© 2014 European Association of Geoscientists & Engineers 361 * gkritik@mred.tuc.gr Near Surface Geophysics, 2014, 12, 361-371 doi: 10.3997/1873-0604.2014013 Comparative study of different inversion techniques applied on Rayleigh surface wave dispersion curves George Kritikakis 1* , Antonis Vafidis 1 , Konstantinos Papakonstantinou 2 and Adam O’Neill 3 1 Applied Geophysics Laboratory, Technical University of Crete, Polytechnioupolis, Kounoupidiana, 73100, Chania, Greece 2 IPI Consulting, Monastiriou 100 st., 10442, Athens, Greece 3 DownUnder GeoSolutions Pty Ltd, Level 3, 76 Kings Park Rd, West Perth, WA 6005, Australia Received July 2012, revision accepted September 2013 ABSTRACT This study examines the performance of different inversion techniques applied on Rayleigh surface wave dispersion curves. The kriSIS algorithms implement the Quasi-Newton method, the L1 norm minimization, smoothness, damping and minimum gradient constraints and their combinations, as well as weighted inversion. Furthermore, any a priori geophysical or/and geotechnical information can be taken into account during the inversion. The proposed methodology is applied on two syn- thetic dispersion curves as well as two synthetic seismic records. Eight inversion parameters were tested per examined model resulting in 7680 tests. Three of them were tested on real data. The main outcome of this comparative study indicates that, for the tested models and real data, the Least Squares (L2 norm) inversion, using smoothness constraint and calculating the Jacobian matrix from analytical relationships or arithmetic differentiation, leads to the most reliable and accurate inver- sion results. The accuracy of an estimated subsurface model is controlled by at least four kinds of errors, which propagate through the seismic acquisition-processing-inversion flow (O’Neill 2003): 1) Raw and transformed data errors (seismic noise, dispersion picking errors, misidentified higher modes, side scattered wavefields). These kinds of errors are the most important ones, since in the case of the picking of wrong dispersion curves, there is no inversion algorithm to produce the correct subsurface Vs model. Recently Dal Moro and Ferigo (2011) and Dal Moro (2011) developed a joint inversion methodol- ogy, using Rayleigh, Love and HVSR data, to reduce the uncertainty of inverting wrong individual data; 2) Inexact forward modelling (plane-wave mode assumptions, body waves not accounted for, one-dimensional (1D) model assumptions in laterally varying media); 3) Inappropriate parameterization (linearization of the disper- sion function, a priori number of layers, elastic assumptions); 4) Detection of the global minimum (very complex objective functions, especially those with sharp stiffness contrasts). Even with infinite data, no errors and perfect parameteriza- tion, the estimated model is non-unique (Luke et al. 2003; Dal Moro, Pipan and Gabrielli 2007; Foti et al. 2009), which is fundamental to all inverse problems. The degree of equiva- lence in surface wave inversion is highly model dependent but, in general, increases with depth (Dal Moro 2011). The INTRODUCTION Shear wave velocity determination from ground roll has undergone rapid development in near surface geophysics in the last few years. Multichannel Analysis of Surface Waves (MASW), initially intro- duced by Park, Miller and Xia (1999), is among the proposed techniques for that purpose. This method requires multichannel seismic records rich in Rayleigh waves. There are several ways to extract experimental (fundamental and higher modes) dispersion curves (Nolet and Panza 1976; Park, Miller and Xia 1999; Lin and Chang 2004; Vignoli et al. 2011), such as from the local maxima of seismic energy on the frequency-phase velocity (f–c) domain (McMechan and Yedlin 1981). The theoretical dispersion curves are calculated for horizontally layered medium using model param- eters, such as P and S-wave velocity (Vp and Vs), thickness (h) and density (ρ) and using forward modelling methods, such as Thomson-Haskell (TH) (Schwab and Knopoff 1972). Dispersion curves are mostly dependent on the shear wave velocity (Vs) (Xia, Miller and Park 1999). Since the other model parameters do not strongly influence the dispersion curves, Vs depth profiles are esti- mated from the Rayleigh dispersion curves, using inversion tech- niques. These depth profiles are set at the centre of the geophone spread (Luo et al. 2009), and subsequently Vs pseudo-sections can be created using roll along acquisition techniques.