b'Coping with ambiguityFeaturewith a quite different problem: he/she has the Effect (the data) and needs to know the Cause (the model that has given rise to the observed effect) in order to design a drill test. This apparent need to reverse the arrow of causality is problematic because there are always infinitely many models that can simulate any given data set (as illustrated in Figure 1), and, to offer one model as an explanation for an anomaly rather than another which may simulate the data equally well or even better, is itself an act of interpretation (and, potentially, subject to the interpreters biases). Interpreters are encouraged to advise their readers of this difficulty in order to help appraise risk (and, perhaps, in the hope of receiving condolences rather than aspersions when an interpretation proves unhelpful). It might therefore seem quite wonderful that, that with the odds of infinity-to-one against selecting the correct model, we come as close as we do (to providing useful results) as often as we do.A world in which the arrow of causality is, or seems, reversed is referred to by philosophers as teleological. For this word, both my Oxford and Webster speak unhelpfully of the religious doctrine of predestination; however, Russell (2000, p84) provides an everyday example by posing the question, Why does the baker make bread?, and answers it with, Because people will be hungry (my italics). The Effect (making bread) precedes the Cause (future hungry people). It is interesting to note that in a teleological world, going from Effect to Cause the baker can proceed in infinitely many ways, and how he/Figure 4.Bouguer gravity map. Map area 850 x 975 m. Contour interval 0.2she goes about it may well affect the result. When looking back mGal. Correction density 2.67 gm/cc. (retrograde in time) from Cause to Effect there can, however, My interpretation relied on the responses of simple shapes asbe only one correct history of the way in which past events described by Nettleton (1940), and I soon satisfied myself fromunfolded. Uniqueness in going from Cause to Effect, be the the shapes of the curves that the source of the ovoid anomaliesrelationship mechanistic or teleological, may not be a universal was more in the nature of a sphere than a vertical cylinderrequirement, but it seems no less important than allowing us to with large depth extent. Both magnetic and gravity contoursmake sense of the world around us. It may be going too far to seem elongated slightly in the NNE direction, so I appliedsuggest it as a precondition for the evolution of intelligent life, Nettletons analysis to lines of data that were parallel and thenbut this would at least be consistent with Hawking (1988, Ch 9), perpendicular to the direction of elongation and came up withwhose sophisticated argument embraces scales ranging from an average depth to centre of 900 m, but the sphere diameterquantum to cosmological.remained unknown and so, too, the depth to the top. The world for the geophysical data interpreter is closer to teleological than mechanistic, and, to seek the physical model Modelling vs. interpretation that best describes what we want to know of our study area is akin to the baker trying to make the best possible bread.Defining the density structure under a local area of the earth and calculating the gravity field that would be measured atAn ancient examplethe surface has been possible since the time of Newton (1642 - 1727)at least for simple shapes like spheres and cylindersIts not just geophysical data that can be ambiguous. Historians even though there may have been little need to do so. Sincereport that an Alexandrian Greek called Eratosthenes (c.276 Newton, other more complicated physical processes like194 BCE) knew that at noon on a certain day when the sun magnetism (magnetostatics) have succumbed to theoreticalshone directly into a well in Upper (southern) Egypt, an obelisk analysis making possible what we now call forward modelling.in Lower Egypt cast a shadow, and, that he used the inherent Significant progress with even more complicated processesparallax to correctly calculate the diameter of the Earth and like electromagnetism was made by Maxwell (1831 - 1879) andprove it to be a sphere. The geometry is shown (not to scale) others before and after him; however, the solution of manyin Figure 5a, but a glance at Figure 5b shows that proof can be practical problems had to wait for the advent of the digitalelusive. Historians seem not to report, or not to have noticed, age, and today EM remains an important field of study. It isthat Eratosthenes data was ambiguous and that he might noted that in defining a model and calculating its response,just as well have been calculating the distance of a burning there can be only one correct answer in the forward modellingrock in the sky above a flat Earth (and if truth were established of any of the physical processes. A world where Cause (theby democratic consensus, the Earth, in ancient times, would model) precedes Effect (the calculated response) is one thatcertainly have been flat).philosophers refer to as mechanistic.Figures 5a and 5b can now be seen as the end members of a While the development of forward modelling algorithms is anrange of infinitely many solutions, all permitted by the data, important endeavour, it is necessarily confined to theoreticianswhich combine different values of sun distance and earth familiar with mathematical aspects of the relevant theories. Adiameter. Eratosthenes could not have known that the suns practicing exploration geophysicist, by contrast, is confrontedrays are essentially parallel, so the truth that came out of his DECEMBER 2022 PREVIEW 46'