Databases of surface wave dispersion

Transcription

1 submitted to Geophys. J. Int. Databases of surface wave dispersion Simona Carannante (1,2), Lapo Boschi (3) (1) Dipartimento di Scienze Fisiche, Università Federico II, Naples, Italy (2) Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy (3) E.T.H. Zürich, Switzerland. Received SUMMARY We derive phase velocity maps from two global databases of surface wave dispersion, and compare them to assess the relative quality of the observations. Although based upon similar sets of seismic records, the databases show some significant discrepancies, which we attempt to trace to the different automated measurement techniques employed by their authors. This exercise is relevant to our current understanding of the Earth s upper mantle, whose elastic structure is most importantly constrained by surface wave observations like the ones in question. Key words: seismic tomography, upper mantle, lateral resolution 1 INTRODUCTION Seismic surface waves are dispersive; their speed of propagation is a function of their frequency, or, in other words, individual harmonic components of the surface wave seismogram (individual modes) propagate over the globe at different speeds. For any given earthquakeseismometer couple, one can isolate from the seismogram each harmonic component, and measure its average speed (phase velocity) between source and receiver. We call dispersion curve a plot of phase velocity against frequency. From a large set of measured dispersion curves, with sources and stations providing a coverage as uniform as possible of the Earth,

2 2 Carannante and Boschi local phase velocity heterogeneities can be mapped as a function of longitude and latitude. At each location, perturbations in phase velocities with respect to a given reference model are weighted averages of seismic heterogeneities in the underlying mantle (Jordan 1978). Measurements of surface wave dispersion provide, through the steps outlined above, the most important global seismological constraint on the nature of the Earth s upper mantle (e.g., Ekström 2). Over the last decade, two large intermediate-period (35-15 s) dispersion databases have been assembled by Trampert & Woodhouse (1995; 21) and Ekström et al. (1997) from global networks of broadband seismic stations, and are now (at least to some extent) available to the public. Both are currently employed in global tomography studies (e.g., Boschi & Ekström 22; Spetzler et al. 22; Antolik et al. 23; Beghein 23; Boschi et al. 24). The two databases are in good, but not complete agreement, and their relative quality is under debate. The main difference between the work of Trampert & Woodhouse (1995; 21) and that of Ekström et al. (1997) rests in the automated algorithms used to determine dispersion curves from individual seismograms. In both cases, theoretical ( synthetic ) seismograms are calculated from theoretical dispersion curves, and compared to the measured one; an inverse problem is then solved to find the theoretical dispersion curve that minimizes the misfit between measured and synthetic seismograms; such optimal dispersion curve is the seeked dispersion measurement; as we shall illustrate below, the two groups have tackled this inverse problem in very different ways. In the following, we apply the same algorithm to derive phase velocity maps, at a discrete set of frequencies, from both databases. We identify specific discrepancies, and attempt to trace them to differences in the measurement procedures. 2 MEASURING SURFACE WAVE DISPERSION Following Ekström et al. s (1997) notation, we start by writing the surface wave seismogram u(ω) intheform u(ω) =A(ω)e iφ(ω), (1)

3 Databases of surface wave dispersion 3 where amplitude A and phase Φ are functions of frequency ω. Φ(ω) and the phase velocity c(ω) are related, Φ(ω) = ωx c(ω), (2) with X denoting propagation path length measured along the great circle. u(ω) canbe calculated, e.g., by surface wave JWKB theory as described by Tromp & Dahlen (1992; 1993). Given an observed seismogram, surface wave dispersion between the corresponding source and receiver is measured by finding the curves A(ω) andc(ω) (hence Φ(ω)) that minimize the misfit between the observed seismogram and u(ω). The best-fitting c(ω) is the seeked dispersion curve. Ekström et al. (1997) and Trampert & Woodhouse (1995; 21) find synthetic seismograms in slightly different, but equivalent ways; both groups write the corrections to amplitude and phase, with respect to PREM (Dziewonski & Anderson 1981), as linear combinations of a set of cubic splines f i (ω), with coefficients b i and d i, respectively, N δa(ω) = b i f i (ω), i=1 N δc(ω) = d i f i (ω), i=1 and the dispersion measurement is reduced to the determination of b i, d i (i =1,..., N). (3) (4) The outlined inverse problem is non-linear, and Ekström et al. (1997) accordingly choose to solve it through the non-linear SIMPLEX method (e.g., Press et al. 1994). They parameterize their dispersion curves in terms of only N = 6 splines; this number being relatively small, curves tend to be smooth, and no further regularization is needed. Here the approach of Trampert & Woodhouse (1995, 21) is quite different; first, their dispersion curves are described by as many as N = 36 splines (Trampert & Woodhouse 21). Secondly, they accomodate the non-linearity of the inverse problem in a very different way: since group velocities are secondary observables easily calculated from the seismograms, they prefer to first measure those, and then derive phase velocity dispersion curves from

4 4 Carannante and Boschi them, now exploiting their linear relationship with the least-squares algorithm of Tarantola & Valette (1982). To our understanding, the procedures of Ekström et al. (1997) and Trampert & Woodhouse (1995, 21) are, in all other respects, equivalent to each other. It is worth mentioning one issue that both groups had to consider while developing their algorithms; notice from equation (1) that the surface wave seismogram is a periodic function of Φ with period 2π; when dispersion is measured, values of Φ different of exactly 2π will provide an equally good fit to the data; and perturbations δφ larger than 2π cannot simply be discarded, because at intermediate periods (say, < 1s), true heterogeneities in the Earth s structure can suffice to cause phase anomalies of more than one cycle. Both groups solve this ambiguity in the same way: at long periods (> 1s) the exact number of full cycles in phase can be determined without ambiguity; this part of the seismic spectrum is then inverted first, and the higherfrequency portion of the dispersion curve is found through subsequent iterations, with the requirement, based on physical considerations, that the dispersion curve be smooth. This is discussed in detail both by Ekström et al. (1997) and Trampert & Woodhouse (1995), and nicely illustrated by figure 3 of Ekström et al. (1997). We show in figures 1 and 2 histograms of Trampert & Woodhouse s (21) and Ekström et al. s (1997) phase delay measurements, grouped by surface-wave type (Rayleigh, Love) and period (data at 35, 6, 1 and 15 s only are shown, to represent the entire databases). At longer periods, both databases standard deviations decrease; at 35 s, where the data are more sensitive to strong crustal or lithospheric heterogeneities, observed phase delays are, as expected, stronger; more importantly, figures 1a and 2a (Love and Rayleigh phase delays, respectively, at 35 s) show the most significant differences between the two databases. 3 PHASE-VELOCITY MAPS We derive Love and Rayleigh wave phase velocity maps at all periods (35 to 15 s) where measurements are available; a separate tomographic inversion is performed at each period, to find an independent phase velocity map; we then compare maps obtained from Trampert

5 Databases of surface wave dispersion 5 & Woodhouse s (21) database with those obtained from Ekström et al. s (1997) one. In order for this comparison to be meaningful, we employ in both cases the same tomographic parameterization (approximately equal-area pixels, of size 5 5 degree at the equator), regularization (a combination of norm and roughness damping), and inversion algorithm (LSQR) (Boschi & Dziewonski, 1999; Boschi, 21). The regularization scheme (constant throughout this work) was chosen after a number of preliminary inversions (Carannante 24). Our results (from both databases) are in general agreement with those of other authors (e.g., Trampert & Woodhouse 1995, 21; Ekström et al. 1997; Boschi & Ekström 22); shorter period data are predominantly sensitive to crustal structure, and the corresponding phase velocity maps are dominated by the ocean-continent signature; as period increases, lithospheric features (upwellings of hot material at mid-oceanic ridges, fast continental roots) become dominant. Also, as a general rule, at any given period Love wave maps are affected by structure at shallower depths than Rayleigh wave ones. Maps derived from the two databases are similar at all periods (Carannante 24). The agreement increases with increasing period. Figures 3 and 4 show phase velocity maps, from both databases, at relatively short periods (35 to 6 s); relatively strong discrepancies are visible at 35 s and 4 s for Love waves (figure 3), and 35 s only for Rayleigh waves (figure 4). Particularly at those periods, maps resulting from Ekström et al. s (1997) database are more clearly dominated by the contrast between slow continents and fast oceans; mid-oceanic ridges, and heterogeneities of various nature within the continents, are only minor, if visible at all. In the maps that we have obtained at the same short periods from Trampert & Woodhouse s (21) database, instead, the dominant ocean-continent signal is accompanied by a more significant shorter spatial wavelength component, associated with the mentioned geophysical features. In practice, particularly for Love waves, phase velocity heterogeneities imaged from Ekström et al. s (1997) data tend to depend on period more strongly than those found from Trampert & Woodhouse s (21) data.

6 6 Carannante and Boschi The most evident discrepancies are those between the 35 s Love wave phase velocity maps of figure 3 (enlarged in figure 5), in Tibet and in the Atlantic Ocean. The map derived from the data of Ekström et al. (1997) is dominated by the main features of crustal thickness (Mooney et al. 1998; Bassin et al. 2), while the one from Trampert and Woodhouse s (21) database is more correlated to longer period phase velocity heterogeneity (i.e. upper mantle structure). To quantify the above observations, we have carried out a spectral analysis of phase velocity maps, finding their spherical harmonic coefficients through least-squares fits; figure 5 shows the least well correlated spectra, found (as expected) from the 35 s Love wave maps. The spectral peaks at harmonic degrees 2 and 5, naturally associated with oceanic/continental plates, are much stronger according to Ekström et al. s (1997) than Trampert & Woodhouse s (21) database; the opposite is true of higher degree coefficients (9 through 14 in figure 5). A last useful information to discriminate between the databases in question is the datafit (variance reduction) achieved when inverting the observations; we give it in figure 6, plotted as a function of period for all the periods considered by Carannante (24). As already noticed by the compilers of the databases, variance reduction of both Love and Rayleigh wave data decreases with increasing period. The fit to Ekström et al. s (1997) data is systematically better; this might mean that Ekström et al. (1997) have selected the data more conservatively, succeeding to clean them from effects of noise that might still be present in Trampert & Woodhouse s (21) database, or that the latter database includes information on heterogeneities of shorter spatial frequency, that our 5 5 pixel parameterization cannot resolve. 4 CONCLUSIONS The dispersion databases of Trampert & Woodhouse (21) and Ekström et al. (1997) provide a very important constraint on the shallow seismic structure of the Earth. They lead to similar, but not entirely consistent images of surface wave phase velocities. Discrepancies

7 Databases of surface wave dispersion 7 we have found are strong enough to alter our understanding of lithosphere and upper mantle; they might result from differences in the networks of seismic stations, and time windows chosen by the authors to collect the original seismic records; more realistically since the phase velocity maps shown here are increasingly better correlated at intermediate to long periods they could be explained in terms of the different algorithms designed by the authors to measure dispersion curves from recorded seismograms. As discussed in section 2, the main difference between the algorithms in question resides in the parameterization of dispersion curves, and in the inversion methods employed to derive them from recorded seismograms. Ekström et al. (1997) chose a coarser parameterization of the dispersion curve (6 splines only), but did not require any further smoothing than that implicit in the parameterization itself, and found dispersion curves through fully nonlinear inversions. At 35 s period, our histogram of their Love wave phase delay observations (figure 1) is characterized by a larger standard deviation than Trampert & Woodhouse s (21); the latter authors, who derive dispersion curves with a linear, damped least squares algorithm, might have over-smoothed them; this would explain the systematically lower variance reduction achieved when inverting their data, and the stronger correlation, in figure 1, between the Love wave phase velocity maps at 35 and 4 s obtained from their data, vs. those obtained from Ekström et al. s (1997) data. In other words, the short period end of Trampert & Woodhouse s (21) dispersion curves might be too strongly anchored to longer periods. On the other hand, maps resulting from Trampert & Woodhouse s (21) database are characterized by a stronger power spectrum at shorter spatial wavelengths (e.g., figure 5); their data might contain meaningful information associated with geophysical features of small spatial extent, that Ekström et al. s (1997) data cannot resolve. Accordingly, the variance reduction plots of figure 6 could simply indicate that our intermediate resolution (5 5 pixels) parameterization cannot adequately describe such narrow heterogeneities. This interpretation, if correct, would invalidate the previous speculations. Carannante (24) has performed an additional set of nonuniform resolution inversions,

8 8 Carannante and Boschi whose results appear to favour Ekström et al. s (1997) database; the problem, however, deserves further analysis, possibly from authors with deeper insight in the measuring techniques, rather than tomographic applications. ACKNOWLEDGMENTS We are particularly grateful to prof. Paolo Gasparini for his help and encouragement. Thanks also to Göran Ekström, Domenico Giardini, Jeannot Trampert, Aldo Zollo. During his stay at Università di Napoli Lapo Boschi was funded by Ministero dell Istruzione, Università e Ricerca. All figures were done with GMT (Wessel and Smith 21). REFERENCES Antolik, M., Gu, Y. J., Ekström, G. & Dziewonski, A. M., 23. J362D28: a new joint model of compressional and shear velocity in the mantle, Geophys. J Int., 153, Bassin, C., Laske, G., and Masters, G., 2. The current limits of resolution for surface wave tomography in North America, Eos Trans. AGU, 81, F897. Beghein, C., 23. Seismic anisotropy inside the Earth from a model space search approach, PhD thesis, Utrecht University, Utrecht, Netherlands. Boschi, L., 21. Applications of linear inverse theory in modern global seismology, PhD thesis, Harvard University, Cambridge, Massachusetts. Boschi, L. & Dziewonski, A., High and low resolution images of the Earth s mantle - Implications of different approaches to tomographic modeling, J. geophys. Res., 14, 25,567 25,594. Boschi, L. & Ekström, G., 22. New images of the Earth s upper mantle from measurements of surface-wave phase velocity anomalies, J. geophys. Res., 17, doi:1.129/2jb59. Boschi, L., Ekström, G. & Kustowski, K., 24. Multiple resolution surface wave tomography: the Mediterranean basin, Geophys. J Int., 157, doi:1.1111/j x x. Carannante, S., 24. Velocità di fase delle onde sismiche di superficie: immagini tomografiche globali a risoluzione variabile, Tesi di laurea, Università di Napoli Federico II, Naples, Italy. Ekström, G., 2. Mapping the lithosphere and asthenosphere with surface waves: Lateral structure and anisotropy, in The History and Dynamics of Global Plate Motions, editedbym. Richards et al., AGU monograph.

9 Databases of surface wave dispersion 9 Ekström, G., Tromp, J. & Larson, E. W. F., Measurements and global models of surface wave propagation, J. geophys. Res., 12, Jordan, T. H., A procedure for estimating lateral variations from low-frequency eigenspectra data, Geophys. J. R. astr. Soc.,, 52, Mooney, W. D., Laske, G., and Masters, G., Crust 5.1: a global crustal model at 5x5 degrees, J. geophys. Res., 13, Spetzler, J., Trampert, J. & Snieder, R., 22. The effect of scattering in surface wave tomography, Geophys. J Int., 149, Tarantola, A. & Valette, B., Generalized non-linear inverse problems solved using the leastsquares criterion, Rev. Geophys. Space Phys., 2, Trampert, J. & Woodhouse, J. H., Global phase velocity maps of Love and Rayleigh waves between 4 and 15 seconds, Geophys. J Int., 122, Trampert, J. & Woodhouse, J. H., 21. Assessment of global phase velocity models, Geophys. J Int., 144, Tromp, J. & Dahlen, F. A., Variational principles for surface wave propagation on a laterally heterogeneous Earth, II, Frequency-domain JWKB theory, Geophys. J Int., Tromp, J. & Dahlen, F. A., Maslov theory for surface wave propagation on a laterally heterogeneous Earth, Geophys. J Int., Wessel, P., and W. H. F. Smith, Free software helps map and display data, Eos Trans. AGU, 72, This paper has been produced using the Blackwell Scientific Publications GJI LaT E Xstylefile.

10 Figure Captions Figure 1. Histograms of Love wave phase delays (seconds) observed by (blue) Ekström et al. (1997) and (green) Trampert & Woodhouse (21), at (a) 35 s, (b) 6 s, (c) 1 s, and (d) 15 s periods. Figure 2. Same as figure 1, Rayleigh wave phase delays. Figure 3. Tomographic maps of Love wave phase velocity (percent perturbations to PREM) from the databases of (left) Trampert & Woodhouse (21) and (right) Ekström et al. (1997), at short to intermediate periods (given in brackets at each panel). Figure 4. Same as figure 3, Rayleigh wave phase velocity maps. Figure 5. Spectral analysis of 35 s Love wave phase velocity maps derived from the databases of (top map, green spectrum) Trampert & Woodhouse (21) and (bottom map, blue spectrum) Ekström et al. (1997). It is at this Love wave frequency that images resulting from the two data sets are most different. Figure 6. Fit of the two databases (Ekström et al. (1997 in blue, Trampert and Woodhouse (21) in green) achieved in our inversions, as a function of period, for both Love (top panel) and Rayleigh (bottom panel) wave observations. The same inversion algorithm and regularization scheme were applied throughout. Results of inversions not discussed above are also included.

11 Figures frequency(%) (a) data(s) frequency(%) (b) data(s) 48 4 (c) 4 (d) frequency(%) frequency(%) data(s) data(s) Figure 1. Histograms of Love wave phase delays (seconds) observed by (blue) Ekström et al. (1997) and (green) Trampert & Woodhouse (21), at (a) 35 s, (b) 6 s, (c) 1 s, and (d) 15 s periods.

12 (a) (b) frequency(%) frequency(%) data(s) data(s) (c) 5 (d) frequency(%) frequency(%) data(s) data(s) Figure 2. Same as figure 1, Rayleigh wave phase delays.

13 LOVE WAVES TRAMPERT EKSTROM (35s) (35s) (4s) (4s) (51s) (5s) (62s) (6s) Figure 3. Tomographic maps of Love wave phase velocity (percent perturbations to PREM) from the databases of (left) Trampert & Woodhouse (21) and (right) Ekstro m et al. (1997), at short to intermediate periods (given in brackets at each panel).

14 RAYLEIGH WAVES TRAMPERT EKSTROM (35s) (35s) (4s) (4s) (51s) (5s) (62s) (6s) Figure 4. Same as figure 3, Rayleigh wave phase velocity maps.

15 LOVE WAVES (35s) TRAMPERT EKSTROM Amplitude(%) TRAMPERT EKSTROM Spherical Harmonic degree Figure 5. Spectral analysis of 35 s Love wave phase velocity maps derived from the databases of (top map, green spectrum) Trampert & Woodhouse (21) and (bottom map, blue spectrum) Ekström et al. (1997). It is at this Love wave frequency that images resulting from the two data sets are most different.

16 variance reduction (%) LOVE WAVES Ekstrom Trampert period (s) variance reduction (%) RAYLEIGH WAVES Ekstrom Trampert period (s) Figure 6. Fit of the two databases (Ekström et al. (1997 in blue, Trampert and Woodhouse (21) in green) achieved in our inversions, as a function of period, for both Love (top panel) and Rayleigh (bottom panel) wave observations. The same inversion algorithm and regularization scheme were applied throughout. Results of inversions not discussed above are also included.