Surface waves and overtones provide excellent constraints on crustal, upper mantle, and transition zone structure.
They offer far better radial resolution of shallow structure than is possible with teleseismic body waves,
while simultaneously having excellent global coverage and signal-to-noise ratios. Indeed, since its development a quarter
century ago (*Woodhouse and Dziewonski*, 1984), the modeling of long period waveforms of surface waves and overtones
using approximate techniques has made possible the development of high resolution models of upper mantle shear wave velocity and radial aniostropy
(*Panning and Romanowicz*, 2006; *Kustowski et al.*, 2008).

However, the ray- and perturbation theory that underlies these efforts can result in modeling errors that exceed the noise level
of the observed waveforms (*Panning et al.*, 2009). In the case of realistic crustal structure, the modeling inaccuracies can
significantly contaminate the retrieved images of mantle velocity and radial anisotropy (*Lekic et al.*, 2009).
Fortunately, the development of computational techniques capable of fully modeling wave propagation through a complex,
heterogeneous medium such as the Earth (Spectral Element Method: e.g. *Capdeville et al.*, 2003)
has enabled tomographers to move away from approximate techniques.

The superior accuracy of the spectral element method comes at a far greater computational cost than that associated with
approximate techniques. In particular, crustal structure comprising thin layers substantially
increases computational costs. At the same time, inaccuracies in existing global crustal models like CRUST2 (*Bassin et al.*, 2000)
can contaminate the retrieved mantle images. Because of this, there is a need for a new crustal model that avoids the meshing of
thin layers while increasing the accuracy of crustal corrections. Long period waveforms lack the resolution necessary for
crustal inversion, so we supplement our waveform dataset using 1x1 Rayleigh and Love group velocity dispersion maps
provided by *M. Ritzwoller* (*personal communication*) spanning the 25-150 sec period range.

Here, we present preliminary results of a joint inversion of group velocity dispersion and long period waveforms for crustal and upper mantle elastic structure.

Tomographic imaging of the Earth's interior using waveforms is a non-linear process requiring an
iterative procedure. Each iteration involves a forward modeling step in
which three-component waveforms with periods longer than 60 s are calculated using
the spectral element method through a 3D model of isotropic shear wavespeed () and radial
anisotropy (). The partial derivatives relating model perturbations to
time-domain misfits between data and synthetics are calculated using non-linear asymptotic coupling theory (NACT: *Li and Romanowicz*, 1995).
Model updates are obtained by following the procedures described in *Mégnin and Romanowicz* (2000) and references therein.

In order to account for non-linear effects of model perturbations on group velocities and develop an unbiased starting crustal model, we
begin by creating 21,000 candidate models which span a variety of crustal (2-4 km/s).
is scaled to compressional wavespeed and density using relations of *Brocher* (2003). In order to avoid meshing thin crustal layers, we fix
crustal thickness to 60 km and mimic the response of a layered isotropic medium by introducing anisotropy
(i.e. is allowed to vary between 0.6 and 1.4). The models are represented as degree 3 polynomials, and their group velocities are calculated
using a modified MINEOS code (*Woodhouse*, 1988).

Once we obtain a starting crustal model, we regionalize it by grouping similar velocity profiles into 4 clusters, and then summarizing each cluster by a single model of mean density and slownesses. For each reference profile, we then calculate group velocity dispersion curves and partial derivatives relating logarithmic group velocity perturbations from the reference values to perturbations in and . The most appropriate regional kernels are then used to obtain a model update which minimizes the logarithmic misfits between predictions and the group velocity dispersion at each point on the Earth. This ensures that the perturbations are always within the linear regime.

Figure 2.35 compares the structure of the uppermost mantle obtained using CRUST2 and long period waveforms alone (A: left) and our new Earth model obtained by jointly inverting long period waveforms and group velocity dispersion constraints (B: right). The differences between the models are prominent at shallow depths, where model B exhibits substantially stronger correlation between anomaly and age of oceanic plates. At 100 km, the models are similar, though further differences emerge at 250 km, at which depth model B shows fewer fast anomalies beneath Asia, save for those corresponding to the Siberian and Finnoscandian cratons.

The model developed using CRUST2 fits Love waves two times worse than Rayleigh waves, even when inverting for radial anisotropy variations. However, by including higher frequency group velocity measurements and inverting for crustal structure, we improve the fits to both Love and Rayleigh waves and bring them closer to parity.

We plan to carry out further iterations and resolution tests to quantify the benefits of joint inversion of long period waveforms and shorter period group velocity dispersion curves.

This research was supported by National Science Foundation grant NSF/EAR-0308750.

Bassin, C., Laske, G. and G. Masters, 2000. The Current Limits of Resolution for Surface Wave Tomography in North America. *EOS Trans AGU 81,* F897.

Brocher, T.M, 2003. Empirical Relations between Elastic Wavespeeds and Density in the Earth's Crust. *BSSA, 95*, 2081-2092.

Capdeville, Y., E. Chaljub, J.P. Vilotte and J.P. Montagner, 2003. Coupling the spectral element method with a modal solution for elastic wave propagation in global Earth m
odels. *Geophys. J. Int., 152,* 34-66.

Lekic, V., M. Panning and B. Romanowicz, 2009. A simple method for improving crustal corrections in waveform tomography. *Submitted to Geophys. J. Int.*.

Li, X.D. and B. Romanowicz, 1995. Comparison of global waveform inversions with and without considering cross-branch modal coupling, *Geophys. J. Int., 121,* 695-709.

Megnin, C. and B. Romanowicz, 2000. The three-dimensional shear velocity structure of the mantle from the inversion of body, surface and higher-mode waveforms. *Geophys. J. Int., 143,* 709-728.

Panning, M. and B. Romanowicz, 2006. A three-dimensional radially anisotropic model of shear velocity in the whole mantle. *Geophys. J. Int., 167*, 361-379.

Panning, M.P., Y. Capdeville, and B.A. Romanowicz, 2009 Seismic waveform modelling in a 3-D Earth using the Born approximation: potential shortcomings and a remedy.
*Geophys. J. Int., 177*, 161-178.

Woodhouse, J.H. and A.M. Dziewonski, 1984. Mapping the upper mantle: three dimensional modeling of Earth structure by inversion of seismic waveforms. *J. Geophys. Res. 89,* 5953-5986.

Woodhouse, J.H., 1988. The calculation of eigenfrequencies and eigenfunctions of the free oscillations of the Earth and the Sun.
*Seismological Algorithms*, ed. Doornbos, D.J., 321-370.

Berkeley Seismological Laboratory

215 McCone Hall, UC Berkeley, Berkeley, CA 94720-4760

Questions or comments? Send e-mail: www@seismo.berkeley.edu

© 2007, The Regents of the University of California