ALBERT

Notes: This paper shows how the performance of a fully non-linear earthquake location scheme can be improved by taking advantage of problem-specific information in the location procedure. The genetic algorithm is best viewed as a method of parameter space sampling that can be used for optimization problems. It has been applied successfully in regional and teleseismic earthquake location when the network geometry is favourable. However, on a series of test events with unfavourable network geometries the performance of the genetic algorithm is found to be poor.We introduce a method to separate the spatial and temporal parameters in such a way that problems related to the strong trade-off between depth and origin time are avoided. Our modified algorithm has been applied to several test events. Performance over the unmodified algorithm is improved substantially and the computational cost is reduced. The algorithm is better suited to the determination of hypocentral location whether using arrival times, array information (slowness and azimuth) or a combination of both.A second type of modification is introduced which exploits the weak correlation between the epicentral parameters and depth. This algorithm also improves performance over the standard genetic algorithm search, except in circumstances where the depth and epicentre are not weakly correlated, which occurs when the azimuthal coverage is very poor, or when azimuth and slowness information are incorporated. On a shallow nuclear explosion with only teleseismic P arrivals available, the algorithm consistently converged to a depth very close to the true depth, indicating superior depth estimation for shallow earthquake locations over the unmodified algorithm.

Notes: Earthquakes in oceanic areas are normally located using traveltime tables which are representative of continental paths, since most seismic stations lie on continents. It should therefore be possible to improve such locations by employing a set of traveltimes more appropriate to paths from oceanic events to continental stations.A comparison has therefore been made between locations for a number of oceanic events using the recent iasp91 global traveltimes and the times for the pac91 model derived from observations of events in the Pacific. Although there were often significant differences in the location estimates for the two models, these were often no larger than the shifts induced by changing the misfit criterion used for determining the location.For events in purely oceanic regions such as Tonga and the Marianas with little nearby continent, the results from the pac91 model either provided a significantly better fit to the data or produced depth estimates in close accord with independent constraints (e.g. centroid moment tensor locations). In these cases the use of a specific set of ‘oceanic’ traveltimes can be recommended. However for marginal zones and island arcs, the situation is less clear and it is probably best to employ the global traveltime set with the use of additional phases to improve depth estimates.

Notes: A large array of short-period, portable seismographs was operated in the Northern Territory of Australia for 3 months in 1986 in order to record earthquakes in the island arcs to the north and east of Australia. The array consisted of 18 digital recorders, 28 analogue tape recorders and the 20 stations of the permanent Warramunga (WRA) seismic array. An unusual aspect of this experiment was the variable station spacing and apertures of the different elements of the hybrid array. The WRA and portable digital arrays had station spacing of 2.2 km and 5–13 km, respectively, and allowed confident identification of phases returned from the upper mantle, whilst the analogue array had station spacing of 40 km and allowed us to track mantle phases across its 500 km aperture.Seismograms from 17 shallow earthquakes (mb 4.3–5.1) in the Indonesian arc are used to investigate the P-wave velocity structure of the upper mantle beneath NW Australia. We combine seismograms from these events into a composite record section covering ranges from 1000 to 2600 km. Strong phases following the first P-wave arrivals in this composite record section clearly indicate the presence of significant structure in the upper mantle. Lateral heterogeneity in the upper mantle causes the timing and amplitudes of mantle phases to vary across the array and among earthquakes. In order to minimize the effects of lateral heterogeneity, we filter and stack the data and concentrate on features in the data that are seen for many individual seismograms and for several earthquakes. We calculate WKBJ and reflectivity seismograms in order to construct a vertical velocity profile that fits the observed traveltimes and waveforms in an average sense. Our preferred model NWB-1 includes second-order velocity discontinuities of 3.7 per cent near a depth of 200 km, 6.1 per cent near 400 km and 3.7 per cent near 620 km in order to reproduce the amplitudes of the later phases. The low amplitudes of the first arrivals in the range from 1600 to 2200 km require either a low-velocity zone below 230 km depth or a low velocity gradient between 230 km and the 400 km discontinuity. Model NWB-1 is smoother than some models that have been previously proposed for this region which may have mapped lateral heterogeneity into vertical velocity profiles.

Notes: Traveltime calculations in 3-D velocity models have become more commonplace during the past decade or so. Many schemes have been developed to deal with the initial value problem, which consists of tracing rays from a known source position and trajectory usually towards some distant surface. Less attention has been given to the more difficult problem of boundary value ray tracing in 3-D. In this case, source and receiver positions are known and one, or more, minimum time paths are sought between fixed endpoints.A new technique for boundary value ray tracing is proposed. The scheme uses a common numerical integration technique for solving the initial value problem and iteratively updates the take-off angles until the ray passes through the receiver. This type of ‘shooting’ technique is made efficient by using expressions describing the geometrical spreading of the wavefront to determine the relationship between the ray position at any time and the take-off angles from the source. The use of numerical integration allows the method to be compatible with a wide variety of structures. These include models with velocity varying smoothly as a function of position and those with arbitrarily orientated surfaces of discontinuity. An examination of traveltime accuracy is given as well as a discussion of efficiency for a few classes of velocity model.To improve upon the first guess pair of take-off angles, a small-scale non-linear inverse problem must be solved. The difference between the receiver position and the arrival point of a ray, on a plane through the receiver, describe a mis-match surface as a function of the two take-off angles of the ray. The shape of this surface can possess local minima and multiple ‘global’ minima even for relatively simple 1-D velocity models. Its study provides some insight into the non-linearities of a small-scale geophysical inverse problem.

Notes: Temporary array deployments of short-period seismometers in northern Australia have been used to build up composite record sections for waves interacting with the upper mantle. Stable measures of the seismic wavefield are provided by stacking the complex envelopes of all the seismic waveforms falling in a 10km distance interval away from the source.Two groups of sources (a) along the Flores Arc, Indonesia with propagation under northwestern Australia, and (b) in New Guinea with paths to the NNE of the array, have been used to construct composite record sections for both P and SV waves over the distance range 1300–2800 km. the timing and amplitude distributions for P waves from the two regions show noticeable differences. Detailed modelling of the record sections yields velocity models with significant variation in velocity for the two sets of propagation paths for which the midpoints are separated by about 1000km.The short-period SV-wave sections indicate efficient propagation of highfrequency S waves in a lithosphere extending down to 210km. Arrivals from the deeper mantle cannot be correlated with confidence because of a loss in high-frequency content revealed by broad-band observations. This requires a significant attenuation zone for S beneath 210 km.

Notes: The effect of the free surface can be removed from three-component seismic recordings to recover the incident upgoing wavefield, if the slowness and azimuth of the current wavefront are known as a function of time. For a single three-component station it is usually possible to estimate an azimuth for an event from the first arriving P-waves, but slowness estimates are less reliable when more than one wavetype is presented in the seismic wavetrain. However, the free surface correction operators are generally slowly varying functions of slowness and so some error in slowness can be tolerated.Effective approximations for the removal of the free surface effects can be made for hard rock sites to cover slowness bands for the main regional phases Pn, Pg, Sn and Lg. By applying these operators in turn over group velocity windows appropriate to the particular phases, the relative amplitude of the P, SV and SH contributions to the wavefield can be estimated. Because the free surface amplification effects have been removed, the amplitudes can be compared directly and provide useful constraints on the radiation characteristics of the source. This procedure is therefore helpful for developing discrimination measures for different classes of sources.

Notes: For quasi-stratified media in which the principal variation in seismic properties is with depth, propagation invariants can be constructed from certain combinations of the displacement and tractions elements of two seismic wavefields. These invariants are independent of depth and vanish for identical wavefields, and are constructed for anisotropic, laterally varying media in the spatial and wavenumber domains.These propagation invariants can be exploited to substantially simplify the construction of reflection and transmission processes in laterally varying media, including coupling between wavenumbers. The implementation of this approach is illustrated by application to the incidence of SH-waves on an irregular interface below a free surface. The results are in excellent agreement with those from other schemes but take about 20 per cent less computation time. Even greater improvements in calculation speed are possible in more complex models.

Notes: Many techniques for the solution of seismic-wave propagation problems depend on the representation of the seismic wavefield in terms of a linear combination of basis functions, as for example in Fourier or Gaussian Beam expansions. A common formal representation encompasses such methods when a preferred coordinate is isolated to track the propagation path. Different techniques can be classified by the dependence of the basis functions on this preferred coordinate. The common representation provides useful insight into the relation between apparently disparate methods and can guide the development of computational techniques. This common framework allows the development of generalized propagator methods and a compact formulation of reflection and transmission problems. A general perturbation approach can be used either to add heterogeneity to an existing structure or to restore features, such as coupling between P and S waves, which have been ignored in an approximate development.

Notes: The surface wave T-matrix formulation which describes scattering from a discrete obstacle embedded in a stratified medium is extended to accommodate scattering from two or more obstacles. By exploiting the translation properties of the vector cylindrical wave functions and employing the definition of the surface wave T-matrix for a single obstacle it is possible to construct a composite T-matrix for a two-obstacle configuration in terms of the individual T-matrices. This procedure can be extended, recursively, to incorporate N obstacles. The scattered field contributions from each obstacle including the entire hierarchy of multiple scattering interactions are clearly identifiable in the resulting expression.The formulation is applied to several two-obstacle configurations over a range of ka to investigate the implications of multiple scattering interactions for regional phases such as Lg propagating in the Earth's crust and upper mantle. The results indicate that the significance of multiple scattering is dependent upon the size of the scatterers, their separation and orientation with respect to the incident wave. Multiple scattering is less pronounced for small scatterers (ka 〈 1.0) and is most significant at separations under a wavelength. For obstacles of ka∼ 1.0, pair interactions result in deviations from the zeroth-order field of less than 10 per cent in the forward scattered power. The effects of multiple scattering are limited to still smaller separations for point scatterers; however the nature of their multipole representations suggests that scattered Love waves may be generated more efficiently through pair interactions than Rayleigh waves in the low-frequency limit. Consideration of multiple scattering becomes essential as the size of the obstacle increases. Large obstacles (ka∼ 10.0) behave as lenses by focusing the majority of scattered energy along a narrow corridor about the forward direction. If two obstacles are aligned parallel to the direction of the incident wave the power in the first-order pair interaction is comparable to the total power scattered from a single obstacle for a wide range of separations.

Notes: Laterally varying interfaces cause coupling between wavenumbers so that seismograms in two-dimensionally layered media can be synthesized by means of ‘supermatrices’, which include the coupled contributions of all the wavenumbers. We introduce reflection and transmission ‘supermatrices’ in order to eliminate numerical problems arising from loss of precision for evanescent waves in the seismogram synthesis. An interface is assumed to be such that the reflected and transmitted wavefields; on its two sides can be represented as purely upgoing and downgoing waves, i.e. the Rayleigh ansatz is imposed. The computational demands of this method can be kept to a minimum by exploiting propagation invariants in the coupled wavenumber domain.The superior performance of this ‘invariant embedding’ approach when compared to propagator or finite difference schemes is illustrated by application to the response of sedimentary basins to excitation by an incident plane wave or a line force. The results are in good general agreement with the other methods, but show greater numerical stability and computational efficiency. In the case of a single interface the ‘invariant embedding’ procedure for P-SV-waves takes 45 per cent less computation time and 29 per cent less memory than the propagator method of Koketsu (1987a, b). The gains are reduced in a multilayer case because of the level of computation required to calculate the addition rules for the large reflection and transmission supermatrices.