L5 - Space Geodesy: GPS and Large-Scale Velocity Fields

Question 1

How does VLBI (Very Long Baseline Interferometry) work? (3)

Answer 1

Look at quasars simultaneously with radio telescopes
As the telescopes move relative to each other, the phase difference will change
Do this for multiple telescope pairs and quasars to estimate telescope relative motions

Question 2

How does SLR (Satellite Laser Ranging) work? (5)

Answer 2

Bounce laser pulses off orbiting reflectors
Measure the travel-time pulse
Do this from multiple stations
Solve for the locations of the reflectors and ground stations
Repeat over time to see stations move

Question 3

How were EQs and fault slip rate estimates first used to construct velocity fields over large areas? (1)

Answer 3

Adding moment tensors of EQs in a region to estimate the spatial and temporal average of the strain

Question 4

What is an EQ moment tensor? (3)

Answer 4

M_ij = M_0(u_in_j + u_jn_i)
M_0 is seismic moment
u(i,j) and n(i,j) are unit vectors

Question 5

What is the Kostrov summation? (2)

Answer 5

Adding up a set of EQ moment tensors to estimate total strain from EQs that’s occurred in a region
Strain rate_ij = 1/(2μVT) * Σ(M(n)_ij) from n=1 to N

Question 6

What is the velocity gradient tensor? (1)
Where can this be obtained for? (1)
Where can it not? (1)

Answer 6

The complete description of how a continuous body deforms
The surface
Not the lithosphere

Question 7

Define the velocity gradient tensor (1)

Answer 7

∂v_x/∂x ∂v_x/∂y ∂v_x/∂z |
| ∂v_y/∂x ∂v_y/∂y ∂v_y/∂z |
| ∂v_z/∂x ∂v_z/∂y ∂v_z/∂z |

Question 8

How can the velocity gradient tensor be split into useful parts? (5)

Answer 8

L = S + A
S = 0.5(L + L^T)
S is strain rate tensor (symmetric)
A = 0.5(L - L^T)
A is vorticity tensor (asymmetric)

Question 9

What are the useful terms within the strain rate tensor? (3)

How do these terms relate? (1)

Answer 9

S_11 = rate of expulsion of material along strike of the zone
S_22 = rate of horizontal shortening across strike of the zone
S_33 = rate of vertical thickening in the zone
S_11 + S_22 + S_33 = 0 as lithosphere incompressible

Question 10

Why does the Kostrov summation give odd focal mechanisms for real EQs? (2)

Answer 10

Not purely double-couple

Slight spatial component

Question 11

How can the spatial variation of strain, and an associated velocity field be worked out? (4)

Answer 11

Split area of interest into polygons (corners = end of faults)
Kostrov summation can give average strain of each polygon
If one boundary held fixed, strains can be integrated inwards
Gives velocity estimates at polygon corners

Question 12

Why is it difficult to obtain a velocity field? (2)

Answer 12

Incomplete knowledge of fault locations and slip rates

Observation time is short so not all active faults have broken in an EQ

Question 13

How can the issues with obtaining velocity fields be overcome? (3)

Answer 13

Enforcing internal consistency
Taking different routes through polygons should give the same strain at each point
Reduces problems from absent observations unless data has big errors

Question 14

What is the benefit of always seeing four or more satellites for GPS? (1)

Answer 14

Can solve for location and time

Question 15

How can GPS be used to construct velocity fields? (1)

Answer 15

Use phase of the carrier signal to get mm accuracy of positions over time

Question 16

What are the problems of using GPS to construct velocity fields? (2)
How are they solved? (2)

Answer 16

Signal propagation delays in the ionosphere need to be corrected for
Frequency-dependent so can be estimated as satellites transmit two different frequencies
Water vapour delays in the troposphere
Effects lessened by recording for long periods of time to average the data

Question 17

What is campaign mode GPS? (4)

Answer 17

Make benchmark
Measure location
Return multiple times and re-measure
Gives time-averaged velocities

Question 18

What is continuous mode GPS? (3)

Answer 18

Leave instrument in the same place
Run continuously
Gives full site motion

Question 19

How do GPS and InSAR differ on measurement density? (2)

Answer 19

GPS is sparse: 10’s to 100’s km

InSAR is v dense: ~100m

Question 20

How do GPS and InSAR differ on time resolution? (2)

Answer 20

GPS is very high ~1s with continuous mode

InSAR takes 10’s of days to years

Question 21

How do GPS and InSAR differ on accuracy? (2)

Answer 21

GPS is high: fractions of mm/yr

InSAR is high but gets atmospheric effects: cm/yr

Question 22

How do GPS and InSAR differ on ease of use? (2)

Answer 22

GPS: need to go to study area = expensive
InSAR: fully remote but dependent on the existence of data

Question 23

How might GPS be used to estimate EQ potential? (1)

Answer 23

Can attempt to see which areas have locked faults

Question 24

How can GPS velocity fields be used to estimate seismic vs aseismic deformation (using Iran as an example)? (3)

Answer 24

All strain happening in EQ in N Iran as seismic magnitude = geodetic, so mostly seismic
In S Iran, geodetic > seismic, strain not happening in EQ, so mostly seismic
Zagros is full of salt diapirism so gets lots of creep on decoupling fault horizons

Question 25

How can GPS be used to estimate regional tectonics (using Iran as an example)? (2)

Answer 25

See E-W left-lateral faulting take up N-S right-lateral shear
Happens by rotations about vertical axes and left-lateral E-W slip

Question 26

What is a potential future use of GPS for EQ safety? (2)

Answer 26

GPS waveforms might be able to inform of EQs before seismic stations can, and of the magnitude
2011 Tohoku: GPS after 157s, seismology took 20 mins to work out magnitude, tsunami took 20-30 mins to hit the coast