A segment of the subject 625-304 Applied Geophysics

On the large scale, the variation in the force of gravity in the Australian region appears to be correlated with geological features. The basis for this correlation is simple and obvious, so that gravity information can readily be incorporated into geological interpretations. In some cases, because of the ability of gravity to report rock variations below the surface, the geological interpretation must be altered to account for these data.

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Parasnis is a standard textbook. Don't forget to look at the AGCRC page for more on the large-scale geophysics data.

• looks at applications of gravity in geological mapping
  

Main objective

to enable the eventual integration of gravity data with other geological data by giving rules of thumb which make the data more accessible.

• Describe physical basis of gravity variations
• Discuss simple theory
• Show responses for simple models
• Case history

Gravity measurements

• measurements of Gravity Acceleration - "g"
• g varies from place to place on Earth
• variations are in response to changes in the density of the underlying rocks.

The force between two masses is:

• Proportional to masses
• Proportional to inverse square of distance

and the formula is:

Force is mass x acceleration
If M is attracting mass, m is accelerated by
gamma is the Universal Gravitational Constant

gamma = 6.674 x 10-11 N.m2.kg-2

For sphere of uniform density, all mass appears located at the Centre of Mass

Earth-average g is 10 m.s-2

This corresponds to result if total mass of Earth is located at its centre

measure radius (geometry) and g and gamma (experiments), and Earth's mass can be computed.

• All masses in Earth contribute to average
• Nearby masses contribute more (inverse square of distance effect)
• If nearby densities more than average, local g will be above average

Consider spherical volume near surface:

• radius 100m,
• depth to centre 200 m,
• density 2 t.m-3

This contributes what to g at P?

Check your answer?

Substitute different material in the same spherical volume:

for example, with density = 3 t.m-3
(basalt replacing sandstones?)

This volume now contributes - what?

g at P will now be - what, compared with average!

Check your answer?

• Moving away from P reduces effect of anomaly
  • (Inverse square of distance effect)
• Departure from average g thus shows existence of departures from average density
  
  
• Anomalies reflect geology!

Change calculated here is about 1 ppm of average gravity

Gravimeters currently available can resolve changes of 10-100 ppb with little difficulty; higher resolution with more care

To play with a simulated gravimeter (and test your German), go here.

• Acceleration: m.s-2
• Special units used in Geophysics:
  • Gal = 0.01 m.s-2
  • milliGal = 10-5 m.s-2
  • gravity unit = 1 mm.s-2
• Last two are "practical units" for measurements in Geology.

"Other Effects"

• Observations also affected by
  • Sun, Moon attractions (moving masses)
  • Earth's rotation (axifugal acceleration)
  • Change in height (changes average g)
• Bouguer gravity anomaly refers to observations adjusted for these effects (that is, the things we know)

Simply:

• Overhead, the moon's gravitational attraction reduces that of the Earth.
• On the horizon, lunar gravity forces make little change.

Magnitude of lunar attraction:

Compare with geological values!

Rotation acceleration also reduces gravitational effect

• At equator, directly "up"
• At pole, zero

Magnitude of rotation effect:

Compare geological signals!

Increasing height above sea level is increasing distance from Earth centre

so Average gravity decreases

Magnitude of this elevation effect:

Compare geological variations!

• Higher elevation = more rock to sea level
• Additional rock causes additional local gravity
• Measure density, thickness (height) and compute effect

Magnitude about 25% of elevation (opposite sign)

Each of these four effects calculable

• know time (solar/lunar forces)
• know latitude (rotational forces)
• know height (elevation effects)
• know densities (surficial effects)

Adjust observations for things we know ("reductions")

Anomalies must be due to unexplained variations!

So, now you know :

• Earth's gravity changes from place to place
• Changes reflect rock densities
• Changes are small but measurable
  
  
• How do we invert them?

Predicting gravity responses

• Simple geometric models, such as spheres and slabs, have easily-calculable responses.
• Response shapes reflect the whereabouts of the source.
• Calculations can be intense, but there are simplifications which are easily applied.

Gravimeters measure vertical acceleration (g is really a vector). So, anomaly due to a sphere, as we move away from it, is more than just Newton's Law .

For extra density d(rho) in a sphere of radius a and depth-to-centre D, the gravity anomaly is:

There are two parts

• (The magnitude term: how much extra mass)
• [The shape term: where it is, in both dimensions]

This really helps interpretation!

The graph is simple. You should try plotting it!

This is widely observed in geophysical responses

• magnitude >> amount of source material
• shape >> location of source material

Simple rules can help with structural interpretation of maps
What is the simplest rule?

Plot the [ ] part of the step-model formula, for four different depths:

• How does the shape change?

Plot the [ ] part of the horizontal cylinder formula, for four different depths:

• How does the shape change?

"Rules of Thumb" 3

Observe that

• The shapes are broader
• The slopes are flatter

if the density anomaly is deeper

- and we can quantify that

For a cylinder model the depth is equal to

• half the width, at half the maximum amplitude

For a step model, the depth is equal to

• half of the distance over which half of the gravity change occurs

A similar rule can be made from the sphere formula ... Try it!

These aren't used for building exact models

• the rules refer to centres-of-mass only
• they will be applied to real data, which is usually more complicated

• The general idea of "half the width at half the maximum" is widely applicable and simple.
• It still needs analysis, to apply it to appropriate pieces of data
• the data should roughly resemble the simple model applied

* for the time being, anyway!

• Thought will confirm that these rules are checkable with algebra.
• More exercise of simple maths leads to other generalizations based on maxima and slope measurements.
• These are almost as simple, given the numerical data.

Inversion and interpretation of gravity maps

• A gravity map reflects the density distribution in the subsurface.
• Two classes of interpretation can be invoked:
  • Qualitative
    • working from shapes in the map
  • Quantitative
    • working from models, with numbers

• Qualitative interpretation requires "only" that the shapes (and their signs) be identified and associated with possible geological sources.
• This is very useful - but more so if rules-of-thumb are remembered to help with the depth dimension.

• Usually, the map must be decomposed into contributions which can be associated with simple models.
• These simple models represent the actual density distribution.
• Some idea of anomaly shapes due to the models is necessary.

• Reserve the word Inversion for the calculation of the size and shape of a model.
  
  
• Use Interpretation to cover the "translation" of that model to a geological context.

Separation

This is necessary to isolate the responses to different sources.

A feedback loop is involved

If models don't fit the components,

• Change the models and try again, or
• Change the separation and try again.

This profile doesn't resemble any of the simple model responses we've seen. We can separate it into two components, though.

Qualitative step:

Break the map into components, in different areas

Quantitative step:

Suggest simple model shapes for the components

Separate the data into contributions from the models

Calculate (rule of thumb?) the model component locations

Interpretation

• In terms of geological models.

Case History - Elura (NSW)

Target: sulphide orebody in siltstone.

Densities:
Sulphides - 4.5 t.m-3
Siltstones - 2.7 t.m-3

Suggests good gravity target.

Shape (from other bodies): probably vertical pipe-like

• Anomaly magnitude - 14 gu
• Roughly-concentric anomaly contours

  Suggests local source
  
  Use sphere model to investigate
  separate into "regional" and "local" contributions
  
  Half-width of local anomaly - 400-500 m

• From maximum position, find location of target centre
• From halfwidth, rule of thumb gives depth ­p; 250-300 m
• From density contrast, depth, and maximum anomaly, find sphere size ­p; 125 m radius

Predictions:

• depth to top - 150 m
• diameter at 250 m - 250 m
• mass of body - 30-40 Mt

Observations:

• depth to top - 100 m (ignoring gossan)
• extent - 200m x 80 m
• tonnage - 27 Mt

Fresh Science!

Early in 2000 BHP announced a scientific and engineering breakthrough — successful gravity data acquisition from an airborne platform with resolution similar to that from reasonably detailed ground work. So far they have only released a few details and images.

The BHP Falcon system measures the vertical gravity gradient - the rate of change of gravity with height - probably to help overcome the severe noise problems which arise from the mobile airborne platform. However it is easy to see that this contains effectively the same information about subsurface density distributions. For the simple sphere anomaly discussed at the beginning of this page, it is easy to show that the gradient will be

in which all of the same model parameters appear, although the shape factor (in [ ] ) will be different from that for a direct measurement. Try plotting the shape of the curve wrto distance (x) for both the gravity and gravity gradient. (If you have a Mac, use the Graphing Calculator.)

Gravity Gradient data contain the same information about anomalies as do conventional gravity data.

Ground gravity data is relatively slow to acquire, and often limited to accessible regions. Airborne gravity data acquisition will mean more, and more-uniform data to be integrated with other earth-science observations in geological exploration.

It is vital that you look for other examples of gravity maps and their use.
Start now to look at geological maps, journals and textbooks, and apply your own inversions and interpretations.

Next: Magnetics

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