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 x 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.
Bibliographical noteFunding Information:
We acknowledge fruitful discussions with Drs. Walter D. Mooney, Marc Monnereau, Mike Navon, Montserrat Fuentes, Motoyuki J.B. Kido and Larry Boschi. We thank Prof. Enzo Boschi for his constant encouragement. This research was supported by geophysics program of the National Science Foundation and C.P. acknowledged also support from the Minnesota Supercomputing Institute and from Center for Research on Computation and its Applications.
Copyright 2007 Elsevier B.V., All rights reserved.
- Transition zone