Traveltime dispersion in an isotropic elastic mantle: strong lower-mantle signal in differential-frequency residuals

Abstract

We study wavefield effects of direct P- and S -waves in elastic and isotropic 3-D seismic structures derived from the temperature field of a high-resolution mantle circulation model. More specifically, we quantify the dispersion of traveltime residuals caused by diffraction in structures with dynamically constrained length scales and magnitudes of the lateral variations in seismic velocities and density. 3-D global wave propagation is simulated using a spectral element method. Intrinsic attenuation (i.e. dissipation of seismic energy) is deliberately neglected, so that any variation of traveltimes with frequency can be attributed to structural effects. Traveltime residuals are measured at 15, 22.5, 34 and 51 s dominant periods by cross- correlation of 3-D and 1-D synthetic waveforms. Additional simulations are performed for a model in which 3-D structure is removed in the upper 800 km to isolate the dispersion signal of the lower mantle. We find that the structural length scales inherent to a vigorously convecting mantle give rise to significant diffraction-induced body-wave traveltime dispersion. For both P- and S-waves, the difference between long-period and short-period residuals for a given source–receiver pair can reach up to several seconds for the period bands considered here. In general, these ‘differential-frequency’ residuals tend to increase in magnitude with increasing short-period delay. Furthermore, the long-period signal typically is smaller in magnitude than the short-period one; that is, wave-front healing is efficient independent of the sign of the residuals. Unlike the single-frequency residuals, the differential-frequency residuals are sur- prisingly similar between the ‘lower-mantle’ and the ‘whole-mantle’ model for corresponding source–receiver pairs. The similarity is more pronounced in case of S -waves and varies between different combinations of period bands. The traveltime delay acquired in the upper mantle seems to cancel in these differential signals depending on the associated wavelengths and the length scales of structure at shallow depth. Differential-frequency residuals may thus prove useful to precondition tomographic inversions for the lower-mantle structure such as to reduce the influence of the upper mantle for certain length scales. Overall, standard deviations of the diffraction-induced traveltime dispersion between the longest (51 s) and the shortest (15 s) period considered here are 0.6 and 1.0 s for P - and S -waves, respectively. For comparison, the corresponding standard deviations of the 15 s residuals are 1.0 s and 2.8 s. In the lower-mantle model, standard deviations are 0.3 and 0.6 s, respectively, which gives an average lower-mantle contribution to the total dispersion of 50 per cent for P -waves and 60 per cent for S -waves.