SEISMOGRAM SYNTHESIS FOR AZIMUTHALLY ANISOTROPIC MEDIA WITH A SINGLE SLOWNESS INTEGRATION

The computation of exact synthetic seismograms for azimuthally anisotropic (AA) models with a frequency-slowness integration method requires two horizontal slowness integrations. However, a single slowness integration that is exact for azimuthally isotropic media requires much less computation time, and has therefore been considered for the AA case as well. As a single slowness integration leads to traveltime and amplitude errors, it should be used for AA media only if these errors are negligible. In this paper we discuss the errors, and outline how they can be estimated. The main contribution to the single-integration traveltime error comes from incorrect group (ray) velocities in the single-integration case. The single-integration group velocities are always greater than or equal to the true group velocities, causing traveltimes to be too small. If there are cusps in the group-velocity surface, not only may the traveltimes be wrong, but there may also be arrivals missing from the seismograms. In layered AA media a minor contribution to the single-integration error arises from not allowing the ray to leave the sagittal plane. The resulting traveltime error is opposite in sign, but much smaller than the traveltime error caused by incorrect group velocities. Amplitudes may be incorrect even though traveltimes are accurate. However, this can only be the case for certain isolated sagittal planes, such as symmetry planes; in other sagittal planes amplitude errors and traveltime errors go together. To decide whether single-integration amplitudes will be accurate one should compute the sagittal velocity curves for single and double integration for a range of azimuths. If the velocity errors are insignificant, then the amplitudes will be accurate for all sagittal planes.