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
1
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
2
3
4
5
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)
6
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• Basic ice thickness, now superseded – Almost...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...)
7
Important results
• Englacial layers indicating xtal orientation – Strongly oriented layers are 2-4% faster than
randomly oriented layers • Subglacial geologic structures: basins, faults
8
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.
9
How to make a sound?
• Explosives • Sledgehammer • Vibrator truck • Compressed-air gun • …
10
11
12
13
14
15
16
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
17
18
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)
19
vp =
s43µ+ k
⇢
vs =
rµ
⇢
Key Measurements
20
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
21
© 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
23
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/
26
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
29
Ice over Water
Seismic body wave velocity
31
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
32
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.
33
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
34
Bulk modulus (k)
35k =Applied hydrostatic pressure P
Fractional volume change �v/v
Shear modulus or Rigidity
36
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