An equivalent source procedure is derived for upward continuation of unevenly spaced gravity and magnetic data. The dipole layer is placed on a topographic relief approximated by a polyhedral surface, the stations being the vertices of the triangular faces. The dipoles have linear magnitudes, being directed along the normal vector over each triangle. The unknown values of the dipole magnitudes at each station are obtained by a suitable modification of the usual integral equation considering the discontinuity of the normal vector at each vertex of the dipole surface. Profile data processing is also studied. A numerical test outlines the accuracy and the limitations of the model for the case of a magnetic field significantly perturbed by a rough topographic relief.
We assembled a database consisting of 5,404 PKIKP/PKiKP observations from 555 events, where PKIKP is the phase sampling the inner core (IC) and PKiKP is the phase reflected at the inner core boundary (ICB). Around 138° distances, their differential arrival times and amplitude ratio are mostly sensitive to the seismic velocity and attenuation structure in the uppermost IC (UIC), respectively. Our observations do not support a large-scale anisotropy in the UIC, but do not exclude its presence in some restricted areas. A robust inversion for the isotropic P-wave velocity perturbations shows a higher velocity cap with a radius of ~60°, approximately centered beneath the Northern Sumatra, with a local low velocity zone beneath the central Indian Ocean. The rest of the UIC, including the Northern part of Eurasia and of the Atlantic Ocean, exhibits mostly lower velocity. Amplitude ratio values of PKIKIP/PKiKP (observed vs. computed) from 548 high signal-to-noise (>5) recordings show a large variance, suggesting only a faint correlation between higher velocity and lower attenuation in the UIC. Our results provide better constraints to the models invoking a heat transfer in the UIC, with a complex temperature pattern near ICB.
S U M M A R YQ P factor at the top of the inner core (IC) is derived using the amplitude spectral ratio (PKPbc versus PKPdf) method applied to the waveforms of suitable, strong (magnitude >6.0) intermediate depth and deep (h > 150 km) earthquakes recorded at some selected South American stations. In most cases, the sampled volume of the IC is centred beneath the Pacific Ocean, but some Q P values correspond to volumes under South Africa and under Northern Atlantic. The obtained value of Q P is 323 ± 16 (at 95 per cent confidence level), close to a normal (Gaussian) distribution. The maximum depth of penetration of the PKPdf phase into the IC is roughly 333 km, suggesting a possible increase of Q P with depth, although the large scatter in data prevents a definite conclusion. As regards the geographical patterns no variation was observed.
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