changing/stripping off url pointed by image using javascript

If you have a reference to the img element, then its parent (parentNode) will be the link (in the structure you've given). Three options:

1. Remove the link entirely
2. Disable the link
3. Change the link's href

1. Remove the link entirely

You can remove the link entirely by doing this:

var link       = img.parentNode,
    linkParent = link.parentNode;
linkParent.insertBefore(img, link);
linkParent.removeChild(link);

That uses parentNode to find the parent and grandparent, insertBefore to move the image, and removeChild to remove the link. Note that this assumes the image is the only thing in the link.

2. Disable the link

If you want to keep the link but render it useless, you can do this:

var link = img.parentNode;
if (link.addEventListener) {
    link.addEventListener("click", function(event) {
        event.preventDefault();
    }, false);
}
else if (link.attachEvent) {
    link.attachEvent("onclick", function() {
        return false;
    });
}
else {
    link.onclick = function() {
        return false;
    }
}

3. Change the href of the link:

This is trivial, just set the href property of the link element (which you can get because it's the parent node of the image) to whatever you want:

img.parentNode.href = /* ...something else */;

For instance:

img.parentNode.href = "http://stackoverflow.com";

...would change the link to point to Stack Overflow.

Live example

Some references:

• DOM2 Core
• DOM2 HTML
• DOM3 Core
• HTML5 Web Application APIs

<a id="anchorWithImage" href="myfile.htm"><img src="rainbow.gif"></a> 

Why not grab the anchor, then set its href to nothing:

var a = document.getElementById("anchorWithImage");
a.href = "javascript:void(0)";

Or grab it and set its click event to cancel the default action, which is to browse to the location of its href property

a.onclick = function(e) {
   e.preventDefault();
}

Or do you want to grab all anchors that have an image as their child element, and strip out their href?

jQuery would make this easy, if that's an option for you

$("a").filter(function() {
    return $(this).children("a").length === 1;
}).attr("href", "javascript:void(0)");

or

$("a").filter(function() {
    return $(this).children("a").length === 1;
}).click(function() { return false; });  //returning false from jQuery handlers
                                         //prevents the default action 

EDIT

If you were to have a reference to the image, and wanted to set its parent's anchor's href, you'd grab it with the parentNode property:

var img = document.getElementById("imgId");
var a = img.parentNode;
a.href = "javascript:void(0)";

With jQuery you could use something similar to this

$("a").has("img").click(function(e).preventDefaults();});

Basically all this line does is identifies all tags within the document containing an tag disables standard event process

From your comment on another answer, it sounds like you actually want to change/eliminate the target of links at a specific position in the page. You could do something like this:

var el = document.elementFromPoint(10, 10);

while(el) {
    if(el.nodeName.toLowerCase() == 'a')
        el.href = 'javascript:';

    el = el.parentElement;
}

This would loop up from the selected element, identify if the element is an anchor, and set the href to something that does nothing.

you can change the href of a tag on window load itself, so you need not worry when it is clicked.

window.onload = fundtion(){
var imgs = document.getElementsByTagName('img');
 for(var i=0;i<imgs.length;i++){
   var parentElem = imgs[i].parentNode;
   if(parentElem.tagName === 'A') 
   parentElem.setAttribute("href", "javascript:void(0)");
 }
};