Conclusions

Presently there are limits of automatic differentiation for the use in exploration geophysical problems. In order to be useful for automatic differentiation of algorithms a preprocessor has to satisfy the following 3 requirements:

1

Since seismic data usually consists of discrete numbers, the preprocessor must allow us to numerically evaluate a given function by supplying either the function or general rule for numerically differentiating the function.

2

Because many algorithms are written as a bundle of subroutine calls, the data dependency analysis must be able to differentiate the subroutines recursively.

3

Index lookup has to be recognized as a numerical function that can be differentiated. (This requirement is closely related to the first.) For example, data(it,ix) must be recognized as a discrete function d(t,x) that can be differentiated.

Preprocessors that meet these requirements would be an extremely useful tool for differentiation of algorithms in exploration geophysics. At present I am in contact with the authors of Padre2 and JAKEF discussing the implementation of the enumerated requirements.