RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 8, ES1002, doi:10.2205/2005ES000185, 2006

Appendix A

[101]  The algorithm of recalculating the paleomagnetic poles (obtained initially using the GAD hypothesis) proceeding from the assumption of the contribution of the non-dipole components G2 and G3 to the geomagnetic field.

[102]  Given: ( j, l ) are the latitude and longitude of the site where paleomagnetic samples were collected; ( F, L ) denote the latitude and the longitude of the paleomagnetic pole calculated using the dipole law; G2 and G3 are the quadrupolar and octupolar coefficients ( G2 = g02/g01; G3=g03/g01 ).

[103]  Required to find ( F32, L32 ) are the latitude and longitude of the respective paleomagnetic pole accounting for the contribution of the non-dipole components.

[104]  Solution: (1) Knowing the coordinates of the sampling site and the coordinates of the pole, we found D and I, which are the declination and inclination of the old geomagnetic field at the sampling site:

j m= arcsin[ sin(j) sin(F) + cos(j) cos(F) cos(L -l)],

j m being the paleolatitude of the sampling site

D= arccos[( sin(F) - sin(jm) sin(j))/( cos(j) cos(j m)]

I= arctan[2times tan(j m)].

[105]  (2) Using the expression

eq001.gif

where I is the inclination of the magnetic field at the site with paleolatitude j m32, we found a new paleolatitude of the sampling site j m32 taking into account the contribution of the non-dipole components.

[106]  (3) Using the conventional technique, we calculated the new coordinates of the paleomagnetic pole:

F32 = arcsin[ sin(j) sin(j m32) + cos(j) cos(j m32) cos(D)]

L32 = -b + l + p, if sin(j m32) < sin(j) sin(F32)

or

L32 = b + l, if sin(j m32) ge sin(j) sin(F32),

where

b = arcsin[ cos(j m32) sin (D)/ cos(F32)].

[107]  (4) As a result, we had the paleomagnetic pole ( F32, L32 ) calculated taking into account the geomagnetic field of the G2 and G3 non-dipole components.


RJES

Citation: Veselovskiy, R. V., and V. E. Pavlov (2006), New paleomagnetic data for the Permian-Triassic Trap rocks of Siberia and the problem of a non-dipole geomagnetic field at the Paleozoic-Mesozoic boundary, Russ. J. Earth Sci., 8, ES1002, doi:10.2205/2005ES000185.

Copyright 2006 by the Russian Journal of Earth Sciences

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