I am interested in
study and modelisation of seismic waves
We measure body wave delays by cross-correlation. To do so requires
a good knowledge of the source time function. The SCARLET scheme (Vallee et al., GJI 183:338, 2010) allows us to do so efficiently and reliably.
The finite frequency sensitivity of seismic delay times is rather
complicated. On the one hand, this enables us to resolve more detail.
But on the other hand, this forces us to parameterize the Earth in
such a way that the detail offered by the sensitivity is not
smoothed away by the coarse parameterization that is usually
adopted in global tomography.
We parameterize the Earth's mantle with about 3.6 millions pixels.
Evidently, we will never be able to resolve each of them. This asks
for new methods of regularization, which are being developed
by Frederik Simons (Princeton), Ignace
Loris (Bruxelles), Ingrid Daubechies (Duke) and us, and which we test on a data set
of multiple frequency delay times originally
compiled by Sigloch et al. (Nature Geosci., 1, 458-462, 2008). The
principle is to find a model that can be fitted with the minimum
number of wavelet coefficients. The choice of wavelets is still
open. In the example above - which shows the input and output
of a checkerboard test over USArray - the logical
choice of wavelets are the Haar wavelets.
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