Data Interpretation - Gravity

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:

  1. Process data to maximize signal-to-noise ratio. This will include:
    • Corrections for deterministic noise,
    • Minimization of statistical noise,
    • Development of a plausible interpretation,
  2. 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 symbolic math 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.

      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 polynomical 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.
  • 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, click the application links below.
    • Follow the instructions provided in the script to load and plot your residual gravity field into the script. In all cases, note that this involves modifying the script, usually by simply replacing a file name with one that contains your observations.
    • 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.