Linear programming approach to moment tensor inversion of earthquake sources and some tests on the three-dimensional structure of the upper mantle

Summary. A new method of moment tensor inversion is developed, which combines surface wave data and P -wave first motion data in a linear programming approach. Once surface wave spectra and first motion data are given, the method automatically obtains the solution that satisfies first motion data and minimizes the L1 norm of the surface wave spectra. We show the results of eight events in which the method works and is stable even for shallow events. We also show one event in which surface wave data and P -wave first motion data seem to be incompatible. In such cases, our method does not converge or converges to a solution which has a large minor (second) double couple component. It is an advantage that the method can determine the compatibility of two data sets without trial and error.
Laterally heterogeneous phase velocity corrections are used to obtain spectra at the source. The method is also applied to invert moment tensors of eight events in two recent three-dimensional (3-D) upper mantle structures. In both 3-D models, variances of spectra are smaller than those in a laterally homogeneous model at 256 s. Statistical tests show that those reductions are significant at a high confidence level for five events out of eight examined. For three events, we examined those reductions at shorter periods, 197 and 151 s. The reduction of variances is comparable to the results at 256 s and is again statistically significant at a high confidence level. Orientation of fault planes does not change very much by incorporation of lateral variations of phase velocity or by doing inversions at different periods. This is mainly because of the constraints from P -wave first motion data. Scatter of phase spectra at shorter periods, especially at 151 s, is great and suggests that surface wave ray paths deviate from great circle paths substantially and these effects cannot be ignored.     

A detailed analysis of the February 1996 aftershock sequence in the eastern Pyrenees, France

Following the 1996 February 18 M _L = 5.2 earthquake in the Agly massif in the eastern French Pyrenees, we installed a temporary network of seismometers around the epicentre. In this paper, we analyse 336 well-located aftershocks recorded from February 19 to February 23 by 18 temporary stations and two permanent stations located less than 35  km from the epicentre. Most aftershocks have been located with an accuracy better than 1.5  km in both horizontal and vertical positions. Their spatial distribution suggests the reactivation of a known fault system. We determined 39 fault-plane solutions using P -wave first motions. Despite their diversity, the focal mechanisms yield an E–W subhorizontal T-axis. We also determined fault-plane solutions and principal stress axes using the method developed by Rivera & Cisternas (1990 ) for the 15 best-recorded events. We obtain a pure-shear-rupture tectonic regime under N–S subhorizontal compression and E–W subhorizontal extension. These principal stress axes, which explain the focal mechanisms for at least 75 per cent of the 39 aftershocks, are different from the axes deduced from the main shock. The post-earthquake stress field caused by the main-shock rupture, modelled as sinistral strike slip on three vertical fault segments, is computed for various orientations and magnitudes of the regional stress field, assumed to be horizontal. The aftershock distribution is best explained for a compressive stress field oriented N30°E. Most aftershocks concentrate where the Coulomb failure stress change increases by more than 0.2  MPa. The diversity of aftershock focal mechanisms, poorly explained by this model, may reflect the great diversity in the orientations of pre-existing fractures in the Agly massif.     

Fully normalized spherical cap harmonics: application to the analysis of sea-level data from TOPEX/POSEIDON and ERS-1

We introduce two sets of fully normalized harmonics for the spectral analysis of functions defined on a spherical cap. The harmonics are the products of Fourier functions and the fully normalized associated Legendre functions of non-integer degree. Using Sturm-Liouville theory for boundary-value problems, we present two convenient and stable formulae for computing the zeros of the associated Legendre functions that form two sets of orthogonal functions. Formulae for the stable numerical evaluation of the fully normalized associated Legendre functions of non-integer degree that avoid the gamma function are also derived. The result from the expansions of sea-level anomaly from altimetry into Set 2 fully normalized cap harmonics shows fast convergence of the series, and the degree variances decay rapidly without aliasing effects. The zero-degree coefficients (Set 2) of sea-level anomaly from TOPEX/ POSEIDON (T/P) and ERS-1 indicate an El Niño event during 1993 January-1993 July, and a La Niño event during 1993 November-1994 July, although the ERS-1 result is less obvious. Ocean circulations over the South China Sea and the Kuroshio area are clearly identified with the low-degree expansions of sea-surface topography (SST) from T/P and ERS-1. A cold-core eddy of 4° in diameter centred at 17.5°N, 118 E was detected with the expansion of SST from T/P cycle 47, and a property of the cap harmonics is used to compute this eddy's kinetic energy. The kinetic energy is at a low in winter and high in summer, and its variation seems to be periodic with an amplitude of 0.4 m² S^-2.