How to make an element inherit a set of CSS rules for another element?

The easiest is to add your someInheritedDiv element to the first rule like this.

div.someBaseDiv,
#someInheritedDiv
{
    margin-top:3px;
    margin-left:auto;
    margin-right:auto;
    margin-bottom:0px;
}

This will tell your #someInheritedDiv to apply the same styles as div.someBaseDiv has. Then you extend this set of styles with more specific to your #someInheritedDiv:

#someInheritedDiv
{
    background-image:url("images/worldsource/customBackground.gif");
    background-repeat:no-repeat;
    width:950px;
    height:572px;
}

This is how specificity in CSS works.