Typical Inversion with the MASW Method

This is the most common type of inversion used with the multichannel approach (MASW).  Goal of the field survey and subsequent data processing before inversion takes place
is to establish the fundamental mode (M0) dispersion curve as accurately as possible, which has been one of the key issues with data acquisition and processing in the history
of surface wave applications.  Theoretical M0 curves are then calculated for different earth models by using a proper forward modeling scheme, the most common type of which
is the one by Schwab and Knopoff (1972), to be compared against the measured (experimental) curve (
Fig. 1).  This inversion approach is based on the assumption that the
measured dispersion curve represents the M0 curve only not influenced by any other modes of surface waves.  On the other hand, the concept of
composite (or apparent)
dispersion curve is used in the
SASW method accounting for the multi-modal influence as the modal separation cannot be accomplished only with two receivers.  
Key issue with this inversion approach has been the optimization technique to search for the
most probable earth model among many other candidates as much efficiently as possible.  The
root-mean-square (R-M-S) error (
Fig. 2) is usually used as an indicator of the closeness between
the two dispersion curves (measured and theoretical), and the final solution is chosen as the 1D
Vs pofile resulting in a preset (small) value of R-M-S error.  Either a deterministic method such as
the least-squares method (Menke, 1989; Xia et al., 1999) or a random approach (Socco and
Boiero, 2008, for example) is taken for the optimization (
Fig. 3).  The former type is usually faster
than the latter type at the expense of the increased risk of finding a local, instead of global,
minimum.  Research issues in each type therefore have been how to reduce the level of this risk
with the former type, whereas how to improve the speed with the latter type.  Another pitfall
common to both types (perhaps intrinsic to all types of inversion) is the risk of numerical artifacts.  
For example, although a solution with a smaller R-M-S error is numerically correct, it may not
necessarily represent a more realistic one (
Fig. 4).
Fig. 1.
Fig. 2.
Fig. 3.