Petroleum Geology for Engineers
Homework problem set 2
Gravity method (due on or before Thursday, February 19, 2015):
The following data are collected from a gravity survey over some suspected buried targets. Column 1 shows the observation stations. The first station, situated at latitude 35° S is the reference station, and the other stations are placed successively in the South with distances in meters from the reference station as shown. Column 2 is the elevation in meters of each station with respect to the datum. Finally, column 3 is the measured gravity value at each station in gravity units (g.u.). Note, as we discussed, the measured values are NOT the absolute gravity, but the relative gravity field or the deviations (anomaly) from the mean gravity.
Station (distance in m from the reference)
Elev (m)
Measured Gravity (g.u)
0
160
170.1
200
120
240.1
400
80
340.5
600
30
438.6
800
10
480.4
1000
60
480.2
1200
100
460.4
1400
120
365.7
1600
130
380.8
1800
140
406.3
2000
160
484.7
2200
170
436.7
2400
180
419.3
2600
190
418.7
2800
195
416.9
3000
192
417.8
3200
199
319.7
3600
198
300.3
3800
193
268.8
4000
197
217.5
4200
195
200.2
4400
196
198.7
4600
197
200.2
4800
199
207.1
5000
200
207.2

• Compute the latitude, free-air, and Bouguer corrections to the measured data at each observation point. For Bouguer correction, assume a density of 2.067 g/cm3. Show each correction in separate columns with headings. • Compute the Bouguer gravity anomaly and display it in another column. So finally, you will generate four additional columns (three for the corrections and one for the computed Bouguer anomaly) to the data provided. Please be careful with the signs of each correction, i.e., whether to add or subtract the computed correction to/from the measured data. • Display the measured anomaly and the Bouguer anomaly at different observation points in a single graph. Please level the graph with correct units, heading, caption, etc. • Bonus Questions (You can get up to 20 additional points if you answer them correctly). • Compare the measured anomaly with the Bouguer anomaly- • Are they similar or different? Please explain with reasons • Mark the regions with gravity anomaly that are possibly due to the sediments • Recall, measured gravity field is mostly controlled by the regional structural trends caused by the smooth basement and any deviation from such trend is caused by the basement above • Consider that you are using this gravity data to detect a structural trap • Which part (or parts) out of the entire line would you recommend further investigations using seismic?
Useful materials from the lecture notes (Reading through this will help)
Latitude correction
Because of the spheroidal shape of the earth, the acceleration due to gravity (g) increases from the equator to the poles. So, if you are conducting a gravity survey in an area and the area of the survey is large, you need to correct the measured data for the variations in latitude between different stations. As discussed, the way to do it is as follows: • You choose a reference station- the first station in this homework. • The latitude correction of the other stations in gravity units (g.u) is 8.139878 Δx sin 2φ where Δx is the component of the distance in meters of the station from the reference station along the N-S direction, and φ is the latitude. • Also note: • If the station location is at higher latitude compared to the reference station (i.e., to further north if the survey is conducted in the northern hemisphere and to further south if it is conducted in the southern hemisphere, you subtract the computed correction from the measured value. If it is at a lower latitude, you then add, and if it is at the same latitude as the reference station (i.e., if it is to east or west), you do not do any latitude correction.
Free-air correction
Elevation of the station causes measured gravity to change. Therefore, the effect of elevation must be removed from the measured gravity field. This is typically done by removing the elevation effect to a datum, usually taken as the mean sea level. Recall from the lecture notes that the free-air correction is given as (1)
In equation 1, g is the acceleration due to gravity and Rsph is radius of the equivalent spherical earth (6371 km). Using a mean g of 9.8305 m/s2, it was also shown that the free-air correction is 3.0865 g.u/m. It is also mentioned that the correct way to do it is use a g value for the survey area, from the intentional gravity formula.

Figure 1: Acceleration due to gravity as a function of latitude.
Because the area here is 35°S, from the international gravity formula (see Figure 1), the value of g for the location is approximately 9.798 m/s2. I recommend that you use this value for g in equation 1 to calculate the free-air correction in g.u/m. Once you calculate it, just multiply it to the elevation in meters for each station as the free-air correction for the station. Obviously, if the elevation is above the datum, the correction is positive and it is negative if it is below. It is a good idea to calculate correction with the correct sign so that you just add the correction to the measured gravity field when computing the Bouguer gravity anomaly.
Bouguer correction
As mentioned in the class, the Bouguer correction is the effect to the measured gravity field due to the additional mass at the elevated areas and due to the lack of mass at the low areas compared to the datum. It is also shown that it is given as 0.4191ρ g.u/m where ρ is the density in g/cm3. So, the Bouguer correction at a given station in g.u is given as 0.4191ρh where h is the elevation of the station in meters.
Computation of the Bouguer gravity anomaly
Here you really need to be careful with the signs: • For the latitude correction in any station: • Add the computed correction to the measured field if the station is at lower latitude with respect to the reference station. • Subtract the correction from the measured field if the station is at higher latitude with respect to the reference station. • Do not apply any correction if the station is at the same latitude as the reference station. • For the free-air correction at any station: • If you calculated the correction with correct sign, i.e. a positive value if the elevation is above the datum and a negative value if the elevation is below datum, you are then all set. Just add your correction to the measured field- the positive numbers will be added and the negative numbers will be subtracted. • For the Bouguer correction at any station: • If you follow the same convention as for the free-air correction, i.e., you computed a positive value if the elevation is above the datum and a negative value if the elevation is below datum, you then need to subtract the computed correction from the measured gravity field.
Display of the results
Please use the correct labels: • Properly annotate the horizontal and vertical axes with correct units. • Use a clear caption or label to differentiate the measured gravity curve from the computed Bouguer gravity anomaly.
Bonus questions
You are not required to answer these questions but it can surely help in your final grades. Because this is a bonus question, I would rather not provide any hint/comment on how you would answer. Just read through the notes and stretch your imagination to provide your best answer. This question and the other such questions you’ll get in future are all meant to test your skills beyond the regular class and your ability to be an effective professional when you start your careers. So, there is no penalty if you do not answer, but if you do there will be an extra reward towards your final grade.
Final remarks
You are encouraged to discuss the homework with others in the class, but your submitted homework must be original. Copying the homework off one another is not acceptable and would give everyone involved with a zero point.