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An open question in geophysics is how small-scale heterogeneities in wave speed are distributed within the Earth's mantle. These heterogeneities can be caused by temperature and/or compositional variations, and are assumed to have a profound influence on mantle dynamics. Conversely, insight into the characteristics of the heterogeneities would provide valuable clues on aspects of mantle dynamics such as mixing. The aim of this study by Laura Alisic with Jeroen Tromp is to utilize scattering of seismic waves by heterogeneities to constrain their characteristics, such as size, directivity, strength and location. Comparison of synthetic seismograms of heterogeneity models with synthetic seismograms of laterally homogeneous models can yield signatures of heterogeneity, which can then be utilized when comparing heterogeneous models with actual seismic data.

Various random distributions of heterogeneities are created, with varying dimensions, strength and depth range. The velocity fields belonging to these distributions are added to a background velocity field, PREM, which is then used as input for the global spectral-element software SPECFEM_GLOBE (references 1, 2). This software package allows for analysis of the full wave field, and no approximation of single scatterers is necessary. The numerical simulations are performed on 384 nodes, and have a shortest period of approximately 11 seconds. A set of differential timeseries is created by substraction of the resulting heterogeneous synthetic seismograms from the reference seismograms, which can then be analyzed. The source-receiver geometry is depicted in Figure 1.

Figure 1: Geometry of source (red) and receivers (blue). Receivers are located at every 2 degrees within arrays A and B.

Several examples for heterogeneity models are constructed, along with synthetics in three components belonging to those models. As source for the synthetics the June 9 1994 Bolivia event is used. The results are shown in Figures 2-5, where all differential seismograms are plotted with equal scaling (1/50th of the original seismogram amplitude).

 

Figure 2: Model 1. Whole mantle model, max. 0.7 % Vp variation, size of heterogeneities 75 km. (a) Heterogeneity model. (b) Vertical component of differential seismogram. (c) Radial component of the differential seismogram. (d) Transverse component of the differential seismogram.

 

Figure 3: Model 2. Lower mantle model, max. 0.7 % Vp variation, size of heterogeneities 75 km in the lowest 1000 km of the mantle. (a) Heterogeneity model. (b) Vertical component of differential seismogram. (c) Radial component of the differential seismogram. (d) Transverse component of the differential seismogram.

 

Figure 4: Model 3. Whole mantle model, max. 2.1 % Vp variation, size of heterogeneities 75 km. (a) Heterogeneity model. (b) Vertical component of differential seismogram. (c) Radial component of the differential seismogram. (d) Transverse component of the differential seismogram.

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Figure 5: Model 4. Whole mantle model, max. 0.7 % Vp variation, size of heterogeneities 30 km. (a) Heterogeneity model. (b) Vertical component of differential seismogram. (c) Radial component of the differential seismogram. (d) Transverse component of the differential seismogram.

The differential seismograms for the Bolivia 1994 event (Figure 2-5) show larger amplitudes for models with stronger heterogeneities, and smaller ones for lower mantle heterogeneity models. pPKKP and other multiples of PKKP are strongly influenced by the presence of heterogeneities in the lower mantle, and the coda to these phases is visible in whole mantle and lower mantle models. Figure 6 shows that PKKP waves can be reflected at shallower levels than the CMB and thus arrive later than the main phase. The transverse and radial components for the Bolivia 1994 event show strong precursors to the SS phase, especially in whole mantle models. SS waves can have a lower reflection point than the free surface, resulting in shorter ray paths, as indicated in Figure 6.

Figure 6: Geometry of scattered ray paths for SS and PKKP paths.

 

 

 

 

 

 

The computation of synthetic seismograms using various heterogeneity models as input for SPECFEM3D_GLOBE allows for identification of seismic phases most likely to be influenced by the presence of scatterers. The models presented here show that SS and pPKKP and multiples are highly interesting to analyze in future steps when real data is considered and compared to synthetics. This approach could then

yield insight into the nature of small-scale heterogeneities in the mantle, in terms of their strength, length scale and depth range.

The numerical simulations for this study were performed on Caltech’s Division of Geological and Planetary Sciences Dell cluster.

References
[1] D. Komatitsch and J. Tromp. Introduction to the spectral-element method for 3-D seismic wave propagation. Geophys. J. Int., 139 (3): 806-822, 1999.
[2] D. Komatitsch and J. Tromp. Spectral-element simulations of global seismic wave propagation-I. Validation. Geophys. J. Int., 149 (2): 390-412, 2002.

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