Improvements in Waveform Modeling and Application to Eurasian Velocity Structure

We introduce several recent improvements to mode-based 3D and asymptotic waveform modeling and examine how to integrate them with numerical approaches for an improved model of upper-mantle structure under eastern Eurasia. There is considerable information on structure in broadband seismograms that is currently not fully utilized. With numerical techniques, such as the Spectral Element Method (SEM), it should be possible to compute the complete predicted wavefield accurately without any restrictions on the strength or spatial extent of heterogeneity. This approach, however, requires considerable computational power.

We have implemented an approach which relies on a cascade of increasingly accurate theoretical approximations for the computation of the seismic wavefield to develop a model of regional structure for the area of Eurasia located between longitudes of 30 and 150 degrees E, and latitudes of -10 to 60 degrees North. The selected area is very heterogeneous, but is well surrounded by earthquakes and a significant number of high quality broadband digital stations, making it an ideal area to test new methods.

Starting Model

The first step in our modeling approach is to create a large-scale starting model including shear anisotropy using Nonlinear Asymptotic Coupling Theory (NACT; Li and Romanowicz, 1995), which models the 2D sensitivity of the waveform to the great-circle path between source and receiver, but neglects the influence of off-path structure. We have recently improved this approach by implementing a new crustal correction scheme, which includes a non-linear correction for the difference between the average structure of several large regions from the global model with further linear corrections to account for the local structure at each point along the path between source and receiver (Marone and Romanowicz, 2006; Panning and Romanowicz, 2006).

We inverted a global dataset augmented by additional data collection for paths which cross the region. To use the global dataset, we correct for structure outside the region using a global anisotropic starting model, SAW642AN (Panning and Romanowicz, 2006). The model in the region includes isotropic S structure parameterized in level 6 spherical splines, which correspond to a lateral resolution of $\sim$ 200 km (figure 30.1). It also includes anisotropy through the parameter $\xi=(V_{SH})^2/(V_{SV})^2$ . This is parameterized with a lateral resolution of $\sim$ 400 km (not shown here).

**Figure 30.1:** Starting isotropic S velocity model for the upper mantle for Eurasia developed using NACT. Values are the percent perturbations in isotropic velocity from PREM. Model is parameterized in radial splines spaced approximately 100 km, and in level 6 spherical splines (spacing $\sim$ 200 km).
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3D Born approximation

This model is further refined using a 3D implementation of Born scattering (Capdeville, 2005). We have made several recent improvements to this method, such as including perturbations to discontinuities. While the approach treats all sensitivity as linear perturbations to the waveform, we have also experimented with a non-linear modification to the approach analogous to that used in development of NACT. This modification allows us to treat large accumulated phase delays determined from a path-average approximation non-linearly, while still using the full 3D sensitivity of the Born scattering approximation.

We have performed some preliminary modeling of a subregion between longitudes 90 and 145 degrees E, and latitudes 15 and 40 degrees N with a subset of the original dataset consisting of the vertical component data from source-receiver pairs contained within the large region. The preliminary model is a relatively low resolution ( $\sim$ 400 km) isotropic velocity model. We show the model derived using the Born approximation with (figure 30.2) and without the non-linear correction (figure 30.3). In these preliminary models, it is difficult to determine which model is better able to image the anomalies.

**Figure 30.2:** Shear velocity model developed using linear Born kernels for 180 events recorded on the vertical component. Values shown are perturbations relative to the isotropic average of the reference model.
$\begin{figure}\begin{center} \epsfig{file=panning06-1-2.eps, width=8cm}\end{center}\end{figure}$

**Figure 30.3:** Same as figure 30.2 for the model developed using the non-linear Born partial derivatives.
$\begin{figure}\begin{center} \epsfig{file=panning06-1-3.eps, width=8cm}\end{center}\end{figure}$

Numerical approaches

Acknowledgements

This project has been funded through the Dept. of Energy, National Nuclear Security Administration, contract no. DE-FC52-04NA25543

References

Capdeville, Y., An efficient Born normal mode method to compute sensitivity kernels and synthetic seismograms in the Earth, submitted to Geophys. J. Int., 2005.

Komatitsch, D. and J. P. Vilotte, The spectral element method: an effective tool to simulate the seismic response of 2D and 3D geological structures, Bull. Seism. Soc. Am., 88, 368-392, 1998

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

Marone, F. and B. Romanowicz, Non-linear crustal corrections in high resolution regional waveform seismic tomography, Geophys. J. Int., in revision, 2006.

Panning, M.P. and B. Romanowicz, A three-dimensional radially anisotropic model of shear velocity in the whole mantle, Geophys. J. Int. online early, doi: 10.1111/j.1365-246X.2006.03100.x, 2006.