Book Review: Basic Wave Analysis

Illustrious geophysicist Enders A Robinson*’s new book Basic Wave Analysis** (BWA) sets out to explain the fundamentals of computer processing in exploration geophysics. After reading the introduction we imagined an exchange between the authors and their editor who asks why there is no mention of big data, artificial intelligence and machine learning. BWA’s introduction is an impassioned answer to our imagined query, and its content an erudite exposé of centuries of‘prior art’.

In the introduction, BWA imagines the task of writing a full waveform inversion (FWI) code. Forget about AI and machine learning. The person must depend upon their own intellect, not upon AI. As a prerequisite, the person would have to be well versed in geophysical theory conveyed by books and journals. Since the 1950s, geophysics has seen major advances from the use of computers. None of these major advances have been the result of machine learning. All of the existing codes have been written by geophysicists. BWA sees a decidedly bleak future for a world dominated by AI where ‘inventive science would disappear’. There may be a time while ‘vast computational algorithms do whatever you like’, but sooner or later ‘something would break down and no one will be able to fix it’. Geophysicists need to learn the basics of computer programs so that geophysical tools, talents and geological models continue to be refined, leveraging increasingly powerful computing.

BWA distinguishes itself from other texts by ‘reminding the reader of our pioneering ancestors of scientific research’. The text is peppered with historical backgrounders to theory with reference to Gauss, Huygens, Leibniz, Newton and many others. Vignettes of the scientific greats introduce elements of wave theory. While not exactly a history of science textbook, BWA provides plenty of pointers to where an inquisitive reader might look for more. BWA closes the circle on the history of science and computing with the observation that today, ‘the bounty of data resources and computing facilities is beyond anything that could have been imagined a few years ago’. As Gauss observed, ‘it is not knowledge but the act of learning, and not possession but the act of getting there, which grants the greatest enjoyment’.

So is BWA enjoyable? Its three parts (of increasing difficulty) address velocity, raypath and wavefront analysis. We have only dipped our toes into the 400-page work but found this rewarding from the broad historical narrative. For instance, a discussion of velocity analysis starts with an account of the impact of the Lisbon earthquake of 1755 that ‘heightened the debate between intellectuals of the age on their views of reason and religion’, and goes on to compare Leibniz’ and Voltaire’s views of the world and of religion that introduced the age of enlightenment. All in the context of an intriguing story of 18th Century science and experimental investigations of isostasy. There is some serious erudition here combined with an entertaining writing style and some fascinating commentary. For instance, Alexander Pope in hisEssay on Criticism (1711) ‘effectively describes the objective function’ in a short poem.

So yes, BWA is immensely enjoyable, but how does it perform as a textbook. Here, our opinion was colored by a recent blog posing from Mat Hall on ‘illuminated equations’ which makes BWA (and perhaps all textbooks) look a bit dowdy. There are some inconsistent levels of explanation. The ‘phasor’ is dumped in as a formula without explanation. This contrasts with Wikipedia’s more complete coverage and elegant graphics. Sometimes the commentary veers into the far side as when a discussion of dimensionality extends to Einstein’s four-dimensional spacetime and the possibility of ‘more than four dimensions of spacetime, string, bosonic and superstring theories’. The discussion comes back down to earth with the observation that geophysics does not generally extend beyond classical physics and itself ‘has enough complications to satisfy the enquiring mind’. But for the key topics, such as full waveform inversion, the explanation of both the science and the math is accessible. BWA takes its time with its expositions.

BWA is replete with historical allusions and sometimes reads like a life of the scientific and geophysical saints. Fermat, Huygens, Morse, Fessenden, von Mintrop … all names to conjure with. BWA provides historical chapter and verse of the early days of geophysics including some background of geophysical contracting companies (deGolyer, Karcher ..). Dirac gets a section but curiously, poor old Joseph Fourier escapes treatment, an oversight that is compensated by the copious (67) references to Fourier math. BWA, is a great addition to the geophysical literature, complementing Geophysics in the Affairs of Mankind that we reviewed back in 2001.

* More on Robinson on the excellent Engineering and Technology History Wiki.

** With co-author Tijmen Jan Moser. SEG Geophysical Monograph Series N° 24, an SEG/EAGE Co-Production. ISBN 978-1-56080-372-0. Available from the Society of Exploration Geophysicists: $106.00 (list); $59.00 (members).

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