Towards Forward Modeling of 3D Heterogeneity in D" region

Akiko To, Yann Capdeville and Barbara Romanowicz


The presence of strong lateral heterogeneity in D" is now well documented, and represents a problem for seismic modeling, when using standard ray or mode approaches, because of the theoretical limits of validity of these methods. Consequently, present tomographic models are only able to represent the large scale, smooth features of the structure. They may also not reflect the amplitudes of lateral variations accurately. We use a coupled normal mode/Spectral Element Method (SEM) (Capdeville et al., 2003) to compute synthetic seismograms of Sdiff in the D" part of a 3D tomographic model (SAW24B16, Mégnin and Romanowicz, 2000) down to a corner frequency of 1/12s. This coupled method is much faster than standard SEM, as the numerical part of the computation is restricted to the D" region. The rest of the mantle is assumed 1D, and there the wavefield is computed using efficient normal mode summation.

Comparison between Observed and Synthetic Waveforms

We compare the synthetics thus obtained with observed waveforms for a collection of 16 deep earthquakes in the Western Pacific. The results from one of the events are shown in Figure 35.1 and Figure 35.2. For deep earthquakes, the effect of strong heterogeneity in the crust and upper mantle is avoided. Observed and synthetic travel time trends are very consistent, although in most cases the observed residuals are significantly larger. Waveform amplitudes are less consistent.

We manually modify the original SAW24b16, and by trial and error try to make a better model which fit the observations (Figure 35.3). The fit becomes better in a few traces, but in many cases it is difficult to fit both amplitude and travel times (Figure 35.4).

Modification of the Velocity Model by a Genetic Algorithm

We try to apply a genetic algorithm to travel time or waveform modeling in the D". The advantages of GAs are that there is no damping and the output models are less controlled by the starting model. These properties are appropriate for modeling strong and complex heterogeneity in the D". The defect of the method is the high computational cost. By limiting the target to a small local region on the CMB, we reduce the number of model parameters. We use ray theory, which is the most expedient method, to calculate travel times, and examine whether a GA is useful for modeling D".

We choose a region of 28 x 28 degree in Northern Pacific, where 58 Sdiff ray paths diffract on CMB. We divided the region to 25 boxes. The number of initial ensemble of models is 30. After 15 to 16 generations, the model converged. We were able to get 35% of variance reduction. In future, we want to apply this method using NACT with the focusing and defocusing effect.

Comparison of Travel Time between Ray Theory and Coupled Mode/SEM

We compared the predicted Sdiff travel time between ray theory and Coupled Mode/SEM (Figure 35.5). Ray theory is a most expedient way to calculate travel times. However, it is an infinite frequency approximation and not appropriate to handle diffracting waves.

For negative residuals, both residuals are almost the same. They distribute around y=x with in 1 to 2 second differences. However, for positive residuals, the predictions from ray theory give larger values by up to 4 seconds. This is consistent with theoretical predictions for the wave front healing effect (e.g. Nolet and Dahlen, 2000).


We thank the National Science Foundation for support of this research.


Capdeville Y., B. Romanowicz and A. To, Coupling Spectral Elements and Modes in a spherical earth: an extension to the ``sandwich'' case. Geophys. J. Int, 154, 44-57, 2003

Capdeville Y., E. Chaljub, J.P. Vilotte and J.P. Montagner, Coupling the Spectral Element Method with a modal solution for Elastic Wave Propagation in Global Earth Models, Geophys. J. Int, 153, 34-66, 2003

Dziewonski A.M., and D.L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, 297-356, 1981.

Mégnin, C., and B. Romanowicz, The shear velocity structure of the mantle from the inversion of of body, surface and higher modes waveforms, Geophys. J. Int, 143, 709-728, 2000

Figure: The ray paths distribution of Sdiff phase whose waveforms are shown in Figure 35.2. The event is 511.2km deep. Dark gray line: the diffracting part. Light gray line: The ray paths at the bottom 370km of the mantle, where 3D heterogeneity is included in synthetic waveform calculation.
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Figure 35.2: Top: Comparison of selected waveforms. Synthetic waveforms are made by couple model/SEM 3D models of the D'' layer. The contribution of heterogeneity from rest of the mantle is calculated by ray theory. Bottom: Travel time residuals and maximum amplitude ratio relative to PREM (Dziewonski and Anderson, 1981) for all traces.
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Figure: The background model is SAW24b16. The blue line shows the region where the anomaly is amplified in each depth. Numbers on the blue line show the factor of amplification. The waveforms calculated from this model is shown in Figure 35.4
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Figure 35.4: Waveforms from modified model as indicated in Figure 35.3. The two waveforms from Event2 show better fit between synthetics from the modified model and the observations. However, the fit between observation and synthetics become worse in the modified model for most of the waveforms from Event1.
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Figure 35.5: Synthetic travel time residuals with respect to PREM for 800 globally distributed Sdiff phase. The 3D velocity model used in the comparison is SAW24b16. The model has 3D heterogeneity in the bottom 370km of the mantle. The travel time residuals calculated using Coupled Mode/SEM are on Y axis. We cross correlated the waveforms constructed from the 3D model and PREM.
\epsfig{file=toh5.epsi, width=8cm}\end{center}\end{figure}

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