Dispersion Imaging Scheme (Passive Roadside MASW)

In spite of the 1-D receiver array used, the dispersion imaging scheme for the passive
remote survey (Park et al., 2004) can also be used if source points are located far away
from the array (e.g., a distance greater than ten times the array size) and therefore
recorded surface waves can be approximated as plane wave propagation.  In this case,
the imaging resolution will be reduced due to the 1-D nature of the array.  On the other
hand, any scheme for an active survey can be used if source points are inline (
Fig. 1a).    

In the case of a passive survey alongside a road, however, points of surface wave
generation are usually on the road since waves are generated when moving vehicles
travel over irregularities on the road surface.  Therefore source points can be fairly close
to the receiver array, violating the plane-wave assumption.  In addition, because the
receiver line is always off the road, the wave propagation is therefore hardly in
accordance with inline propagation although being close to it when sources are at far
distances on a fairly straight road.  If strong waves from nearby source points are
recorded and their offline nature is not accounted for during dispersion analysis, phase
velocities are overestimated approximately in inverse proportion to the cosine of the
azimuth. Furthermore, considering relatively strong energy from nearby source points,
the dominating mode of propagation may be not only offline but also cylindrical with a
wavefront whose curvature cannot be ignored (
Fig. 1c).  

Park and Miller (2005) account for these offline and cylindrical characteristics and
compare results to those from the conventional analysis scheme based on the inline
plane wave propagation.  The offline nature is accounted for by the passive remote
scheme (Park et al., 2004) that scans through a possible range (180 degrees because
of the 1-D array) of incoming azimuths of dominating waves for each frequency
component.  Then, all the energy in this phase velocity-azimuth space is stacked
(summed) along the azimuth (theta) axis to account for multiple energy peaks that may
represent different modes and sources.  During this azimuth scanning before the
stacking, however, an attempt is made to account for the cylindrical nature by an
additional scheme that calculates the approximate distance between a specific receiver
and a possible source point, which is in turn determined from the consideration of
azimuth and approximate distance between the receiver line and the road (
Fig. 2).  This
consideration can correct for the overestimation to some degree but not completely,
indicating that a true 2-D array has to be used for the most accurate estimation.  The
incomplete correction becomes more significant for longer wavelengths.  Tests with
specific field data sets show the overestimation caused by the conventional inline
processing that considers all the recorded wavefields as being perfectly inline can be
as large as 30 percent, but the overestimation can be reduced to less than 10 percent
by using this scheme (
Fig. 3).

Two options are proposed in Park and Miller (2008).  One is to use the scheme for the
passive remote survey (Park et al., 2004) with azimuth scanning range of 0-180
degrees.  This can be the choice if the array is relatively remote (e.g., distance to the
nearest road is 5-10 times the array size) or surface waves may come from multiple
roads running in different azimuths.  This first option covers the case of offline plane
propagation.  The second option is to consider offline cylindrical propagation by
modifying the previous scheme slightly.  The modification takes place in azimuth-energy
mapping where previously for a given azimuth the same phase shift was considered for
all the receiver points because of the plane-wave assumption.  The necessary phase
shift now changes with the receiver location because of the finite distance between the
source and receiver points according to the distance calculation principle depicted in
Fig.  2.  The vertical offline distance (dy) is the distance between the receiver array and
the center of the road.  This option may be the choice when the survey takes place near
a road that is fairly straight and is the only major road in the vicinity.    
Fig. 1.  Three different types of possible surface wave propagation with a roadside survey
method employing a 1-D linear receiver array parallel to road (from Park and Miller, 2008)
(Right) Fig. 2.  Distance calculation for each receiver point to account for the offline
cylindrical (OC) propagation.

(Below) Fig. 3.  Actual field data example of dispersion curves from different types of surveys
at the same site indicating different degrees of deviation from the most reliable result from
the survey with a 2-D receiver array (from Park and Miller, 2008).