18-Geol-A7 Applied Geophysics · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2018 — 18-Geol-A7 Applied Geophysics. Three-hour, closed-book exam; approved Casio or Sharp calculator permitted. The paper offers a choice of six of the following ten questions, each worth 16.66% of the total mark, and every question requires an essay-format answer — this is a genuinely all-essay sitting with no numeric data, formula sheet, or figure supplied in the source. All ten questions are answered below so the set stands as a complete study resource for choose-N-of-M exams.
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics (2nd ed.) — the primary reference for every method touched in this paper (electrical/EM methods, seismic refraction/reflection, radiometrics, magnetics, gravity, well logging); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration (3rd ed.) — survey design, array geometry, data acquisition and processing; Blakely, Potential Theory in Gravity and Magnetic Applications — magnetic-mineral behaviour and gravity reduction (Q5, Q7); Selley & Sonnenberg, Elements of Petroleum Geology — well-logging tool context (Q8).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Three ordered-magnetism types. All three arise from strong quantum-mechanical (exchange) coupling between neighbouring atomic magnetic moments in a crystal lattice, but differ in how those moments align. In ferromagnetism, all neighbouring moments align parallel, producing a large net spontaneous magnetization even with no applied field; pure metallic iron and nickel are the classic examples, but pure ferromagnetism is rare among natural rock-forming minerals. In antiferromagnetism, neighbouring moments align antiparallel in two sublattices of exactly equal magnitude, which cancel completely — the mineral has essentially zero net magnetization; ilmenite and the low-temperature form of hematite are geological examples. In ferrimagnetism, neighbouring moments again align antiparallel in two sublattices, but the sublattices are of unequal magnitude, so they do not fully cancel and a substantial net magnetization remains — magnetite (Fe$_3$O$_4$), by far the dominant magnetic mineral in most rocks, and pyrrhotite are ferrimagnetic. In everyday geophysical usage, "ferromagnetic" is often used loosely to describe magnetite-bearing rocks, but strictly their behaviour is ferrimagnetic.
Induced vs. remanent magnetization. Induced magnetization $M_i=\kappa H$ is proportional to, and aligned parallel with, the Earth's present-day field $H$; it vanishes if the field is removed. Remanent magnetization $J_r$ is a permanent magnetization locked into the rock at the time it formed — thermoremanent magnetization (TRM) as an igneous rock cools through its Curie temperature in the ambient field, detrital remanent magnetization (DRM) as magnetic grains settle and align in sediment, or chemical remanent magnetization (CRM) as new magnetic minerals grow during alteration — and it persists independently of, and can point in a completely different direction from, today's field.
Quantifying the relative sizes: the Koenigsberger ratio. Geophysicists compare the two via
$$Q_n=\dfrac{J_r}{\kappa H}$$
the ratio of remanent to induced magnetization in the present field. $Q_n<1$ means induced magnetization dominates the rock's total response; $Q_n>1$ (common in strongly-TRM'd basalts, and in many massive sulphide bodies) means remanence dominates.
Dealing with remanence in interpretation and modelling. Several strategies are used, in increasing order of rigour. (1) In low-$Q_n$ terrain, remanence is simply neglected and the anomaly is forward-modelled/inverted using susceptibility alone. (2) Where paleomagnetic or drill-core remanence measurements exist for the target rock unit, the known remanent vector (magnitude and direction) is added to the induced vector and both are included explicitly in the forward model. (3) Where no direct measurement is available, the total magnetization direction can itself be treated as an unknown and solved for as part of the inversion (e.g. amplitude/analytic-signal inversion methods, which are constructed to be largely insensitive to the magnetization direction and so remain valid whether the anomaly is induced-, remanent- or mixed-source). (4) At minimum, an anomaly whose observed shape and polarity are inconsistent with a purely induced-source model at the survey's magnetic latitude should be flagged as a probable remanence indicator rather than forced into an induced-only fit.
Example. Basalt flows and mafic dykes that cooled during a geomagnetic reversal carry a strong reversed TRM, and pyrrhotite-rich massive sulphide bodies can carry strong remanence in a direction unrelated to today's field; a magnetic survey over such a body can show an anomaly with a low or even negative (reversed-polarity) peak, or an anomaly displaced laterally from the true body location, that a purely induced-source model at the site's actual magnetic latitude cannot reproduce — a clear field signature that remanent magnetization, not induced magnetization alone, is controlling the response.
