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Progress in modeling deep mantle isotropic shear and compressional velocity structure using waveform inversion

Mark Panning and Barbara Romanowicz


Seismic tomography is an important tool for determining the structure and dynamics of the Earth's mantle. It is a technique which utilizes geophysical inverse theory to use large amounts of seismic data (both travel times and waveforms) to model the elastic structure of the Earth. With the use of nonlinear asymptotic mode coupling theory (NACT) (Li and Romanowicz, 1996) and three component body and surface waveform data, we are able to model 3D isotropic shear and compressional velocity structure throughout the mantle.

Figure 34.1: (A) Comparison of SAW24B16 and the isotropic S velocity model in the core-mantle boundary region. Inversions are also shown for only the L component data and only the Z component data. (B) P velocity models P16B30 (Bolton, 1996) and WEPP2 (Fukao et al., 2001) are shown for comparison.
\epsfig{file=panning02_1_1.epsi, width=8cm}\end{center}\end{figure}

While simultaneous models of shear and compressional velocity (or alternatively shear and bulk sound velocity) with P sensitivity based primarily on travel times (i.e. Masters et al., 1999) have been developed, very little work has been done to explore $V_P$ modeling using waveforms due to the higher dominant frequency of $V_P$ data.

Degree 24 Isotropic S Velocity Model

We inverted 3 component body and surface wavepackets for mantle S velocity. We used SAW24B16 (Mégnin and Romanowicz, 2000), an SH velocity model based only on T component data, as a starting point. However, since our new model uses all three components of data, it is a model of isotropic $V_S$ perturbations. The model obtained has similar T component variance reduction to SAW24B16, while performing significantly better for L and Z component data. Features in the uppermost mantle are what we would expect due to SV/SH anisotropy observed in other upper mantle models (e.g. Ekström and Dziewonski, 1998: Montagner and Tanimoto, 1991). An interesting difference can be seen between the two models in the western Pacific in the core-mantle boundary region (figure 34.1). The isotropic model has a pronounced fast anomaly in this area, while it is slow in the SH model. Resolution tests indicate this feature to be robust. Since this model differs from the SH model by including L and Z component data, we inverted only the latter datasets to see where the signal originates. While L component data produces a model similar to the SH model, the model from Z component data is quite different. Since most S sensitivity in the core-mantle boundary region is from vertically arriving phases such as SKS and Sdiff, which will primarily show up on the L component, this provides a hint that the signal may originate from $V_P$ energy. This enters our model through an assumed $d(\ln{V_S})/d(\ln{V_P})$ scaling relationship. Figure 34.1 also shows two $V_P$ mantle models. While the models differ, both show a fast anomaly in the western Pacific.

Waveform Inversion for P Velocity Structure

Due to the apparent $V_P$ contamination in the isotropic $V_S$ model, we tested whether we could perform a direct waveform inversion for $V_P$ structure. Coverage tests indicate that there is some coverage throughout the mantle, although significantly less than $V_S$ sensitivity. For the inversion, the S velocity was fixed to that of SAW24B16 truncated to degree 12, and the P velocity was perturbed from the PREM velocities. The degree 8 $V_P$ model in figure 34.2 gives a variance reduction of 45% compared to 39% for truncated SAW24B16 with no P model. For long wavelengths, it is quite similar to P16B30 (Bolton, 1996),

Figure 34.2: Comparison of P velocity models up to degree 8 for this study (left) and P16B30 (right).
\epsfig{file=panning02_1_2.epsi, width=8cm}\end{center}\end{figure}

indicating the method has potential. With a more optimal datset (with periods shorter than 32s cutoff here and wavepackets detter defined for P phases), a waveform inversion for $V_P$ mantle structure appears to be feasible.


The degree 24 isotropic $V_S$ model differs from SAW24B16 in several areas of the mantle. While these changes can be due to SV/SH anisotropy or other causes, the differences in the models in the core-mantle boundary region appear to be caused by $V_P$ signal, indicating a potential breakdown in $d(\ln{V_S})/d(\ln{V_P})$ scaling relationships. Although more data coverage is needed, preliminary tests indicate modeling $V_P$ structure using waveform inversion is possible.


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


Bolton, H., Long period travel times and the structure of the mantle. Ph.D. Thesis, La Jolla, 204 pages, 1996.

Ekström, G. and A.M. Dziewonski, The unique anisotropy of the Pacific upper mantle, Nature, 394, 168-172, 1998.

Fukao, Y., S. Widiyantoro and M. Obayashi, Stagnant slabs in the upper and lower mantle transition region, Rev. of Geophys., 2001.

Li, X.D., and B. Romanowicz, Global shear velocity model developed using nonlinear asymptotic coupling theory, Jour. Geophys. Res., 101, 22,245-22,272, 1996.

Masters, G., H. Bolton, and G. Laske, Joint seismic tomography for P and S velocities: How pervasisve are chemical anomalies in the mantle? EOS Trans. AGU, 80 S14, 1999.

Mégnin, C., and B. Romanowicz, The 3D shear velocity of the mantle from the inversion of body, surface, and higher mode waveforms, Geophys. Jour. Intl., 143, 709-728, 2000.

Montagner, J.P., and T. Tanimoto, Global anisotropy in the upper mantle inferred from the regionalization of phase velocities. Jour. Geophys. Res., 95, 4797-4819, 1990.

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