Research School of Earth Sciences


A global dataset of frequencydependent bodywave travel times: towards a global finitefrequency tomography of the Earth's mantleChristophe Zaroli^{1}, Eric Debayle^{1} and Malcolm Sambridge^{2} 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
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). Finitefrequency theory (Dahlen et al. 2000) incorporates single scattering into the formulation, and has been developed for long period bodywaves. 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 "bananadoughnut" (BD) kernels because of their shape (See Figure 1). The actual benefit of a finitefrequency 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 finitefrequency 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 traveltime datasets. Until now, most finitefrequency studies have been made using long period traveltimes 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 traveltimes measured by crosscorrelation 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 traveltime, so that it can be associated with a finitefrequency kernel carrying the same frequency information. Secondly, by measuring finite frequency traveltimes 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 traveltime 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 finitefrequency is still active, we believe that significant progress can be achieved by building a new dataset of massive long period body phases traveltimes measured over a broad frequency range. To date, there is no such global database of frequencydependent bodywave traveltime 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 finitefrequency SH or SVwave tomography, but can be easily extended to Pwave 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 traveltimes on SH components in different frequencybands covering the period range 668 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.

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