Spherical Cap Complete Bouguer Correction: Grid Examples
Following on from my traverse examples, I now want to share examples of the Spherical Cap Complete Bouguer Correction computed for gravity observations in Tasmania, as well as theoretical examples on a grid mesh for Tasmania and Hawaii.
Example 1 – Tasmania Grid Mesh
Tasmania is an island to the southeast of Australia. Not so many years ago an emu could walk there from the mainland, but sea level rise has isolated it. To the east, west, and south a narrow continental shelf plunges to a complex abyssal plain. Onshore topography is rugged, but peaks rarely exceed 1500 meters high.
I have computed the Spherical Cap Complete Bouguer Correction on a 30 arc-second grid for stations located on land including offshore islands and islands in the Bass Strait. A datum level of -6000 meters was used and so the correction includes both terrain and water models.
The first image shows the spherical cap terrain correction superimposed on the bathymetry. Terrain corrections have a mean value of 16.7 milligals with a standard deviation of 4.3 milligals.
You can see a gradient from north to south which is caused by the water model, the contribution of which is shown in the next image. The water contributes to a slope of about 3 – 4 milligals across the island.
Example 2 – Tasmania Observed Gravity
I have computed the terrain correction for observed gravity stations on Tasmania. The gravity dataset is sourced from Geoscience Australia but dates back to 2009. A total of 75694 observations were processed. The station locations are shown on the map below. You can see that coverage and station density is highly variable.
Next is an image of the Complete Bouguer Anomaly. CBA has been calculated by adding the Spherical Cap Complete Bouguer Correction to the Free Air Gravity acquired from Geoscience Australia.
For comparison, I have included an image acquired from Geoscience Australia of the CBA as computed by them. The image is from the same era as the source database, but I can’t guarantee it was produced from exactly the same observation database. They compare generally well, but there are differences and the closer you look the more you find. Move the slider to the right to see my CBA data and move the slider to the left to see the Geoscience Australia CBA data.
Example 3 – Hawaii Grid Mesh
If you were crazy enough to try to do an onshore gravity survey at Hawaii, what kind of terrain corrections would you need to make?
Hawaii is dominated by the peaks of Mauna Loa and Mauna Kea, both approximately 4200 meter high shield volcanos. However, the terrain above sea level is bested by the bathymetry. The volcano plunges another 5500 meters to the seafloor and the total height of the volcano is closer to 9700 meters. It is Earth’s most impressive isolated topographic feature, in my opinion.
I computed spherical cap terrain corrections for Hawaii on a 30 arc-second grid. I computed the correction for two different datum levels. Firstly, I used a datum level of 0 meters. In this scenario only terrain above sea level contributes to the model, meaning bathymetry data and a water model are not used. Secondly, I used a data level of -6000 meters. This incorporates bathymetry and water into the model.
The first image is the spherical cap terrain correction for a datum level of 0m. Contours are at an interval of 2 milligals. The correction ranges from 0.38 to 73.7 milligals.
The next image is the spherical cap terrain correction for a datum level of -6000m. Contours are at an interval of 2 milligals. The correction ranges from 18.0 to 103.5 milligals.
Finally, here is an image of the difference between the TCC for a datum level of -6000 and the TCC for a datum level of 0. Contour interval is 2 milligals. The difference ranges from 15.3 to 48.1 milligals. Along the east coast the difference becomes extreme very close to the coast line.
Here is a slider image for the terrain correction for datum level 0 (left) and -6000 (right).
Here is a slider image for the terrain correction for datum level 0 (left) and the difference (right).
I hope these examples have been instructive and thought provoking!