Looking at the Inside of the Earth with 3-D Wavelets: A Pair of New Glasses for Geoscientists

Current seismic tomographical models produce databases with increasing size and higher spatial resolution. Consequently, direct visual inspection and interrogation of the seismic database are becoming more and more an arduous and time-consuming task. Recently, it has been shown that feature extraction can be emphasized and simplified by the use local spectra extraction (LSE) obtained from Gaussian wavelet transform (Bergeron et al., 1999). For example, such a feature may be the subducting slab under Japan or a plume-like object beneath the transition zone under Iceland. A drawback of the LSE is that the physical space dimensionality is added by 1, thus increasing greatly the information content. Our approach is to assimilate and synthesize the set of local spectra by using two proxy quantities: the spatial distributions of the local maxima of the L2-norm, E-max, and the associated local wavenumber, k-max. We propose to test this new computer vision method with two types of noisy synthetic data in order to emphasize the basic strengths and features of this novel method. We show that even if the signal to noise ratio is very low (less than 1dB), the presence of a slab and a plume or columnar structure can be detected in the k-max spatial distribution. The E-max proxy detects background fluctuation modulated by the sharp peaks in the spatial patterns. Without any a-priori knowledge, we cannot perceive these subtleties by a direct visual inspection of the raw data set. With our numerical experiments, we have developed a database of synthetic patterns, as in a dictionary, which can prove to be useful for the geophysical community for comparing with new local tomographic models. Examples of this operation can be viewed on the web. The P1200 tomographical model from Zhou (1996) is also analyzed and zoomed "in" with wavelets. Most prominent of this geophysical example are the significant depth extent of the plate-tectonic boundaries around Asia and the signature of the megaplume under the East African rift.