In reflection seismology, we create a source with an airgun and then use receivers to register acoustic waves (an approximation) at the surface. From these measurements, we can predict a velocity field $c=c(x)$. This can be seen in the figure below taken from a research group Karlsruhe Institute of Technology at this link.
The 2D model pictured here shows (the red, yellow, and black colorbar) shows a model of P-wave velocity. This picture shows you the geometry of material interfaces of the subsurface. However, it does not directly tell you anything directly about rock composition. Table 5.4a at this link suggests that it would be hard to tell the difference between limestone and sandstone at 30% porosity. This would make predicting a P-wave velocity field possibly less useful than a direct map of the rock type.
Motivated by the discussion above, my questions are below.
(1) Is rock type not that important and geometry all that matters for the purpose of exploration geophysics? For reservoir modeling, is knowing the rock type important?
(2) If I get a core out of just one spot and map rock type with depth, can I then infer rock type over the whole field? For example, in this image, if I saw the black part correlates with, say, limestone, can I just blindly say "okay everywhere else in this image where I see black is probably limestone" (of course, this may lead to errors but seems a reasonable approach to me)?
(3) If I am able to extract a porosity, permeability field, an S-wave velocity field, and possibly many other fields, can I infer the rock type or at least, decrease my uncertainty in predicting rock type?
(4) In light of (1)-(3), I imagine that on large projects, geophysicists give their images to people more experienced with stratigraphy and the like. What kinds of questions can geophysicists answered with reasonable confidence? What kinds of questions can stratigraphers answer with/without given images from a geophysicist?
NOTE: I identify as an applied mathematician, so feel free to over-explain any geology.