Traveltime computation is an important part of seismic imaging algorithms. Conventional implementations of Kirchhoff migration require precomputing traveltime tables or include traveltime calculation in the innermost computational loop . The cost of traveltime computations is especially noticeable in the case of 3-D prestack imaging where the input data size increases the level of nesting in co...

Traveltime computation is an important part of seismic imaging algorithms. Conventional implementations of Kirchhoff migration require precomputing traveltime tables or include traveltime calculation in the innermost computational loop . The cost of traveltime computations is especially noticeable in the case of 3-D prestack imaging where the input data size increases the level of nesting in co...

In this note, we explain how to model (ir)reducibility of rewriting on ground terms using (dis)equational constraints. We show in particular that innermost (ir)reducibility can be modeled with a particular narrowing relation and that (dis)equational constraints are issued from the most general unifiers of this narrowing relation.