It is possible to use the waveform data not only to derive the source mechanism of an earthquake but also to establish the hypocentral coordinates of the ‘best point source’ (the centroid of the stress glut density) at a given frequency. Thus two classical problems of seismology are combined into a single procedure. Given an estimate of the origin time, epicentral coordinates and depth, an initial moment tensor is derived using one of the variations of the method described in detail by Gilbert and Dziewonski (1975). This set of parameters represents the starting values for an iterative procedure in which perturbations to the elements of the moment tensor are found simultaneously with changes in the hypocentral parameters. In general, the method is stable, and convergence rapid. Although the approach is a general one, we present it here in the context of the analysis of long‐period body wave data recorded by the instruments of the SRO and ASRO digital network. It appears that the upper magnitude limit of earthquakes that can be processed using this particular approach is between 7.5 and 8.0; the lower limit is, at this time, approximately 5.5, but it could be extended by broadening the passband of the analysis to include energy with periods shorter that 45 s. As there are hundreds of earthquakes each year with magnitudes exceeding 5.5, the seismic source mechanism can now be studied in detail not only for major events but also, for example, for aftershock series. We have investigated the foreshock and several aftershocks of the Sumba earthquake of August 19, 1977; the results show temporal variation of the stress regime in the fault area of the main shock. An area some 150 km to the northwest of the epicenter of the main event became seismically active 49 days later. The sense of the strike‐slip mechanism of these events is consistent with the relaxation of the compressive stress in the plate north of the Java trench. Another geophysically interesting result of our analysis is that for 5 out of 11 earthquakes of intermediate and great depth the intermediate principal value of the moment tensor is significant, while for the remaining 6 it is essentially zero, which means that their mechanisms are consistent with a simple double‐couple representation. There is clear distinction between these two groups of earthquakes.

S U M M A R YWe have developed model S40RTS of shear-velocity variation in Earth's mantle using a new collection of Rayleigh wave phase velocity, teleseismic body-wave traveltime and normalmode splitting function measurements. This data set is an order of magnitude larger than used for S20RTS and includes new data types. The data are related to shear-velocity perturbations from the (anisotropic) PREM model via kernel functions and ray paths that are computed using PREM. Contributions to phase delays and traveltimes from the heterogeneous crust are estimated using model CRUST2.0. We calculate crustal traveltimes from long-period synthetic waveforms rather than using ray theory. Shear-velocity perturbations are parametrized by spherical harmonics up to degree 40 and by 21 vertical spline functions for a total of 35 301 degrees of freedom. S40RTS is characterised by 8000 resolved unknowns. Since we compute the exact inverse, it is straightforward to determine models associated with fewer or more unknowns by adjusting the model damping. S40RTS shares many characteristics with S20RTS because it is based on the same data types and similar modelling procedures. However, S40RTS shows more clearly than S20RTS the abrupt change in the pattern of shear-velocity heterogeneity across the 660-km phase transition and it presents a more complex patern of shear-velocity heterogeneity in the lower mantle. Utilities to visualise S40RTS and software to analyse the resolution of S40RTS (or models for different damping parameters) are made available.

A model of three-dimensional shear wave velocity variations in the mantle reveals a tilted low velocity anomaly extending from the core-mantle boundary (CMB) region beneath the southeastern Atlantic Ocean into the upper mantle beneath eastern Africa. This anomaly suggests that Cenozoic flood basalt volcanism in the Afar region and active rifting beneath the East African Rift is linked to an extensive thermal anomaly at the CMB more than 45 degrees away. In contrast, a low velocity anomaly beneath Iceland is confined to the upper mantle.

A method is presented for the inversion of waveform data for the three-dimensional distribution of seismic wave velocities. The method is applied to data from the global digital networks (International Deployment of Accelerometers, Global Digital Seismograph Network); the selected data set consists of some 2000 seismograms corresponding to 53 events and 870 paths. The moment tensors of the earthquakes are determined through an iterative procedure which minimizes the corrupting influence of lateral heterogeneity. A global model is constructed for shear wave velocity, expanded up to degree and order 8 in spherical harmonics, and described by a cubic polynomial in depth for the upper 670 km of the earth's mantle. Although no a priori information is incorporated, the model predictions reproduce much of what is known about the dispersion of mantle waves, for example, high phase velocities for shields, low velocities at ridges, and a strong degree 2 pattern for Rayleigh waves. Since the method makes use of complete waveforms, overtone data are also included. It is shown that the model is reproducible in that substantially the same model can be constructed from each half of the total data set considered independently. The model shows that shields and ridges are major features in the depth interval 25-250 km. The ridges of the southern Pacific and the larger shields persist to 350 km, but the SouthEast Indian Rise is underlain by a high-velocity anomaly at this depth, as is much of the Mid-Atlantic Ridge. At 450-650 km the major features are a broad region of high velocities incorporating South America, much of the South Atlantic and parts of West Africa, a broad region of low velocities in the central and eastern Pacific, high velocities in the western Pacific, and a low-velocity anomaly beneath the Red Sea and the Gulf of Aden. In the absence of a crustal correction, degrees 2 and 3 show a high positive correlation with the geoid;paradoxically, this is largely destroyed when the distribution in crustal thickness is taken into account. Spherical harmonic degrees 4-7 show a significant negative correlation. INTRODUCTIONThe aim of this study is to map the three-dimensional structure of the earth's upper mantle, using the information contained in long-period seismic recordings. The delineation of earth structure is, of course, one of the primary goals of seismology as a whole, since it is only by seismic methods that we may obtain, by more or less direct observation, information concerning local conditions deep in the earth's interior. The accumulation of digital data from the global networks, International Deployment of Accelerometers (IDA) and Global Digital Seismograph Network (GDSN), has only now made it possible to take a global perspective and to begin to construct reliable three-dimensional representations of earth structure, independently of an assumed regionalization.The data used in this study consist of seismic waveforms at periods greater than 135 s, and the technique we adopt is that of adjusting structural pa...

[1] Our understanding of large-scale mantle dynamics depends on accurate models of seismic velocity variation in the upper mantle transition zone (400-1000 km depth). With the Mode Branch Stripping technique (MBS) of van Heijst and Woodhouse [1997] it is possible to extract the dispersion characteristics of overtone surface wave signals from single source-receiver overtone waveforms. Such data provide new global transition zone constraints. We combined more than a million measurements of path-average overtone phase velocity with normal-mode splitting functions and body wave travel times to construct model S20RTSb of shear velocity heterogeneity throughout the mantle. We discuss in detail the resolution of structural heterogeneity in the transition zone. The main observations are the following: (1) Large-scale shear velocity variations (15%) in the upper 250 km of the mantle are at least 5 times larger than deeper in the mantle. Highvelocity keels of Archean cratons extend to about 200 km depth. Low velocities related to mid-ocean ridge upwelling are confined to the upper 150 km of the mantle. (2) The 220-km discontinuity in PREM cannot be reconciled with Rayleigh wave dispersion, especially in oceans. (3) The velocity below the oceanic lithosphere (350-400 km depth) is 1-1.5% lower than beneath the continental lithosphere. (4) High-velocity slabs of former oceanic lithosphere are conspicuous structures just above the 670-km discontinuity. They extend to about 1100 km depth in the South American, Indonesian, and Kermadec subduction zones, indicating that slabs penetrate through the 670-km phase transition in several subduction zones. (5) We observe lower-than-average shear velocity below the lithosphere at eight hot spots (including Hawaii, Iceland, Easter, and Afar). It is, however, difficult to accurately estimate their depth extent in the transition zone because of the limited vertical resolution.

Data from the Global Digital Seismograph Network were used to obtain ‘centroid‐moment tensor’ solutions using the method of Dziewonski et al. (1981). Results were obtained for 201 earthquakes ranging in seismic moment from 7×1023 to 3×1027 dyne‐cm. The wide dynamic range of the SRO/ASRO stations allows us to investigate, using the same algorithm, series of events among which the smallest and the largest may differ in moment by a factor as large as 1000. Among the events studied is a particularly interesting series, in January 1981, off the island of Honshu. The main shock was preceded by three foreshocks and followed by four aftershocks all falling within the range of our analysis. There is an indication that the source mechanism changes with the size of the event. Statistical analysis of the results for all earthquakes reveals that the half duration of shallow and intermediate events is approximated by 1.6×10−8 M01/3. The shifts in origin time for deep‐focus earthquakes are indicative of the general complexity of these events, which depends only weakly on the seismic moment. The extreme departures from a double couple mechanism seem to depend both on the moment and on the focal depth. While for shallow earthquakes these departures decrease, from a maximum at about 1025 dyne‐cm, with increasing moment, the reverse appears to be true with respect to deep‐focus earthquakes. Shallow earthquakes north of New Guinea and along the Solomon Islands show systematic and substantial departures from the double couple mechanism.

Travel‐time residuals of the PKIKP phase observed between 170° and 180° show an axisymmetric pattern of degree 2 with an amplitude of about 2 seconds. The effect at shorter distances is much less pronounced and the entire data set cannot be explained by a physically realistic radial distribution of (isotropic) heterogeneity. We propose that, in addition to the general (isotropic) heterogeneity, the inner core is anisotropic with cylindrical symmetry aligned with the earth's rotation axis. Average P‐velocity along this axis is about 1 percent faster than in the equatorial plane.

Previous hypotheses concerning the cause of anomalous splitting in free oscillation spectra have led to models which are difficult to accept from the physical point of view ‐ involving either substantial heterogeneity in the fluid outer core or large topographic variations in the core‐mantle boundary and the inner core boundary and heterogeneity of several percent in inner core properties. Furthermore, other seismological evidence, some of it pre‐existing and some of it very recently discovered, militates against these models. Within the framework of isotropic earth models there appears to be no acceptable explanation of the modal observations. Here we show that anisotropy in the inner core can produce an effect which is of the correct magnitude and which varies from mode to mode in approximately the observed manner. The data currently available are insufficient to objectively map the anisotropy, but the simple assumption of a constant elastic tensor which is invariant under rotations about the Earth's rotation axis (i.e. is transversely isotropic in the plane of the equator) matches well the gross features of the modal observations. This model does not entirely reconcile the modal data with traveltime observations; it is argued, however, that there exists an anisotropic model which will do so.