Inversion of shallow-seismic wavefields: II. Inferring subsurface properties from wavefield transforms

The problem of inferring subsurface properties from shallow-seismic data is solved by a two-stage scheme that fits the full wavefield by its synthetic counterpart. In a first stage (described in a companion paper) I derive Fourier-Bessel expansion coefficients for the recorded data through a wavefield transformation. The present paper describes the joint inversion of these coefficients together with P-wave arrival times to infer subsurface properties. In this way we exploit the full signal-content including the dispersion of higher-modes, leaky-modes, their true amplitudes, and, at least partly, body waves. Owing to the multi-mode character of shallow-seismic field-data conventional techniques of dispersion analysis are not applicable. Since an initial model appropriate for inversion of full seismograms is rarely available in shallow seismics, the direct inversion of waveforms is not feasible. The wavefield transformation removes a remarkable amount of non-linearity from the data. In consequence the proposed method is robust even in the absence of a priori information. In distinction to the inversion of dispersion curves, it does not require the identification of normal-modes prior to inversion. The method performs well when applied to the multi-mode wavefields present in most shallow-seismic data sets. Compared to waveform fitting, it can be more efficient by about a factor of ten, because we need not evaluate the Bessel-expansion and therefore need less calculations of the forward problem. Subsurface properties are derived for the two sets of field-data that were already presented in the first paper. One of them includes a pronounced low-velocity channel. For both we observe a remarkably good resolution of S-velocity down to the bedrock, which is found in 6 and 16 m depth, respectively. In both cases it would not be possible to infer the depth of bedrock from P-wave data alone. Synthetic seismograms calculated from the final model match the recorded waveforms surprisingly well, although no waveform fitting was applied. A subsequent waveform inversion becomes feasible with initial models taken from the results of this method. Finally it is shown by example, that conventional techniques of dispersion-curve fitting are likely to give misleading results when applied to our field-data.