Surface seismic imaging by multi-frequency amplitude inversion

We have developed a new full-waveform inversion scheme for crosshole seismic imaging. In this paper, we adapt it to surface seismic imaging in which only the spectral amplitudes are used. We perform numerical experiments to test the known source signature algorithm (KSS) against two other inversion schemes?one which estimates the source signature from the shot gathers (ESS) and the other which avoids knowledge of the source by using normalized data (NDI). All three approaches rely on a finite element method for the 2D/2.5D acoustic modelling, and operate in the frequency domain. Three shallow subsurface models were considered, representing buried karst topography, dipping blocks, and isolated waste ponds. The synthetic experiments involved only a limited number of 'surveys' with just 8, 3, or 1 shots into variable-length geophone arrays. In all cases, conventional seismic data processing fails to recover the structure. The spectral inversions, which use frequencies over the range 50?400 Hz, involve the entire seismograms, including primaries, multiples, direct waves, etc. The features in the models typically have dimensions of 5?20 m, which can be compared with the geophone spread length of 40 m (8 shots) to 100 m (3 or 1 shot). The 8 shot inversion performed best for all the models. In fact, it was not possible to recover the karst structure with just 1 or 3 shots, but the other models were recovered, albeit with less accuracy, using such a small number of shots. ESI and NDI perform remarkably well on the dipping-block and waste-pond models. KSS yielded superior results to the other two schemes. The estimated source spectra were close to but did not exactly match the known wavelets. Imaging results are most impressive for such a small number of shots.