Surface wave methods gained in the past decades a primary role in many seismic projects. Specifically, they are often used to retrieve a 1D shear wave velocity model or to estimate the V S,30 at a site. The complexity of the interpretation process and the variety of possible approaches to surface wave analysis make it very hard to set a fixed standard to assure quality and reliability of the results. The present guidelines provide practical Electronic supplementary material The online version of this article

SUMMARY 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 full‐wavefield 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. The potential to reconstruct the full waveform from the transform is confirmed by two field‐data examples, which are recorded with 10 Hz geophones at effective intervals of about 1 m and spreads of less than 70 m length and are excited by a hammer source. Their transforms are discussed in detail, regarding aliasing and resolution. They reveal typical properties of shallow surface waves that are at variance with assumptions inherent to conventional inversion techniques: multiple modes contribute to the wavefield and overtones may dominate over the fundamental mode. The total wavefield may bear the signature of inverse or anomalous dispersion, although the excited modes have regular and normal dispersion. The resolution at long wavelengths (and thus the penetration depth of the survey) is limited by the length of the profile rather than by the signal‐to‐noise ratio at low frequencies. Finally, this approach is compared with conventional techniques of dispersion analysis. This illustrates the advantage of conserving the full wavefield in contrast to the reduction to one dispersion curve.

SUMMARY 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.

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Full-waveform inversion (FWI) of Rayleigh waves is attractive for shallow geotechnical investigations due to the high sensitivity of Rayleigh waves to the S-wave velocity structure of the subsurface. In shallow-seismic field data, the effects of anelastic damping are significant. Dissipation results in a low-pass effect as well as frequency-dependent decay with offset. We found this by comparing recorded waveforms with elastic and viscoelastic wave simulation. The effects of anelastic damping must be considered in FWI of shallow-seismic Rayleigh waves. FWI using elastic simulation of wave propagation failed in synthetic inversion tests in which we tried to reconstruct the S-wave velocity in a viscoelastic model. To overcome this, Q-values can be estimated from the recordings to quantify viscoelasticity. Waveform simulation in the FWI then uses these a priori values when inferring seismic velocities and density. A source-wavelet correction, which is inevitable in FWI of field data, can compensate a significant fraction of the residuals between elastically and viscoelastically simulated data by narrowing the signals' bandwidth. This way, elastic simulation becomes applicable in FWI of data from anelastic media. This approach, however, was not able to produce a frequency-dependent amplitude decay with offset. Reconstruction, therefore, was more accurate when using appropriate viscoelastic modeling in FWI of shallowseismic Rayleigh waves. We found this by synthetic inversion tests using elastic forward simulation as well as viscoelastic simulation with different a priori values for Q.