One linguistic tool I highly appreciate is the portmanteau, where we combine two or more words to create a new word, usually with some compaction effect by removing overlapping sounds. Common portmanteau words include favourites such as guesstimate, brunch, spork, and skort. In the geoscience community, we often use “geo” in things like company names, like those who include “geoconsultants” in their company or department name, or jokes, “geofantasy”. One may consider these as simply using the prefix, “geo”, but, really, we mostly mean geoscience of one field or another.


There are times when we forget the practicalities of the problem that we are trying to solve.

There is the old joke about the cattle ranchers who asked a mathematician how many cows they can get to market using the railway. The mathematician opened his presentation with, “Consider a spherical cow.” The mathematical world is a fantasy world that we imagine so that we may simplify our calculations. Sometimes those simplifications go too far.

Other times the imaginary world of mathematics works out great. Many of the fundamentals of seismic data processing are based on assumptions that we violate constantly, yet we are somehow able to create interpretable images of subsurface structures and stratigraphic features – and, on a good day, predict lithology and presence of hydrocarbons.

Other times, these mathematical fantasies are purely that: fantasy. Elliptical anisotropy is a perfect example. The argument goes that assuming the velocity variation with respect to direction is elliptical in shape is a simplifying assumption. That logic is sound, but elliptical anisotropy does not exist in nature. To get elliptical anisotropy, Thomsen’s epsilon and delta are assumed to be equal. If epsilon and delta were equal, then Alkhalifah’s anisotropic parameter, eta, would be zero and we would never see the hockey-stick effect on NMO-corrected CMP gathers. The typical observation of the upturned hockey stick indicates positive eta, which means epsilon is greater than delta. Backus averaging of periodic thin layering will only yield values of delta less than epsilon. All of the rock physics studies that I have seen over the years, the most comprehensive of which come from Lev Vernik, show that delta is typically much smaller than epsilon in clastic rock samples. Elliptic anisotropy does not represent real rocks and it will not correct non-hyperbolic moveout, which it assumes doesn’t exist.

Orthogonal fracture sets are another fantastical phenomenon. When I asked a group of structural geologists about orthogonal fracture sets, a few squirmed and said that anything is possible. Not the answer I was seeking to justify the study of orthorhombic anisotropy. Fractures tend to be aligned at oblique angles, theoretically 60° apart and not 90°. Our other orthorhombic case, fractures orthogonal to bedding, is also uncommon, but it is more common than orthogonal fracture sets. Those of us seeking an exploration application of orthorhombic anisotropy may be limited to horizontal layers with a dominant horizontal stress direction, like in Wyoming, where azimuthal moveout is observed.

The two criteria for separating mathematics from mathemythology are: (1) do we see our assumption in the real world; and (2) can our assumption, though flawed, still solve a measurable problem?


I recently heard this word while teaching a course. It is certainly important to understand the structure and processes involved in reef building, but some may interpret a week of snorkelling the Caribbean to be more like a holiday than a rigorous work week. When I have been on field courses where there is hiking or snorkelling all day, then noting, drawing, and mapping in the evening, it surely doesn’t feel like a vacation. It can be an adventure and a lot of fun, but those characteristics don’t diminish the productivity, learning opportunity, or the challenges both mentally and physically. Some of the camaraderie and adventure aspects of field courses and field mapping will also increase the engagement of the geoscientist and increase the effectiveness of the study.

Sometimes management concerns about the geoliday can limit the effectiveness of resource exploration, due to insufficient field work. One interpreting geophysicist told me about working fourteen hour days, measuring fractures and dips in 40° heat during daylight hours and making maps after dark. Her frustration was that management felt that this wasn’t real work, yet sitting in her comfy chair in an air conditioned office was somehow ‘real work’.



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