Rayleigh-wave phase velocities in French Polynesia

b
Rayleigh-wave phase velocities are investigated in the period range 17–100 s by the two-station method over several paths covering most of French Polynesia. Our results confirm the validity of theoretical models obtained through regionalization of data pertaining to longer paths. They also exhibit a 2–3.5 per cent anisotropy, with the axis of maximum velocity oriented in the direction of spreading of the plate. Part of this anisotropy is, however, due to the presence of the Tuamotu archipelago; when this is removed, the remaining anisotropy (about 1.5 per cent) correlates with the present direction of spreading, indicating that a relaxation of the anisotropy has taken place since the East Pacific ridge jump. Finally, the presence of the Tuamotu Islands explains anomalous waveshapes for surface waves travelling in their vicinity, due to multipathing through their faster structure.     

Orthogonality and mean squares of the vector fields given by spherical cap harmonic potentials

It is well known that the vector fields derived from spherical harmonics are orthogonal over the sphere. It is now shown that the vector fields derived from spherical cap harmonics are orthogonal over the cap, to the same extent as the cap potentials are, and expressions are given for their mean squares.     

Post-seismic rebound of a spherical Earth: new insights from the application of the Post–Widder inversion formula

The post-seismic response of a viscoelastic Earth to a seismic dislocation can be computed analytically within the framework of normal-modes, based on the application of propagator methods. This technique, widely documented in the literature, suffers from several shortcomings; the main drawback is related to the numerical solution of the secular equation, whose degree increases linearly with the number of viscoelastic layers so that only coarse-layered models are practically solvable. Recently, a viable alternative to the standard normal-mode approach, based on the Post–Widder Laplace inversion formula, has been proposed in the realm of postglacial rebound models. The main advantage of this method is to bypass the explicit solution of the secular equation, while retaining the analytical structure of the propagator formalism. At the same time, the numerical computation is much simplified so that additional features such as linear non-Maxwell rheologies can be simply implemented. In this work, for the first time, we apply the Post–Widder Laplace inversion formula to a post-seismic rebound model. We test the method against the standard normal-mode solution and we perform various benchmarks aimed to tune the algorithm and to optimize computation performance while ensuring the stability of the solution. As an application, we address the issue of finding the minimum number of layers with distinct elastic properties needed to accurately describe the post-seismic relaxation of a realistic Earth model. Finally, we demonstrate the potentialities of our code by modelling the post-seismic relaxation after the 2004 Sumatra–Andaman earthquake comparing results based upon Maxwell and Burgers rheologies.     

Assessment of regional geomagnetic field modelling methods using a standard data set: spherical cap harmonic analysis

Various methods that take account of the potential nature of the field have been proposed for modelling geomagnetic data on a regional scale. Several of these have been applied to a standard data set based on annual mean values from observatories in Europe. Here, we examine some of the properties of spherical cap harmonic analysis when applied to this data set, and compare the quality of fit with that of the other models. It is found that, for this data set, rectangular polynomial analysis provides a compact fit to main field data, but that in most other cases, for both main field and anomaly data, spherical cap harmonic analysis provides the better fit. Although relatively insensitive to chosen cap size, spherical cap harmonic analysis deteriorates more rapidly than the other methods when the number of coefficients is reduced.