Four lava flows at a single site give the following mean directions (declination…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch The geomagnetic field: potential, spectrum, induction and the palaeomagnetic record

Problem

Four lava flows at a single site give the following mean directions (declination DD measured clockwise from north, inclination ImagI_{\rm mag} positive downward). Data: flow 1, D=10.0∘D=10.0^\circ, Imag=55.0∘I_{\rm mag}=55.0^\circ; flow 2, D=20.0∘D=20.0^\circ, Imag=60.0∘I_{\rm mag}=60.0^\circ; flow 3, D=0.0∘D=0.0^\circ, Imag=58.0∘I_{\rm mag}=58.0^\circ; flow 4, D=15.0∘D=15.0^\circ, Imag=62.0∘I_{\rm mag}=62.0^\circ. ((a)) Add the four directions as unit vectors to find the resultant length RR, the Fisher precision parameter k=(N−1)/(N−R)k = (N-1)/(N-R), and the semi-angle of the 95%95\% cone of confidence α95≈140∘/Nk\alpha_{95} \approx 140^\circ/\sqrt{Nk}. ((b)) Give the mean declination Dˉ\bar D and mean inclination Iˉ\bar I. ((c)) The site is at latitude 55.0∘ N55.0^\circ\,\mathrm{N}. Reduce the mean direction to a virtual geomagnetic pole: state its latitude and its longitude measured east of the site's longitude, choosing the correct branch of the longitude formula.

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