We address various issues associated with the applicability of the generalized Radon transform (GRT) inversion to global seismic data:(i)Holes' in the data acquisition manifold, (ii) The irregular(source-receiver) sampling of the acquisition manifold, and (iii) The high levels of coherent (harmonic) and random noise propagating through the inversion operator applied to the data. The degree of redundancy in the data is used in partly resolving these issues.
Concerning the first issue, we analyze the procedure of data continuation. Data continuation is decribed by an elliptic minimal projector derived from annihilators of the data, and provides us with the insight what `imperfections' of the acquisition manifold are permissible. Concerning the second issue, we discuss the optimal quasi-Monte Carlo sampling that yields the (sparse) discretization of the inversion operator. We briefly touch upon the third issue and introduce the notion of mixed-effects statistical models connected with the GRT. The common element in the treatments of the various issues is the analysis and sampling of the range of the Fourier integral operator that models the relevant part of the data.
We illustrate the application of our inverse scattering procedure to core-mantle boundary (CMB) imaging below Central America from earthquake generated data: We use the S (SH) coda wave containing the ScS phase (topside CMB reflection) and the SKS (SV) coda wave containing the SKKS (underside CMB reflection) for this purpose.
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