ALBERT

Notes: The location of seismic events can be improved if accurate picks can be assigned for later seismic phases, which requires both the detection of an arrival and the recognition of its character. Such phase identifications are particularly valuable if they can be provided in real-time as the seismic disturbance passes across a broad-band seismic recording station.A simple but promising scheme for characterizing arrivals can be constructed by analysing the energy content of the seismic trace as a function of time. Such an approach can be used to detect arrivals by using a method comparing the short-term average energy to a long-term average, with averaging windows that are adaptive to the local frequency of the seismic disturbance. The phase detector can be tuned to different classes of arrivals by utilizing three-component records. By comparing the energy on the vertical component of motion to that in the horizontal plane, it is possible to start to separate P and S arrivals. Phase assignments can be refined by the use of adaptive filtering and by including polarization information.With an estimate of the azimuth of propagation it is possible to use approximate projection methods which attempt to compensate for the influence of the free surface, since the surface corrections are not a strong function of slowness for teleseismic arrivals. By this means, an instantaneous estimate can be made of the relative contributions of P, SV and SH arrivals which can be very helpful in determining the phase assignment for a particular arrival.

Notes: New empirical traveltime curves for the major seismic phases have been derived from the catalogues of the International Seismological Centre by relocating events by using P readings, depth phases and the iasp91 traveltimes, and then re-associating phase picks. A smoothed set of traveltime tables is extracted by a robust procedure which gives estimates of the variance of the traveltimes for each phase branch. This set of smoothed empirical times is then used to construct a range of radial velocity profiles, which are assessed against a number of different measures of the level of fit between the empirical times and the predictions of the models. These measures are constructed from weighted sums of L2 misfits for individual phases. The weights are chosen to provide a measure of the probable reliability of the picks for the different phases.A preferred model, ak135, is proposed which gives a significantly better fit to a broad range of phases than is provided by the iasp91 and sp6 models. The differences in velocity between ak135 and these models are generally quite small except at the boundary of the inner core, where reduced velocity gradients are needed to achieve satisfactory performance for PKP differential time data.The potential resolution of velocity structure has been assessed with the aid of a non-linear search procedure in which 5000 models have been generated in bounds about ak135. Msfit calculations are performed for each of the phases in the empirical traveltime sets, and the models are then sorted using different overall measures of misfit. The best 100 models for each criterion are displayed in a model density plot which indicates the consistency of the different models. The interaction of information from different phases can be analysed by comparing the different misfit measures. Structure in the mantle is well resolved except at the base, and ak135 provides a good representation of core velocities.

Notes: Much modelling of the seismic wavefield is undertaken with an acoustic approximation in which the influence of shear waves is neglected. Although such calculations can predict the correct traveltimes for compressional-(P-) wave propagation, they can he very misleading with respect to the distribution of seismic amplitudes, especially at larger offsets. At the seabed, the acoustic approximation predicts total reflection for P waves incident beyond the critical angle. However, once the presence of shear waves in the solid material below the sea-floor is taken into account, P waves in the sea water incident beyond the critical angle can give rise to transmitted S waves, with a consequent major change in the propagation pattern. Such effects are very important for areas with high velocities at the sea-floor, as commonly occurs in tropical waters, such as the north-west shelf of Australia. The character of the water-borne noise in these conditions depends on whether the shear wavespeed at the seabed lies above or below the P-wave velocity in the sea water above. For high shear velocities, two distinct sets of critically reflected multiples can be produced to give a very energetic noise train trapped in the water column. Conversion of P to S in transmission at the sea-floor can often be important and give rise to significant arrivals on the outer traces from long marine cables. Further, the conversion of energy to S waves reduces the energy available for P-wave multiples and dramatically reduces the influence of waterbottom multiples compared with a purely acoustic situation. Synthetic seismogram calculations for large offsets and equivalent calculations in the slowness-times domain, with selective control of the level of multiples and conversion at each interface, provide a convenient tool for characterizing the expected water-borne energy and the influence of converted shear waves on the pressure field recorded in the water.

Notes: A number of techniques which exploit the waveforms of seismic surface waves depend on simple approximations for the character of the propagation process from source to receiver based on the representation for a stratified medium. Commonly the propagation path is assumed to lie along a great circle and to be representable by a path-averaged structure. The influence of structure near the source and near the receiver is included by using local modal formulations. However, the terms that depend on source depth and receiver depth in the stratified medium results are not purely local in character, and so care has to be taken to ensure a simple mapping between the modal shapes for the different structures.For frequencies less than 0.03 Hz, different crustal structures can be used at the source, near the receiver, and along the propagation path, provided that the change in crustal thickness is not more than 10 km between contiguous structures. Furthermore, for frequencies up to 0.035 Hz, it should be possible to use a single modal set in non-linear waveform inversions for perturbations of up to 5 per cent in lithospheric velocities along the propagation path.For propagation paths of length from 1000 to 4000 km, typical of a continental scale, the path-averaged structure approximation should be suitable for waveform fitting for frequencies in the range 0.01-0.03 Hz. The lower limit depends on the use of asymptotic approximations and the upper on the influence of heterogeneity on the modal content of the seismograms.Where surface waves cross a major structural boundary such as the continent-ocean transition, some aspects of the wavefield can still be represented using the path-averaged approximation.

Notes: The advent of broad-band seismology has meant that use is being made of a wide range of seismic phases, for many of which ellipticity corrections have not been readily available. In particular, when many seismic phases are used in location schemes, it is important that the systematic effects of ellipticity are included for each phase.An efficient and effective procedure for constructing ellipticity corrections is to make use of the ray-based approach of Dziewonksi & Gilbert (1976), as reformulated by Doornbos (1988), in conjunction with the rapid evaluation of traveltimes and slownesses for a given range using the tauspline procedure of Buland & Chapman (1983).Ellipticity coefficients have been tabulated for a wide range of seismic phases and are available in electronic form. The ellipticity correction procedures have been extended to include an allowance for diffraction phenomena, for example Pdiff, Sdiff diffracted along the core-mantle boundary. Corrections for additional phases can be generated by building the ellipticity coefficients from suitable combinations of the coefficients for different phase segments.

Notes: Reference earth models can be retrieved from either body waves or normal-mode eigenperiods. However, there is a large discrepancy between different reference earth models, which arises partly from the type of data set used in their construction and partly from differences in parametrization. Reference models derived from body-wave observations do not give access to density, attenuation factor and radial anisotropy. Conversely, reference models derived from normal modes cannot provide the correct locations for the depth of seismic discontinuities, nor the associated velocity jump. Eigenperiods derived from reference models constructed using body-wave data together with classifical attenuation models differ significantly from the observed eigenperiods.The body-wave and normal-mode approaches can be reconciled. The V' and V, velocities given by body-wave models are considered as constraints, and an inversion is performed for parameters that cannot be extracted from body waves in the context of a radially anisotropic model, i.e. the density p, the quality factor Q, and the anisotropy parameters 5, (b and q. The influence of anelasticity is very large, although insufficient by itself to reconcile the two types of model. However, by including in the inversion procedure the density and the three anisotropic parameters, body-wave models can be brought into complete agreement with eigenperiod data. A number of reference models derived from body waves were tested and used as starting models: iasp91, sp6, and two new models ak303 and ak135. A number of robust features can be extracted from the inversions based on these different models. The quality factor Q, is found to be much larger in the lower mantle than in previous models (e.g. prern). Anisotropy, in the form of transverse isotropy with a vertical symmetry axis, is significant in the whole upper mantle, but very small in the lower mantle except in the lower transition zone (between the 660 km discontinuity and 1000 km depth) and in the D'-layer. Compared with prem there is an increase of density in the D'-layer and a decrease in the lower transition zone. The attenuation estimates have been derived using velocity dispersion information, but are in agreement with available direct measurements of normal-mode attenuation. Such attenuation data are still of limited quality, and the present results emphasize the need for improved attenuation measurements.

Notes: A full treatment of topographic effects on the seismic wavefield requires a 3-D treatment of the topography and a 3-D calculation for the wavefield. However, such full 3-D calculations are still very expensive to perform. An economical approach, which does not require the same level of computational resources as full 3-D modelling, is to examine the 3-D response of a model in which the heterogeneity pattern is 2-D (the so-called 2.5-D problem). Such 2.5-D methods can calculate 3-D wavefields without huge computer memory requirements, since they require storage nearly equal to that of the corresponding 2-D calculations.In this paper, we consider wave propagation from a point source in the presence of 2-D irregular topography, and develop a computational method for such 2.5-D wave-propagation problems. This approach is an extension to the 2.5-D case of the discrete wavenumber-boundary integral equation method introduced by Bouchon (1985) and Gaffet & Bouchon (1989) to study 2-D topographic problems. One of the most significant advantages of the 2.5-D calculations is that calculations are performed for a point source and so it is possible for us to take into account the 3-D radiation pattern from the source. We demonstrate that this discrete wavenumber-boundary integral equation procedure, coupled with a Green's function decomposition into P-and S-wave contributions, provides a flexible and effective means of evaluating the wavefield.