For all the non-philosophers reading this post, we define theory as a set of mathematical principles on which an activity is based. The set of principles that underlie the study of geophysics is that radio waves and sound waves for instance have different levels of penetration. When a sound wave is reflected it can tell us the density and depth of an object, like a rock. These principles are based on physics, and not on the actual program that models the depth and density of rock. Doing that would be putting the cart before the horse. If we change the way we model the results of our acoustic test, we do not change the underlying principles of physics.
A method is a procedure to accomplish something. Methods are generally activities that can be done by pen and paper (although sometimes they are easier when automated) in which we determine the steps, for instance, to find out how to tell what is beneath a particular surface. The implementation is the tool that is used to do implement the method. This is usually as a computer algorithm. So, an algorithm is a tool that is based on a method that is underpinned by a theory. Seems simple enough, but this is often misinterpreted.
