Dispersion Image Inversion

This type of inversion includes the use of dispersion image data (also called phase velocity spectra) instead of dispersion curve(s) that does not even involve the extraction of
modal curves at all (Ryden and Park, 2006; Forbriger, 2003a; 2003b) (
Fig. 1).  
This higher mode domination, largely ignored until recently, occurs more often than historically speculated.  Causes include special velocity (Vs and Vp) structure that, in turn,
includes not only reverse and irregular but also
normal velocity change with depth, damping (attenuation) effects of different modes, energy partitioning between different modes
at the time of surface wave generation (this often referred as
excitability), and effects from data acquisition and processing.  

The mode-mix problem means an extracted dispersion curve encompasses more than one mode.  For example, a curve of 10-30 Hz range may actually represent the
fundamental mode in the lower frequencies of, say, 10-15 Hz, while the rest follows the trend of a higher mode.  This also occurs more often than normally speculated
traditionally.  It happens when the energy domination of surface waves shifts from one mode (e.g., M0) to different mode (e.g., M1) as frequency (therefore wavelength) changes
from a certain range to another, which can be largely predicted from the concept of modal excitability.  Another cause for the mode-mix is the damping effect of surface waves that
changes with modes.  For example, although the M0 may dominate at the time of surface wave generation, the domination may get shifted to a higher mode after they travel a
certain distance because of the different attenuation history each mode has experienced.  This energy shift from one mode to another in a dispersion image can be observed as
either gradual or abrupt and, in turn, can be a result of an actual physical phenomenon, data processing effects, or a combination of both.
This approach eliminates such drawbacks with the modal-curve-based inversion as the mode-misidentification (Fig. 2)
and mode-mix (
Fig. 3) problems, both of which were not acknowledged until recently.  Mode-misidentification means
the incorrect mode identification for the extracted dispersion curve.  For example, a higher mode can be easily extracted
as the M0 curve if data acquisition and subsequent processing are not properly performed.  On the other hand, an
extracted curve originally identified as the first higher mode (M1) may actually be the second (M2) or third (M3), etc.,
mode.  A dispersion curve with incorrect modal identity can result in a significantly erroneous Vs profile because of the
lack of compatibility in the inversion process trying to match measured and theoretical curves.  
Fig. 1.
Fig. 2.
Fig. 3.