© 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.