Get JSONArray without array name?

You don't need to call json.getJSONArray() at all, because the JSON you're working with already is an array. So, don't construct an instance of JSONObject; use a JSONArray. This should suffice:

// ...
JSONArray json = new JSONArray(result);
// ...

for(int i=0;i<json.length();i++){                        
    HashMap<String, String> map = new HashMap<String, String>();    
    JSONObject e = json.getJSONObject(i);

    map.put("id",  String.valueOf(i));
    map.put("name", "Earthquake name:" + e.getString("eqid"));
    map.put("magnitude", "Magnitude: " +  e.getString("magnitude"));
    mylist.add(map);            
}

You can't use exactly the same methods as in the tutorial, because the JSON you're dealing with needs to be parsed into a JSONArray at the root, not a JSONObject.

JSONArray has a constructor which takes a String source (presumed to be an array).

So something like this

JSONArray array = new JSONArray(yourJSONArrayAsString);