ONeill_SurfaceWave_discuss

Seismic surface waves in shallow site investigations
Part I: Higher-mode observations and inversion issues
Adam O’Neill*, Jamhir Safani, Keiji Nagai and Toshifumi Matsuoka
Department of Civil and Earth Resources Engineering, Kyoto University, Japan
adam@earth.kumst.kyoto-u.ac.jp
http://earth.kumst.kyoto-u.ac.jp/~adam
*Presently:
DownUnder GeoSolutions, Subiaco, Western Australia
adamo@dugeo.com
http://www.dugeo.com
ABSTRACT
A major limiting restriction for accurate, rapid surface wave inversion is in correct mode identification and
modeling. Smooth transitions to higher modes at low frequency can occur if both shear wave velocity contrast
(scaled by the overburden layer thickness) is from 50-150% and S-wave velocity of half-space is from 50-150%
of the P-wave velocity in the top layer. This makes them more likely to be observed at sites with low Poisson’s
ratio. Leaky modes can also become dominant at low frequency, but only when the S-wave velocity of a given
layer is less than the P-wave velocity of the overlying layer.
Love waves can exist where a Low Velocity Layer (LVL) exists below a stiff surface, however, propagate as
increasingly higher modes with increasing frequency and mode-identification is difficult, and unlike Rayleigh
waves, where a High Velocity Layer (HVL) exists at shallow depth below a soft surface, Love wave propagation
is dominated by the fundamental mode. Incorporating more higher surface wave modes in the inversion process
increases vertical resolution, particularly where the low-frequency data is limited, common in active-source
surveys with short geophone spreads.
Introduction
In a recent special issue on ‘seismic surface waves’ (O’Neill, 2005), three primary issues with the method for its use
in shallow site investigation were consistently raised:
(1) Higher modes,
(2) Wavefield scattering, and
(3) Acquisition parameters
The higher-mode problem invariably arises when large stiffness contrasts and velocity reversals exist, and
wavefield scattering occurs when surveying around lateral geological, cultural or topographic variations. Acquisition
parameter effects are by far the least problematic issue – especially in ideal sites (flat, normally dispersive layering).
In this paper (Part I), using previously published and new models and data, some problems with higher modes
identified by other researchers are quantitatively investigated and reiterated with numerical and field datasets. In a
following paper (O’Neill et al., 20xx, hereafter referred to as Part II), measurement and imaging issues with wavefield
scattering and acquisition parameters are investigated, and a discussion of some unusual surface wave dispersion due
to side-scattering is offered.

Higher Modes at Low Frequency
Synthetic Tests
Bodet et al., (2005) showed by physical modeling using a laser-Doppler system the limitations with linearised,
fundamental mode inversion when a large elastic contrast is present. When a stack of many layers is used, the vertical
smoothing of the estimated shear-wave velocity (VS) model between the over- and underlying layer increases with the
depth of the half-space interface. One problem arose where the overlying layer was relatively thin. It was noticed that
the observed dispersion at low frequency does not follow the theoretical fundamental mode but coincides with the first
higher modes, a pitfall described earlier by Socco and Strobbia (2005).
The 4 mm PMMA plate profile of Bodet et al., (2005) was synthetically modeled using the full-wavefield
reflectivity method of O’Neill et al., (2003). The same acquisition geometry was employed – 101 traces at 0.4 mm
spacing, from 10 mm near-offset – however, dimensions were scaled up by 1000 (millimetres to metres), thus
frequencies down by 1000 (kHz to Hz). As shown in Fig. 1, the observed ‘effective’ dispersion does transition to the
first higher mode at low frequency, at a so-called ‘osculation point’ (Denil, 2005), which is where the dispersion
function roots (i.e. wavenumbers) approach in frequency-phase velocity space.
Inversion of the observed dispersion using the full-wavefield kernel, with similar frequency limits and
parameterisation as the original publication, is shown in Fig. 2. Since the low frequency dispersion is not assumed as
the fundamental mode, the underlying aluminium stiffness correctly estimated, whereas in Bodet et al., (2005) it was
overestimated by nearly 30%.
Similarly, Denil (2005) showed by numerical simulations of a 2-layered case, that where there is a large stiffness
contrast, transitions to dominant higher modes can occur. It is interesting to note, that the synthetic shear wave
velocity model 1d of Denil (2005) (a 5 m layer of 330 m/s over 960 m/s half-space) shows very similar scaled shear
wave velocity ratios to the physical models of Bodet et al., (2005) (both 3 mm and 6 mm layers of 1280 m/s over 3200
m/s substrate) - that is, 2.9 and 2.5 respectively. A simulation of models 4a and 4d of Denil (2005) is shown in Fig. 3.
In model 4a (Figs 3 (a) and (b)) there is a definite transition to a higher mode at low frequency. However, even though
the shear wave velocity contrast in model 4d is much higher, the dispersion is dominated by the fundamental mode
(Figs 3 (c) and (d)).
Empirical Rules
Based on the 2-layer models of Bodet et al., (2005) and Denil (2005), it can be seen that jumps to dominant higher
modes at low frequency occur only when both the following two empirical conditions are satisfied:
0.5 < VS2/(VS1*h1) < 1.5 (1)
0.5 < VS2/VP1 < 1.5 (2)
Or, in other words:
(i) Shear wave velocity contrast at a stiff interface (scaled by the overburden layer thickness) ranges from 50-150%,
and
(ii) S-wave velocity of half-space is from 50-150% of the P-wave velocity in the top layer.
These parameter combinations are typical of field scenarios where a stiff half-space of moderate Poisson’s ratio (e.g.
gravels/rock) underlies a thin overburden of low(er) Poisson’s ratio (e.g. dry sands). If the overburden is of high

Poisson’s ratio (e.g. saturated sand or clay), then Equation 2 will not be satisfied, thus higher modes probably not
generated.
Applying Equations 1 and 2 to the models of Denil (2005), the results are given in Table 1. Only Models 1d (not
shown here) and 4a (Fig. 3a) show a jump to higher modes at low frequency, since both Equations 1 and 2 are
satisfied. Levshin and Panza (2005) show a similar case, where VS2 = 1.5VP1, similar to model 4d of Denil (2005), but
illustrating how an osculation point exists between the fundamental and first higher modes. This is due to critical
reflected P-waves in the waveguide becoming trapped as part of the Rayleigh wavefield. However, that model does
not satisfy Equation 1 (VS2/(VS1*h1) = 1500/(500*10) = 0.3), thus higher modes are not expected.
Field Example 1: Low Poisson’s Ratio
Shot data and associated dispersion at a field site in Australia (O’Neill, 2003) is shown in Fig. 4. This site
comprises unconsolidated gravel/sand/silt overburden over weathered bedrock, with fresh granite at about 6.5 m depth.
The direct P-wave velocity is in the order of 1000 m/s, making the near-surface Poisson’s ratio about 0.35. The sharp
phase velocity increase at about 40 Hz appears very much like that in Fig. xx, where the fundamental mode transitions
smoothly to the first higher mode.
Assuming a similar VP/VS ratio for the crystalline rock as in the overburden, the dispersion was inverted using the
full-wavefield modelling of O’Neill et al., (2003) and the results shown in Fig. 5. The layer interfaces were
constrained to those of the lithological contrasts identified in a shallow auger log, except for the uppermost 0.9 m of
the profile, which was sub-divided into two, 0.45 m thick units.
The theoretical modal and effective dispersion curves associated with the best-fitting model are shown in Fig. 6,
along with the field dispersion. The transition from the fundamental to the first higher mode at about 40 Hz is clearly
visible. The empirical rules of Equations 1 and 2 are not exactly applicable in this case, due to the multi-layered,
irregular velocity structure. However, if representative 2-layer averages are taken as VS1 = 500 m/s, VS2 = 1300 m/s,
h1 = 5 m and VP1 = 1000 m/s, then both are satisfied (0.52 and 1.5 respectively).
Field Example 2: High Poisson’s Ratio
Kaufmann et al., (2005) showed near-coincident land and marine data where a limestone layer was known to exist
below a sandy overburden at about 5 to 9 m depth. Using commercial software, limited to a fundamental mode
assumption, and ‘blindly’ parameterized to 10-layers, the inversion results showed a shear wave velocity gradient in
the ‘bedrock’. The data and dispersion from that on-land site is shown in Fig. 7. As in the original publication, there is
a sharp discontinuity in the main dispersion lobe at about 13 Hz, and at even lower frequency, there is possibly a leaky
mode component (O’Neill and Matsuoka, 2005).
Inversion of the effective dispersion curve, using the full-wavefield modelling of O’Neill et al., (2003) is shown in
Fig. 8. The image is cropped at 25 Hz for clarity, but the same input dispersion frequency range (8 to 40 Hz) and layer
parameterisation as Kaufmann et al., (2005) has been duplicated. The estimated ‘Final’ model shows a large stiffness
contrast at about 5-7 m depth, compared to the 10-layered model of Kaufmann et al., (2005), represented by the ‘True’
profile.
It was originally thought that the large discontinuity at 13 Hz was due to a dominant higher mode. Such
discontinuities have been observed in both field and synthetic data, where a large elastic contrast exists at shallow
depth (O’Neill et al., 2003). However, upon calculating the modal dispersion response of the newly estimated model,
it can be seen that the dispersion is apparently dominated by the fundamental mode, as shown in Fig. 9. This seems
reasonable, since the Poisson’s ratio of the uppermost layer(s) are high (for the shot gather used here, a P-wave

velocity of 2050 m/s is interpreted from the first arrivals), thus Equation 2 (VS2/VP1 = 550/1250 = 0.44) is not
satisfied.
One possible problem with the original 10-layer inversion result of Kaufmann et al., (2005) comes from the
estimated VP/VS ratio of the top of the limestone. They estimated 2400 m/s for the limestone (averaged over the entire
line), thus at a nominal 7 m depth, if the estimated S-wave velocity is taken as 260 m/s, the VP/VS ratio of the upper
portion of the limestone is in the order of 7.9 to 9.2 (Poisson’s ratio exceeding 0.49). Even the homogenous half-space
S-wave velocities of 450 m/s in both the 10- and 3-layered models of Kaufmann et al., (2005) give a VP/VS ratio of
4.7-5.5. While a P-wave velocity of 2400 m/s is plausible even for highly weathered and porous rock, and even
though there is no theoretical limit to the maximum bulk- to shear-modulus ratio for a grain-pore assemblage, given
by the Hashin-Shtrickman bounds (Mavko et al., 1998), such low S-wave velocities of limestone are unlikely.
The full-wavefield inversion result gives an S-wave velocity of 530-560 m/s, thus a VP/VS ratio for the limestone of
about 3.7 to 4.5 (Poisson’s ratio around 0.47). Empirical tests show that water-saturated limestones obey a VP-VS
best-fit relationship of (Mavko et al., 1998: p. 236):
VS = -0.05508 VP
2
+ 1.0168 VP – 1.0305 (3)
Thus, for a P-wave velocity range of 2000-2500 m/s, the VP/VS ratio should be around 2.1 to 2.5. The full-wavefield
inversion result is closer to this value, and the dispersion fit makes the estimate more likely. While the refraction
model may be nonunique (Foti et al., 2003), it is more probable that in the original work of Kaufmann et al., (2005),
VS of the limestone (especially the upper part) was systematically underestimated, possibly from modelling
inconsistency or inversion parameterization, but apparently not due to higher-mode mis-identification at low
frequency.
Leaky Mode Contributions
Synthetic Tests
In the field and numerical simulations above, often very high phase velocity is observed at the lower limits of
measurable frequency. Park et al., (2005) showed a 2D finite-difference simulation of a 3-layered structure where the
first higher mode was dominant at low frequency. A 1D reflectivity simulation of this model, using 96-channels at 1
m spacing and 2.5 m near-offset is shown in Fig. 10 (every second trace decimated for clarity). When the effective
dispersion curve is overlain on the modal dispersion function, shown in Fig. 11, it can be sent hat the first higher mode
becomes dominant at frequencies below the 30 Hz osculation point, as also observed by Park et al., (2005). The
compound matrix calculation is only valid for real values of the dispersion function, however, the
reflectivity-observed dispersion shows even higher phase velocities at low frequency, following the real root of the
complex dispersion function. This result is similar to the model 4a of Denil (2005), shown in Fig. 3 (b), and
constitutes leaky mode propagation, which is where S-wave energy is radiated into the half-space.
In both Figs. 3 and 11, it appears that leaky mode propagation can arise when
VSi+1 < VPi , i = 1, .., No. of layers (4)
that is, the S-wave velocity of a given layer does not exceed the P wave velocity of the overlaying layer. A useful
indication can be made from the direct P-wave arrivals - if the low-frequency phase velocity is approaching the

refracted P-wave velocity, it is best to exclude these frequencies if using a fundamental mode assumption. This,
however, does still not account for dominant higher ‘normal’ surface wave modes (Equations 1 and 2), thus, unless a
full-wavefield modeling kernel is used in the inversion, the presence of both leaky and higher normal modes must be
identified before inverting the observed dispersion.
Higher Modes at High Frequency
Synthetic Tests and Filtering Pitfalls
If the overburden layer comprises a very thin veneer of very low Poisson’s ratio (e.g. dry sand over limestone), such
as model 3 of Denil (2005), transitions to higher modes can occurs abruptly, unrelated to osculation points (points
where modal dispersion curves approach in frequency-phase velocity space). The wavefield simulation results in Figs
12 and 13 show this complicated pattern, with a possible leaky mode contribution at very low frequency: At low
frequency (below 25 Hz), phase velocities are approaching the P-wave velocity of the second layer (1100 m/s). The
model is consistent with Equation (4) so leaky modes are indeed likely.
Ivanov et al., (2005) suggested a time-offset muting procedure as a method to remove these kinds of higher modes
which may prevent automatic fundamental mode identification. The higher modes in the 75-125 Hz band have phase
velocities above 350 m/s. It was suggested even a slight over-muting is not detrimental, thus a 300 m/s window was
first applied, shown in Figs 14 (a) and (b). There is still higher mode presence in the shot gather, and the dispersion
image shows little change, but slightly increased phase velocities at low frequency, a side-effect also noticed by
Ivanov et al., (2005). Applying an even harsher mute (175 m/s) corrupts the plane wave dispersion at both high- and
low-frequency ends, shown in Figs. 14 (c) and (d).
In cases with very strong higher modes, this simple muting procedure may not be suitable when accurate, automatic
picking of the fundamental mode is desired. One possible use may be in muting P-wave arrivals
(direct/refracted/guided) and other early- and late-time noise, before plane-wave transform of the shot gather.
Love Wave Modes
Full-Wavefield Synthetic Tests
Safani et al., (2005) showed how independent inversion of the Love and Rayleigh wavefields can provide a measure
of transverse isotropy in shallow sediments. Further to that work, a full-wavefield SH-wave modeling was developed,
extending the method of O’Neill et al., (2003) to include Love wave ‘effective mode’ inversion. Love wave behaviour
in profiles when a stiff layer exists at the surface and buried at shallow depths was then studied.
For example, the results of modeling the shallow LVL and HVL profiles in O’Neill and Matsuoka (2005) are
shown in Fig. 15. The LVL case (Fig. 15 (a) and (b)) shows mode transitions at higher frequencies, similar to the
Rayleigh wave case, but the discontinuities are of much larger amplitude and rapidly approach the S-wave velocity of
the top layer at high frequency. Although these ‘channel waves’ generally follow the normal-mode roots, unique
mode-identification is difficult, especially since some effective-mode ‘segments’ can smoothly transition between
normal mode. This pattern was also noticed in field data by Strobbia (2005), and Levshin and Panza (2005) point out
the insufficiencies of modal modeling to realistically simulate this kind of dispersion. Conversely, for the HVL case
(Fig. 15 (a) and (b)), unlike the dominant higher Rayleigh mode(s) which exist at 8-16 Hz, the Love wave dispersion
is dominated by the fundamental mode. This makes inversion more simple and nonlinearity will be greatly reduced
compared to the Rayleigh wave case.

Field Example
To illustrate the effects of even a modestly stiff surficial layer, Love and Rayleigh wave data were collected at a
compacted site in Japan. The field data in Fig. 16 shows coincident P-SV and SH wave shot gathers and dispersion
images. The Rayleigh wave dispersion is relatively smooth, indicative no major stiffness contrasts. However, the Love
wave dispersion shows multiple discontinuities, similar to the full wavefield modeling of Fig. 15(b). Inversion of the
Rayleigh wave dispersion, shown in Fig 17, shows a thin, high velocity layer at the surface. Below this surficial layer,
the estimated model agrees nearly perfectly with a downhole S-wave velocity log about 50 m away. The surficial
stiff-layer presence, causing the multiple Love-wave modes, seems reasonable since the surface wave data were
collected over compacted road base, which was either not present at the time of, or not sampled by, the borehole
logging.
Love Wave Advantages
O’Neill and Matsuoka (2005) showed the pitfalls associated with higher Rayleigh wave modes, namely large
discontinuities which can have a strong leaky mode component, or, where the observed effective dispersion crosses
several mode boundaries, both of which can arise when a steep, nonlinear stiffness gradient exists at the surface.
However, using the full SH-wavefield modelling method mentioned above, in this kind of profile, the Love wave
dispersion is smooth and dominated by the fundamental mode. These modeling results are shown in Figs 18 and 19.
Embedding this full-wavefield modeling kernel into the inversion procedure used by Safani et al., (2005) allows
rapid inversion of the ‘effective’ Love wave dispersion curve. The results shown in Fig. 20 show how the nonlinear
stiffness gradient in the upper 2.5 m is recovered well, however, due to poor resolution, the profile at depth is less well
estimated, and the homogenous half-space shear-wave velocity underestimated by about 70% (true value 2150 m/s).
Love waves may be beneficial or advantageous where either a shallow, stiff layer exists at shallow depth, or, where
a nonlinear stiffness gradient exists at the surfaces. However, there is always the risk that in cases where a stiff
surficial layer exists, difficult mode-identification of the Love wave data may prevent its inversion, thus Rayleigh
wave data is best collected simultaneously to reduce risk.
Multimode Global Inversion
Synthetic Test
Higher modes need not always be a pitfall. Indeed, if they are well separated and uniquely identifiable, they can be
profitably employed to reduce inversion nonuniquness. The only possible practical problems are the invariable weak
and band-limited nature of higher modes, especially in normally dispersive cases. Yamanaka (2005) showed how a
Genetic Algorithm (GA) inversion of the fundamental mode over the 2-30 Hz band can successfully estimate the
structure of a Low Velocity Layer (LVL) model. However, there were two features of that work which lacked
field-realism: (i) Higher modes are naturally generated where a shallow LVL is present (O’Neill, 2003), and; (ii) The
frequency range of active source field surveys does not usually provide data below about 5 Hz.
Model 2 of Yamanaka (2005) was used for a full P-SV wavefield simulation, assuming a Poisson’s ratio of 0.45 for
all layers. A 48-channel spread, at 5 m near offset and 1 m geophone spacing, with a 40 Hz impact source at the
surface and 4.5 Hz geophones is simulated, the results shown in Fig. 21. When overlain on the modal dispersion
function (Fig. 22), it can be seen that they comprise the fundamental mode, then higher modes in monotonically
ascending order, i.e. 1st, 2nd, etc. One possible pitfall is the small phase velocity transition between the third and

fourth higher modes at about 75 Hz, where in a field dataset they may be interpreted as a single mode. Yamanaka
(2005) used a frequency range of 2-30 Hz for inverting the fundamental mode. In the simulations here, the lower
frequency limit is 6 Hz.
The forking GA of Nagai et al., (2005) was used to invert the multimode dispersion, employing the same 4-layer
parameterisation and search limits as used by Yamanaka, except for the top layer maximum thickness bound set as 4
m instead of 8 m. The results of inverting the theoretical fundamental mode from 2-30 Hz and the full-wavefield
calculated fundamental mode dispersion from 6-30 Hz are shown in Figs 23 (a) and (b). All models with an L2-norm
data fit up 20 m/s are plotted. Figure 23 (a) shows a similar result to that of Yamanaka (2005), particularly where the
GA overestimated the depth of the homogenous half-space. When frequencies from 2-6 Hz are excluded (Fig. 23 (b))
there is much larger nonuniqueness, the deeper portion exhibiting a gradational appearance, similar to that estimated
by linearised inversion methods (O’Neill et al., 2003).
However, by incorporating 2 modes (fundamental and first-higher), even with a lower frequency limit of 6
Hz, the inversion results are accurate, as shown in Fig 24 (a). When 5 modes are used, the result is shown in Fig 24 (b).
Compared to the fundamental-mode only inversion over the same bandwidth, nonuniqueness is markedly reduced, as
seen by the fewer number of and narrow spread of equivalent models within the allowed data misfit, and shallow
parameter recovery is better. Similar reduction in sensitivity at depth when low-frequency data is limited, and the
improvements provided by higher-modes, was noted by Feng et al., (2005). Combining passive- and active-source can
provide data in both the low- and higher-frequency ranges respectively, as illustrated by Malovichko et al., (2005) and
Park et al., (2005).
Field Example
A multimode Rayleigh wave dispersion pattern was observed at a field site over compacted soil in Australia. The
48-channel shot gather and dispersion image are shown in Fig. 25 and the picked dispersion curves in Fig. 26. While
the fundamental and first two higher modes are quite uniquely identified, the highest observed mode may actually
comprise the 3rd
and 4th
modes, the transition frequency at about 70 Hz. This higher mode mi-identification problem
was noted in the previous synthetic test of Figs 21 and 22.
The dispersion was inverted using 1, 2, 3 and 4 modes in turn (the latter truncated at 66 Hz due to the above
mis-identification possibility). The results with common GA parameterisation and boundaries are shown in Fig. 27 (a)
to (d), within an RMS data fit of up to 10 m/s. Also included are the linearised inversion results, using a 12-layer stack,
with thicknesses starting from 0.5 m and ending at 2.5m, with the homogenous half-space at 20 m. It can be seen that
the 1- and 2-mode inversions are quite nonunique, whereas the 3- and 4-mode inversion results are more robust. To
resolve the low-velocity layer, which is certainly present, a minimum of 3 modes are required.
Note how in the interpreted fundamental-mode dispersion curve, there is a sharp, phase velocity increase at low
frequency, which is suggestive of a possible jump to higher mode or leaky mode, as described above. This also
occurred with the model of Yamanaka (2005) when a low Poisson’s ratio (0.25) was assumed. For these reasons, a
full-medium impulse-response modeling kernel would be preferred to the conventional propagator matrix method
used here.
Conclusions
Numerical modeling and interpretation of profiles with large elastic contrasts, supported with field data, reveal the
following about the multi-mode characteristics of surface waves:

(i) Higher modes at low frequency can become dominant if both shear wave velocity contrast (scaled by the
overburden layer thickness) is from 50-150% and S-wave velocity of half-space is from 50-150% of the P-wave
velocity in the top layer. This makes them more likely to be observed at sites with low Poisson’s ratio;
(ii) Leaky modes can also become dominant at low frequency. Although large velocity contrasts are not necessary, the
S-wave velocity of a given layer cannot be more than the P-wave velocity of an overlying layer. Low frequency phase
velocities approaching the refracted P-wave velocities are an indication of leaky mode contribution;
(iii) Love waves can exist where a Low Velocity Layer (LVL) exists below a stiff surface, however, propagate as
increasingly higher modes with increasing frequency and mode-identification is difficult. Unlike Rayleigh waves,
where a High Velocity Layer (HVL) exists at shallow depth below a soft surface, Love wave propagation is
dominated by the fundamental mode; and,
(iv) Incorporating more higher Rayleigh wave modes in the inversion process increases vertical resolution,
particularly where the low-frequency data is limited (in active-source surveys with short geophone spreads).
In a companion paper (Part II), acquisition-parameter dependencies and the effects of lateral subsurface and
topographic variations causing wavefield scattering are quantitatively investigated.
Acknowledgements
This work was conducted during a post-doc position at Kyoto University, funded by the Japan Society for the
Promotion of Science (JSPS). Students of the Engineering Geology and Geophysics labs are thanked for both field
and computing assistance. Ron Kaufmann is thanked for providing a field data example.
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Table 1. Empirical ‘rules of thumb’ suggesting the conditions whether higher modes are expected, for the synthetic
models of De Nil (2005).
Model no.> 1a 1d 4a 4d
Eqn. 1 value 0.33 0.58 0.65 1.2
Eqn. 2 value 0.49 0.87 0.98 1.7
Higher
mode
expected?
No Yes Yes No

0 2000 4000 6000
0
5
10
15
Phase velocity (m/s)
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 200 400 600
1000
1500
2000
2500
3000
3500
4000
Reflectivity
Compound matrix
Figure 1. Synthetic Rayleigh wave modelling results of
the 4 mm PMMA on aluminium physical model of
Bodet et al. (2005): (a) Velocity models (with effective
dispersion curves overlain), and (b) Effective dispersion
curves (overlain on the sign of the modal dispersion
function).
Frequency (Hz)
Phasevelocity(m/s)
(a) RMS error: 0.02 %
0 100 200 300 400 500 600 700
1000
1500
2000
2500
3000
3500
Measured
Initial
Final
0 1000 2000 3000 4000
0
1
2
3
4
5
Shear wave velocity (m/s)
Depth(m)
(b) RMS error: 18.0 %
True
Initial
Final
Inter.
Figure 2. Full P-SV wavefield inversion results of the
synthetic dispersion for the 4 mm PMMA model of
Bodet et al. (2005): (a) Dispersion image, measured
from shot gather using the same geometry as Bodet et
al., 2005) with observed and calculated dispersion
curves, and (b) True and estimated shear-wave velocity
models.
VS
VP
PSV
0 500 1000 1500 2000
0
5
10
15
20
25
30
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 10 20 30 40 50
200
400
600
800
1000 Reflectivity
Compound matrix
0 500 1000 1500 2000
0
5
10
15
20
25
30
Depth(m)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 10 20 30 40 50
200
400
600
800
1000
Figure 3. Synthetic P-SV modeling results of the models
of Denil (2005): (Left) Velocity models (with effective
dispersion curves overlain), and (Right) Effective
dispersion curves (overlain on the sign of the modal
dispersion function) for the models (a) and (b) Model 4a,
and (c) and (d) Model 4d.
5 10 15 20 25 30
0
0.05
0.1
0.15
0.2
0.25
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 50 100 150 200
200
400
600
800
1000
1200
1400
1600
1800
2000
Figure 4. Vertical component field data from a site in
Australia of residual soils over shallow granitic
basement: (a) Shot gather, and (b) Dispersion image
(with picked dispersion curve).

0 20 40 60 80 100 120 140 160 180
0
500
1000
1500
2000
Frequency (Hz)
Phasevelocity(m/s)
Measured
Initial
Final
0 500 1000 1500 2000
0
1
2
3
4
5
6
7
8
Sandy gravel
Silty sand
Saprolite
Granite (EOH)
Shear velocity (m/s)
Depth(m)
(b)
Initial
Final
Inter
10
0
10
1
10
2
0
1
2
3
4
5
6
7
8
Percent (%)
Depth(m)
(c)
σβ
Figure 5. Full P-SV wavefield inversion results from
site in Australia of residual soils over shallow granitic
basement: (a) Dispersion curves, (b) Estimated shear
wave velocity models (with nearby auger borehole log),
and (c) Shear wave velocity standard deviation.
0 500 1000 1500 2000
0
2
4
6
8
10
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 50 100 150 200
200
400
600
800
1000
1200
1400
1600
1800
2000
Field data
Compound matrix
Figure 6. Synthetic P-SV modelling results of the
best-fitting profile from the soil over granite site: (a)
Velocity models (with effective dispersion curves
overlain), and (b) Effective dispersion curves (overlain
on the sign of the modal dispersion function).
10 20 30 40
0
0.2
0.4
0.6
0.8
1
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 10 20 30 40 50
50
100
150
200
250
300
350
400
450
500
550
Figure 7. Vertical component field data from the on-land
site of Kaufmann et al. (2005): (a) Shot gather, and (b)
Dispersion image (with picked dispersion curve).
Frequency (Hz)
Phasevelocity(m/s)
5 10 15 20 25
50
100
150
200
250
300
350
Measured
Initial
Final
0 200 400 600
0
5
10
15
20
Depth(m)
True
Initial
Final
on-land site data of Kaufmann et al. (2005): (a)
Dispersion image, measured from shot gather using the
same geometry as Bodet et al., 2005) with observed and
calculated dispersion curves, and (b) Estimated
shear-wave velocity models, where the ‘True’ model is
that of Kaufmann et al. (2005).
0 500 1000 1500 2000 2500
0
5
10
15
20
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60
0
100
200
300
400
500
600
Field data
Compound matrix
Figure 9. Synthetic P-SV modelling results of the
best-fitting profile from the on-land site of Kaufmann et
al. (2005): (a) Velocity models (with effective
function).

0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
200
400
600
800
1000
1200
1400
1600
1800
2000
Figure 10. Synthetic P-SV full-wavefield modeling of
the profile from Park et al. (2005): (a) Shot gather, and
(b) Dispersion image (with picked effective dispersion
curve).
0 500 1000 1500 2000 2500
0
5
10
15
20
25
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
200
400
600
800
1000
1200
1400
1600
1800
2000
Reflectivity
Compound matrix
Figure 11. Synthetic P-SV modeling results of the
3-layer profile from Park et al. (2005): (a) Velocity
models (with effective dispersion curves overlain), and
(b) Effective dispersion curves (overlain on the sign of
the modal dispersion function).
10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 50 100 150 200
100
200
300
400
500
600
700
800
900
1000
Figure 12. Synthetic P-SV full-wavefield modelling of
profile 3 from De Nil (2005): (a) Shot gather, and (b)
Dispersion image (with picked dispersion curve).
0 500 1000 1500 2000
0
5
10
15
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 50 100 150 200
100
200
300
400
500
600
700
800
900
1000
Reflectivity
Compound matrix
Figure 13. Synthetic P-SV modeling results of profile 3
from De Nil (2005): (a) Velocity models (with effective
function).
10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 50 100 150 200
200
400
600
800
1000
10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 50 100 150 200
200
400
600
800
1000
profile 3 from De Nil (2005), and the effects of various
top-mute filters as described by Ivanov et al. (2005): (a)
and (b) 300 m/s top mute, and (c) and (d) 175 m/s top
mute.

10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Offset (m)
Time(s)
(a)
Frequency (Hz)Phasevelocity(m/s)
(b)
0 20 40 60 80 100
150
200
250
300
10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Offset (m)
Time(s)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 20 40 60
50
100
150
200
250
300
Figure 15. Synthetic SH full-wavefield modelling of the
low- and high-velocity layer Cases 2 and 3 from O’Neill
and Matsuoka (2005): (a) and (b) Low velocity layer,
and (c) and (d) High velocity layer.
5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
100
150
200
250
300
350
5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 20 40 60 80 100
100
150
200
250
300
350
Figure 16. Field data from a compacted site in Japan: (a)
and (b) Vertical component, and (b) Transverse
component.
0 10 20 30 40 50 60 70
100
200
300
400
500
Frequency (Hz)
Phasevelocity(m/s)
Measured
Initial
Final
0 200 400 600
0
5
10
15
20
25
Depth(m)
(b)
True
Initial
Final
Inter
10
0
10
1
10
2
0
5
10
15
20
25
Percent (%)
Depth(m)
(c)
σβ
∆β
vertical component field data in Fig. 16: (a) Dispersion
curves, (b) Shear-wave velocity models (‘True’ model is
downhole SH log from a nearby borehole), and (c)
Relative standard deviation and differences with nearby
borehole log.
0 20 40 60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80
100
200
300
400
500
600
700
800
Figure 18. Synthetic SH full-wavefield modelling of the
nonlinear stiffness gradient model from O’Neill and
Matsuoka (2005): (a) Shot gather, and (b) Dispersion
image (with picked dispersion curve).

0 200 400 600 800 1000
0
5
10
15
20
Velocity (m/s)
Depth(m)
(a)
VS
VP
SH
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80
100
200
300
400
500
600
700
800
Figure 19. Synthetic SH modeling results of the
nonlinear stiffness gradient model from O’Neill and
Matsuoka (2005): (a) Velocity models (with effective
function).
0 10 20 30 40 50 60 70 80
200
400
600
800
Frequency (Hz)
Phasevelocity(m/s)
Measured
Initial
Final
0 100 200 300 400 500 600 700
0
5
10
15
20
Depth(m)
(b)
True
Initial
Final
Inter
10
0
10
1
10
2
0
5
10
15
20
Percent (%)
Depth(m)
(c)
σβ
∆β
Figure 20. Full SH wavefield inversion results of the
synthetic data in Fig. 19: (a) Dispersion curves, (b)
Shear-wave velocity models, and (c) Relative standard
deviation and differences with nearby borehole log.
10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
50
100
150
200
250
300
the low-velocity layer model 2 of Yamanaka (2005): (a)
Shot gather, and (b) Dispersion image (with picked
dispersion curve).
0 200 400 600
0
2
4
6
8
10
12
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
50
100
150
200
250
300
Figure 22. Synthetic P-SV modeling results of the
low-velocity layer model of Yamanaka (2005): (a)
Velocity models (with multimode dispersion curves
overlain), and (b) Multimode dispersion curves
(overlain on the sign of the modal dispersion function).
(a)
0 200 400 600 800
0
2
4
6
8
10
12
Shear−wave velocity (m/s)
Depth(m)
Best
Inter.
True
(b)
0 200 400 600 800
0
2
4
6
8
10
12
Depth(m)
Best
Inter.
True
Figure 23. Genetic Algorithm inversion results of the
fundamental-mode P-SV dispersion in Figure 22, using
the same parameterization as Yamanaka (2005): (a) 2-30
Hz range, and (b) 6-30 Hz band.

(a)
0 200 400 600 800
0
2
4
6
8
10
12
Depth(m)
Best
Inter.
True
(b)
0 200 400 600 800
0
2
4
6
8
10
12
Depth(m)
Best
Inter.
True
multimode P-SV dispersion in Figure 22, using the same
parameterization as Yamanaka (2005): (a) Fundamental
and first-higher modes, and (b) Fundamental to
fourth-higher modes inclusive.
10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
150
200
250
300
350
Figure 25. Vertical component field data from a site in
Australia: (a) Shot gather, and (b) Dispersion image
(with picked dispersion curves).
0 20 40 60 80 100
150
200
250
300
350
Frequency (Hz)
Phasevelocity(m/s)
(a)
Fundamental
1st−higher
2nd−higher
3rd−higher (and 4th?)
150 200 250 300 350 400
0
5
10
15
20
25
Approx. shear velocity (m/s)
Approx.depth(m)
(b)
Figure 26. Multimode dispersion curves of Fig 25: (a)
Phase velocity versus frequency, and (b) Approximate
shear wave velocity versus depth (0.9*phase velocity
and 0.4*wavelength).
(a)
0 100 200 300 400 500 600
0
5
10
15
Depth(m)
Best
Fitting
Linear
(b)
0 100 200 300 400 500 600
0
5
10
15
Depth(m)
Best
Fitting
Linear
(c)
0 100 200 300 400 500 600
0
5
10
15
Depth(m)
Best
Fitting
Linear
(d)
0 100 200 300 400 500 600
0
5
10
15
Depth(m)
Best
Fitting
Linear
field data in Figure 26: (a) Fundamental-mode only, (b)
2 modes, (c) 3 modes, and (d) 4 modes. ‘Linear’
indicates the solution with the same number of modes,
by the linearised optimization method of Safani et al.
(2005).

Seismic surface waves in shallow site investigations
Part 2: Lateral variation and acquisition parameter effects
Adam O’Neill*, Masafumi Kato, Toshinau Yasui and Toshifumi Matsuoka
Department of Civil and Earth Resources Engineering, Kyoto University, Japan
adam@earth.kumst.kyoto-u.ac.jp
http://earth.kumst.kyoto-u.ac.jp/~adam
*Presently:
DownUnder GeoSolutions, Subiaco, Western Australia
adamo@dugeo.com
http://www.dugeo.com
ABSTRACT
A major concern with applying surface wave inversion for shallow site investigation are the effects of 2D/3D
geological and topographic effects. Full-wavefield modelling suggests that the active-source surface-wave
response is dominated by the material in the near-half of the recording spread, thus the spread midpoint may not
be optimal nominal location. A Low Velocity Layer (LVL) will be imaged with less shot dependency that a High
Velocity Layer (HVL), however, the extent of a LVL pinchout will be overestimated by up to 20% of the spread
length. Similarly, the location of a cavity will be estimated at least 25% beyond the spread midpoint, away from
the shot, and by rollalong 1D inversion, the cavity appears as a low-velocity anomaly, sloping diagonally down
towards the shot location at about 30-40 degrees.
Acquisition parameters have little effect on observed dispersion, at least for very shallow applications, and the
little dependence on coupling makes landstreamer acquisition viable. Side-scattering from hard objects and/or
topographic undulations introduces discontinuities into the observed ‘effective’ dispersion, similar to dominant
higher modes due to velocity reversals, and an overestimate of low-frequency phase velocity, and cannot be
readily discriminated.
Introduction
In a previous paper (O’Neill et al., 20xx, hereafter referred to as Part I), higher surface-wave modes and both the
potential problems and advantages of their use in shallow site shear wave velocity imaging were outlined. In this Part
II companion paper, two remaining issues – subsurface and topographic variations causing wavefield scattering and
acquisition-parameter dependencies of the observed dispersion – are quantitatively investigated.
The combined effects of these two aspects suggests that there is still no clear-cut method to distinguish between
‘noise’ due to higher-mode presence versus that from wavefield-scattering. Indeed, they are inherently related: Lateral
variations can give rise to mode-conversions, that is, surface waves (Rayleigh / Love / guided / flexural) both to and
from body waves. A discussion, supported with 3D modeling results, is offered to demonstrate the unusual dispersion
which may be observed at some field sites where cultural (e.g. retaining walls) or topographic (e.g. quarry faces) are
parallel to the recording spread.

Lateral Variations and Wavefield Scattering
Literature Review
Shallow profiling with surface wave inversion is now routinely commercially applied for shallow geological
mapping in engineering and environmental problems, both on-land (Miller et al., 1999a; Feng et al., 2004) and
marine (Bohlen et al., 2004; Kugler et al., 2005). This is becoming even more apparent with rapid acquisition
systems such as 'land-streamers' (Inazaki, 2004) and 'auto-juggie' (Tian et al., 2003), and often used to support
and complement shallow reflection (Miller et al., 1999b) and refraction (Ivanov et al., 2000) data sets.
However, unlike seismic refraction, where inversion models can rigorously accommodate 2D and 3D velocity
structure and topography, the shear-wave velocity profiles produced by surface wave inversion are in fact only
'pseudo-2D' or '1.5D' since they employ the following practise:
1. Observe phase velocity dispersion from either:
(a) Rollalong, raw shot gathers (Miller et al., 1999a), or,
(b) Sliding offset windows along a single shot gather by multichannel (Al-Equabi and Herrmann, 1991; Kugler
et al., 2005), or two-channel (Suzuki et al., 2001) methods,
(c) CMP cross-correlated gathers (Hayashi and Suzuki, 2004; Nagai et al., 2005), or,
(d) Stacked plane-wave transforms from several shot-offsets (O’Neill, 2003; Zhang et al., 2002),
2. Invert the observed dispersion to a flat-layered model, assumed located at the centre of the recording window,
and;
3. Align the 1D models and contour or smooth for representative 2D (or 3D) ‘pseudo-sections’ or ‘slices’.
Theory by Kuo and Nafe (1962) showed how as the distance between receivers becomes infinitesimal, the
effective phase velocity approaches the local phase velocity, which is independent on propagation direction. The
lateral smearing is based on the fact phase velocity dispersion represents the path average over the recording
array. However, in practise, (at least for active MASW), such a ‘local’ phase velocity is not measurable, and the
maximum resolvable wavelength (thus depth of penetration) is limited to 40% of the spread length (O’Neill,
2004; Bodet et al., 2005). Therein lies the tradeoff between ‘vertical’ and ‘horizontal’ resolution.
Smoothly varying lateral variations are known to be well-imaged with 1D surface wave inversion, which has
been exploited in global earthquake seismology (Sambridge and Mosegaard, 2002). From a shallow seismic
perspective, dipping interfaces were first studied by physical modeling (Kuo and Thompson, 1963). Numerical
modelling by Suzuki et al., (2001) showed how both MASW and SASW phase velocity dispersion curves over a
dipping interface will give the depth to the interface below the array midpoint. Laser-Doppler physical modeling
by Bodet et al., (2005) showed similar results, however, without reliable a-priori information of the average
depth (from refracted arrivals) the interpreted depths were closer to the average below the near half of the
recording array.
A lateral stiffness gradient was simulated by 2D numerical modeling by Bohlen et al. (2004), where rollalong
1D inversion from overlapping trace windows reproduced the 2D structure well. In field data, interpreted
horizons correlate well with conventional reflection profiling images (Kugler et al., 2005). For visually improved
images, spatially interpolating the inversion results between 1D midpoints is not considered detrimental (Badal

et al., 2004) and the effects of shot-receiver geometry can be partially addressed by statistically ‘deblurring’ the
final sections (Xia et al., 2005). Group velocity tomography, which represents the average structure over the
source-receiver path, provides similarly blurred images in 3D (Long and Kocaoglu, 2000).
However, when the lateral variations are more abrupt, wavefield scattering becomes more of a problem. When
a vertical fault-step is crossed, dispersion discontinuities arise in the vicinity of the vertical contacts, however,
both numerical (Nagai et al., 2005) and field tests (Hayashi and Suzuki, 2004) showed how high density, 1D
inversion can provide a reliable, albeit laterally ‘smeared’ image of the fault step. Reflected waves have always
been known to contaminate the observed dispersion curves, both from vertical boundaries (Sheu et al., 1988) and
topographic slopes (O'Neill et al., 2004). While these can be used for buried object imaging (Herman et al.,
2000; Grandjean and Leparoux, 2004), in 1D inversion, such lateral variations cause gross systematic
propagation of error into the estimated layer elastic parameters.
Horizontal Resolution and Acquisition Geometry
To quantitatively illustrate 2D effects, a numerical ‘sand-filled sinkhole’ model was constructed, inspired by the
photographs of Fig. 1, which are cave-collapse sinkholes. The model is shown in Fig. 2, and the soil parameters in
Table 1. These were assigned based on the field data interpreted sections in Crice (2005) and O’Neill (2003), which
showed similar ‘soft-zones’, bounded by hard rock. Poisson’s ratio is 0.4 for all layers, and density QP and QS are 1.8
g/cc, 100 and 40 respectively. Geologically, it represents a veneer of soft sand over a thick, stiff layer (such as
limestone or laterite), below which is a velocity reversal (e.g. clay/silt/sand), with a stiff contrast arbitrarily added at
50 m depth (to simulate fresh basement rock). The ‘sinkhole’ is where the stiff third layer is absent, replaced by soft,
homogenous 400 m/s material, and no air cavity is present.
The forward calculation used for the 2D simulation is an elastic Finite Difference (FD) method, the same as used in
Nagai et al., (2005). The reliability of this code, from a 1D perspective, was tested by comparison to a simulation
using full-wavefield reflectivity of O’Neill et al., (2003). Fig. 3 indicates how it is a difficult case even from a 1D
perspective, since the stiff layer causes several higher modes to become dominant at low frequency. Based on this
result, the 2D FD data is thus deemed suitable to be inverted with the 1D reflectivity code without systematic model
error (at least in zones where layering is flat).
Using the 2D FD code, shot gathers were simulated over the sinkhole model, with a 96-channel spread at 1 m
geophone spacing and 2.5 m near offset. Both forward (pushing from the left) and reverse (pulling form the right)
acquisition geometries were ‘collected’ in rollalong fashion, with a 2 m shot spacing. Each shot gather was passed
through a processing and inversion flow comprising: Dispersion observation by frequency-slowness transform, and;
Unconstrained, linearised inversion by the full-wavefield method of O’Neill et al., (2003). The nominal location of the
estimated model for each shotpoint is positioned in the middle of the recording spread, each covering a ‘strip’ of 2 m,
i.e. the shot spacing. Thus, there is considerable overlap and spatial redundancy – the same as used in commercial
practise, however, no gridding or smoothing is applied. The processing-inversion of all data was done entirely
automatically – once initial parameters were set (e.g. frequency and phase velocity ranges) no manual user input was
made.
The inverse imaging results are shown in Figs. 4 (a) and (b) for the forward and reverse shot directions respectively.
The half-space horizon at 50 m depth was not the target here, intended to be used for reflection imaging tests, so the
plots are cropped at 30 m depth for clarity. There is a definite, yet repeatable asymmetry due to the source-receiver
orientation. Even though the model is constructed through inversion using a 1D full-wavefield model at each midpoint,
the edges are detected well. However, there are artifacts at depth, which occur below the stiff-layer terminations, but

dependent on acquisition geometry.
To better indicate the zones where scattering is strong, the dispersion curves as phase velocity versus reduced
wavelength (i.e. approximate depth) are shown in Figs. 5 (a) and (b), for both forward (pushing from the left) and
reverse (pulling from the right) shot directions respectively. Each is plotted vertically at the spread ‘midpoint’,
wavelengths are scaled to depth by a factor of 0.4. Most scattering occurs at the edge of the ‘hard’ zone, and only
when the shot is over the sinkhole, i.e. at the right hand edge when shot is pushing from the left, and vice-versa. Note
too how there is still a stiff-layer dispersion anomaly over the soft-zone, indicative of the lateral averaging of the 95 m
spread.
To illustrate the dependence on acquisition geometry, consider a 96-channel spread centred symmetrically over the
right-hand edge of the soft-zone. The inversion results for the forward and reverse shot dispersion for this midpoint
are shown in Fig. 6. The ‘True’ model is the 1D profile beneath the shot – where the forward shot is over the stiff zone
and the reverse shot is over the soft zone. Two immediate observations are:
(i) When the surface waves are propagating from a soft to hard zone, scattering (and thus estimated model error) is
more influential than the opposite case, that is, the wavefield propagating from a stiffer into a softer zone, and;
(ii) The estimated model does show a kind of ‘smeared’ image of the average stiffness, however, seems to be more
representative of the material below the first half of the shot gather, that is, nearer the shot.
This kind of surface wave profiling could be used for estimating overburden shear-wave velocity for use in S-wave
and PS-wave seismic reflection static corrections and depth migration models, as shown by O’Neill et al., (2006b). In
cases with large vertical and lateral velocity contrasts and reversals, static methods employing arrival times (refraction,
tomography etc.) can produce less-unique velocity models, leading to error and uncertainty in the stacked and
migrated reflection images.
Thin Layer Terminations
Nagai et al., (2005) showed the lateral smoothing effect when dispersion measured from CMP cross-correlated data
across a vertical fault model is inverted, and how over-parameterisation (of the number of layers) causes apparent
‘pinchouts’ of near-surface layers. Further to that work, a 2D pinchout with both real low- and high-velocity layer
pinchouts was synthetically modeled and inverted. Accurate mapping of this kind of structure is important both
onshore and offshore, for infrastructure foundations and pipeline trenching.
The models are shown in Figs. 7 (a) and (b). They are based on the low and high-velocity layer models used in
O’Neill and Matsuoka (2005). In each, the layer at 2 m depth terminates abruptly at the central shotpoint. Using the
same 2D FD code as Nagai et al., (2005), shot gathers were simulated, with a 96-channel spread at 1 m geophone
spacing and 2.5 m near offset. Both forward (pushing from the left) and reverse (pulling form the right) acquisition
geometries were ‘collected’ in rollalong fashion, with a 2 m shot spacing. Surface wave dispersion was measured from
the raw shot gathers by frequency slowness transform with no pre-processing (e.g. CMPCC stacking).
The dispersion curves, aligned vertically at each ‘midpoint’ and plotted at relative scales for both forward and
reverse shot directions, are shown in Figs. 8 (a) and (b) respectively. Wavelengths are scaled to depth by a factor of
0.4.
The inversion results, using the 1D full-wavefield method of O’Neill (2003) at each midpoint, are shown in Figs 9
(a) and (b) for the forward and shot data (pushing the spread from the left) and in Figs 9 (e) and (f) for the reverse shot

data (pulling the spread from the right), for each layering case respectively.
The LVL pinchout is quite well-imaged, without any major artifacts. While the image does show it extending about
5-10 m beyond the point of the termination with the 96-channel array used, there is no major dependence on
acquisition geometry i.e. shot direction. The HVL image, however, shows similar features to that observed in the
previously described sinkhole model, that is:
(i) The artifacts at depth below the edge of the termination of the layer at the central shotpoint, and
(ii) The lateral extent of the termination is slightly overestimated when the shot is to the left, and underestimated when
the shot is to the right.
An overestimate of the lateral extent of a hard layer may lead to problems if it is intended to be used for a foundation,
and an underestimate may be problematic if the aim is to avoid the hard layer, e.g. for pipeline trenching.
Individual results around the position of the pinchout, for both models and forward and reverse shots, are shown in
Fig. 10. For the LVL case (Figs. 10 (a) and (c)), the result is nearly independent of shot direction. However, for the
HVL case (Figs. 10 (b) and (d)), the 1D model more closely resembles the profile below the shot and nearer-offset
traces.
Shot Direction Effects
The estimated model dependence on acquisition geometry (i.e. shot direction) was noticed in the physical modeling
tests by Bodet et al., (2005), where for dipping interface, when the shot is up-dip (i.e. over shallower overburden) the
depth to the half-space is underestimated, and vice-versa. Similarly, in the numerical ‘pseudo-2D’ profiles of Nagai et
al., (2005), the edge of the vertical fault (higher velocity block) was imaged about 10-20 m in the direction of the
raised block, when the shot (i.e. nearer offsets) were over deeper/softer material.
The sinkhole and pinhchout modeling here shows similar effects: that is, with active-source surface-wave response,
the phase velocity dispersion (and thus estimated model) is dictated by the material around the shot and/or in nearer
traces, rather than a reciprocal average over the recording spread. Thus, arbitrarily positioning the inverted 1D model
at the center of the spread may not be the best alternative.
Further work is needed to investigate other acquisition and processing effects, such as different spread lengths and
near-offsets, and measuring dispersion from CMP gathers versus stacked plane-wave transforms.
Field Example: Mud Volcano
Data were acquired at a site in Niigata, Japan, where a ‘mud volcano’ (overpressured mud and methane gas,
surfacing from formations at depth) exists. A 24-channel landstreamer with 4.5 Hz geophones at 2 m spacing was
used. Shotpoints were 2 m apart and 5 stacks of a wooden mallet impacting on the asphalt used as energy source. Shot
location was ‘pushing’ from the left at a near-offset of 10 m (O’Neill et al., 2006a).
The 2D ‘pseudosections’, created from aligning the inverted models from each shot at the spread midpoints, are
shown in Fig. 11. In addition, the dispersion curves at each midpoint are plotted vertically as approximate depth
versus phase-velocity, in the vicinity of the model. Fig 11 (a) comprises ‘coarsely’ parameterized models: 12 layers,
0.5 m thick at the surface and increasing to 2.5 m thickness, with the homogenous half-space at 20 m depth. Fig 11 (b)
is more ‘finely’ parameterized, with twice the number of layers, each about half the thickness of the ‘coarse’ inversion.
Moreover, in the ‘fine’ inversion, the smallest allowed damping parameter is twice that of the ‘coarse’ inversion (i.e.
less roughness allowed) and it is smoothed laterally with a 3-point median filter (i.e. taking the median estimated VS at
each depth between the models from 3 adjacent shotpoints).
The patterns of both the rollalong dispersion curve sand imaged shear-wave velocity sections are remarkably

similar to the LVL pinchout of Figs. 8 (a) and 9 (a). At either end of the field profile, there is apparently laterally
homogenous ground. The soft horizon between about 2 m to 5 m depth appears to pinch out at about location 80 m
and from about location 85 m there is a stiffer zone imaged at depth. In the vicinity of the LVL pinchout, from about
75-85 m, the dispersion curves become anomalous, which is reflected in the VS image at depth. However, even though
the spread is 46 m long, the only departure from a relatively repetitive pattern occurs within a zone of about 6
shotpoints (10 m).
The individual 1D inversion results at positions 48 m, 86 m and 102 m are shown in Fig. 12. At the two end
locations (Figs. 12 (a) and (c)), relatively smooth dispersion with predictable higher modes provide typical soft-layer
and stiff-layered profile estimates respectively. In the vicinity of the imaged LVL pinchout (Fig. 12 (b)), the
dispersion image shows discontinuities apparently unrelated to dominant higher propagating modes. It appears these
lobes are due to scattered surface waves, and occur in a similar frequency band (20-30 Hz) as in the synthetically
modeled case. Based on the above numerical tests, it is likely that the position of the pinchout is probably
overestimated, which assuming 20% of the spread length (46 m), would put it about 9 m to the left, between positions
70-75 m.
While the laterally smoothed section is visually more appealing, there are some portions which may be
mis-represented. For example, in Nagai et al., (2005), the abrupt termination of a shallow zone due to
overparameterisation was noted at the point where a vertical fault plane is crossed (from hanging wall to footwall).
Here, while the LVL pinchout is a real effect, the deep, stiff zone in the right of the image is probably better estimated
as a gradual, lateral stiffness increase and/or dipping horizon due to weathering or expected basement structure.
Cavity Presence and Detection
Cavity detection is generally made through the differences in observed dispersion between reciprocal shot
directions (Luke and Calderon-Macias, 2005) and/or or amplitude/phase anomalies (Cull et al, 2005) in the vicinity of
the buried object.
Gelis et al., (2005) showed numerical simulations over various cavity models, using a new 2D staggered-grid
finite-difference method (FDM). An alternative to FDM is the Discrete Element Method (DEM), which employs a
spring-dashpot analogy for wave propagation through the model material. Only recently has this method been used for
elastic wave modeling (Valle-Garcia and Sanchez-Sesma, 2003). This method is stable even in the presence of very
thin and/or abrupt elastic contrasts, allowing cavities, vertical trenches, cracks and fracture swarms to be incorporated.
The rectangular cavity model of Gelis et al., (2005) was used in a DEM simulation, with the same acquisition
parameters. The shot gather (Fig. 13(a)) shows similar weak surface wave backscatter from the left hand edge of the
cavity (at 12 m offset), plus anomalous low frequency dispersion (Fig. 13(b)).
A similarly cavity, albeit larger, but at the same depth (10 m wide, 4 m high, 2 m depth to top) was then modeled,
embedded in a homogenous half-space of similar stiffness (VP of 857 m/s, VS of 350 m/s, density 1.8 g/cc). The ‘air’
Vp and Vs are both set as 1 m/s. For this, the 2D FD code of Nagai et al. (2005) was employed, simulating a
48-channel spread at 1 m geophone spacing and 2.5 m near offset. Again, both forward (pushing from the left) and
reverse (pulling form the right) acquisition geometries were ‘collected’ in rollalong fashion, with a 2 m shot spacing.
Dispersion was measured from the raw shot gathers by frequency slowness transforms.
The dispersion curves as phase velocity versus reduced wavelength (i.e. approximate depth) are shown in Figs. 14
(a) and (b), for both forward (pushing from the left – solid curves) and reverse (pulling from the right – dashed curves)
shot directions respectively. Each is plotted vertically at the spread ‘midpoint’ and wavelengths are scaled to depth by
a factor of 0.4. There is a markedly reduced phase velocity, over and within about 5 m either side of the cavity edges.

This response is asymmetric, and suggests, as above, that the response is dominated by the material beneath the
nearer-offset traces. Note too the increased forward-scattering (solid curves, to the right of the cavity), which
manifests from the point where the shot is over the cavity, and continues for shotpoints 20 m or beyond the cavity
edges. Conversely, back-scattering from the cavity (soil curves, to the left of the cavity) has minimal effect on the
observed dispersion.
The rollalong inversion results, again using the 1D full-wavefield modeling of O’Neill et al., (2003), are shown in
Figs. 15 (a) and (b) for the forward and reverse shot directions, respectively. Like the end of the LVL pinchout, the
location of a cavity is estimated at least 25% beyond the spread midpoint, away from the shot. Again, there is the
asymmetry due to acquisition geometry, causing a sloping anomaly, dipping down towards the direction in which the
shot is located at about 30-40 degrees. It is unlikely that this anomaly would be interpreted as a cavity, especially in
more complicated layering and geology.
Acquisition Parameters
Source/Geophone Type and Spread Geometry
Harry et al., (2005) showed how analysis of the surface waves in datasets originally collected for seismic reflection
can provide useful models of the shallow zone. The ‘non-ideal’ parameters used in that work, along with accepted
‘ideal’ acquisition parameters are given in Table 2.
The ‘ideal’ parameters are of course arguable, these values taken from personal experience and as representative of
those suggested in O’Neill (2005). By comparing the synthetically modeled responses of their field estimated profiles,
using the above two acquisition parameter combinations, it was suggested that short near-offsets and spread lengths
and high frequency geophones were suggested to be not detrimental. In fact, the so called ‘non-ideal’ parameters
actually allowed high frequencies to be accurately recorded, with reduced attenuation with offset and less influence of
spurious phase and amplitude geophone response. Fig. 16 show s further evidence for this conclusion, in the mean
spectral power measured from both the raw traces and along the ridge in plane-wave transform space (the picked
dispersion curve). The assumed ‘non-ideal’ power curves correlate well with those observed from field data.
Seismic Landstreamers
Landstreamers are becoming more commonly used, however, reported tests of their use– for surface waves at least
– are scarce. Crice (2005) shows an imaged shear-wave velocity section from data collected across a gravel/sand to
grass transition, from data collected with a landstreamer, and Wisen and Christiansen (2005) used geophones on
baseplates to collect data on asphalt road.
However, quantitative comparisons between landstreamer and coincident planted geophones was first presented by
O’Neill et al., (2006a), and those results are summarized here. First, the effect of coupling and geophone frequency is
shown in a field dataset from Japan. Fig. 17 compares compares shot gathers and dispersion images collected with
coincident 4.5 Hz landstreamer geophones and planted 28 Hz geophones, with the same source. In Fig 18 (a), the
observed dispersion is almost entirely equivalent, and in Fig 18 (b), the spectral power (along the picked dispersion
curve in frequency-slowness space) of the landtreamer is as good as or better than the plants.
One point of note is the dispersion discontinuity at 50 Hz. With the 4.5 Hz landstreamer, it is relatively gentle, and
the dispersion would most likely be interpreted as the fundamental mode. However, in with 28 Hz spiked geophones,
it is more abrupt, instantly recognizable as a higher mode. Note too how the higher frequency geophones also record
more strongly the higher mode above 80 Hz.

Certainly, if an operator already owned a set of high frequency geophones, there would be little need to buy or rent
low-frequency ones to do surface wave surveys. One possible exception to this rule, was noted by O’Neill (2003),
where the use of undamped, 8 Hz refraction geophones produced anomalously high measured phase velocities around
32 Hz, suspiciously close to the second octave above the natural frequency. However, this only occurred only with a
sledgehammer source, less so with a 12-gauge shotgun source down a 30 cm hole.
A second test was done to confirm the dispersion data quality in very poor geophone coupling. Figs. 19 (a) and (b)
shows a shot gather and dispersion image (with picked effective dispersion curve) with the landstreamer on an asphalt
sealed road, and Figs. 19 (c) and (d) show the same measurement, but with the streamer moved laterally off the road,
onto a grassy verge. The two lines are parallel, about 5 m apart, and there is a 30 cm square concrete drainage running
midway between them. A 170 m/s top-mute, with 25 ms cosine taper, was applied before processing, to mute the
air-wave and other early-time noise. Nonetheless, note how the air-wave is suppressed when streamer is on the grass.
In spite of the obviously very poor coupling when on the grass (some baseplates were in fact ‘floating’ on sticks
and leaves, up to 5 cm above the soil), the measured dispersion curves (Fig. 20) agree to within 5% over most of the
recorded bandwidth, which - considering possible lateral geological variation - is below the noise threshold. Note,
however, how there is an apparent dominant higher mode above 25 Hz in the data collected on the asphalt. Note too
the sharp increase in phase velocity below about 5 Hz, which is possibly a higher surface wave or leaky mode, as
discussed above.
Discussion:
Wavefield Scattering and Mode Discrimination
Topographic Side-Scattering
Two issues with the field data of Harry et al., (2005) data are possible higher-modes and side-scattering from
compacted road edges and a vertical quarry wall, parallel to the recording spread. Certainly, there is the phase velocity
‘stepping-up’, the dispersion discontinuities at high frequency suggesting higher modes, indicative of a profile with a
shallow LVL. Inversion of the ‘effective dispersion’ by full-wavefield modeling is shown in Fig. 21. The ‘True’
model is that estimated in the original publication of Harry et al., (2005), where a fundamental mode-assumption
inversion was used. The full-wavefield modeling accounts for the higher modes and estimates a much more irregular
profile, in particular a stiffer surficial layer and deep zone.
However, over the 50-100 Hz band, there is some distortion in the ‘mode-jumping’ pattern associated with the
velocity reversal. That data was collected on a road, parallel to and close to the top of a quarry face. It is possible that
either the edge of the compacted road, or the topographic ‘drop-off’ may have caused side scattering, contaminating
the dispersion.
The effects of a collecting data alongside a vertical cliff-face, parallel to the recording spread, were modeled using
an elastic 3D FD code on an 8-CPU Linux cluster. The layered model is the LVL Case 2 used in O’Neill et al., (2003),
which produces dominant higher surface waves at high frequency, similar to that observed by Harry et al., (2005). The
cliff-face is 10 m from, and parallel to, the recording spread of 48 channels at 1 m spacing and 5 m near-offset, shown
schematically in Fig. 22. Figs 23 (a) and (b) show the flat-topography response and Figs. 23 (c) and (d) show the
response with the cliff present. The effects of the cliff are to introduce more dispersion discontinuities and of larger
amplitude than due to the LVL alone. In particular, the dispersion around 20 Hz is particular affected, with possibly an
extra surface wave mode being interpreted.
Examination of the shot gathers shows that where the cliff is present, there is a strong, hyperbolic arrival after the

main ground-roll wavetrain. However, this arrival may not be so easily identified, since a profile with a LVL also
generates high-frequency arrivals showing apparently hyperbolic moveout, and Love waves also show similar
hyperbolic arrivals in a LVL case (See Part I).
With respect to the Harry et al., (2005) field data, the question remains: Were the discontinuities due to higher
modes (due to velocity reversals) or topographic side scattering (from the quarry cliff face)? Most likely, a
combination of both are in effect, and the corruption of lower frequency data has possibly introduced systematic error
into the estimated model.
To illustrate the challenge in correctly identifying the ‘true’ surface wave modes from side-scattering effects,
reciprocal shot field datasets collected at a site in Japan with a landstreamer and 4.5 Hz geophones along an asphalt
road are shown in Fig. 24. Here, there was a 1.5 m drop-off on one side of the road, and a 3-4 m embankment rise on
the other. Moreover, shallow (0.5 m) concrete lined drainage channels were embedded alongside both kerbs. A 128
ms AGC is applied to highlight any late hyperbolic arrivals, and it appears that there is similar anomalous response
around the 20-50 Hz band, possibly associated with side-scattering.
Hard Boundary Side-Scattering
The effects of collecting surface waves alongside a hard, parallel boundary, e.g. a concrete retaining wall, drainage
channel or floodbank, were numerically investigated using the same 3D FD code. Three cases were modelled: (i)
Concrete wall above ground only (e.g. concrete blocks or pads at the surface), (ii) Below ground-level only (e.g.
retaining wall or concrete-lined drainage channel), and; (iii) Above and below ground (e.g. an external building wall
and footing). The recording spread runs parallel to the ‘wall’, shown in Fig. 24 and the elastic parameters of the soil
and concrete are shown in Table 3.
The modeling results are shown in Fig. 25. The dispersion images of Figs. 25 (d) and (f), show a discontinuity at 40
Hz, similar to the pattern due to a jump to a higher mode, typical of a weak LVL below a thin, moderately stiff surface,
with a stiff substrate at depth. When the concrete is purely above ground the discontinuity, albeit less pronounced, is
still present, supporting a comment by a practitioner in O’Neill (2005) that concrete blocks at the surface corrupt the
dispersion curve. Note too how the difference in the amplitude of the discontinuity between Figs. 25 (a) and (d) is
similar to that in Figs. 17 (b) and (d) – the latter due to purely to different geophone frequency.
Inspection of the shot gathers shows a hyperbolic arrival after the main ground-roll wave train, which are surface
waves reflected from the boundary, similar to the field and numerical data suffering from topographic side-scatter.
The artificially higher phase velocities observed in the plane wave transform, compared to the homogenous case (Fig.
25 (h)), would be expected for waves arriving obliquely to the spread. However, the slightly reduced phase velocity
below 40 Hz is contradictory to expectation and these effects would be difficult to discriminate in field data. Tools
such as 3-C recording and wavefield scattering theory (Blonk and Herman, 1996; Herman et al, 2000) may be key to
better combatting this problem
Conclusions
Rapid surface wave inverse modeling is restricted to two basic assumptions:
(i) Smooth, normal-mode propagation, in
(ii) Flat (1D), homogenous layering.
In real sites, surface waves invariably propagate with complex mode structures, and are scattered by lateral (2D/3D)
geologic and topographic variations. These issues are certainly more important than other effects, such as the

dependence of active-source surface-wave phase-velocity dispersion on acquisition and processing methods, which is
shown to be negligible.
Numerical modeling of 2D/3D structures, support ed with field tests, reveal the following:
(i) The active-source surface-wave response over 2D/3D subsurface is dominated by the material in the near-half of
the recording spread, thus (with only a single shot direction) models are suggested to be plotted nearer to the shot
(rather than the spread midpoint),
(ii) A Low Velocity Layer (LVL) will be imaged with less shot dependency that a High Velocity Layer (HVL).
However, the extent of a LVL pinchout will be overestimated by up to 20% of the spread length (from the spread
midpoint, in the direction away from the shot);
(iii) Similarly, the location of a cavity will be estimated at least 25% beyond the spread midpoint, away from the shot.
By rollalong 1D inversion, the cavity appears as a low-velocity anomaly, sloping diagonally down towards the shot
location at about 30-40 degrees;
(iv) Acquisition parameters (number of geophones, spacing and center frequency, and source bandwidth and offset
etc.) have little effect on observed dispersion, at least for very shallow applications. The little dependence on coupling
makes landstreamer acquisition viable; and
(v) Side-scattering from hard objects and/or topographic undulations introduces discontinuities into the observed
‘effective’ dispersion, similar to dominant higher modes due to velocity reversals. In all cases, an overestimate of
low-frequency phase velocity arises, which cannot be readily discriminated.
Further work into the side-scattering problem would be an ideal research project – with the dual aims of either
wavefield scattering removal and/or its use in subsurface imaging. A successful method would have applications at
both material testing scale (e.g. concrete crack detection), field engineering construction sites (e.g. piling and grouting
evaluation) and on-land petroleum seismic exploration (e.g. converted and S-wave reflection statics).
Acknowledgements
This work was conducted during a post-doc position at Kyoto University, funded by the Japan Society for the
Promotion of Science (JSPS). Students of the Engineering Geology and Geophysics labs are thanked for both field
and computing assistance. Dennis Harry is thanked for providing a field data example.
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Table 1. Model parameters of the numerical sand-filled ‘sinkhole’
Layer Thickness
(m)
VS
(m/s)
VP
(m/s)
1 2 350 857
2 2 400 980
3 8 600 1470
4 38 400 980
5 Inf 1000 2450
Table 2. Comparison between the ‘non-ideal’ field parameters used by Harry et al., (2005) and more ‘ideal’ field
parameters for routine surveys, suggested by O’Neill (2003).
Parameter ‘Non-
ideal’
‘Ideal’ Reason
No. of
channels and
spacing (m)
12 at
1 m
24 at
1 m
Resolve longer
wavelengths
Near-offset 1 m 5 m Reduce
near-field effects
Geophone
resonance
100 Hz 4.5 Hz Gain low
frequency
response
Source
frequency
~100 Hz 40 Hz More power of
dominant
wavelength
Table 3. Elastic parameters representing ‘soil’ and ‘concrete’ used in 3D FD modeling of a ‘wall’ parallel to the
seismic recording spread.
Parameter ‘Soil’ ‘Concrete’
VP (m/s) 490 4300
VS (m/s) 200 2150
Density (kg/m3
) 1800 2250
QP 100 1000
QS 45 450

(a)
(b)
Figure 1. Exposed sinkholes showing a thick, apparently
stiff, horizon at shallow depth, below a thin surficial
veneer, with softer material at depth:
(a) From http://www.stoptranspark.org/sinkholes.html ,
and;
(b) From
http://www.coonawarradiscovery.com/goodies4u.asp
Depth(m)
Distance (m)
−80 −60 −40 −20 0 20 40 60 80
0
5
10
15
20
25
30
VS
(m/s)
250
300
350
400
450
500
550
600
650
700
Figure 2. 2D finite-difference model designed to
simulate a shallow sand-filled sinkhole within a stiff
limestone layer.
500 1000 1500 2000 2500
0
10
20
30
40
50
60
Depth(m)
(a)
VS
VP
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
300
350
400
450
500
550
1D reflectivity
2D finite−difference
Figure 3. Synthetic P-SV modelling results (both 1D
reflectivity and 2D finite-difference) of the sinkhole
model, over the zone where the stiff layer exists: (a)
Velocity models (with effective dispersion curves
overlain), and (b) Effective dispersion curves (overlain
on the sign of the modal dispersion function).
(a)
Depth(m)
Distance (m)
−80 −60 −40 −20 0 20 40 60 80
0
5
10
15
20
25
30
VS
(m/s)
250
300
350
400
450
500
550
600
650
700
(b)
Depth(m)
Distance (m)
−80 −60 −40 −20 0 20 40 60 80
0
5
10
15
20
25
30
VS
(m/s)
250
300
350
400
450
500
550
600
650
700
Figure 4. Shear-wave velocity imaging results by full
P-SV wavefield inversion of the rollalong 2D
finite-difference data over the sinkhole model, for
acquisition geometries: (a) Shot ‘pushing’ from the left,
and (b) Shot ‘pulling’ from the right.

(a)
Depth(m)
Distance (m)
−100 −80 −60 −40 −20 0 20 40 60 80 100
0
10
20
30
40
50
60
VS
(m/s)
250
300
350
400
450
500
550
600
650
700
(b)
Depth(m)
Distance (m)
−100 −80 −60 −40 −20 0 20 40 60 80 100
0
10
20
30
40
50
60
VS
(m/s)
250
300
350
400
450
500
550
600
650
700
Figure 5. Stacked dispersion curves plotted as
approximate depth (0.4 wavelength) versus arbitrary
velocity, at each spread-midpoint of the rollalong 2D
finite-difference data over the sinkhole model, for
acquisition geometries: (a) Shot ‘pushing’ from the left,
and (b) Shot ‘pulling’ from the right.
(a)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 0.16 %
0 50 100 150 200
320
340
360
380
400
420
440
460
480
500
Measured
Initial
Final
0 200 400 600 800 1000
0
10
20
30
40
50
60
Depth(m)
RMS error: 29.3 %
True
Initial
Final
(b)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 0.08 %
0 50 100 150 200
320
340
360
380
400
420
440
460
480
500
Measured
Initial
Final
0 200 400 600 800 1000
0
10
20
30
40
50
60
Depth(m)
RMS error: 19.4 %
True
Initial
Final
synthetic rollalong 2D finite-difference data over the
sinkhole model, at the spread midpoint over the
right-hand edge of the soft-zone, for acquisition
geometries: (a) Shot ‘pushing’ from the left, and (b)
Shot ‘pulling’ from the right. The ‘True’ model is the
profile below the shotpoint.

(a)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
150
200
250
300
350
(b)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
100
150
200
250
300
350
Figure 7. 2D finite-difference models designed to simulate shallow pinchouts: (a) Low Velocity Layer (LVL), and (b)
High Velocity Layer (HVL).
(a)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
150
200
250
300
350
(b)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
100
150
200
250
300
350
(c)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
150
200
250
300
350
(d)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
100
150
200
250
300
350
Figure 8. Stacked dispersion curves plotted as approximate depth (0.4 wavelength) versus arbitrary velocity, at each
spread-midpoint of the rollalong 2D finite-difference data over the pinchout models: (a) LVL, with shot ‘pushing’
from the left; (b) HVL, with shot ‘pushing’ from the left; (c) LVL, with shot ‘pulling’ from the right; (d) HVL, with
shot ‘pulling’ from the right.

(a)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
150
200
250
300
350
(b)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
100
150
200
250
300
350
(c)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
150
200
250
300
350
(d)
Depth(m)
Distance (m)
−60 −40 −20 0 20 40 60
0
2
4
6
8
10
12
14
16
18
20
22
VS
(m/s)
100
150
200
250
300
350
Figure 9. Shear-wave velocity imaging results by full P-SV wavefield inversion of the rollalong 2D finite-difference
data over the pinchout models: (a) LVL, with shot ‘pushing’ from the left; (b) HVL, with shot ‘pushing’ from the left;
(c) LVL, with shot ‘pulling’ from the right; (d) HVL, with shot ‘pulling’ from the right.
(a)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 0.79 %
0 20 40 60 80 100
120
140
160
180
200
220
240
Measured
Initial
Final
0 100 200 300 400 500
0
5
10
15
20
25
Depth(m)
RMS error: 23.8 %
True
Initial
Final
(b)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 5.90 %
0 10 20 30 40 50 60 70
50
100
150
200
250
Measured
Initial
Final
0 100 200 300 400 500
0
5
10
15
20
25
Depth(m)
RMS error: 40.1 %
True
Initial
Final
(c)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 0.79 %
0 20 40 60 80 100
120
140
160
180
200
220
240
Measured
Initial
Final
0 100 200 300 400 500
0
5
10
15
20
25
Depth(m)
RMS error: 20.1 %
True
Initial
Final
(d)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 2.57 %
0 10 20 30 40 50 60 70
50
100
150
200
250
Measured
Initial
Final
0 100 200 300 400 500
0
5
10
15
20
25
Depth(m)
RMS error: 34.2 %
True
Initial
Final
Figure 10. Full P-SV wavefield inversion results of the synthetic rollalong 2D finite-difference data over the pinchout
models, at the spread midpoints directly over the pinchout termination (position 0 m): (a) LVL, with shot ‘pushing’
from the left; (b) HVL, with shot ‘pushing’ from the left; (c) LVL, with shot ‘pulling’ from the right; (d) HVL, with
shot ‘pulling’ from the right. For each, the ‘True’ model is the profile below the shotpoint.

(a)Depth(m)
Distance (m)
50 55 60 65 70 75 80 85 90 95 100
0
5
10
15
20
25
VS
(m/s)
50
100
150
200
250
300
(b)
Depth(m)
Distance (m)
50 55 60 65 70 75 80 85 90 95 100
0
5
10
15
20
25
VS
(m/s)
50
100
150
200
250
300
P-SV wavefield inversion of the data collected by
landstreamer (on asphalt road) at the Niigata ‘mud
volcano’ site. Each comprises models plotted at the
centre of the rollalong spreads, with the stacked
approximate-depth dispersion curves overlain: (a)
‘Coarse’ layered models, (b) ‘Fine’ layered models
(with lateral 3-point median filter). Data acquired with
24-channels at 2 m spacing and 10 m near-offset, with
shot ‘pulling’ from the right.
(a)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 1.25 %
0 10 20 30 40 50
50
100
150
200
250
Measured
Initial
Final
0 50 100 150 200 250
0
5
10
15
20
25
Depth(m)
Final
Range
(b)
Frequency (Hz)Phasevelocity(m/s)
RMS error: 0.86 %
0 10 20 30 40 50
50
100
150
200
250
Measured
Initial
Final
0 50 100 150 200 250
0
5
10
15
20
25
Depth(m)
Final
Range
(c)
Frequency (Hz)
Phasevelocity(m/s)
RMS error: 1.81 %
0 10 20 30 40 50
50
100
150
200
250
300
350
400
Measured
Initial
Final
0 100 200 300 400
0
5
10
15
20
25
Depth(m) Final
Range
Figure 12. Full P-SV wavefield inversion results at
various midpoints along the Niigata ‘mud volcano’ line:
(a) Position 48 m (soft zone), (b) Position 82 m
(pinchout/scattering zone), and (c) Position 102 m
(stiff zone).

5 10 15 20 25
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 50 100 150 200
250
300
350
400
450
500
Figure 13. Synthetic P-SV full-wavefield modeling
results by the 2D discrete element method (DEM), over
the rectangular cavity model Gelis et al. (2005),
employing the same acquisition parameters: (a) Shot
gather, and (b) Dispersion image (with picked effective
dispersion curve).
−100 −80 −60 −40 −20 0 20 40 60 80 100
0
5
10
15
Depth(m)
Distance (m)
Figure 14. Stacked dispersion curves plotted as
approximate depth (0.4 wavelength) versus arbitrary
velocity, at each spread-midpoint of the rollalong 2D
finite-difference data over the cavity model of Gelis et al.
(2005). Solid curves are from shot ‘pushing’ from the
left; Dotted curves from shot ‘pulling’ from the right.
(a)
Depth(m)
Distance (m)
−100 −80 −60 −40 −20 0 20 40 60 80 100
0
5
10
15
VS
(m/s)
50
100
150
200
250
300
350
400
(b)
Depth(m)
Distance (m)
−100 −80 −60 −40 −20 0 20 40 60 80 100
0
5
10
15
VS
(m/s)
50
100
150
200
250
300
350
400
P-SV wavefield inversion of the rollalong 2D
finite-difference data over the over the cavity model of
Gelis et al. (2005): (a) Shot ‘pushing’ from the left, and
(b) Shot ‘pulling’ from the right.

0 50 100 150 200 250 300
−6
−4
−2
0
Frequency (Hz)
Power(dB)
(a)
Seismograms
Dispersion
0 50 100 150 200 250 300
−6
−4
−2
0
Frequency (Hz)
Power(dB)
(b)
Seismograms
Dispersion
0 50 100 150 200 250 300
−6
−4
−2
0
Frequency (Hz)
Power(dB)
(c)
Seismograms
Dispersion
Figure 16. Power spectra along the picked effective
dispersion curve in frequency-slowness space,
comparing the effects of acquisition geometry: (a) Field
data of Harry et al. (2005); (b) Synthetic data, using the
model and acquisition parameters of (a), and; (c)
Synthetic data, using the same model, but more ‘ideal’
acquisition parameters (24 channels at 1 m spacing and
5 m offset, 4.5 Hz geophones and a 40 Hz source
wavelet).
5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
100
150
200
250
300
5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 20 40 60 80 100
100
150
200
250
300
Figure 17. Shot gathers and dispersion images
comparing (a) and (b) 28 Hz planted geophones, and (c)
and (d) 4.5 Hz landstreamer geophones.
0 20 40 60 80 100
100
150
200
250
300
350
Frequency (Hz)
Phasevelocity(m/s)
(a)
4.5 Hz landstreamer
28 Hz spiked
0 20 40 60 80 100
−6
−5
−4
−3
−2
−1
0
Frequency (Hz)
Power(dB)
(b)
Figure 18. (a) Dispersion curves, and (b) Spectral power
comparing 28 Hz planted and 4.5 Hz landstreamer
geophones.
10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 10 20 30 40 50
100
200
300
400
500
10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Offset (m)
Time(s)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 10 20 30 40 50
100
200
300
400
500
Figure 19. Shot gathers and dispersion images from
landstreamer data recorded on (a) and (b) Sealed asphalt
road, and (c) and (d) Adjacent grass verge.
0 10 20 30 40 50
0
100
200
300
400
500
600
700
800
900
Frequency (Hz)
Phasevelocity(m/s)
(a)
On asphalt
On grass
100 120 140 160 180 200
0
2
4
6
8
10
Approx. shear velocity (m/s)
Approx.depth(m)
(b)
Figure 20. Dispersion curves comparing landstreamer
data recorded on a sealed asphalt road and the adjacent
grassy verge.

Frequency (Hz)
Phasevelocity(m/s)
0 50 100 150 200 250 300
100
150
200
250
300
Measured
Initial
Final
0 100 200 300 400
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Depth(m)
True
Initial
Final
field data of Harry et al. (2005): (a) Dispersion image,
with observed and calculated dispersion curves, and (b)
True and estimated shear-wave velocity models, where
the ‘true’ model is that from the fundamental-mode
inversion of Harry et al. (2005).
0
10
20
30
40
50
60
70
0
5
10
15
20
25
30
0
5
10
15
Inline (m)
Crossline (m)
Depth(m)
Source
Receiver
Figure 22. Model used for 3D finite-difference
simulations of the effects on the observed surface wave
dispersion of a vertical ‘cliff’ parallel to the recording
spread.
10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 20 40 60 80 100
120
140
160
180
200
220
240
10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 20 40 60 80 100
120
140
160
180
200
220
240
Figure 23. Synthetic P-SV full-wavefield modeling
results by the 3D finite-difference method, using the
LVL model from O’Neill et al (2003): (a) Flat
topography, and; (b) With a vertical ‘cliff’ parallel to
and 10 m from the geophone spread.
5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(a)
Frequency (Hz)
Phasevelocity(m/s)
(b)
0 50 100 150 200
100
150
200
250
300
5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
Offset (m)
Time(s)
(c)
Frequency (Hz)
Phasevelocity(m/s)
(d)
0 50 100 150 200
100
150
200
250
300
Figure 24. Reciprocal shot gathers and dispersion
images from landstreamer data recorded on an asphalt
road, with an embankment rise on one side and drop on
the other side of the road: (a) and (b) Forward shot, and
(c) and (d) Reverse shot.

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