Three sites give palaeomagnetic declinations

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

Three sites give palaeomagnetic declinations D1=350∘D_1 = 350^\circ, D2=5∘D_2 = 5^\circ and D3=10∘D_3 = 10^\circ (all measured clockwise from north, 0∘0^\circ to 360∘360^\circ). Someone argues: 'The mean declination is the arithmetic mean of the three angles, Dˉ=(350∘+5∘+10∘)/3=121.7∘\bar{D} = (350^\circ + 5^\circ + 10^\circ)/3 = 121.7^\circ.' ((a)) Find the error in this working. ((b)) Compute the correct mean declination by averaging the corresponding unit vectors, as the vector-averaging method for palaeomagnetic directions requires.

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