Gravity Data Reduction and Interpretation
BACKGROUND
Geologists and engineers often perceive the interpretation of geophysical data as "geomagic" because of
the mathematical complexity of the underlying theory. This need not be the case if all of the partners in a
project (geologists, engineers, and geophysicists) concentrate on the exploration process. The last exercise
introduced you to the application of formal engineering design techniques to the planning of a
geophysical survey. In this exercise, we will study how the same kind of
structured decision-making processes
can be applied to the interpretation of geophysical data.
Perhaps the most common failing of data interpreters is to become committed to their first interpretation
too quickly. Once they have settled on their first interpretation, they tend to try to force all of the data to
fit that interpretation. Unfortunately, because of the inherent uncertainty in geophysical data, it often is
possible to force a set of data to fit a number of different models. Even though the data fits their first
interpretation, there is no guarantee that it is the most likely interpretation. Using a well-defined, structured
approach to the interpretive process can minimize the chance of delivering the wrong interpretation -- or
can at least demonstrate that the preferred interpretation is suspect. This sort of "honesty" is what leads to
trust between client and contractor, and both gain in the end.
OBJECTIVES
There are four learning objectives:
- Gain experience with both data presentation and modeling,
- Develop an understanding for the kinds of corrections applied to gravity data, with special
emphasis on the empirical corrections that require interpolation between reference points,
- Codify the steps involved in processing and interpreting geophysical data,
- Get exposure to the problem of matching gravity anomalies with possible geologic sources.
If you have not already done so, you first need to
generate a gravity data set using your survey parameters
and download them to your computer.
As you can see from the plot of the observations, they look much more complex than would be expected from
the anomaly produced by a simple tunnel.
The objective in this exercise is to attempt to enhance the gravity
anomaly due to the target and interpret that anomaly in terms of the location, shape, and condition of the
target. There are two milestones in the process of accomplishing this objective:
- Process data to maximize signal-to-noise ratio. This will include
- Corrections for deterministic noise,
- Minimization of statistical noise,
- Development of a plausible interpretation,
- Validation of interpretation and estimates of model confidence. This will
include
- A parametric sensitivity analysis of the plausible interpretation,
- Determination of all possible models and selection of preferred model,
- Validation and calculation of likelihood of preferred interpretation,
- Identification and analysis of other anomalies, if any.
PROCEDURE
For this exercise, you will need the gravity observations generated from your
survey, a spreadsheet, and one of the Java packages pointed to below.
Once you have these, you can begin on the following procedure.
- Process the data to remove or minimize all variations not deriving from
the target.
- Load the generated gravity observations into your spreadsheet and generate
a plot of gravity versus position along the line. Notice that the data
file that you have generated contains three columns of data. The first
gives the location of the observations along the line (location is specified
using the client
specified survey coordinates). The second gives the time at which
the gravity observation at that location was taken, and the third is the
gravity observation in mGals. Notice
that one position on the line has multiple gravity readings. This position
should correspond to the location of your base station. If you requested
multiple readings at each station in an effort to reduce reading errors,
only a single reading will be listed in the file, because these multiple
readings have been averaged for you.
- Using your spreadsheet and the techniques developed in the Observation
Assignment, correct the data
for temporal variations (drift and tides).
- At this stage one would normally apply latitude,
elevation, slab,
and topography corrections to the data. We will assume that these do not
need to be applied for this survey.
- Correct data for long-wavelength spatial variations caused by deep geologic
structure or distant topography. There are a number of ways you can estimate
the regional gravity anomaly. Probably one of the simplest is to fit some
low-order function to the data (say a straight line, or a quadratic function).
Then subtract the gravity predicted by this function from the observed
gravity values. Another way to estimate the regional gravity anomaly is
to use gravity observations from other, more spatially dispersed, gravity
surveys. Most areas within the continental US have a complete enough gravity
coverage to allow this to be done. The National
Geophysical Data Center provides gravity observations from across
the US on CD-ROM.
This data is ideally suited for estimating regional gravity anomalies.
For this exercise, we will use gravity observations derived from the CD-ROM
to estimate the regional gravity anomaly. (In Australia, both the Australian
Geological Survey Organisation (AGSO) and State geological surveys can
supply reconnaissance-scale gravity data for a fee.)
Gravity observations from around the city of Golden were used to construct
a map of the regional
gravity field around the survey. Using this map, estimate the shape
of the regional gravity field along the profile and subtract the contribution
of the regional field from your gravity observations as follows:
- Print the map, or import it into a graphics program, draw grid
lines on the printout or adjust the size to scale in a graphics display,
and pick the value of the regional gravity at selected points along
the profile.
- For the selected points you can use your gravity stations, or you
can pick fewer points and use linear interpolation or a polynomial
curve fit to approximate the values of the regional gravity contribution
at your gravity stations. If you do the latter, choose the interval
between points so that the approximation errors are small.
- In your processing spreadsheet, subtract the regional gravity values
from your corrected gravity observations.
- If necessary, smooth the resulting residual gravity field to minimize
random variations and emphasize the anomaly due to the target. Before
doing this, look critically at your data, and make sure that the "random
variations" are not in fact the result of mistakes in the reduction
process.
- Note: check the actual values in each column, and
make sure that there are no numbers in "scientific" format
(such as 0.1E-1). It is best to use the spreadsheet number-formatting
settings to avoid this. The Java interpreter may have difficulties
with exponent formats.
- Preliminary Data Presentation and Interpretation
- Plot the resulting residual gravity field versus position along the
line. Are there interpretable gravity anomalies present in the profile?
- Identify geologic models that should be considered in interpreting the
data.
- Evaluate whether an anomaly associated with the target of interest
can be seen in the data.
- Identify all anomalies that appear to derive from local geologic
features.
- Determine which geologic models could be the source of those local
anomalies.
- Formal Data Interpretation
- From your spreadsheet, output a data file that contains two columns.
The first should be location along the gravity profile, the second should
be the residual gravity field. Do not output column names as the first
line in the file.
- To interpret the gravity observations, download one of the scripts pointed
to below to your machine.
- Follow the instructions provided in the script to load and plot your
residual gravity field into the script.
- By now varying the model parameters that specify the location, depth,
size, and density contrast of the tunnel, attempt to match that portion
of the observed residual gravity field that you think might be due to
a tunnel. To do this, remember to use the rules that describe the physics
of the problem that were requested as an appendix in your survey
bid.
- Once you have found a preferred model(s), estimate the uncertainties
in the model parameters. Do this by systematically varying the model parameters
about your preferred values and find all values that fit the observed
data to within the data uncertainties.
- Finally, are there other models that could fit the data equally as
well as your preferred model that have very different parameters? If these
models are geologically plausible, describe what they are and give your
rationale for choosing a preferred model(s).
OUTCOMES
You will submit two reports on the basis of the work described in this
exercise. The first will cover those questions raised in milestone 1
listed above, and the second will cover those listed in milestone 2.
In this sense, the first report represents a preliminary report of work
in progress to the client, the second report will represent the final result
of your efforts. Each report should be in the form of a summary report to
your client. The heading can be in standard memo format. Each should include:
- A brief review of the basis for the survey design (statement of the
problem),
- A summary of the data-processing and interpretation procedures (you
may want to refer to a flow chart in the appendices), and
- A clear and concise statement of your preliminary interpretation and
an indication of the action that will be required to refine and validate
that interpretation.
As usual, the body of each report must be no longer than two pages. However,
it is important to provide enough information (in the appendices) for the
client's geophysical staff or consultant to be able to check any of your
work. This would include:
- A tabulation of the field data,
- A description of each processing step, including formulas and outcomes,
- For any "standard" corrections that were not done, a description of
how they normally would have been done and an explanation of why they
were not necessary in this case,
- A narrative discussion of how and why you chose the "possible" models
for each anomaly, and
- A description of any other anomalies that the survey turned up that
could not be caused by a mine tunnel.
As always, remember that your reports are also sales documents; in this
case, instead of selling your services, it is selling your competence and
the quality of your work. Also remember that your clients are busy executives
that probably are out of touch with the technical state of the art. Your
report must communicate quickly and effectively and should convey a sense
of competence and professionalism.
There are some
examples of reports for viewing or download here.
