Ice streams, shear margins, and glacier stick-slip motion v (m/yr) - - PowerPoint PPT Presentation

Ice streams, shear margins, and glacier stick-slip motion

a

v (m/yr) 1.5 5 20 75 300 1000 4000

Rignot et al., 2011

Part 1. Background on ice streams

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Ice Ridge Ice Stream Ice Ridge Ice Ridge Ice Stream Ice Shelf

How certain is future Antarctic mass balance?

Mass in 15 Ice Streams 1 km thickness 50 km width 1 km/yr flow velocity (other smaller mass fluxes, see Shepherd et al., 2012) Mass out Mass imbalance Imbalance is equal to the discharge of just two ice streams. How sure are we that this calculation will remain the same?

Current state-of-the-art ice sheet models

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a

v (m/yr) 1.5 5 20 75 300 1000 4000

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1.5 5 20 75 300 1000 4000

α (Pa yr/m)1/2 50 100 150

Morlighem et al. 2013 Model Observed Tuned “Basal Sliding Parameter”

• The simulations shown are 3D, thermo-viscous creeping flow simulations with real bathymetric data.
• Variation in flow speeds results largely from the tuned basal sliding parameter rather than from actual

physical processes.

• For this reason, such a description may have some utility if interpreted as a linearization about current

conditions, but

• it is unlikely that models such as this can forecast complex future changes.

Direction of ice flow 800 m ice thickness 120 km ice stream width x y z Bed Ice z x

Rapid ice velocities are primarily controlled by subglacial conditions.

Basal Shear Stress

Direct observation of the ice-bed interface: the WISSARD experiment

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JPL Photo

• 1. Fast sliding is facilitated by glacial till.

GPS stations Floating Ice Grounded Ice ˚ ˚ ˚ 1 7 ˚ W ˚ ˚W ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚

Direct observation of the ice-bed interface: the WISSARD experiment

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JPL Photo

Image Width ~ 0.15 m

• 2. Subglacial water pressures can be very high.

GPS stations Floating Ice Grounded Ice ˚ ˚ ˚ 1 7 ˚ W ˚ ˚W ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚

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JPL Photo

Image Width ~ 0.15 m

Fast flowing ice streams exist because of the lubricating effect of a water-saturated subglacial till. Direct observation of the ice-bed interface: the WISSARD experiment

Ice Ridge Ice Stream Ice Ridge Ice Ridge Ice Stream Ice Shelf Shear Margin

Ice stream shear margins

Shear margins are the lateral boundaries of the ice

• streams. This causes a large velocity gradient.

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Suckale et al 2014

Ice stream shear margins

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Suckale et al 2014

The shear margin velocity gradient causes shear heating.

Subglacial hydrology

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Part 2. Ice stream variability

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GPS observations

• B. Map of the Whillans Ice Plain (WIP)

180˚ 180˚ 1 7 ˚ W 1 7 ˚ W 160˚W 160˚W 1 5 ˚ W 1 5 ˚ W 5 8 ˚S 8 5 ˚ S 4 8 ˚S 8 4 ˚ S 3 8 ˚S 8 3 ˚ S GPS stations Floating Ice Grounded Ice ˚ ˚ ˚ 170˚W ˚ ˚W ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ GPS stations Floating Ice Grounded Ice ˚ ˚ ˚ ˚ ˚ 160˚W ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚

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The Whillans Ice Stream is decelerating.

Beem et al. 2014 2018

Sliding Velocity (mm/s)

0.2 0.4 0.6 0.8 1

180˚ 180˚ 170˚W 170˚W 160˚W 160˚W 1 5 ˚ W 1 5 ˚ W 5 8 ˚S 8 5 ˚ S 4 8 ˚S 8 4 ˚ S 3 8 ˚S 8 3 ˚ S

˚ ˚ ˚ 1 7 ˚ W ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚

Floating Ice G r

• u

n d e d I c e Direction of ice flow Total duration of sliding is 30 min.

Episodic ice motion

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Winberry et al., 2014

Slip event dynamics

μ

• 1000

1000 2000 3000 4000

GPS velocity (m/d)

10 20 30 40 50 60

Vmax ~50 m/d initial acceleration (~200 s) gradual deceleration (~1500 s)

Time (s) μ (a) M7 slip event (GPS data)

GPS Velocity (m/day)

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Time (s) Particle Velocity (nm/s)

500

• 500

Data from IRIS

Seismic tremor occurs during sliding.

Jan 12 Jan 13 Jan 14 Sliding Velocity (m/day)

Seismic Particle Velocity (nm/s)

500

• 500

Grounding Zone

• 2. Tremor during ice stream slip events

0 s 1000 s 2000 s 3000 s

Long term goal: to quantify the processes that determine the strength of the ice-bed interface. I validate an improved glacier sliding law against two observations:

• 1. Ice stream stick slip motion

μ

• 1000

1000 2000 3000 4000

GPS velocity (m/d)

10 20 30 40 50 60

Vmax ~50 m/d initial acceleration (~200 s) gradual deceleration (~1500 s)

Time (s) μ (a) M7 slip event (GPS data)

Stick-Slip Cycles: the Sequence of Events

Upstream station Downstream station Flow direction

Stick-Slip Cycles: the Sequence of Events

Ice compresses in the upstream direction Steady upstream motion Minimal downstream motion

Stick-Slip Cycles: the Sequence of Events

During a slip event, ruptures propagate across the ice stream. Direction of slip Direction of rupture propagation

Stick-Slip Cycles: the Sequence of Events

During a slip event, ruptures propagate across the ice stream. Not yet sliding Rupture front Direction of slip Sliding

Stick-Slip Cycles: the Sequence of Events

The slip events ends when accumulated strain has been relieved.

The balance of forces

Push from upstream ice Ocean Tides (Elastic) Shearing Basal shear acts everywhere x y Direction

• f

ice flow

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• B. Map of the Whillans Ice Plain (WIP)

GPS stations Floating Ice Grounded Ice 180˚ 180˚ 1 7 ˚ W 1 7 ˚ W 1 6 ˚ W 1 6 ˚ W 150˚W 150˚W 5 8 ˚ S 85˚S 4 8 ˚ S 84˚S 3 8 ˚ S 83˚S

The balance of forces

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The balance of forces

Inertia Longitudinal driving stresses Vertical elastic shear Basal shear

Our simplified ice sheet model represents a depth integrated, cross- stream profile of an ice stream. Inertia plays only a limited role in our simulations, but including it serves as a check on our predictions. Most of the interesting dynamics come from the basal shear stress term.

Designing a stick-slip sliding law

During sliding with Coulomb Friction, the frictional coefficient instantaneously jumps from a static to a dynamic value.

𝜐 = 𝑔 𝜏

Coulomb Friction cannot explain the re-strengthening that causes repeatable slip events and leads to numerical ill-posedness due to the infinitely sharp transition in strength.

Sliding Velocity Friction Coefficient Time V1 Static coefficient

• f friction

Dynamic coefficient

• f friction

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Designing a stick-slip sliding law

We use a Rate- and State- Dependent Frictional sliding law. Important properties: 1. An instantaneous strength increase during acceleration (a stabilizing feature), 2. Evolution to a steady state value over a slip scale L. Sliding is said to be rate weakening if b>a.

Sliding Velocity Friction Coefficient ~ a Normalized Slip, u/L ~ b V1 V0

1 2 3 4

• 1
• 2
• 3

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• 3. Supports both steady and unstable sliding
• 4. The weakening length scale L is thought to scale with the grain

size of the sheared material.

Designing a stick-slip sliding law

Traditional glacier sliding laws (i.e., Weertman, 1957) are inconsistent with stick slip cycles. Stick-slip in the presence of steady loading requires a basal sliding law that results in cyclic acceleration and deceleration. Importantly, traditional glacier sliding laws exhibit unrealistic unbounded strength and may therefore

• verestimate the resistance to

forces that favore ice acceleration.

Log ( ) Shear Stress Log ( ) Sliding Velocity

One sliding law, two behaviors

The transition between steady sliding and stick-slip occurs because of a balance between frictional weakening and elastic restoring force:

Friction Coefficient ~ a Normalized Slip, u/L ~ b

1 2 3 4

• 1
• 2
• 3

Slip Stress

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Fast slip and Slow Slip

40 50 100 150 200 500 1000 500 1000

Time (s)

1 2 3 50 100 150 200 250

Time (s)

5 10 15 50 100 150 200 100 200 20 40 60

Time (hr)

0.01 0.02 0.03

Velocity (mm/s)

50 100 150 200 20 40 60

Time (hr)

A. B. C. D. E. F.

Distance (km) Distance (km) Distance (km)

W/Wc = 2.0 W/Wc = 1.1 W/Wc = 0.8 100 km 125 km 150 km

Time (s)

Smooth tidal modulation Whillans-style slip event Inertially-limited slip event

Slow slip events happen in a unique range of parameter space:

• Pore pressures are low enough to cause stick—slip cycles, yet
• Pore pressures are high enough to avoid inertial ruptures.

Whillans Ice Plain: “Slow-Slip”

Quasi-steady tidal modulation Inertial rupture

High pore pressure Low pore pressure

Stick-slip cycles are consistent stagnation

• 1. Low water pressure causes stick-slip cycles:

frictional weakening due to sliding > elastic resistance to slip

Absolute strength and weakening rate both depend on effective pressure.

depends on water pressure Also depends on water pressure

Details: The critical pore pressure p∗ results from a linear stability analysis of perturbations to steady frictional sliding with rate and state friction (see, for example Rice et al., 2001; Lipovsky and Dunham, 2016).

• 2. Lower water pressure increases the absolute level of resistive shear stress

~

?

Basal Resistive Stress > Driving Stresses

• B. Map of the Whillans Ice Plain (WIP)

0.1 0.2 0.3 0.4 0.5 500 1000 1500 2000

Time (s)

0.1 0.2 0.3 0.4 0.5

• C. Slip event stack
• A. Simulation

Sliding Velocity (mm/s) Sliding Velocity (mm/s)

GPS stations Floating Ice Grounded Ice 1 8 ˚ 1 8 ˚ 170˚W 170˚W 160˚W 160˚W 1 5 ˚ W 1 5 ˚ W 5 8 ˚ S 8 5 ˚ S 4 8 ˚ S 8 4 ˚ S 3 8 ˚ S 8 3 ˚ S

Rupture Dynamics

A picture of conditions at the bed

Direction of ice flow 43

A picture of conditions at the bed

Rupture propagation occurs as the onset of slip moves from one weakening zone to another.

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We still have not addressed the details of the weakening zones…

Seismic Particle Velocity (nm/s)

500

• 500

Surface Velocity (m/day)

• 1. Ice stream stick slip motion
• 2. Tremor during ice stream slip events

0 s 1000 s 2000 s 3000 s

Part 3. Glacier microseismicity

Seismic tremor occurs during slip events.

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• ne second

100 nm/s

This shows 20 earthquakes per second.

Same log-power color-scale in both figures

Simulation Data

GPS Data GPS Data

Periodic earthquakes have periodic spectra.

Frequency

1/T 2/T 3/T 4/T

…

Power

…

Time

Amplitude T

…

T T T T

Periodic earthquakes have periodic spectra.

Frequency

1/T 2/T 3/T 4/T

…

Power

…

Time

Amplitude T

…

T T T T 100 nm/s Lipovsky and Dunham, 2016

Whillans Ice Plain, ~120 km cross stream Lipovsky and Dunham, 2016

Strain Accumulation

No slip

• n fault

Steady slip Steady slip

Most strain in the bed Limited strain in ice

Whillans Ice Plain, ~120 km cross stream Lipovsky and Dunham, 2016

Slip

More elastic rebound Less elastic rebound

Whillans Ice Plain, ~120 km cross stream Lipovsky and Dunham, 2016

Net Motion Over Cycle

Net displacement No net displacment

Tremor and slow slip: Both modeled with same sliding law

Models of tremor episodes reveal a tremendous amount of information about subglacial conditions:

• Seismic parameters: slip, rupture velocity, fault dimension
• Till properties: elastic modulus, grain size, water pressure
• The temporal variation of these properties.
• B. Basal fault patch:

Net displacement No net displacment

No slip

• n fault

More elastic rebound Less elastic rebound

Steady slip Steady slip

Most strain in the bed Limited strain in ice

Lipovsky and Dunham, 2016

Seismic parameters: slip, rupture velocity, fault size

Surface Velocity (m/day) Time (s)

Slip = Velocity x Recurrence Time ~ 50 microns

Seismic parameters: slip, fault size, seismic velocity amplitudes

Elastic Whole Space Bimaterial Interface

Subduction zone tremor and slow slip

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Rogers and Dragert (2003)

Subduction zone tremor and slow slip

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Liu and Rice (2008)

A picture of conditions at the bed

100 m scale 100 km scale

Interevent time is increasing.

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Winberry et al., 2014

Temporal variation in bed rigidity

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Mechanical and hydrologic properties of Whillans Ice Stream till: Implications for basal strength and stick-slip failure

• J. R. Leeman1, R. D. Valdez1, R. B. Alley1, S. Anandakrishnan1, and D. M. Saffer1

1Department of Geoscience, Penn State, University Park, Pennsylvania, USA

Details: The change in the bed effective shear modulus can be computed through an effective medium (e.g.., Voight-Reuss) description. The shear modulus is inversely related to the porosity because bulk averge shear modulus decreases when there is a higher water fraction.

Dilatancy during rapidly sliding phase Compaction during stick-phase

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The ice sheet bed is stiffening

(e)

Recent (post-2010) style Long Wait Time > 18 hr Past (pre-2010) style: Short Wait Time < 18 hr Shear modulus inferred from models of small, repeating earthquakes (Lipovsky and Dunham, 2016)

Bed Shear Modulus, MPa 10 20 30 Frequency