Dynamics of the transition zone under Europe inferred from wavelet cross-spectra of seismic tomography

Tomographical results are commonly presented in the form of color images and not much statistical quantification has been
carried out on the derived models. Correlation between different depths can shed important light concerning the dynamics.
We have generalized the application of multidimensional wavelets to investigate the products of two field variables, such as
the cross-spectrum, which is of paramount importance for quantifying the correlation between two depth levels of seismic
tomography with a multiple-scale character. For two multidimensional fields A and B, we calculate the correlation C by
projecting this as an Hermitian inner product in physical space with a two-dimensional (2D), fourth derivative of the Gaussian
wavelet as the weighting function. The correlation function C becomes now a multi-scaled function, a map cast in terms of
both the scale and location of the wavelet transform. Having calculated C, we can delineate the locations and length-scales
of the prominent features in the landscape of the correlation function. This wavelet formulation is very general and can be
extended to other types of statistical analysis, for example in a Kalman filter system. We have used a high-resolution (finer
than 1◦) seismic tomographical model for analyzing the extent of mantle layering under Europe by focussing on the different
length-scales in the correlation function involving the 3D seismic anomalies lying between 400 and 600 km depth. Between
the depths of 500 and 600 km under Europe, the wavelet correlation analysis shows that an ellipse-shaped object exists with
an area of 2000 km × 4000 km having a strong correlation for length-scales of around 400 km, and weaker correlation for
shorter length scales of around 150 km. On the other hand, between depths of 400 and 600 km, the correlation deteriorates
on the long length scales and becomes even worse at the short length scales. From the wavelet correlation spectra, we can
extract an horizontal characteristic length scale of around 100 km, which may be related to the boundary interaction between
the slab and the ambient mantle. The correlation results suggest that the thickness of the recumbent fast (cold) material in the
transition zone is between 100 and 150 km. This large elliptical pattern of presumably cold material would act to inhibit the
vigor of mantle convection locally beneath Europe today.

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