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

[email protected] http://earth.kumst.kyoto-u.ac.jp/~adam

*Presently:

DownUnder GeoSolutions, Subiaco, Western Australia [email protected]

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.

References Bodet, L., van Wijk, K., Bitri, A., Abraham, O., Cote, P., Grandjean, G. and Leparoux, D., 2005, Surface-wave inversion limitations from laser-Doppler physical modeling: J. Env. and Eng. Geophys., 10 (2), 151-162. De Nil, D., 2005, Characteristics of surface waves in media with significant vertical variations in elasto-dynamic properties: J. Env. and Eng. Geophys., 10 (3), 263-274. Feng, S., Sugiyama, T. and Yamanaka, H., 2005, Effectiveness of multi-mode surface wave inversion in shallow engineering site investigations: Exploration Geophysics, 36, 26-33. Foti, S., Sambuelli, L., Socco, V. L. and Strobbia, C., 2003, Experiments of joint acquisition of seismic refraction and surface wave data: Near Surface Geophysics, 1, 119-129. Ivanov, J., Park, C. B., Miller, R. D. and Xia, J., 2005, Analyzing and filtering surface-wave energy by muting shot gathers: J. Env. and Eng. Geophys., 10 (3), 307-321.

Kaufmann, R. D. Xia, J., Benson, R. C., Yuhr, L. B., Casto, D. W. and Park, C. B., 2005, Evaluation of MASW data acquired with a hydrophone streamer in a shallow marine environment: J. Env. and Eng. Geophys., 10 (2), 87-98. Levshin, A. L. and Panza, G. F., 2005, Caveats in modal inversion of seismic surface wavefields: [http://users.ictp.trieste.it/~pub_off/np/IC2005_16to30.html], 20pp. Malovichko, A. A., Anderson, N. L., Malovichko, D. A., Shylakov, D. Y. and Butirin, P. G., 2005, Active-passive array surface wave inversion and comparison to borehole logs in southeast Missouri: J. Env. and Eng. Geophys., 10 (3), 243-250. Mavko, G., Mukerji, T. and Dvorkin, J., 1998, The rock physics handbook: Tools for seismic analysis in porous media: Cambridge University Press, UK. Nagai, K., O'Neill, A., Sanada, Y. and Ashida, Y., 2005, Genetic Algorithm inversion of Rayleigh wave dispersion from CMPCC gathers over a shallow fault model: J. Env. and Eng. Geophys., 10 (3), 275-286. O'Neill, A., 2003, Full-waveform reflectivity for modelling, inversion and appraisal of seismic surface wave dispersion in shallow site investigations: PhD thesis (Unpublished), The University of Western Australia, School of Earth and Geographical Sciences [http://earth.kumst.kyoto-u.ac.jp/~adam/]. O'Neill, A., 2005, Seismic surface waves special issue guest editorial: J. Env. and Eng. Geophys., 10 (2), 67-85. O'Neill, A., Dentith, M. and List, R., 2003, Full-waveform P-SV reflectivity inversion of surface waves for shallow engineering applications: Expl. Geophys., 34 (3), 158-173. O'Neill, A. and Matsuoka, T., 2005, Dominant higher surface-wave modes and possible inversion pitfalls: J. Env. and Eng. Geophys., 10 (2), 185-201. O’Neill, A., Kato, M., Yasui, T. and Matsuoka, T., 20xx, Seismic surface waves in shallow site investigations - Part 2: Lateral variation and acquisition parameter effects (submitted). Park, C. B., Miller, R. D., Ryden, N., Xia, J. and Ivanov, J., 2005, Combined use of active and passive surface waves: J. Env. and Eng. Geophys., 10 (3), 323-334. Safani, J., O'Neill, A., Matsuoka, T. and Sanada, Y., 2005, Applications of Love wave dispersion for improved shear-wave velocity imaging: J. Env. and Eng. Geophys., 10 (2), 135-150. Socco, L. V. and Strobbia, C, 2004, Surface-wave method for near surface characterization: a tutorial, Near Surface Geophysics, 2 (4), 165-185. Strobbia, C., 2005, Love wave analysis for the dynamic characterisation of sites: Bollettino di Geofisica Teorica ed

Applicata, 46, (2-3), 135-152. Yamanaka, H., 2005, Comparison of the performance of heuristic search methods for phase velocity inversion in the shallow surface wave method: J. Env. and Eng. Geophys., 10 (2), 163-173. 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

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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.

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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.

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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).

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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).

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Figure 8. Full P-SV wavefield inversion results of the 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).

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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 dispersion curves overlain), and (b) Effective dispersion curves (overlain on the sign of the modal dispersion function).

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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).

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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).

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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).

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Figure 13. Synthetic P-SV modeling results of profile 3 from De Nil (2005): (a) Velocity models (with effective dispersion curves overlain), and (b) Effective dispersion curves (overlain on the sign of the modal dispersion function).

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Figure 14. Synthetic P-SV full-wavefield modelling of 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.

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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.

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Figure 16. Field data from a compacted site in Japan: (a) and (b) Vertical component, and (b) Transverse component.

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Figure 17. Full P-SV wavefield inversion results of the 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.

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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).

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Figure 19. Synthetic SH modeling results of the nonlinear stiffness gradient model from O’Neill and Matsuoka (2005): (a) Velocity models (with effective dispersion curves overlain), and (b) Effective dispersion curves (overlain on the sign of the modal dispersion function).

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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.

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Figure 21. Synthetic P-SV full-wavefield modelling of the low-velocity layer model 2 of Yamanaka (2005): (a) Shot gather, and (b) Dispersion image (with picked

dispersion curve).

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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).

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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.

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Figure 24. Genetic Algorithm inversion results of the 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.

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Figure 25. Vertical component field data from a site in Australia: (a) Shot gather, and (b) Dispersion image (with picked dispersion curves).

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Figure 27. Genetic Algorithm inversion results of the 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

[email protected] http://earth.kumst.kyoto-u.ac.jp/~adam

*Presently:

DownUnder GeoSolutions, Subiaco, Western Australia [email protected]

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.

References Al-Equabi, G. I. and Herrmann, R. B., 1993, Ground roll: A potential tool for constraining shallow shear-wave structure: Geophysics, 58, 713-719. Badal, J., Dutta, U., Seron, F. and Biswas, N., 2004, Three-dimensional imaging of shear wave velocity in the uppermost 30 m of the soil column in Anchorage, Alaska: Geophys. J. Int., 158, 983-997.

Blonk, B. and Herman, G. C., 1996, Removal of scattered surface waves using multicomponent seismic data: Geophysics, 61 (5), 1483-1488. Bodet, L., van Wijk, K., Bitri, A., Abraham, O., Côte, P. Grandjean, G. and Leparoux, D., 2005, Surface-wave inversion limitations from laser-Doppler physical modeling: J. Env. and Eng. Geophys., 10 (2), 151-162. Bohlen, T., Kugler, S., Klein, G. and Theilen, F., 2004, 1.5D inversion of lateral variation of Scholte-wave dispersion: Geophysics, 69, 330-344. Crice, D., 2005, MASW, the wave of the future; Editorial: J. Env. and Eng. Geophys., 10 (2), 77-79. Cull, J., Jung, G. and Massie, D., 2005, Cavity detection using single-fold frequency analysis: J. Env. and Eng. Geophys., 10 (2), 80-81. Feng, S., Sugiyama, T. and Yamanaka, H., 2004, Applications of multi-mode Rayleigh wave phase velocity inversion: Proc. 110th SEGJ (Spring) Mtg., 31-34. In Japanese. Gelis, C., Leparoux, D., Virieux, J., Bitri, A., Operto, S. and Grandjean, G., 2005, Numerical modeling of surface waves over shallow cavities: J. Env. and Eng. Geophys., 10 (2), 111-121. Grandjean, G. and Leparoux, D., 2004, The potential of seismic methods for detecting cavities and buried objects: experimentation at a test site: J. Appl. Geophys., 56, 93-106. Harry, D. L., Koster, J. W., Bowling, J. C. and Rodriguez, A. B., 2005, Multichannel analysis of surface waves generated during high-resolution seismic reflection profiling of a fluvial aquifer: J. Env. and Eng. Geophys., 10 (2), 123-133. Hayashi, K. and Suzuki, H., 2004, CMP cross-correlation analysis of multi-channel surface-wave data: Exploration Geophysics, 35, 7-13. Herman, G. C., Milligan, P. A., Huggins, R. J. and Rector, J. W., 2000, Imaging shallow objects and heterogeneities with scattered surface waves: Geophysics, 65, 247-252. Inazaki, T, 2004, High-resolution seismic reflection surveying at paved areas using an S-wave type land streamer: Exploration Geophysics, 35, 1-6. Ivanov, J., Park, C. B., Miller, R. D., Xia, J., 2000, Mapping Poisson's ratio of unconsolidated materials from a joint analysis of surface-wave and refraction events: Proc. SAGEEP, 11-19. Kugler, S., Bohlen, T., Bussat, S. and Klein, G., 2005, Variability of Scholte-wave dispersion in shallow-water marine sediments: J. Env. and Eng. Geophys., 10 (2), 203-218.

Kuo, J. T. and Nafe, J. E., 1962, Period equation for Rayleigh waves in a layer overlying a half-space with a sinusoidal interface: Bull. Seism. Soc. Am., 52, 807-822. Kuo, J. T. and Thompson, G. A., 1963, Model studies on the effect of a sloping interface on Rayleigh waves: J. Geophys. Res., 68, 6187-6197. Long, L. T., Kocaoglu, A. H. and Martin, J., 2000, Shallow S-wave structure can be interpreted from surface-wave group-velocity tomography: Proc. SAGEEP, 39-45. Luke, B. and Calderon-Macias, C., 2005, Detecting anomalous inclusions in soil profiles: Encouraging the use of geophysics to solve engineering problems: J. Env. and Eng. Geophys., 10 (2), 82-84. Miller, R. D., Xia, J., Park, C. B. and Ivanov, J. M., 1999a, Multichannel analysis of surface waves to map bedrock: The Leading Edge, 12, 1392-1396. Miller, R. D., Xia, J., Park, C. B., Davis, J. C., Schefchik, W. T. and Moore, L., 1999b, Seismic techniques to delineate dissolution features in the upper 1000 ft at a power plant site: Proc. 69th SEG Int. Mtg, 492-495. Nagai, K., O'Neill, A., Sanada, Y. and Ashida, Y., 2005, Genetic Algorithm inversion of Rayleigh wave dispersion from CMPCC gathers over a shallow fault model: J. Env. and Eng. Geophys., 10 (3), 275-286. O'Neill, A., 2003, Full-waveform reflectivity for modelling, inversion and appraisal of seismic surface wave dispersion in shallow site investigations: PhD thesis (Unpublished), The University of Western Australia, School of Earth and Geographical Sciences [http://earth.kumst.kyoto-u.ac.jp/~adam/]. O’Neill, A., 2004, Shear velocity model appraisal in shallow surface wave inversion: Proc. ISC-2 on Geotechnical and Geophysical Site Characterization, Viana da Fonseca, A. and Mayne, P. W. (eds.), 539-546, Millpress, Rotterdam. O’Neill, A., 2005, Seismic surface waves special issue; Guest editorial: J. Env. and Eng. Geophys., 10 (2), 67-76. O’Neill, A., Dentith, M. and List, R., 2003, Full-waveform P-SV reflectivity inversion of surface waves for shallow engineering applications: Expl. Geophys., 34 (3), 158-173. O’Neill, A., Matsuoka, T. and Tsukada, K., 2004, Modelling topographic effects in seismic surface wave surveying on artificial river floodbanks: Proc. 7th SEGJ Int. Symp., 415-420. O’Neill, A., Safani, J., and Matsuoka, T., 2006a, Landstreamers and surface waves: Testing and Results: Proc. SAGEEP. 10pp. O’Neill, A., Safani, J. and Matsuoka, T., 2006b, Rapid S-wave velocity imaging with seismic landstreamers and surface wave inversion: Preview, No. 121 (April), 25-30 (Aust. Soc. Expl. Geophys.).

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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

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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

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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.

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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.

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RMS error: 0.16 %

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RMS error: 29.3 %

True InitialFinal

(b)

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Dep

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RMS error: 19.4 %

True InitialFinal

Figure 6. Full P-SV wavefield inversion results of the 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)

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m)

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S (m/s)

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Figure 7. 2D finite-difference models designed to simulate shallow pinchouts: (a) Low Velocity Layer (LVL), and (b) High Velocity Layer (HVL).

(a)

Dep

th (

m)

Distance (m)−60 −40 −20 0 20 40 60

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S (m/s)

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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)

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th (

m)

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S (m/s)

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S (m/s)

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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)

Pha

se v

eloc

ity (

m/s

)

RMS error: 0.79 %

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Dep

th (

m)

RMS error: 23.8 %

True InitialFinal

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Frequency (Hz)

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RMS error: 5.90 %

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RMS error: 40.1 %

True InitialFinal

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th (

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RMS error: 34.2 %

True InitialFinal

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) D

epth

(m

)

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S (m/s)

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S (m/s)

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Figure 11. Shear-wave velocity imaging results by full 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)

Pha

se v

eloc

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m/s

)

RMS error: 1.25 %

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th (

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Frequency (Hz)P

hase

vel

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/s)

RMS error: 0.86 %

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RMS error: 1.81 %

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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).

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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).

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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.

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Figure 15. Shear-wave velocity imaging results by full 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.

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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).

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Figure 17. Shot gathers and dispersion images comparing (a) and (b) 28 Hz planted geophones, and (c) and (d) 4.5 Hz landstreamer geophones.

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Figure 18. (a) Dispersion curves, and (b) Spectral power comparing 28 Hz planted and 4.5 Hz landstreamer geophones.

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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.

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Figure 20. Dispersion curves comparing landstreamer data recorded on a sealed asphalt road and the adjacent grassy verge.

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epth

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Figure 21. Full P-SV wavefield inversion results of the 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).

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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.

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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.

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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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Figure 25. Model used for 3D finite-difference simulations of the effects on the observed surface wave dispersion of a ‘concrete’ wall, parallel to the recording spread: (a) Above ground only; (b) Below ground only; (c) Extending both above and below ground.

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Figure 26. Synthetic P-SV full-wavefield modeling results by the 3D finite-difference method, of a 200 m/s half-space, with the geophone spread parallel to, and 10 m from, a ‘concrete’ wall which is: (a) Above ground only; (b) Below ground only; (c) Extending both above and below ground, and (d) No wall (homogenous half-space).

ONeill_SurfaceWave_discuss

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