The default background of the log on screen can be found under
/System/ Library/CoreServices and file is named "DefaultDesktop.JPG".
Before replacing this file by another, it's nice to have a copy stored somewhere else (in case of restore is required).
Image properties of the new picture should be 2560 × 1600 pixel with a resolution of 72 pixel per inch (for Mac Book 13,3''). (optional)
Afterwards the new picture is renamed into "DefaultDesktop.JPG". Go to the directory /System/ Library/CoreServices and overwrite the old default background with the new picture.
Change can be seen after reboot.