bats do it dolphins do it glaciologists do...

Bats do it... Dolphins do it... Glaciologists do it

• Active Source Seismology: • Make a sound and listen for an echo • How long did it take for the echo? (velocity)

– That tells us how thick the ice is. • Echos from subglacial layers

– That tells us what is below the ice

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Discover ice/rock properties at depth

• Passive source seismology: wait for earthquakes to occur, record them, use their travel path, travel time, travel amplitudes for:

– Structure of the ice sheet and planet – Thermal and physical properties at great depth

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Important Results

• Glacier bed properties – Flow of glaciers depends on bed

• Physical properties <==> Elastic properties – Till properties: seismic velocities (P & S) – Soft vs. hard till - acoustic impedance – Areal distribution of sediments – (physical <==??==> electrical)

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Important Results

• Basic ice thickness, now superseded – Almost... some ice still troublesome for radar :)

• Water: Lakes and Ice Shelves • Water: sheets and channels • Water: moulins (to be done...)

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Important results

• Englacial layers indicating xtal orientation – Strongly oriented layers are 2-4% faster than

randomly oriented layers • Subglacial geologic structures: basins, faults

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Active Source Seismology

• When did the echo come? – How deep is the ice... and how thick are the sub-

glacial layers? • How strong is the echo?

– How rigid is the rock? Is it water-saturated? • What is the shear-wave velocity profile?

– Water.

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How to make a sound?

• Explosives • Sledgehammer • Vibrator truck • Compressed-air gun • …

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Refracted Energy

CriticallyRefracted

Reflection

Direct

V1

V2

z

1.7

1.8

1.9

2.0

800 1600 2400Tw

o-W

ay

Tra

ve

lTim

e (

Se

co

nd

s)

Source - Receiver Offset (Meters)

0 4520

WAIS Divide

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Seismic velocity of body waves

• Velocity = (elastic modulii / density)1/2

• Reflection is related to change in seismic velocity and change in density.

• Reflection is related to phase change (P-SV)

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vp =

s43µ+ k

⇢

vs =

rµ

⇢

Key Measurements

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Direct

V1

V2

h

Reflection Coefficient

R =⇢2v2 � ⇢1v1⇢2v2 + ⇢1v1

t(x) =1

v1

px

2 + (2h)2

x RS

Till Properties - from time only

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© Nature Publishing Group1986

Blankenship et al., 1986

Vp = 1600 m/sVs = 150 m/s

© Nature Publishing Group1986

Reflection Coefficient

22Holland and Anandakrishnan, 2009

A1 = A0 ⇥R(✓)⇥ �1 ⇥ exp(�↵d1)�1 = Spreading Losses; Free Surface

↵ = Attenuation

d1 = PathLength

R(✓) = Reflectivity

✓ = Angle

A0 = SourceAmplitude

A1 = ReceiverAmplitude

Multiple Bounce @ Normal

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Direct

V1

V2

h

Reflection Coefficient

x RS

Multiple Reflection

A0 =A2

2

A1

d12

R(✓1) =A1

A0

1

�1exp(↵d1)

Seismic params• Firn: Vp = 1-3 km/s, 𝛒=.4-.8 g/cc • Ice: Vp = 3.9 km/s, Vs = 1.9 km/s, 𝛒=0.92 g/cc

– Highly anisotropic, small temperature dependence

– Water: Vp=1.5 km/s, Vs = 0 • Tills: Vp = 1.6-2.4 km/s, Vs = is .05-1 km/s, 𝛒

depends on porosity - important for fast flow • Sediments vs. crystalline rocks: roughness,

erosion potential, fracture potential, water transport... 24

Seismic AVO Theory

P-P Reflection

θiICE

SUBGLACIAL BED

VS, ice

VP, iceρice

VS, bed

VP, bedρbed

REFLECTION!!!

Reflection Amplitude vs Offset

• AVO or AVA - partitioning of energy at an interface that includes P and S conversions

• so-called Zoeppritz equations – see Shuey (1985), Aki & Richards (1980) – https://bruges.readthedocs.io/en/latest/

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R(✓) ⇠= R(0) +G sin2(✓)

G =1

2

�vpvp

� 2v2sv2p

✓�⇢

⇢+ 2

�vsvs

◆

27GMT 2006 Mar 2 11:20:48 Volumes/UserP/Users/sak/GMT/2poles.gmt

South Pole

Radar from the S. Pole

South Pole Lake region

UTIG Radar Data

5 km

100 m

0 10 20 30 40 50 60 70 80 90-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Angle of Incidence (degrees)

Be

d R

efl

ec

tiv

ity

Bedrock

Water

Frozen/Consolidated Seds.

Soft/Dilatant Seds.

Vp (m/sec) Vs (m/sec) Density (kg/m³)

3780 1860 920

5800 3200 2800

3000 1200 2200

1650 200 1700

1500 0 1000

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Ice over Water

Seismic body wave velocity

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Vp=

s�43µ + k

�

⇢

Vs=

rµ

⇢⇢=density

Influences on modulii and density---velocity

• Rock type, porosity – Till vs. basement; water content; deformation

rate • Fluid presence and type

– Water • Temperature, microcracks, fabric, ...

– Flow law of ice

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Summary

• Seismic energy is sensitive to changes in elastic properties.

• Reflection seismic profiling can image at & below the base of the ice sheet.

• For fast-flowing glaciers (and rapidly-changing glaciers), conditions at the base & below the base are extremely important.

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What are the elastic modulii?

• Bulk modulus or incompressibility (k) • Shear modulus or rigidity (μ) • Young’s modulus (E) • Poisson’s ratio (ν) • Any two, along with density will define the

seismic body wave velocity

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Bulk modulus (k)

35k =Applied hydrostatic pressure P

Fractional volume change �v/v

Shear modulus or Rigidity

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µ =shear stress ⌧

shear strain ✏

Young’s Modulus

37E =uniaxial stress �11 = �F/A

uniaxial strain ✏11 = �L/L

Poisson’s Ratio

38E =radial strain ✏22 = �W/W

axial strain ✏11 = �L/L