Besides establishing a theorem's correctness, mathematical communication serves to illustrate and motivate its application. Often, the reader of a mathematical proof may believe its soundness but studies the chain of arguments to clarify its mechanism and its implications. However in applied sciences, like geophysics, theorems are usually further supplemented by relevant applications of the derived algorithm. In complex applications, adequate examples are often considered more convincing than dogmatic proof or theory.

In his publication's Claerbout Karrenbach (1993) automates the reproduction of discrete seismic processing results using a vast array of computer and program tools. This reproducibility safeguards that no step in the data processing goes undocumented. Additionally, Claerbout's true multimedia environment allows users to change the input parameter or the code to study the algorithm's characteristics. Especially since the introduction of Xtpanel Cole and Nichols (1992), the interactivity enables the audience to learn about an algorithm heuristically by easily supplying their own test cases.

Contrary to the production of illustrating data examples, Claerbout publishes only outlines of his theorem's mathematical derivations. Most of of these theorems are easily understood, but potentially the verification of the published argument chains can be time consuming and difficult.

Previous work Abma (1992); Cook et al. (1992) suggested symbol-manipulating computer programs, like MACSYMA, Maple, Mathcad, Mathematica, or Theorist, as convenient research environment for small scientific problems.

In this appendix, I demonstrate how symbolic mathematical computer languages (SMCL) can document and reproduce mathematical discussions. Integrating mathematical derivations, they offer tools to extend Claerbout's concept of reproducibility upstream from computer algorithms.

11/17/1997