Environmental Geodesy
Lecture 3 (February 1, 2011): Earth's Shape
- Earth's mean shape
- Endogenic processes and Earth's shape
- Exogenic processes and Earth's shape
- Oceans, hydrosphere and cryosphere and Earth's shape
Earth's Mean Shape
The meaning of the terms "figure of the Earth" and "shape of the Earth"
depends on context, e.g.
(1) topography of the solid Earth;
(2) surface of solid Earth including oceans, terrestrial hydrosphere and
cryosphere.
ETOPO1 Global
Relief Model
ETOPO1 includes ocean bottom topography and ice mass surfaces, i.e., it is
in between (1) and (2).
Earth's Mean Shape
The meaning of the terms "figure of the Earth" and "shape of the Earth"
depends on context, e.g.
(1) topography of the solid Earth;
(2) surface of solid Earth including oceans, terrestrial hydrosphere and
cryosphere.
(2) is the surface on which most geodetic in situ measurements are carried
out
(2) is too complex for mathematical descriptions of characteristics of the
solid Earth or the Earth system
Soffel (1989) describes four different phases related to the view of the Earth's
shape and dynamics and the main target of research (see Lecture 1).
Earth's Mean Shape
Four different phases of geodesy related to the view of the Earth's shape and
dynamics and the main targets of research.
A: From 200 BC up to the middle of the 17th century: the radius of a
spherical Earth; simple geometrical form.
B: From the middle of the 17th century to the middle of the 19th century: the
oblateness of a rotational ellipsoid; geometrical form resulting from
rotational dynamics.
C: From the middle of the 19th century to the middle of the 20th century: the
geoid; gravitational field in addition to a purely geometrical form.
D: Since the middle of the 20th century: dynamics of the Earth's surface and
relativistic models of the Earth system; changes in the shape instead of mean
shape; dynamical instead of static view.
Earth's Mean Shape
B: From the middle of the 17th century to the middle of the 19th century: the
oblateness of a rotational ellipsoid; geometrical form resulting from
rotational dynamics.
Rotational ellipsoid is uniquely defined by two numbers:
- two dimensions (i.e., two axes),
- one dimension (axis0 and a number representing the difference between the
two dimensions.
Earth's Mean Shape
B: From the middle of the 17th century to the middle of the 19th century: the
oblateness of a rotational ellipsoid; geometrical form resulting from
rotational dynamics.
Rotational ellipsoid is uniquely defined by two numbers:
- two dimensions (i.e., two axes),
- one dimension (axis0 and a number representing the difference between the
two dimensions.
Geodesists, by convention, use the semimajor axis and flattening:
- Size of ellipsoid: radius a at the equator; i.e. semimajor axis of the crosssectional ellipse
- Shape of the ellipsoid: flattening f, which indicates how much the ellipsoid
departs from spherical.
Long sequence of attempts to determine accurate values for a and f.
Earth's Mean Shape
Earth's Mean Shape
A key open question relates to rotational ellipsoid:
- Is the rotational figure of the Earth in hydrostatic equilibrium?
Rotation of the Earth is decreasing (LOD
increasing) over time (due to tidal friction):
LLR: +2.3 ms/cy (cy=century)
Historical record of eclipses: +1.70 ± 0.05 ms/cy
This indicates a quadratic term: +31 s/cy²
As a result, oblateness should be decreasing,
depending on the viscoelastic response of the
Earth to the changing gravitational potential .
SLR:
Question relates to the "Love Number" k2 (will be explained later), which is
relevant for many secular geodynamic problems
Earth's Mean Shape
Topography deviates from reference ellipsoid by +8848 m and -10,911 m
- deviations are small (only 0.17% of the radius)
- deviations are relevant for many practical applications
Sea level
- adjusts to gravitation field, not geometry;
- it follows a equipotential surface of the gravitational potential, if
undisturbed by tides, winds, currents, ...
Geoid is a equipotential surface of Earth's gravitational potential (including
both gravitational and centrifugal forces).
Geoid deviates from reference ellipsoid by about -110 m and +85 m.
Earth's Mean Shape
Geoid deviates from reference ellipsoid by about -110 m and +85 m.
Earth's Mean Shape
Reigber et al. (2005).
Improvement of the Earth’s gravity field models.
From top left to bottom right:
GRIM-5S1: SLR data only (best gravity field model before CHAMP and GRACE);
EIGEN-CHAMP03S: Gravity field from CHAMP;
EIGEN-GRACE03S: Gravity field from GRACE;
EIGEN-CG03C: Gravity field from GRACE combined with terrestrial data.
Earth's Mean Shape
After removing tides, waves, atmospheric forcing (including surges), sea level
can deviate up to 2 m from the geoid.
"Mean" dynamic sea surface topography due to influences of ocean
circulation, ocean temperature, salinity.
Accurate "static' geoid required for determination of mean dynamic sea
surface topography, which is required for ocean circulation and climate
models.
Currently, most accurate static geoid from the Gravity Recovery and Climate
Experiment (GRACE).
GRACE is particularly strong in measuring geoid variations at sub-monthly
time scales and down to 300 km spatial scales (see Lecture 4).
Significant improvements of static geoid expected from the Gravity field and
steady-state Ocean Circulation Explorer (GOCE) .
Earth's Mean Shape
Significant improvements expected from the Gravity field and steady-state
Ocean Circulation Explorer (GOCE).
Launched on 17 March 2009.
Earth's Mean Shape
Relation of the various surfaces used in geodesy
1. Ocean
2. Ellipsoid
3. Local plumb
4. Continent
5. Geoid
Endogenic Processes
Endogenic processes change the Earth shape on time scales from seconds to
million of years
Endogenic Processes
Earthquakes cause significant 3-d deformations within seconds to minutes
Endogenic Processes
A 2.3 m coseismic displacement has distorted the railroad
track near the railway station Tepetarla in the region
between Sapanca Lake and Izmir Gulf, Turkey
(www.geopages.co.uk/news/rev002.html).
Endogenic Processes
Earthquakes cause significant "static"/permanent 3-d deformations within
seconds to minutes.
Predicted coseismic displacement field of the Sumatra-Andaman 2004 earthquake.
Endogenic Processes
GPS observes the static, co-seismic
offset
Large tsunamis are associated with
loading signals on the order of 10
mm
Observed coseismic displacement field of the Sumatra-Andaman 2004 earthquake.
Endogenic Processes
April 4, 2010 Mayor-Cucapah M 7.2
earthquake
Seismic waves have amplitudes of
several > 100 mm in large distances from
the epicenter
Endogenic Processes
Displacement field of Hector Mine
earthquake observed with InSAR
G. Peltzer, UCLA
Endogenic Processes
More on earthquakes; goal to give an impression of the changes in earth
shape ...
Endogenic Processes
Seismic Free Oscillations of the Earth deform the earth with periods from 53
minutes down to seconds and can last for several days.
Theoretical representation through spherical harmonics.
http://icb.u-bourgogne.fr/Nano/MANAPI/saviot/terre/index.en.html
Endogenic Processes
Seismic Free Oscillations of the Earth deform the earth with periods from 53
minutes down to seconds
Theoretical representation through spherical harmonics.
http://icb.u-bourgogne.fr/Nano/MANAPI/saviot/terre/index.en.html
Endogenic Processes
More on post-seismic deformations
Endogenic Processes
Subsurface processes associated
with volcanoes and magma
transport induce local to regional
changes in shape.
InSAR (ERS) has revealed that four
Andean volcanoes thought to be
inactive, are now known to be
rapidly deforming. Each color cycle
corresponds to 5 cm of deformation.
The top three volcanoes are
inflating and Robledo is deflating
(Pritchard & Simons, 2002).
Endogenic Processes
Plate tectonics induce secular changes in shape on the order of 10 cm/yr
horizontally
Endogenic Processes
Secular changes
Endogenic Processes
Secular strain rates caused by
plate tectonics and plate
boundary processes
Kreemer et al. (2003)
Exogenic Processes
Exogenic variations in Earth's shape include:
- Tides of the solid Earth caused by the tidal potential of moon, sun, and
planets (see Lecture 4);
- Rotational perturbations caused by exchange of momentum between core
and mantle, angular momentum exchange with atmosphere and ocean,
external torque caused by tidal forces, ... (see Lecture 5);
- surface loading due to mass relocation on the Earth's surface.
Exogenic Processes
Surface loading due to mass relocation on the Earth's surface include:
- mass redistribution in atmosphere: low/high pressure areas;
- mass relocation in the ocean: tsunamis, tides, storm surges, wind-driven
circulation, other circulation;
- redistribution of water stored on land;
- mass changes in land-based glaciers, ice caps and ice sheets;
- mass exchange between any of these reservoirs in the global water cycle;
- sediment transport and deposition;
- anthropogenic mass relocation (coal mining, oil mining, groundwater
mining, ...)
Loading
- deforms the solid Earth,
- changes the gravity field (both due to the surface mass relocation and the
deformation of the solid Earth) and
- impacts Earth rotation.
Exogenic Processes
Response of solid Earth has an elastic (instantaneous) and viscous (delayed)
contribution.
Elastic response dominate for loading at sub-seasonal to interannual time
scales (e.g., tides, seasonal cycle);
Viscous contribution important for interannual to secular time scales (e.g.
coal mining, postglacial rebound).
Elastic deformations range from up to 20 mm for atmospheric loading, 50
mm associated with ocean loading (tides and surges);
Visco-elastic deformations range from sub-mm/yr for hydrologic changes
(droughts), 1 mm/yr in coal mining areas, several mm/yr for recent ice load
changes, more than 50 mm/yr during major deglaciation periods.
Post-mass relocation deformations are triggered by surface loads but then
dominated by endogenic processes.
More details on this during subsequent lectures.
Oceans, Cryosphere, and Terrestrial Hydrosphere
Oceans:
- Time-variable surface, both as spatial average and locally
- global sea level variations caused by mass exchange with other reservoirs
and changes in heat contents,
- variability on a wide range of spatial and temporal scales
Ice surfaces:
- Time-variable surface height and extent;
- large variations in mass balance;
- seasonal, interannual, decadal time scales;
- ice ages on time scales of 100 kyrs.
Land water storage:
- Time-variable surface water storage (e.g., floods, droughts), also including
significant anthropogenic changes;
- Time-variable subsurface water storage (includes also significant
anthropogenic changes)
Oceans, Cryosphere, and Terrestrial Hydrosphere
More details in subsequent lectures.