The direction of a secondary magnetization component is found from the intersection point of converging remagnetization circles using a method based on the least-squares fitting of great circles to points on a sphere. The technique may be applied to any problem that requires the best intersection point of convergent great circles and is thus useful in other fields besides palaeomagnetism, such as structural geology, plate tectonics and astronomy.

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A palaeomagnetic pole position, derived from a precisely dated primary remanence, with minimal uncertainties due to secular variation and structural correction, has been obtained for China’s largest dyke swarm, which trends for about 1000 km in a NNW direction across the North China craton. Positive palaeomagnetic contact tests on two dykes signify that the remanent magnetization is primary and formed during initial cooling of the intrusions. The age of one of these dykes, based on U–Pb dating of primary zircon, is 1769.1 ± 2.5 Ma. The mean palaeomagnetic direction for 19 dykes, after structural correction, is D = 36°, I = − 5°, k = 63, α95 = 4°, yielding a palaeomagnetic pole at Plat=36°N, Plong=247°E, dp = 2°, dm = 4° and a palaeolatitude of 2.6°S. Comparison of this pole position with others of similar age from the Canadian Shield allows a continental reconstruction that is compatible with a more or less unchanged configuration of Laurentia, Siberia and the North China craton since about 1800 Ma

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A paleomagnetic study involving alternating field (AF) and thermal cleaning, baked contact tests, and the measurement of hysteresis and other magnetic properties has been carried out on 21 Keweenawan diabase dikes (age ~1.1 Ga) from Baraga and Marquette Counties, northern Michigan. The main results are as follows.(1) The dikes exhibit a steep, negatively inclined remanence, which is shown to be a thermoremanent magnetization (TRM) acquired parallel to the ambient field at the time of initial magma cooling.(2) A secondary component, more resistant to magnetic cleaning than the primary TRM, and with west-northwest declination and positive inclination is occasionally found in the dikes, especially those from Baraga County.(3) Despite an early pole position obtained by Graham, which suggested that the dikes in Michigan were potentially important in defining the depth of the Logan Loop, most of them, from Marquette County, yield a pole that lies on the loop's western arm. The region of the projected apex of the loop thus still remains without reliable data.(4) The pole position of the Marquette dikes (48.4°N, 213.5°E; dp = 5.2°; dm = 6.2°) obtained from 14 sites is virtually identical to that obtained from 17 reversely magnetized dikes from the Thunder Bay district in Ontario, but appears to be distinct from poles derived from other Keweenawan units. Both dike swarms are thus interpreted to represent parts of the same magmatic pulse, and one that occurred in the centre of Lake Superior during an early opening phase of the Keweenawan rift system.

Dykes often grow next to other dykes, evidenced by the widespread occurrence of dyke swarms that comprise many closely-spaced dykes. In giant dyke swarms, dykes are observed to maintain a finite spacing from their neighbors that is tens to hundreds of times smaller than their length. To date, mechanical models have not been able to clarify whether there exists an optimum, or natural spacing between the dykes. And yet, the existence of a natural spacing is at the heart of why dykes grow in swarms in the first place. Here we present and examine a mechanical model for the horizontal propagation of multiple, closely-spaced blade-like dykes in order to find energetically optimal dyke spacings associated with both constant pressure and constant * 710 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA, 15261, USA Email address: bunger@pitt.edu (Andrew P. Bunger) Preprint submitted to Earth and Planetary Science Letters May 9, 2013influx magma sources. We show that the constant pressure source leads to an optimal spacing that is equal to the height of the blade-like dykes. We also show that the constant influx source leads to two candidates for an optimal spacing, one which is expected to be around 0.3 times the dyke height and the other which is expected to be around 2.5 times the dyke height.Comparison with measurements from dyke swarms in Iceland and Canada lend initial support to our predictions, and we conclude that dyke swarms are indeed expected to have a natural spacing between first generation dykes and that this spacing scales with, and is on the order of, the height of the blade-like dykes that comprise the swarm.