VẬT lý địa CHẤN intruduction geophysics

Some Gravity BasicsFor the case of a mass above the earth we can re-write the previous equation using M as the mass of the Earth, m as the mass of the object, and R as the distance betw

Introduction to Geophysics

What is Geophysics??

geophysical techniques as possible

Geophysics at the Coarsest Scale

• What techniques do we have to look at a region at the coarsest scale?

– Satellite imagery – ie Landsat, SPOT

– Satellite altimetry

– Satellite gravity

– Satellite magnetism

– DEMs

• Digital elevation models

– DEMs from space – SRTM

• Shuttle radar topography mission

Some Gravity Basics

• We will cover gravity in more detail later in the class – but for now here are the important concepts:

Newton’s Law of Gravitation states that the force of attraction F

respect to the distance r between them is given by the equation below,

m1 m2

r

Some Gravity Basics

For the case of a mass above the earth we can re-write the previous equation

using M as the mass of the Earth, m as the mass of the object, and R as the

distance between the centers of the objects

GM F

Force is related to mass by acceleration, and the term g is known as the

Some Gravity Basics

The gravitational field can be defined in terms of the gravitational potential, U:

R

GM

U =

Gravitational acceleration g is a vector quantity, having both magnitude and

direction The gravitational potential U is a scalar, having only magnitude The

first derivative of U in any direction is the component of gravity in that direction

Equipotential surfaces are those on which the gravitational potential is constant,

ie the geoid

The ocean surface is an equipotential surface, and defines the geoid

Shape of the Earth

The geoid is one way of defining the shape of the earth, but we can also use the ellipsoid The earth is not a perfect sphere, it is an oblate spheroid

We can approximate the shape of the earth by an ellipsoid

•Radius from center to equator = 6378.16 km

•Radius from center to pole = 6356.77 km

•Polar shortening of 1 part in 298.25 – often referred to as flattening

The geoid and the ellipsoid are not coincident as the earth is not

homogeneous

From http://rst.gsfc.nasa.gov/Intro/Part2_1b.html

Shape of the Earth

Similarly, a satellite orbiting the earth moves up and down along its orbit as it is affected by the same gravitational forces that produce the geoidal surface

From http://rst.gsfc.nasa.gov/Intro/Part2_1b.html

Sandwell et al, bathy workshop.

Large geoid low over India (~100 m) – mass defficency

A ship going from Darwin, Australia, to the southern tip of India is going downhill!

Geoid highs over trenches – old and cold subducted slabs

Satellite Altimetry

Satellites do not carry accelerometers

Gravity variations can be calculated from changes in the position (shifts in

orbital height) of a satellite as it orbits due to variations in gravity

•Tracking of radio signals (using Doppler shifts in frequency) from the

satellite help to determine these variations

•Locating the position of the satellite with satellite laser ranging

•Measure the changing height of the surface (sea level with reference to the ellipsoid) with radar or laser altimetry

The presence of extra mass on the seafloor

is to cause a deviation of gravitational attraction such that water above the seamount “bunches up”

Sandwell et al, bathy workshop.

Satellite Altimetry

The satellite uses a radar pulse to measure the distance to the sea surface Repeating this pulse every 0.001

seconds allows the noise levels to be reduced (waves etc) The difference between this distance and that to the theoretical ocean surface is the geoid anomaly

Note that each height value represents

an average of observations taken during

1 second when the satellite moves about

7 km over the ground Height precision is

on the order of 3 cm

Sandwell et al, bathy workshop.

Gravity from Space

As the geiod (gravitational

potential) and the gravity

field are related, the

gravity field can be

calculated from a map of

the geoid This is one of

the first methods used to

get a detailed image of the

seafloor

Deriving the gravity field

from space is only good

for looking at coarse

Geoid and gravity maps

of part of the Gulf of Mexico

Gravity from Space

Tonga-Kermadec Trench,

Louisville Seamount Chain

Southern Oceans around Antarctica

The obvious way to collect bathymetry data for the oceans is using acoustic

methods along sparse ship tracks The above map shows survey ship tracks in the South Pacific at the scale of the continental US Making a map of the US using only data from along these tracks would obviously be very ineffective A systematic

survey of the oceans by ships would take more than 200 years of survey time at a cost of billions of U.S dollars

Bathymetry from Space

In contrast A complete satellite survey can be made in five years for under

$100M This has not yet been done, but we are part of the way there

Gravity is correlated with bathymetry at short wavelength

tracks and the corresponding satellite gravity values, a function can be derived to convert satellite gravity data to bathymetry where there are no ship tracks

Bathymetry from Space

There are a number of sources of topography – many are the domain of

geographers, ie:

•Maps (USGS, etc)

•Conventional Digital elevation models (DEM)

•Many of these are derived from contour maps (digitized)

•Popular GIS programs can display and analyze these

Geophysicists get involved when the technology gets a little more complicated For example:

•Imaging radar systems (for example the SIR-A, -B, and –C flown on the Space Shuttle) typically use variations in the signal bounced back from the ground to create an image

From http://spaceplace.jpl.nasa.gov/en/kids/srtm_makemap3.shtml

Imaging Radar

In this image, the color scene comes from

a Landsat image from the Sahara desert

in NW Sudan The diagonal strip is from

an image acquired from SIR-A flown in

Nov 1981 Because the sand is dry and

has a low dielectric constant the radar

waves penetrate up to 3 m, imaging not

just the sand, but also the bedrock below

Radar Interferometry

Radar imagery taken on two different dates can be compared, and the phase

difference determined to calculate the distances to point targets This was taken to the next level with the Space Shuttle Topography Mission (SRTM) in 2000

•Rather than compare two images taken on different dates, two images were collected simultaneously from slightly different locations

difference when collecting interferometric sidescan data

•Two adjacent transducer arrays

•Both receive at the same time

•As they are next to each other they are receiving basically the same signal

•However, the signal coming to array A may have traveled slightly further than that arriving at array B

•This translates into a phase difference

•The phase difference can be used to determine the angle from which the signal came

•Combined with travel time, this tells us the distance to that point on the seafloor

A similar principle can be used from space, but the transducers (antenna) have to

be further apart – in this case 60 m

The two signals received at both ends of the baseline show a phase shift due to different signal paths Through the

calculation of the relationship between target-receiver distances and the phase difference one obtains elevation

information which can be turned into digital elevation models and maps

Using this method, near global topography has been generated at a pixel size of

1 arc-second (approximately 30 m) So far, data at this resolution is only available for the continental US For other regions the data is available at a pixel size of 3 arc-seconds (90 m)

The above image compares 90 m SRTM data for the Papuan Peninsula with the previously available 30 arc-second data (~1 km grid size)

References Used

1 Basic gravitational theory:

• Kearey, P., M Brooks, and I Hill, An Introduction to Geophysical Exploration.

2 The geoid, satellite altimetry

• http://rst.gsfc.nasa.gov/Intro/Part2_1b.html

3 Calculating bathymetry from satellite gravity

• http://topex.ucsd.edu/marine_topo/text/topo.html

• Smith, W H F and D T Sandwell, Bathymetric prediction from dense satellite

altimetry and sparse shipboard bathymetry, J Geophys Res., 99,

21803-21824, 1994.

• Sandwell, D.T., Gille, S.T., and W.H.F Smith, eds., Bathymetry from Space: Oceanography, Geophysics, and Climate, Geoscience Professional Services, Bethesda, Maryland, June 2002, 24 pp.,