Waveform Inversion of Body Waves by Mode Sums
Barbara Romanowicz
Xiang Dong Li
Seismographic Station, UC Berkeley, Berkeley CA

The accumulation of high quality digital broadband data from the new generation Global Seismological Network allows to combine recent theoretical developments in wave propagation with analysis of such data to achieve better resolution in global mantle tomographic modeling.

Classical waveform tomography relies on the "path average approximation" (PAVA), in which the sensitivity of seismic waves to lateral heterogeneity is restricted to the horizontally averaged structure along the slice of earth spanned between the source and the receiver (Woodhouse and Dziewonski, 1984). While valid for surface waves, this approximation fails to describe the ray character of body waves (Li and Tanimoto, 1993). In order to improve the resolution in the lower mantle, travel time data can be added to the inversion (e.g. Woodward and Masters, 1991; Woodward et al., 1993). This however only helps in some regions of the mantle, sampled by well isolated phases on the seismograms. Also, the sensitivity of the travel times to structure is generally assumed to be uniformly distributed along the ray. This assumption, valid in the high frequency limit, becomes less justified at lower frequencies, such as used in waveform inversions. On the other hand, it is possible to improve this situation by modifying the normal mode theory to include coupling terms between different normal mode branches that make up each bodywave train, which are ignored in the path average approximation.

While other, more exact approaches are being actively pursued (e.g. Geller and Hara, 1993; Lognonne, 1991), we have developed a procedure to invert waveforms on the global scale using the non-linear asymptotic coupling theory (NACT) which includes, to first order, coupling effects between appropriate mode branches (Romanowicz, 1987; Li and Tanimoto, 1993; Li and Romanowicz, 1994). The data used presently are SH waveforms of surface waves as well as body waves of various types (S, multiple S, Sdiff, ScS...) at periods greater than 80 sec and 32 sec respectively. A total dataset of over 6000 surface wave and over 7000 body wave seismograms are included and the model is expressed in spherical harmonics up to degree and order 12. Our tests indicate a significant improvement in resolution of structure in the mid and lowermost mantle using the NACT technique as compared to the PAVA (Figure 1).

Another powerful procedure, not commonly applied so far in waveform modelling, is that, within each body wave trace, we assign different weights to each wavegroup, which may contain more than one bodywave phase. This improves the sampling of certain regions in the mantle by emphasizing phase groups whose amplitudes have a good signal to noise ratio, but are overwhelmed by other phases in the seismogram.
Our current models (e.g. Li and Romanowicz, 1995) show many features that are in agreement with other mantle tomographic models (e.g. Johnson et al., 1994; Su et al., 1994), but it also presents several characteristics of interest to the current geodynamical debate (Figure 2):

1) slab related features in the western Pacific and south America (figure 1) appear to extend across the 670 km discontinuity down to at least 800 km depth, in agreement with more detailed regional studies (Fukao et al., 1992; Grand, 1994) and numerical simulations with temperature dependent viscosity.

2) The profile of total rms amplitude of lateral heterogeneity as a function of depth is characterized by large amplitudes at the top and the bottom of the mantle, with a zone of increased rms near the core-mnantle boundary confined to a narrower zone (about 350 km thick) than in some other models.

3) There is a zone of increased rms centered around the 670 km discontinuity, which we have tested to be a stable feature of our models.

4) The spectrum of our model as a function of depth is characterized by the fact that the region of increased rms around the 670 km discontinuity is strongly dominated by degree 2, similarly to what is observed at the very bottom of the mantle, whereas in the mid-lower mantle, the spectrum is much more flat, possibly indicating the existence of a thermal boundary layer at the 670 km discontinuity.

There are still some gaps in the distribution of available data: the northern hemisphere is much better sampled than the more oceanic, southern hemisphere, resulting in poorer resolution in the lower half of the lower mantle in the southern ocean and Antarctica. The addition of global IRIS stations on islands in the southern Pacific and Atlantic ocean, as well as the deployment of semi-permanent broadband ocean floor observatories will enable to rectify this unbalance, which repeatedly brings up questions on the reliability of features seen by global seismic tomography, especially at shorter scales.