Extrapolation of low frequencies and application to physical modeling data

Scott Keating, Kristopher A. H. Innanen

A projection onto convex sets (POCS) based frequency extrapolation is tested on 1D synthetic and physical modeling data sets, with the goal of obtaining sufficient low frequencies for inversion. The effects of both noise and available frequency band are also investigated. The addition of noise is found to restrict the effectiveness of our inversion in recovering small impedance changes. Broad frequency ranges at high frequency are shown to produce similar results after extrapolation as small frequency ranges at low frequency. Application to physical modeling data met with moderate success, but offered substantive improvements in the inversion as compared to that of the original band-limited data.