Abstract The problem of prediction of in-situ pore pressure (ahead of the bit), on the basis of seismic data, has had a long history of study. It was recognized early that low seismic velocity in a given interval can be caused by high pore pressure in that interval. However, low velocity can also be caused by high porosity, soft lithology, or hydrocarbons, the occurrence of which may be correlated in-situ with high pore pressure. Hence the deduction of pore pressure from seismic information is formally non-unique. Commonly used prediction techniques empirically fit some equation to a shallow "normally pressured" interval, then extrapolate to greater depths, comparing the observed interval velocity to this reference, independently at each depth point. Such a "point algorithm" reflects a physicist's view of the earth's layers as being independent, like samples in a laboratory. Instead, we adapt a geophysical view, regarding the various layers as being coupled through geological proc-esses, in ways which we partially understand. Hence our prediction for the pore pressure in a given layer depends upon data from shallower layers as well. As a "global algorithm", it is embodied in a decision tree, rather than an equation. Since it is different in kind from other algorithms, it can offer independent corroboration of, or alternatives to their predictions. Using uphole VSP data acquired during drilling, it can refine its surface-seismic-based predictions below the bit. It can incorporate a priori information of any sort to condition its predictions. Its predictions lead naturally to the delineation of "subsurface fluid compartments", ie zones several thousand feet thick, each with a local hydrostatic gradient and an elevated hydraulic head, separated by thin seals, with horizontal extents of several km to hundreds of km. Worldwide applications show that its predictions can be useful for prospect evaluation as well as for drilling safety and efficiency.