σ2 σ2 on the fault plate: σS shear stress Normal stress σ and shear stress σ σ N S remote principal stress remote principal ()σ ( ) σ N =1 2 σ1 +σσ 2 −1 2 σ1 −σ 2 cos 2ϑ

σ1 S =1 2( 1 − 2 )sin 2θ

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

Local stresses on fault: σ1 > σ2 > σ3 positive GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Construction of Mohr stress circle: shear stress vs. normal stress

σS axis

o Maximum shear stress = ½ (σ1 - σ2) when θ = 45 σ max P S σS (σ1 - σ2)/2 2θ σN axis σ2 σN σm σ1

Any point on circle has coordinates (σN, σS) σwhere: 1 2(σ ) 1 2( )cos 2 σ N = σ 1 +σσ 2 − σ 1 −σ 2 ϑ (σ1 + σ2)/2 S =1 2( 1 − 2 )sin 2θ

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD