Techniques are well established for source depth and source mechanism inversion from long-period recordings for large seismic events. However, for smaller events at shorter periods, which are important in monitoring a comprehensive test-ban treaty, such inversion routines are not well developed. The primary discriminants between man-made events and earthquakes are the depth of the source and whether the source mechanism has an explosive component. For small, short period events we need to include the full set of crustal reflections near the source and receiver. For shallow events the interference between the main arrivals and surface reflections is important. The relative amplitudes of the main arrivals and the surface reflections are controlled by the source mechanism, whereas the time separation depends on the source depth and epicentral distance.
Teleseismic modelling needs to take into account the differences of structure near the source and the receiver in the upper mantle. We have therefore adopted a hybrid approach in which differing source and receiver structures are represented as horizontally stratified regions composed of uniform layers and beneath the common base of the source and receiver structures a spherical model representation of the mantle structure is employed. A slowness-frequency domain approach in terms of the reflection and transmission properties of the medium is employed because this allows for physically based approximations to the response. By this means we can generate synthetic seismograms for teleseismic arrivals (between 30 and 90) at relatively high frequencies including the direct P and S waves, their surface reflections and crustal reverberations (see fig 10). The formulation can be readily adapted to include anisotropy in the source and receiver structures.
Single slowness methods have usually been used to construct long-period synthetic seismograms at teleseismic distances. However, for higher frequencies the differences in slowness between the direct P and S waves and their surface reflections can become more important. We have implemented a method using a bundle of slownesses around the prediction of geometrical ray theory which is able to achieve good accuracy in modelling.
Figure 10: Variation in P-wave slowness-time response as a function of distance for the moment tensor source of the Derby WA event at 10 km depth, together with the associated P wave radiation pattern.
Most current methods for the analysis of seismic surface waves depend on the assumption that propagation lies along, or close to, the great-circle between source and receiver. However, for shorter period surface waves there is clear evidence of multi-pathing. Such scattered surface wave energy carries information about the nature of the 3-D velocity structure which could complement the conventional analysis. The problem is providing a satisfactory description of the complex propagation process which has to allow for both changes in the direction of propagation and possible interaction between the different surface wave modes being used to represent the surface wave train. This can be achieved by representing each modal contribution locally as a spectrum of plane waves propagating in different directions in the horizontal plane. The influence of three-dimensional structure is then included by allowing coupling between different modal branches and propagation directions which leads to a set of coupled two
This representation of the guided wave field requires the inclusion of a full set of modes, so that, even for isotropic models, both Love and Rayleigh modes appear as different polarisation states of the modal spectrum. The coupling equations describe the interaction between the different polarisations induced by the presence of the three-dimensional structure. The level of lateral variation within the three-dimensional model is not required to be small. Horizontal refraction or reflection of the surface wave field is included by allowing for transfer between modes travelling in different directions.
The coupling matrices which lie at the core of the calculation involve inter-mode and inter-angle coupling and their variation can provide significant insight into the way in which the wavefield interacts with rapid changes of structure as e.g. at the ocean-continent transition and the edge of the craton.
Comments on the maintenance of these frames to Brian Kennett:
brian@rses.anu.edu.au