ALBERT

Notes: Many methods for the analysis of long-period and broad-band S-waveforms depend on a representation of the seismic wavefield in terms of a sum of modes of a reference structure. In addition it is frequently assumed that the propagation of the modal contributions from source to receiver may be regarded as independent. This assumption may not be warranted if there is significant heterogeneity in seismic properties along the propagation path.The interaction between modal components in different styles of heterogeneity model for the upper mantle is examined using a coupled mode propagation technique (Kennett 1984) which allows direct construction of reflection and transmission matrices with full allowance for intermode interactions for 2-D heterogeneity structures.The first type of structure considered has been proposed to explain amplitude and traveltime anomalies in body wave studies of upper mantle phases. This heterogeneity has an amplitude of about 1 per cent and is distributed with a horizontal scale of around 300-400km and a vertical scale which increases from 70km in the uppermost mantle to 200 km at 900 km depth. Horizontally travelling S-waves are hardly affected by this class of heterogeneity for frequencies less than 0.07 Hz.The second heterogeneity model was based on the WEPL3 model proposed by Nolet (1990) from waveform inversion for the structure under the NARS array in western Europe. The heterogeneity reaches 5 per cent deviation from the reference model PREMC in organized regions 700 km or more in length. For this structure surface wave modes with group velocity below 4.2kms-’ can be regarded as propagating independently up to 0.020Hz. The body wave group of modes with higher group velocity succumbs to significant interaction above 0.040 Hz. The frequency limit for largely independent propagation for the body wave group of modes can be extended to about 0.05 Hz for a velocity model with up to 1 per cent additional variability superimposed on WEPL3. Such a composite heterogeneity model would be consistent with both body wave and surface wave behaviour.The errors introduced into the analysis methods by ignoring mode interactions above these frequency limits will depend on the distribution of energy across the modes imposed by the source, and the criterion used for waveform matching between observed and theoretical seismograms.Theoretical seismograms for the heterogeneity structures based on WEPL3 including full allowance for intermode coupling show a distinct phase shift for the fundamental mode when compared with the corresponding calculations for the reference model PREMC: as is indeed observed at the NARS stations. The parts of the seismograms which show the largest influence from the presence of lateral heterogeneity are those which depend on interference phenomena, such as Su. The disruption of the phase patterns can have a profound influence on the appearance of the waveforms. The presence of small-scale heterogeneity has very little influence on the seismograms below 0.035 Hz but becomes more important as the frequency increases, especially for the body wave phases.