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How the first-order structure of the magnetic field changed through geological time is one of the most long-living and hotly debated questions in geomagnetism. For the last 5 Ma, the geomagnetic field is found to be essentially dipolar with about 5 per cent quadrupole term and, possibly, still smaller octupole term. Proving this became possible after accumulation of a large set of globally distributed reliable palaeomagnetic data and their analysis in the coordinates tied to the rotation axis. For older times, the data are less reliable, scarce and unevenly distributed, while tectonic motions destroyed the global coordinates. In this paper, a method to determine the geomagnetic field structure for a single plate is discussed. It is suggested that the coordinate system for analysis can be derived from great circles, each being drawn through a sampling point and the corresponding palaeomagnetic pole (SP-circle). Such circles are to intersect at a true (i.e. pure dipole) pole that is largely purified from the contributions of non-dipole zonal terms and inclination shallowing. The scrutiny of late Permian (270–250 Ma) palaeomagnetic poles from Northern Eurasia revealed two distinct groups: one includes several poles from a limited area in South France (SF), and the other consists of tightly clustered nine poles from locations spread over a large part of Eurasia. Tentatively, the former group can be explained by either rotation of SF with respect to main Eurasia, or less likely, remagnetization in Early Triassic time; irrespectively, these poles cannot be used for calculation of the true dipole pole nor for computation of the apparent polar wander path of Eurasia. The poles from the main part of Eurasia were used to find the position of the true dipole pole of this plate and for analysis of the field. The minimum of residual dispersion of the observed data is found for the quadrupole and octupole terms of less than 10 per cent when each term is varied separately. When both terms are varied together, the best fit is observed for the quadrupole and octupole terms of −4 and 12 per cent, respectively. Our analysis shows that the position of the true dipole pole is robust, while the estimates of non-dipole terms are not. We argue that these estimates should be regarded as the upper limits on the non-dipole contributions to the Late Permian geomagnetic field; at the same time, we are pretty sure that octupole term of 20 per cent or more are not permitted by the data. [ABSTRACT FROM AUTHOR]

In this paper, we present inversion results for regional Pg and Sg phases for the Eurasian continent to explore its use for understanding upper crustal velocity structure. Tomographic inversion of traveltimes from first arriving compressional and shear waves for velocity structure has been applied with great success at all length scales, ranging from the laboratory bench-top to the entire Earth, while inversion of later arriving phases has been much more limited. Our inversion is performed using a damped, smoothed LSQR implementation that solves for site and event terms as well as for velocity along great circle paths between the source and receiver. Results are broadly consistent with published upper crustal velocities for Eurasia, with predominantly high velocities in cratonic regions. Generally, but not always, lower velocities are observed in orogenic and extensional areas and in deep sedimentary basins. A spot-comparison of VP/ VS from local and regional studies compares well with the ratio of observed Pg to Sg velocities from our study where resolution is high. Resolution is determined through the use of checkerboard tests, and these suggest that in regions where data density is high we can resolve features down to at least 2°, with 4° possible over broader areas. rms residual reductions are on the order of 25 per cent for Sg and 30 per cent for Pg. [ABSTRACT FROM AUTHOR]