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.     

New techniques for the analysis of earthquake sources from local array data with an application to the 1993 Scotts Mills, Oregon, aftershock sequence

We analysed aftershocks recorded by a temporary digital seismic network following the moderate M _w = 5.5 1993, Scotts Mills, Oregon, earthquake. A technique to retrieve source moment tensors from local waveforms was developed, tested, and applied to 41 small earthquakes ( M _w ranging from 1.6 to 3.2). The derived focal mechanisms, although well resolved, are highly variable and do not share a common nodal plane. In contrast, the majority of the events, relocated with a joint hypocentre determination algorithm, collapse to a well-focused plane. The incompatibility of the nodal planes of most events with the plane defined by their locations suggests that the aftershocks did not occur on the fault plane, but tightly around it, outlining the rupture area rather than defining it. Furthermore, the moment tensors reveal stable P -axes, whereas T  -axes plunges are highly dispersed. We detect a rotation of average T  -axis plunge with depth, indicating a change from shallower, predominantly dip-slip mechanisms to deeper strike-slip mechanisms. These characteristics are difficult to explain by remnant stress concentrations on the main-shock rupture plane or asperity- and barrier-type models. We suggest that the aftershocks occurred under the ambient regional stress, triggered by a sudden weakening of the region surrounding the main-shock slip, rather than from a shear stress increase due to the main shock.     

Vertical profile of effective turbidity reconstructed from broadening of incoherent body-wave pulses—I. General approach and the inversion procedure

A method is developed for the reconstruction of a non-uniform distribution of scattering properties in the upper layers of the Earth using data on broadening of an incoherent body-wave group or pulse along a number of rays. The theoretical basis for this reconstruction is a linear integral formula after Bocharov (1985, 1988), which is employed to design a linear inversion procedure. The inversion is performed in terms of a single scalar parameter of effective turbidity. This parameter presents an adequate generalization of the common turbidity parameter used in the isotropic scattering case; it describes, simultaneously, scattering attenuation, pulse broadening and backscattering or coda formation. As a preliminary step, necessary conditions of applicability of the transport equation approach for the analysis of regional high-frequency seismic waves are verified. A new compact derivation of Bocharov's formula is then presented. A linear least-squares inversion procedure for recovering a layered turbidity structure is proposed and tested on synthetic data of onset-to-peak delays of incoherent body-wave pulses. A few practical aspects of the application of the general approach to seismological data are analysed, including the correctness of the low-angle approximation, the use of peak delay observations instead of pulse centroid, the effects of a realistic spatial spectrum of inhomogeneity field, the potential bias produced by intrinsic loss, and the distortions produced by a non-spherical (double dipole) source radiation pattern. The latter point is considered as critically important, as one can expect significant data contamination by nodal arrivals. An efficient robust estimation procedure is designed and tested that is capable of suppressing distortions from nodal and near-nodal data.     

A definitive model of the geomagnetic field and its secular variation for 1965 — I. Derivation of model and comparison with the IGRF

Summary. Using a very large body of post-1955 data, a spherical harmonic model of the geomagnetic field and its secular variation is derived for 1965.0. This model is compared with the original International Geomagnetic Reference Field (IGRF) and with individual models used, or proposed for use, in producing the IGRF. Positions of the dip-poles, the geomagnetic poles and the eccentric dipole are derived from the model, together with their rates of change, and comparisons are made with other estimates of these positions.