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9.8 Option –Geophysics: 1. The physical Earth
Extract from Physics Stage 6 Syllabus (Amended
October 2002). © Board of Studies, NSW.
[Edit 30 June 09]
identify data sources, gather and process information to discuss Newton’s proposal for the shape of the Earth using data gathered from investigations involving pendulum measurements
- identify data sources by first
choosing a strategy for finding the kind of information you
need. You will need to find information on Newton’s
proposal, as well as information on pendulum experiments
conducted by Newton’s contemporaries and on why the
issue was controversial. Your data sources may be physics
books or journals, the Internet or CDs. Two web sites that
have some interesting reading are:
Variability of Pendulum Vibrations
Sacred Texts, and
The meridian arc measurement in Peru 1735-1745, Jim R
Smith, UK.
- Gather only the information that would
be useful in answering a question directly on this topic.
Write notes about this information in your book.
- Process the information from various sites to decide which is the most reliable.
Sample discussion
In his Principia, published in 1687, Newton considered the diurnal circular motion of the Earth and concluded that the Earth must be flattened at the poles, i.e. an oblate spheroid, not a perfect sphere.
Newton did no direct experiments with the pendulum to support his hypothesis; instead, he used data collected by Picard, and also by French scientists including Jean Richer, in 1671 at Cayenne in French Guiana. Richer measured the period of a pendulum and found that it beat faster in Paris than it did in Cayenne.
Picard’s and Richer's data suggested that the period of a pendulum changes with latitude, being lesser towards the poles and increasing towards the equator.
Using his law of universal gravitation Newton concluded that the period of a pendulum would be less if it were closer to the centre of the Earth, where g is greater, and that the pendulum would beat more slowly if it were farther from the centre from the Earth, since all other variables that could affect the pendulum period remained constant in Picard’s and Richer’s experiments.
Newton used this reasoning to argue that the surface of the Earth is closer to the centre at higher latitudes nearer to the poles than it is towards the equator and that the shape of the Earth is therefore an oblate spheroid.
Useful Links:
Jean Richer , University of St Andrews, Scotland.
describe the properties of earth materials that are studied in geophysics — particularly elasticity, density, thermal, magnetic and electrical properties
- Elasticity of materials, their ability
to return to their original shape, size or condition after
a deforming stress is removed, is compared in terms of
their elastic modulus.
The elastic modulus of a material, given as stress/strain, changes with pressure and temperature. Pressure tends to increase the modulus; temperature tends to decrease the modulus. There are two different elastic moduli: the shear modulus, if the stress is a shear, and the bulk modulus if the stress is compressional.
Most rocks are surprisingly elastic when compared to an elastic band. When a stress is suddenly released, such as in an earthquake, the change in strain of the rock travels outwards as an elastic seismic wave.
- Density is the mass of material per
unit volume.
Density is one determining factor for the velocity with which a seismic wave travels through a medium. The velocity in the medium is inversely dependent on the density of the medium. Seismic wave reflection and refraction at rock type boundaries is dependent on the relative densities of the layers.
- Thermal conductivity is defined as the
rate at which heat flows through a unit area of a body and
is precisely defined as the quantity of heat that passes in
unit time through unit area of a plate, when its opposite
faces are subject to unit temperature gradient. Rocks of
higher thermal conductivity are more efficient at
transferring heat energy.
The thermal gradient is the rate at which the Earth’s temperature changes with depth. Its average is about 30ºC per kilometre of depth near the surface, but decreases with depth as the temperature increases.
Heat flow rate measures the amount of heat passing through a given area of rock plate in unit time. It is proportional to both thermal conductivity and temperature gradient.
Global Heat Flow, Judson L. Ahern, Ohio State
University, USA. This site has some good diagrams.
- Magnetic susceptibility is the
material property which determines the magnetic response of
different materials. It is defined as the intensity
(strength) of magnetisation of that material when placed in
a magnetic field of unit intensity. The magnetic
susceptibility depends on the amount of ferromagnetic
minerals (e.g. magnetite) present in the rock.
Magnetic Surveys Delta Mine Training Centre,
Alaska, USA. [table of range of magnetic susceptibility for
different rock types].
Rock magnetism occurs in sedimentary rocks that contain magnetic minerals that align with the Earth’s magnetic field as the sediments settle and retain their orientation as the rock hardens. Magnetic minerals in molten materials also align with the Earth’s magnetic field when they cool through the Curie temperature (usually around 550° C), preserving the direction of the Earth’s magnetic field in the solid rock when they cooled through that temperature. This alignment is maintained as long as the temperature of the rock remains below the Curie point.
- Electrical properties
Electrical conductivity of a rock is a measure of how easily that material allows an electrical current to pass through it. Electrical conductivity is the ratio of the current density to applied electric field.
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current and is the quantity usually cited in geophysics. It is the inverse of electrical conductivity. Different rock types have a characteristic range of resistivities.
Magnetic Surveys Delta Mine Training Centre,
Alaska - contains a table of range of electrical
resistivity for different rock types.
identify the principal methods used in geophysics as seismic, gravitational, magnetic, palaeomagnetic, electrical, electromagnetic, radiometric and geothermal, and describe the type of information that two of these methods can provide
- The principal methods used in geophysics are seismic,
gravitational, magnetic, palaeomagnetic, electrical,
electromagnetic, radiometric and geothermal.
- Note: Make sure that you describe the
type of information provided by these
methods, not just the method itself. You only need to be
able to describe the type of information that TWO of these
methods can provide but four have been provided to give you
further examples.
- Seismic methods involve the study of
the way acoustic shock waves are modified by the earth
materials and structures they pass through. They travel
faster in more rigid and in denser bodies and are reflected
from and refracted at the boundaries between various rock
types. Utilising the concept of travel times, geophysicists
are able to infer the density, shape and structure of
materials in the part of the Earth through which the waves
have travelled. This allows them to interpret the geologic
structure of the underlying rock strata and also to form an
image of the internal structure of the Earth.
- The Gravity Method uses variations in
gravity over localised areas on the Earth. The strength of
the gravitational field at a point on the Earth’s
surface depends upon the density distribution below. Using
highly sensitive balances or very sophisticated absolute
gravity meters, geophysicists can determine lateral
variation in gravity. Gravity surveys typically distinguish
the major rock types found in a survey
area, or are used to assist in the delineation and
identification of very dense ore deposits
on a smaller scale. Gravity is also used to delineate
structures associated with oil such as diapiric salt domes.
Early gravitational methods were used to investigate the
Earth’s size and shape by studying pendulum motion
variations.
- Radiometric Methods exploit the
natural radioactivity of many minerals. Scintillation
counters and gamma-ray spectrometers are used, either on
the ground or by air, to record the spectral signatures of
the radiation emitted. These can be compared to the
characteristic spectral signatures of certain rock types to
identify the source of the radiation.
Radiometric methods can also be used to measure the proportions of different radioisotopes in a rock sample. The known half-lives of the isotopes are then used to calculate the age of the rock.
- Geothermal Methods: Thermal rock
properties can provide information on lithology, structure
and the nature of fluids in porous rocks, and can aid in
understanding the thermal history of, for example, a
prospective hydrocarbon-rich geological basin. This is of
economic importance, as expensive drilling can be limited
to areas where the potential for the presence of
hydrocarbons is high.
Measurement of heat flow through the Earth’s surface provides information about tectonic structure with the majority of heat being released by volcanism associated with mid-ocean ridges, active mountain belts, rifts, hot spots, and so on.
plan, choose equipment or resources for, and perform first-hand investigations to gather data and use the available evidence to analyse the variation in density of different rock types
- As you plan this investigation, think about how you
would explain why your chosen procedure is appropriate for
this task. Perform a risk assessment of each planned step.
- Choose equipment that will allow you
to test the rock samples non-destructively. Select a range
of different rock types (eg volcanic, sedimentary, igneous,
metamorphic, ores).
- Perform your investigation using safe
work practices.
- Prepare a suitable form in which to record your
gathered data before you begin. Plan a
number of replicates of each trial to increase the
reliability of your data.
- Analyse the information comparing your
data to sample data on density variation obtained from
other sources (e.g. the internet). Also consider whether a
destructive method of testing would have given different
results. Use your evidence to organise your rock samples
into some cohesive order.
Obtain a number of rock samples which will slide into a large measuring cylinder (preferably plastic for safety reasons).
Measure the mass of each sample using a balance (mechanical or electrical).
Repeat each process at least 3 times to obtain accurate and reliable data.
Tie light twine to each of these samples in turn and measure their volume by observing the amount of water displaced when each rock is completely immersed in the water (difference between final and initial readings on the measuring cylinder).
Repeat each process at least 3 times to obtain accurate and reliable data.
Record the data in a suitable table, calculate the averages and use these to calculate density for each sample.
Organise the samples into rock types Sedimentary, Metamorphic, Igneous (plutonic) and Igneous (volcanic).
Obtain secondary data on the variation of rock type ( internet).
Analyse your data by comparing it to the secondary data collected.
Helpful Links
Rock density: specific gravity [method] , Stephen Fuller,
Kansas City, Missouri, School District [alternative procedure
using Archimedes’ principle].
Density variations of earth materials , Thomas M. Boyd,
University of Melbourne.
Densities of common rock types , Andrew Alden,
Geology,about.com.
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