1. Geodesy & Crustal Deformation
Geology 6690/7690
Geodesy & Crustal Deformation
29 Sep 2017
GPS Reference Frames
• GPS Reference Frame relates Earth-fixed to satellite
motion; reference frame effects are part of position error
• Glacial isostatic adjustment (GIA) is a transient effect
that is ~secular on decadal timescales; has vertical, horizontal
(including plate-like!) expression
• Early GPS reference frames were updated annually; now ~2x
per decade… Still find small adjustments to plate motion rates
• Geological evidence also exists for changes in plate motion
(perturbations of Australian hotspot paths during Ontong-Java
Plateau collision; decreasing Nubia-South America rates)
Read for Fri 29 Sep: Wahr § (67-75)
© A.R. Lowry 2017

2. Read for Monday, Oct 2:
Herring et al. (2016) Plate Boundary Observatory and related
networks: GPS data analysis methods and geodetic
products, Reviews of Geophysics, 54(4),

3. Introduction to Gravity
Gravity, Magnetic, & DC Electrical methods are all examples
of the Laplace equation of the form:
 2u = f (sources),
Where u is a potential,
is the gradient operator
Notation: Here, the arrow denotes a vector quantity;
the carat denotes a unit direction vector.
Hence, the gradient operator is just a vector form of slope…
Because Laplace’s eqn always incorporates a potential u,
we call these “Potential Field Methods”. → ^

4. Gravity We define the gravitational field as
And by Laplace’s equation,
(1)
given a single body of total mass M; here
G is universal gravitational constant = 6.672x10-11
Integrating equation (1), we have
(2)
Nm2
kg2

5. IF the body with mass M is spherical with constant (or
radially symmetric) density, equation (2) has a solution
given by:
Here r is distance from the center of mass (CoM);
is the direction vector pointing toward the CoM
Newton’s Law of gravitation:
So expresses the acceleration of m due to M!
has units of acceleration  Gal in cgs (= 0.01 m/s2)
On the Earth’s surface,
m/s2

6. HOWEVER, r is not radially symmetric in the Earth…
so is not constant!
Gravity methods look for anomalies, or perturbations,
from a reference value of at the Earth’s surface:
gobs
gref r1 r0

7. Example:
Global Free-Air Gravity Field from GRACE + GOCE + surface measurements…
WGM2012 model from Bureau Gravimetríque International

8. Gravity Measurements:
I. Absolute Gravity:
Measure the total field  time of a falling body
prism
vacuum
laser
~2m
Must measure time to ~10-11 s;
distance to ~10-9 m
for 1 mgal accuracy!
Nevertheless this is the most
accurate ground-based
technique
Disadvantages: unwieldy; requires
a long occupation time to
measure

9. Gravity Measurements:
II. Relative Gravity:
Measure difference in at two locations
Pendulum: difference in period
Errors in timing of period T  ~0.1 mgal
Mass on a spring: MDg = kDl
or Dg = kDl/M
Worden and Lacoste-Romberg
are of this type
(“zero-length” spring of L-R yields
errors around 6 mgal) l
mass M
length l
spring
constant k

10. Gravity Measurements:
III. Satellite Gravity:
Measure (from space) the height of an
equipotential surface (called the geoid, N)
relative to a
reference
ellipsoid

11. Gravity Measurements:
III. Satellite Gravity:
Measure (from space) the height of an equipotential
surface (called the geoid, N) relative to a reference
ellipsoid
Ocean Altimetry: Measure the height of the ocean
surface using radar or laser (e.g., JASON)
Satellite Ranging: Satellite orbits follow the geoid
Measure orbits by ranging from the ground to the
satellite or ranging between two satellites
(e.g., GRACE) N

12. Global Free-Air Gravity Field from GRACE
Example:
Global Free-Air Gravity Field from GRACE
Image from UT-CSR/NASA

13. GRACE and the modern
static (i.e., time-invariate)
geoid…
Note that the free air
gravity anomaly field
can be calculated
directly from the geoid.