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A global dataset of frequency-dependent body-wave travel times: towards a global finite-frequency tomography of the Earth's mantle

Christophe Zaroli1, Eric Debayle1 and Malcolm Sambridge2

1 Institut de Physique du Globe de Strasbourg, Ecole et Observatoire des Sciences de la Terre, Centre National de la Recherche Scientifique and Universit&e de Strasbourg, France
2 Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia


Figure 1. Fréchet Kernels at 20s period for a) P wave and b) S wave.

With the growth in the number of seismic stations, the increase in computational power and the development of new analysis tools that extract more information from seismograms, the resolution of global seismic tomographic models has improved significantly in the last 25 years. For example the lateral resolution of surface wave velocity and anisotropy models of the upper mantle has decreased from 5000 km (Woodhouse and Dziewonski (1984), Nataf et al., 1984) to about 1000 km in the most recent seismic models, allowing the anisotropic behaviours between continents to be distinguished (Debayle et al., 2005).

Finite-frequency theory (Dahlen et al. 2000) incorporates single scattering into the formulation, and has been developed for long period body-waves. It is known that long period body waves are sensitive to the wave speed over a broad 3D volume surrounding the geometric ray. The corresponding 3D kernels have become known as "banana-doughnut" (BD) kernels because of their shape (See Figure 1).

The actual benefit of a finite-frequency theory remains controversial (Sieminski et al., 2004, de Hoop and van der Hilst, 2005a; Dahlen and Nolet, 2005; de Hoop and van der Hilst, 2005b; Montelli et al., 2006a; van der Hilst and de Hoop, 2006; Boschi et al., 2006). These authors suggest that the effect of the improved theory could be smaller than that of practical considerations such as the level of damping, the weighting of different data sets and the choice of data fit, especially when considering the relatively small amount of finite-frequency data (~90 000 long period body waves) compared with the large number (~1 500 000) of travel time data analysed with ray theory (e.g. van der Hilst et al. 2005).

Other limitations come from the travel-time datasets. Until now, most finite-frequency studies have been made using long period travel-times measured for ray theory applications. These travel times are not well suited for an inversion using Dahlen et al. (2000) kernels which are designed for travel-times measured by cross-correlation of a broadband seismic phase with a synthetic. To take a full advantage of Dahlen (2000) finite frequency theory, it is necessary to keep control of the frequency content of the waveform associated with a given travel-time, so that it can be associated with a finite-frequency kernel carrying the same frequency information. Secondly, by measuring finite frequency travel-times over different frequency ranges, it is possible to extract more information from each seismic phase. According to Dahlen et al., (2000), the width of a given BD kernel increases with the dominant period of the corresponding body waveform. Therefore, by measuring the travel-time of a seismic phase at several frequencies, there is a potential for increasing the amount of independent information in the inverse problem, as at each frequency, the waveform "senses" a different weighted average of the structure, through a different Banana Doughnut kernel. 

If the debate about the real benefit of finite-frequency is still active, we believe that significant progress can be achieved by building a new dataset of massive long period body phases travel-times measured over a broad frequency range. To date, there is no such global database of frequency-dependent body-wave travel-time measurements.

A first result from this project is an automated approach for measuring long period body wave travel times at multiple frequencies. The approach has been designed to built a dataset for global finite-frequency SH or SV-wave tomography, but can be easily extended to P-wave tomography. The travel times are computed by cross correlation and are fully compatible with the kernels provided by Dahlen, (2000). Currently, our approach allows us to measure in an automated way S, ScS,  SS travel-times on SH components in different frequency-bands covering the period range 6-68 s. Frequency dependent crustal and attenuation corrections for WKBJ synthetics can also be incorporated.

The figures show the finite frequency kernels together with maps showing the coverage of the new data set. The automated procedure has been used to build a global dataset of finite frequency travel times, using 30 years of data from IRIS and GEOSCOPE networks. This will be the basis of future work on mantle imaging.

Figure 3. Arrival times of S, ScS and SS phases retained in the final dataset.

Figure 2. Ray density maps at different depth of the new dataset.