Inversion of shallow-seismic wavefields: I. Wavefield transformation

I calculate Fourier-Bessel expansion coefficients for recorded shallow-seismic wavefields using a discrete approximation to the Bessel transformation. This is the first stage of a fullwavefield inversion. The transform is a complete representation of the data, recorded waveforms can be reconstructed from the expansion coefficients obtained. In a second stage (described in a companion paper) I infer a 1-D model of the subsurface from these transforms and P-wave arrival times by fitting them with their synthetic counterpart. The whole procedure avoids dealing with dispersion in terms of normal modes, but exploits the full signal-content, including the dispersion of higher modes, leaky modes and their true amplitudes. It is robust even in the absence of a priori information. I successfully apply it to the near field of the source. And it is more efficient than direct inversion of seismograms. I have developed this new approach because the inversion of shallow-seismic Rayleigh waves suffers from the interference of multiple modes that are present in the majority of our field data sets. Since even the fundamental-mode signal cannot be isolated in the time domain, conventional phase-difference techniques are not applicable.