Global surface wave diffraction tomography

Abstract

[1] We determine the effect of replacing geometrical ray theory in surface wave tomography with scattering theory. We describe a tomographic method based on a simplified version of the scattering sensitivity kernels that emerge from the Born or Rytov approximations in which surface wave travel times are a weighted average of phase or group slowness over the first Fresnel zone of the wave. We apply this ''diffraction tomography'' to Rayleigh and Love wave group velocity measurements to produce group velocity maps from 20 to 150 s period on a 2°Â 2°grid globally. Using identical data and damping parameters, we also produce maps using ''Gaussian tomography'' which is based on ray theory with intuitive Gaussian smoothing constraints. Significant differences in the amplitude and geometry of the imaged features appear primarily at long periods but exist even in the short-period maps in regions where average path lengths are large. Diffraction tomography, therefore, is significant in most oceanic regions at all periods, but it is also important on continents at long periods at least. On average, diffraction tomography produces larger velocity anomalies in a period-dependent band of spherical harmonic degrees, and diffraction and Gaussian tomography maps decorrelate past a critical spherical harmonic degree that also depends on period. The widths of resolving kernels that emerge from diffraction tomography are systematically larger than those from Gaussian tomography. Finally, mantle features inferred from diffraction tomography tend to have larger amplitudes and extend deeper than those from Gaussian tomography.

Arrival angle anomalies of Rayleigh waves observed at a broadband array: a systematic study based on earthquake data, full waveform simulations and noise correlations

“…One particular consequence of the very strong deviations at short period is that it may be so large that taking into account finite frequency effects based on kernels or Fresnel zones (e.g. Wang & Dahlen 1995;Ritzwoller et al 2002;Yoshizawa & Kennett 2002;Zhou et al 2004) around the great-circle may be inadequate. The data from the present study should allow better quantifying and possibly fostering tools to correct for these effects.…”

Ambient noise surface wave tomography of the Iberian Peninsula: Implications for shallow seismic structure

“…The tomography method is that of Barmin et al [2001], which approximately accounts for the spatially extended frequency-dependent sensitivity of the waves by using Gaussian lateral sensitivity kernels. Although the use of spatially extended sensitivity kernels has only a small effect on the estimated maps at the periods considered [Ritzwoller et al, 2002], they help to provide a more accurate estimate of spatial resolution. This scalar quantity, instead of being obtained using the information from the resolution matrix, is determined as follows: for each grid point of the model we constructed a resolution kernel, which is a row of the resolution matrix, and we fit a 2-D spatial Gaussian function to the kernel and identified the resolution as twice the standard deviation of the Gaussian.…”

The state of the upper mantle beneath southern Africa

“…Significant derivations from great-circle propagation have been observed for shorter period (b40 s) surface waves (Alsina et al, 1993;Cotte et al, 2000), but surface wave ray tracing in earth models (Yoshizawa and Kennett, 2002) similar to the one presented here confirms that off-great circle propagation can reasonably be neglected for the fundamental and first few higher modes at periods greater than ∼40s and for paths less than ∼10,000 km. Ritzwoller et al (2002) examined the effects of off-great circle propagation and found that for short path lengths (∼5000 km) such as those primarily used in this study, the great circle assumption was adequate but led to increasing bias in the inverted model as path length increased. Sieminski et al (2004) show that using a dense path coverage of relatively short paths and assuming ray theory, it is possible to detect heterogeneity with length scales smaller than the wavelength of the data set.…”