Correct the Raw Gravity Data

Now that we have the survey elevations we can corret the gravity data. As we are not interested in absolute gravity measurements, but gravity anomalies due to changes in surface geology, we must make corrections to the gravity data.  As you learned in the provided exert from Lille's text, it is common to make two corrections to measured gravity:
  1. Theoretical Correction
  2. Free-Air Correction
  3. Bouguer Correction
We will need two additional datasets to make these corrections (1) latitude and (2) elevation.  In the next sections, we will use the field calculator to make these corrections to the gravity data.
 

Theoretical Gravity

To find the theoretical gravity (the gravity field expected for an oblate sphere) we must remove the effect of change in latitude and elevation on gravitational acceleration. 

Theoretical Gravity:

The calculation can be accomplished using the field calculator, and the given latitudes for each station.  The sine function in field calculator wants radians rather than degrees, so first create a field (under Options...) called Lat_rad (Float, Precision 12, Scale 6) and convert latitude degrees to latitude radians using radians=deg*3.1415926/180.

Create another field called g_t (Float, Precision 12, Scale 6) for the theoretical gravity. Use the field calculator to find theoretical gravity based upon the latitude in radians. Note that the syntax for field calculations can be frustrating, so before you calculate, copy the equation using the "copy" button on your keyboard.  That way if it doesn't calculate you can paste it back into the field calculator and start from there. The syntax should be, similar to this, with the use of parentheses to separate terms:

978031.85 *(1 +0.005278895* ( Sin ( [Lat_Rad] ) )^2 +0.000023462 * Sin ( [Lat_Rad] )^4)

As a check, the theoretical gravity for station #2 should be 980373.8 mGal. If it looks OK, make sure you save your edits.

Free-Air Correction

We are now ready to find the Free-Air gravity anomaly using our elevation data.  Recall that the free-air anomaly is

Add a field called "g_fa" to the table (Float, Precision 12, Scale 6).  Use the field calculator to calculate the free air gravity, according to the formula given above. Save the edits to your table.

As a check, the Free-Air gravity anomaly for Station #2 should be +9.81 mGal.

Bouguer Correction

The final correction to the data is the Bouguer Correction. The Bouguer Correction accounts for the gravitational mass of above a datum plane, usually sea level. The objective is to remove the amount of mass that would be between the measurement elevation and sea level, such that gravity anomalies are due to DENSITY rather than elevation.

There are different Bouguer corrections applied to gentle topography, rugged topography, and sub-oceanic gravity measurements. Here, we will use the correction for gentle land topography:

Add a new field to your table "g_b" and use the field calculator to make the Bouguer correction to your data. As a check, the Bouguer anomaly for Station #2 should be -44.06.

Create a map of the Bouguer anomaly data using a scaled symbolization. You should see that the anomaly is higher in the uplands due to the greater density of the bedrock. Add a scale, north arrow, and title, and turn this map in.

 

 

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