Geoid_Modelling

This repository contains the code for Regional Geoid Modelling.

Members

• Ayush Gupta
• Shubhi Kant

Steps 1

1. Download the observed airborne gravity data i.e. GRAV-D from here.

2. Read the downloaded GRAV-D data file using Get_Data_Points, as shown below:

[lat, lon, elevation, obs_grav] = Get_Data_Points('NGS_GRAVD_Block_MS01_Gravity_Data_BETA1.txt', 32.5, -106, 1.0);

Step 2

1. Download the height anomaly and gravity anomaly for the GGM from here.

2. Read the GGM files downloaded using GGM_Data, as shown below:

array = ['points1_GGM.dat'; 'point10001_GGM.dat'; 'point20001_GGM.dat'];
[lon_ggm, lat_ggm, height_anomaly_ggm, gravity_anomaly_ggm] = GGM_Data (array);

3. Compute orthometric height by adding flight elevation to GGM height, as shown below:

ortho_height = elevation + height_anomaly_ggm';

Step 3

1. For computing the free air anomaly use compute_free_air_anomaly, as shown below:

FAA = compute_free_air_anomaly(obs_grav, lat, ortho_height, 'WGS84'); 

Step 4

1. For getting the short wavelength component of gravity subtract the GGM gravity anomaly from free air anomaly, as shown below:

anomaly_smw = FAA - gravity_anomaly_ggm';

Step 5

1. For compute the correction to remove gravity attraction due to atmosphere use compute_atm_correction, as shown below:

atm_correction = compute_atm_correction(ortho_height);
anomaly_smw_atm = anomaly_smw - atm_correction;

Step 6

1. To convert the gravity anomaly which is in vector for to a grid, use create_grid, as shown below:

[lons, lats, dg_smw_atm] = create_grid(anomaly_smw_atm, 0.01, lat, lon);

Step 7

1. Download the DEM file for your study area from here as a GeoTIFF file, and convert it into a grid, as shown below:

Heights = imread('srtm_15_06.tif'); % Reading DEM file

lat_dem = linspace(32.45, 33.55, 1320);  % Defining the latitude range taking a buffer of 0.5 degree
lon_dem = linspace(-106.1, -105, 1320);  % Defining the longitude range taking a buffer of 0.5 degree
[X_dem, Y_dem] = meshgrid(lon_dem, lat_dem);
H_dem = double(Heights(6000-1319:6000,2941:4260)); 

2. For computing the terrain correction use Terrain_Correction, as shown below

TC = Terrain_Correction(X_dem, Y_dem, H_dem);

3. Remove the buffer region from the resulting terrain correction matrix, and compute the Faye anomaly by subtracting the Terrain correction from short wavelength gravity anomaly grid computed in Step 6

Step 8

1. For computing the disturbing potential due to reduced gravity anomaly using strokes integral use strokes_integral, as shown below:

Tr = stokes_integral (lons, lats, g_faye, 'WGS84', 0.01);

Step 9

1. Compute the undulations due to short wavelength using Bruns equation by dividing disturbing potential by normal gravity, as shown below:

Nr = Tr./compute_normal_grav(lats, 'WGS84');

Step 10

1. Download the height anomaly for all the grid points from here.

2. Compute the cogeoid by adding the undulation due short wavelength grid to GGM height anomaly grid, as shown below:

N = reshape(height_anomaly_gg, [101,101])'; % Reshaping the heigth anomaly to form a grid
N_cogeoid = Nr + N;

Step 11

1. Compute the indirect effect due to terrain on the undulation using compute_indirect_undulation, as shown below:

dN = compute_indirect_undulation(H_dem, 1/1200, X_dem, Y_dem, 'WGS84');

2. Compute the final geoid by adding the indirect effects to the cogeoid, as shown below:

N_geoid = N_cogeoid + dN;

Note: For information regarding input and output to each of the function use:

help "function_name"