Splitting .tif image into several tiles?

I propose two solutions: the first one using QGIS, the second one using Python (GDAL).

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Solution using QGIS

In QGIS you may create a VRT mosaic.

Please follow this procedure (see the image below):

1. Load the raster in the Layers Panel;
2. Right-click on it and choose Save As...;
3. Check the Create VRT option;
4. Choose the folder where your outputs will be saved;
5. Set the extent (if you want to work on the whole raster, don't modify anything);
6. Choose if using the current resolution (I suggest to leave it as default);
7. Set the max number of columns and rows (in your case, it should be 20000 columns and 2000 rows);
8. Press the OK button.

For example, the using of the parameters in the above dialog on this sample raster (the parameters I set are chosen randomly):

will generate 100 tiles in the path specified at step 4:

Loading them in QGIS, they look like this:

As @bugmenot123 correctly said in the comments, the result looks weird just because the style of each image fits itself to the distribution of values per image (but the data are perfectly fine).

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Solution using Python (GDAL)

Another way to obtain the same result is the using of GDAL (gdal_translate).

With reference to the same example described above, you may use this script:

import os, gdal

in_path = 'C:/Users/Marco/Desktop/'
input_filename = 'dtm_5.tif'

out_path = 'C:/Users/Marco/Desktop/output_folder/'
output_filename = 'tile_'

tile_size_x = 50
tile_size_y = 70

ds = gdal.Open(in_path + input_filename)
band = ds.GetRasterBand(1)
xsize = band.XSize
ysize = band.YSize

for i in range(0, xsize, tile_size_x):
    for j in range(0, ysize, tile_size_y):
        com_string = "gdal_translate -of GTIFF -srcwin " + str(i)+ ", " + str(j) + ", " + str(tile_size_x) + ", " + str(tile_size_y) + " " + str(in_path) + str(input_filename) + " " + str(out_path) + str(output_filename) + str(i) + "_" + str(j) + ".tif"
        os.system(com_string)

You obviously need to adapt the values to your specific case.

Don't split

You gdalbuildvrt, you can create virtual tiles that will only use a few bytes on your disk. Then you can use most softwares that will take your vrt's as input to perform your processing.

Alternatively, I would rather look for a tool that can work with a 1Gb image than split and merge an image. For instance, OTB has most of the capabilities for standard (and sometimes advanced) image processing with large images. You can wrap OTB for Python or run it from QGIS or from command lines.

Another solution using GDAL is the gdal_retile.py tool:

mkdir image_tiles
gdal_retile.py -v -r bilinear -levels 1 -ps 20000 20000 -co "TILED=YES" -co "COMPRESS=JPEG" -targetDir image_tiles big_input_image.tif

For more Information see: http://www.gdal.org/gdal_retile.html