CE678_PROJECT

Geoid modelling ce678 project

REGIONAL GEOID MODELLING

MEMBERS

Jainam
Vyush
Sachin

How to use

This is a guide on how to use this software We use classical remove-restore method to find geoid height in this code.

If stuck anywhere use this guide or type help corresponding to the function in Matlab.

There is a also a file project.ipynb that we have created to demonstrate our code on Nebraska,USA.

Also project.pdf is the project report file.

Step 1

Download the airborne gravity data from here by choosing any state tile.
Use the import_airborne_gravity_data.m function to import the data from the file of gravity data.
Save the matrix into vectors . Ex -

T = import_airborne_gravity_data('file_path');`

latitude = T(:,1);

longitude = T(:,2);

elipsoidal_height = T(:,4);

gravity_filtered = T(:,3);

Step 2

Download the geoid heights of GGM model from here
You can import them with import_geoid_heights
Code can be written as -

nggm = import_geoid_heights('filepath',latitude,longitude)
Calculate the Orthometric height by adding nggm to ellisoidal_height using this function-

orthometric_height = calc_orthometric_height(elipsoidal_height,nggm)

Step 3

Calculate the free air anomaly using the formula

$\Delta g=\left(g_{\text {observed }}+\delta g_{\text {Free air }}\right)-\gamma$

Code -

free_air_anomily = calc_free_air_anomaly(gravity_filtered,latitude,Ellipsoid,orthometric_height)

Here Ellipsoid is a struct used for storing important constants of Earth.For example ,You can use it by initiating as -

Ellipsoid = make_Ellipsoid('WGS84')

Step 4

From the free-air gravity anomaly, remove the effect of a global gravity field model, a long- wavelength gravity anomaly $\Delta g_{\mathrm{GGM}}$

$\Delta g_{\mathrm{s} \& \mathrm{mw}}=\Delta g-\Delta g_{\mathrm{GGM}}$

The resultant reduced gravity anomaly

$\Delta g_{\mathrm{s} \& \mathrm{mw}}$

contains only the medium and the short wave- lengths.

Download gravity anomaly of any GGM model from here.

TIPS on choosing-

Choose latitude and longitude range within the tile of our gravity airborne data we got in 1st step.
The website doesent allow resolution less than about 0.01. So make sure choose appropriate resolution so that code does not take long time to execute.

Code-

To import the data

del_g_ggm = import_grav_anomaly('filepath',latitude,longitude)

del_g_s_and_mw = remove_g_ggm(free_air_anomily,del_g_ggm);

Step 5

A correction to account for the gravitational attraction of the attraction must be applied

$\Delta g_{\mathrm{s} \ell \mathrm{mw}}^{\mathrm{atm}}=\Delta g_{\mathrm{s} \& \mathrm{mw}}-\delta g_{\mathrm{atm}}$

$\begin{aligned} \delta g_{\mathrm{atm}}=0.871-& 1.0298 \times 10^{-4} H+5.3105 \times 10^{-9} H^{2}-2.1642 \times 10^{-13} H^{3}+9.5246 \times 10^{-18} H^{4}-2.2411 \times 10^{-22} H^{5} \end{aligned}$

Code-

g_atm_and_s_mw = remove_g_atm(del_g_s_and_mw,orthometric_height)

Step 6

Convert the gravity anomaly $\Delta g_{\mathrm{s} \& \mathrm{mw}}^{\mathrm{atm}}$ data points into a grid

Ex Code -

[Latitude_grid,Longitude_grid] = create_grid(latitude,longitude,0.01);

g_atm_and_s_mw = griddata(latitude,longitude,g_atm_and_s_mw,Latitude_grid,Longitude_grid);

Step 7

Download the DEM data from here in ASCII format and of 5'x5' resolution. Remember to use all the tiles that cover up your intereseted area.
create a string array of filePaths

files = ["file1path","file2path"...]

Apply gravimetric terrain reduction $\delta g_{\mathrm{T}}$ to compute the Faye anomaly $\Delta g_{\text {Faye }}$ .