How to access SVG elements with Javascript

In case you use jQuery you need to wait for $(window).load, because the embedded SVG document might not be yet loaded at $(document).ready

$(window).load(function () {

    //alert("Document loaded, including graphics and embedded documents (like SVG)");
    var a = document.getElementById("alphasvg");

    //get the inner DOM of alpha.svg
    var svgDoc = a.contentDocument;

    //get the inner element by id
    var delta = svgDoc.getElementById("delta");
    delta.addEventListener("mousedown", function(){ alert('hello world!')}, false);
});

Is it possible to do it this way, as opposed to using something like Raphael or jQuery SVG?

Definitely.

If it is possible, what's the technique?

This annotated code snippet works:

<!DOCTYPE html>
<html>
    <head>
        <title>SVG Illustrator Test</title> 
    </head>
    <body>

        <object data="alpha.svg" type="image/svg+xml"
         id="alphasvg" width="100%" height="100%"></object>

        <script>
            var a = document.getElementById("alphasvg");

            // It's important to add an load event listener to the object,
            // as it will load the svg doc asynchronously
            a.addEventListener("load",function(){

                // get the inner DOM of alpha.svg
                var svgDoc = a.contentDocument;
                // get the inner element by id
                var delta = svgDoc.getElementById("delta");
                // add behaviour
                delta.addEventListener("mousedown",function(){
                        alert('hello world!')
                }, false);
            }, false);
        </script>
    </body>
</html>

Note that a limitation of this technique is that it is restricted by the same-origin policy, so alpha.svg must be hosted on the same domain as the .html file, otherwise the inner DOM of the object will be inaccessible.

Important thing to run this HTML, you need host HTML file to web server like IIS, Tomcat