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# Surface wave attenuation in the shallow subsurface from multichannel–multishot seismic data: a new approach for detecting fractures and lithological discontinuities

- Tatsunori Ikeda
^{1}Email author and - Takeshi Tsuji
^{1}

**Received:**20 May 2015**Accepted:**10 June 2016**Published:**8 July 2016

## Abstract

Surface wave analysis generally neglects amplitude information, instead using phase information to delineate near-surface S-wave velocity structures. To effectively characterize subsurface heterogeneities from amplitude information, we propose a method of estimating lateral variation of attenuation coefficients of surface waves from multichannel–multishot (multifold) seismic data. We extend the concept of the common midpoint cross-correlation method, used for phase velocity estimation, to the analysis of attenuation coefficients. Our numerical experiments demonstrated that when used together, attenuation coefficients and phase velocities could characterize a lithological boundary as well as fracture zone. We applied the proposed method to multifold seismic reflection data acquired in Shikoku Island, Japan. We clearly observed abrupt changes in lateral variation of estimated attenuation coefficients around fault locations associated with a lithological boundary and with well-developed fractures, whereas phase velocity results could detect only the lithological boundary. Our study demonstrated that simultaneous interpretation of attenuation coefficients and phase velocities has the potential to distinguish localized fractures from lithological boundaries.

## Keywords

- Surface wave attenuation
- Surface waves
- Discontinuity
- Fracture
- Geological heterogeneity

## Introduction

Surface wave analysis is a technique for estimating shallow S-wave velocity structures (e.g., Xia et al. 2009; Socco et al. 2010). S-wave velocity profiles are obtained mostly from inversion of experimental dispersion curves of surface waves under the assumption of horizontally layered media (e.g., Xia et al. 1999). Extraction of dispersion curves generally relies on phase information of seismic data. Multichannel analysis of surface waves (MASW; Park et al. 1998, 1999) is currently the most effective method to estimate dispersion curves from multichannel seismic data. To overcome the assumption of one-dimensional velocity structures in surface wave analysis, several workers have proposed methods to estimate quasi-two-dimensional dispersion curves with high spatial resolution (e.g., Hayashi and Suzuki 2004; Boiero and Socco 2010; Bergamo et al. 2012; Ikeda et al. 2013).

The S-wave velocity structure derived from surface wave analysis is frequently used to characterize shallow lithology. However, it is difficult to detect localized near-surface fractures from phase velocity of surface waves derived from conventional surface seismic data. The detection of such fractures is important in various engineering applications (e.g., CO_{2} storage).

Although amplitude information is usually neglected in surface wave analysis, the amplitude of surface waves contains important information for characterizing lithology. Several workers have proposed methods for inversion of layered S-wave quality factors from attenuation coefficients of surface waves using multichannel seismic data (e.g., Lai et al. 2002; Xia et al. 2002; Foti 2004; Werning et al. 2013). Recently, Misbah and Strobbia (2014) proposed a method for jointly estimating modal attenuation and velocity from multichannel–multishot (multifold) data.

In the presence of sharp lateral heterogeneities, however, reflection of surface waves strongly influences estimation of attenuation coefficients of surface waves (Foti, 2004; Bergamo and Socco 2014). To detect these discontinuities associated with scattering (e.g., reflection), Bergamo and Socco (2014) applied the autospectrum method (Zerwer et al. 2005) and the attenuation analysis of Rayleigh waves (Nasseri-Moghaddam et al. 2005). Also, borehole logging can use amplitude information from Stoneley waves (surface waves traveling at the interface between the borehole and the surrounding material) to detect formation boundaries and permeable fractures (e.g., Saito et al. 2004).

In this paper, we propose a method for effectively estimating lateral variation of the attenuation coefficients of surface waves from multifold seismic data. The method is similar to the common midpoint cross-correlation (CMPCC) method, which focuses on phase information between possible pairs of receivers on common midpoints (CMPs) (Hayashi and Suzuki 2004; Tsuji et al. 2012; Ikeda et al. 2013), but our proposed method relies on amplitude information. In particular, we use it to characterize subsurface heterogeneities along with the conventional phase velocity analysis in numerical experiments on heterogeneous models. We also apply our proposed method to multifold reflection data from Shikoku Island, Japan, where lateral heterogeneity is expected from the presence of the median tectonic line (MTL; Ikeda et al. 2009). The results show that our attenuation analysis method is effective in identifying sharp lateral discontinuities (localized fractures and lithological boundaries) associated with faults. Furthermore, we show that simultaneous use of phase velocities and attenuation coefficients has the potential to distinguish localized fractures from lithological boundaries, which is not feasible from phase velocities alone.

## Theory and method

*u*of surface waves in a laterally homogeneous dissipative media can be written as follows (e.g., Strobbia and Foti 2006):

*I*(

*ω*) is the amplitude spectrum of the source,

*R*(

*ω*) is the site response for the dominant mode,

*α*(

*ω*) is the attenuation coefficient for the dominant mode,

*k*(

*ω*) is the wavenumber, \(\phi_{0}(\omega)\) is the phase spectrum of the source, and

*r*is the source to receiver distance.

*α*from multifold data such as seismic reflection or refraction data is based on the following six data processing steps.

- 1.
Seismic data received by the

*j*th receiver from the*s*th source are converted into frequency-offset domain data*u*_{ sj }by Fourier transform. - 2.Amplitude data
*U*_{ sj }are calculated by removing the effect of geometrical spreading of surface waves as follows:$$U_{sj} (\omega ) = \sqrt {r_{sj} } \left| {u_{sj} (\omega )} \right|.$$(2) - 3.For each (
*s*th) shot gather, amplitude ratios*A*_{ c }between*U*_{ sj }for the*j*th receiver and*U*_{ sn }for the*n*th receiver are calculated:where d$$A_{\text{c}} (\omega ,{\text{d}}r) = \frac{{U_{sj} (\omega )}}{{U_{sn} (\omega )}} = {\text{e}}^{{ - \alpha (\omega ){\text{d}}r}} ,$$(3)*r*is the receiver spacing between the*j*th and*n*th receivers and*c*is the CMP number defined at the midpoint between the*j*th and*n*th receivers. Note that the data with the longer offset should be the numerator in Eq. 3. If*N*receivers are employed in data acquisition,*N*(*N*− 1)/2 pairs are generated from each shot gather. - 4.The amplitude ratios in Eq. 3 with the same CMP are grouped together (Fig. 1a, b). We refer to the grouped data as the “amplitude ratio gather.” The amplitude ratio gathers correspond to the CMPCC gathers in the CMPCC method (Hayashi and Suzuki 2004). Amplitude ratio data with the same CMP can be stacked, as in the CMPCC method, if their receiver spacings are the same. Alternatively, we can suppress scattered data by computing mean values of the amplitude ratio data within a specified range of receiver spacing (e.g., Lin et al. 2011). The amplitude ratio gathers are generated in the frequency domain because seismic data in the time domain are converted into the frequency domain data by step 1. In the frequency domain, surface wave analysis usually requires many fewer data samples than in the time domain. This enables us to reduce computational demands in generating amplitude ratio gathers, compared with time domain analyses such as the CMPCC method.
- 5.
The value of

*α*can be estimated by the linear regression of d*r*versus ln(*A*_{c}) (e.g., Foti et al. 2014) through the origin. - 6.
By performing steps 4 and 5 for other CMPs, local attenuation coefficients

*α*can be obtained as a function of the CMPs.

In their two-dimensional attenuation analysis, Bergamo and Socco (2014) separately estimated local attenuation coefficients for each shot because the seismic energy at a reference point, corresponding to the intercept of their linear regression for estimating attenuation coefficients, differs from each shot. In our proposed method, however, we can simultaneously use multishot data in estimating local attenuation coefficients because the initial source amplitude is canceled out in generating the amplitude ratio gather with Eq. 3, and the amplitude ratio gather does not depend on the source amplitude or source location. Also, the midpoints between receiver pairs in the amplitude ratio data are coincident with local points (CMPs). Therefore, local points can be assigned greater weight, compared with the previous attenuation analysis.

In the presence of sharp discontinuities (e.g., faults), scattered surface waves can be observed (e.g., Xia et al. 2007; Hyslop and Stewart 2013; Strobbia et al. 2014; Bergamo and Socco 2014; Hyslop and Stewart 2015). In such laterally heterogeneous media, estimated values of *α* not only reflect attenuation coefficients related to quality factors but also include the effect of scattering (e.g., reflection) due to lateral heterogeneity. To detect lateral discontinuities, Bergamo and Socco (2014) utilized lateral variation of attenuation coefficients related to scattered surface waves. They estimated two attenuation coefficients at each local point (i.e., CMP in this study) from positive- and negative-offset data (e.g., Fig. 1c). Their results demonstrated that a distinct difference between the lateral variation of attenuation coefficients from positive- and negative-offset data is a good indication of the locations of a sharp lateral discontinuity. To effectively characterize lateral heterogeneities, we also focus on spatial variation of local attenuation coefficients related to scattering and separately estimate attenuation coefficients at each CMP from positive- and negative-offset data.

### Numerical experiments

Parameters of P-SV finite-difference modeling for the simulated models

Size of grid cells | 1 m |

Number of cells | 1600 (horizontal) × 300 (vertical) |

Time interval | 0.2 ms |

Number of time steps | 10,000 |

Number of absorbing grids for each side | 100 |

We define CMP positions at every 10 m. We also define positive- and negative-offset data for the sources at the left and right sides of the CMPs, respectively (Fig. 1c). CMPCC gathers and amplitude ratio gathers are computed at each CMP. Phase velocities at each CMP are obtained by applying the MASW for the CMPCC gathers, in which the number of receiver pairs is given as the weighting function to enhance lateral resolution (Ikeda et al. 2013). At each CMP, attenuation coefficients are obtained from the linear regression of the amplitude ratio data, in which we use mean values of the observed amplitude ratio data within 8-m receiver spacing bins in a natural logarithmic scale. Bins with fewer than 10 data samples are discarded. Note that we did not apply the correction of geometrical spreading in Eq. (2) because of the absence of geometrical spreading of surface waves in 2D modeling.

Thus, our numerical experiments clearly demonstrated differences between phase velocities and attenuation coefficients in their sensitivity to heterogeneities (whether lithological boundaries or fractures). Because the proposed attenuation analysis is based on the theory of one-way surface wave propagation, backscattered surface waves are not included in the theory. However, our results showed that the lateral heterogeneity associated with backscattered surface waves can be characterized as the lateral variation of attenuation coefficients. We use such apparent attenuation coefficients to detect heterogeneities in the following field data analysis.

### Application to field data

At the CMP at 220 m on the profile (magenta square in Fig. 5c), the mean values of observed amplitude ratio data at 15.1 Hz from positive- and negative-offset data were well consistent with the corresponding fit lines (Fig. 6a). The negative value of attenuation coefficient *α* estimated from negative-offset data could not be explained by frequency-dependent attenuation of surface waves propagating in laterally homogeneous media, but they could appear near lateral discontinuities as a result of amplification at the boundary (Fig. 3f). The estimated attenuation coefficient from positive-offset data showed the opposite trend (positive value) consistent with the effect of scattering associated with a sharp lateral discontinuity (Bergamo and Socco 2014; Fig. 3e).

*α*, estimated values of

*α*were plotted as a function of one-third wavelength (roughly corresponding to depth) at each CMP (Fig. 7a, b; Additional file 3: Figure S3a, b) because depth sensitivity of Rayleigh waves is concentrated at about one-third wavelength (e.g., Hayashi 2008). In the conversion from frequency to depth, we also considered the effect of topography. The wavelengths for each CMP were obtained from the fundamental mode of dispersion curves estimated by the CMPCC analysis by Ikeda et al. (2013) (Fig. 7d; Additional file 1: Figure S1b; Additional file 3: Figure S3c). Note that the CMPCC analysis by Ikeda et al. (2013) used positive- and negative-offset data simultaneously in the phase velocity estimation for each CMP.

At ~250 m on the profile in Fig. 7, we observed an abrupt change in the values of *α* estimated from positive- and negative-offset data (Fig. 7a, b). Values of *α* from positive-offset data decreased with distance along the profile, opposite to their trend from negative-offset data. To evaluate the degree of change in *α* with horizontal direction, we examined the derivative values of *α* with respect to horizontal distance (Fig. 7c), calculated from the average value of *α* over 40- to 50-m elevation. The derivative values of *α* calculated from positive- and negative-offset directions had large values but opposite signs at ~250 m. This contrast in opposite attenuation trends marks the locations of sharp lateral discontinuities (Bergamo and Socco 2014) caused by scattering or amplification at the boundary (Fig. 3e, f) and, indeed, the lithological boundary on the MTL (MBMTL) near here (Figs. 5c, 7). Lateral variation near the MBMTL is apparent in the dispersion curves of Fig. 7d.

At ~150-m horizontal distance, we also observed an abrupt change in the values of *α* estimated from positive-offset data (Fig. 7a), although we had no negative-offset data here (Fig. 7b; Additional file 2: Figure S2). The increasing trend also corresponded to large derivative values (Fig. 7c). A plausible cause of this lateral variation of *α* is the nearby Kawakami fault (MTLAFS; Figs. 5c, 7). Interestingly, phase velocity data could not resolve this discontinuity because the dispersion curves near the MTLAFS do not show clear lateral variations (Fig. 7d). Our result agrees with the simulation study for the fracture model (Fig. 4).

We also observed vertical, frequency-dependent variation of the estimated attenuation coefficients mainly caused by S-wave quality factors (e.g., Xia et al. 2002). The values of *α* generally decrease with increasing wavelength (pseudo-depth) as clearly seen on the south side of the negative-offset result (Fig. 7b).

As with phase velocity estimation, there is a trade-off between spatial resolution and the length of a moving window when estimating attenuation coefficients at a local point (Bergamo and Socco 2014). Longer receiver spacing yields more reliable attenuation coefficients, whereas the effect of lateral heterogeneity around a CMP can be reduced by excluding data with longer receiver spacings. As Ikeda et al. (2013) demonstrated in CMPCC analysis, the spatial window can be applied for our proposed attenuation method. In this study, the maximum receiver spacings were about 180 m at each CMP. In our field example, lateral variation in the estimated values of *α* north of 300 m on the profile was similar when the maximum receiver spacings were reduced to 100 m (Additional file 4: Figure S4), but the opposite trend in the estimated values of *α* appeared south of 300 m. This opposite trend might be related to lateral discontinuities other than MBMTL and MTLAFS.

## Discussion

When we applied our proposed method to field data, we estimated significant lateral variations in attenuation coefficient *α* at locations matching two faults, MBMTL and MTLAFS, in the study area (Fig. 7a–c). However, a study using phase velocities (Ikeda et al. 2013) showed significant lateral variation only at the fault that constitutes a lithological boundary (MBMTL, Fig. 7d). The lateral variation in phase velocities estimated by surface wave analysis mainly reflects lithological differences (most sensitive to differences in S-wave velocities) (e.g., Fig. 3a–c and MBMTL; Fig. 7d). Because the effects of backscattered surface waves with negative-phase velocities can be reduced in frequency-wavenumber analysis (e.g., MASW), the effect of scattering due to lateral discontinuities (lithological boundaries or localized fractures) is suppressed in phase velocity estimations. Furthermore, since the resolution of phase velocity estimation is not enough to resolve the localized fracture (i.e., small-scale velocity anomaly), clear lateral variation cannot be observed in the estimated phase velocities around localized fractures (Fig. 4a–c and MTLAFS; Fig. 7d). On the other hand, attenuation coefficients vary as a result of both lithological differences and localized fractures (Figs. 3d–f, 4d–f, 7a, b). Around the MTLAFS, scattering by the fracture would be dominant in the estimated attenuation coefficients because the phase velocity result would not detect a lithological contrast. The estimated attenuation coefficients increased near the MTLAFS (Fig. 7a) as the simulation study also showed (Fig. 4d–f), whereas the effect of scattering and amplification at the lithological boundary was indicated near the MBMTL from the opposing trends in the *α* estimated from positive- and negative-offset data (Figs. 3e, f, 7a–c).

However, we observed a single high-attenuation anomaly between the MTLAFS and MBMTL (Fig. 7a). Because of the absence of the negative-offset result around the MTLAFS, the contribution of the fracture (i.e., MTLAFS) for the attenuation anomaly is not clear. To investigate the contribution of the fracture, we performed a simulation of the inverted velocity model based on phase velocity analysis (Ikeda et al. 2013; Fig. 5d) by the same procedure in the section of numerical experiments.

*f*

_{ m }and the

*l*th CMP based on Bergamo and Socco (2014),

*α*

_{ lm }is the attenuation coefficient for

*f*

_{ m }and the

*l*th CMP, \(\left\langle {\alpha _{m} } \right\rangle\) is the mean value of the attenuation coefficients among all CMPs for

*f*

_{ m }, and stdev(

*α*

_{ m }) is the standard deviation of that mean value. The normalized attenuation coefficients can emphasize the lateral variation of attenuation coefficients and reduce the effect of frequency-dependent attenuation coefficients.

Parameters of 3D finite-difference modeling for the simulated model

Size of grid cells | 2 m |

Number of cells | 300 (orthogonal to the survey line) × 700 (parallel to the survey line) × 200 (vertical) |

Time interval | 0.12 ms |

Number of time steps | 21,000 |

Number of absorbing grids for each side | 30 |

Compared with the results of 2D or 3D numerical simulation, the dipping attenuation structure was masked and the high-attenuation anomaly was shifted to the north in the field results of positive-offset data. Because the fault is branched into several planes in the shallow formation due to low effective pressure (Tsuji et al. 2014), the fracture zone could be developed along the trace of large fault (i.e., MTL). Therefore, the fracture zone associated with the MTL fault system has possibility to cause increase in attenuation coefficients in the field data case (Fig. 8c). If so, it would increase the attenuation coefficients between the MTLAFS and MBMTL and mask the dipping attenuation structure observed in the simulation results for positive-offset data (Figs. 8a, 10a, c). Because of well-developed fracture zone, the high-attenuation zone in the simulation results would be shifted to the north, where it would coincide with the result of the field data analysis (Fig. 8c).

The presence of a fracture zone near the MTLAFS enables us to explain the differences between the attenuation coefficients from the simulation and the field data analysis. Thus, both a fracture and a lithological boundary are possibly needed to account for the lateral variation of the estimated attenuation coefficients in the field data.

However, we also observed the difference between the simulation and field results for negative-offset data (Figs. 8b, d, 10b, d). In the simulation results, we observed a dipping low-attenuation anomaly near the MBMTL, probably related to the slope of the lithological boundary. It is difficult to clearly explain the reason for the absence of the dipping structure in the field results of negative-offset data. Since the effect of surface wave attenuation is not considered in constructing the simulated model (Fig. 5d), the difference could be caused by sensitivity differences between the attenuation and phase velocity to localized structural heterogeneities. Although we computed normalized attenuation coefficients to reduce the effect of frequency-dependent attenuation coefficients, such anelastic attenuation included in only field data would also be responsible for the difference.

Because attenuation coefficients has the possibility to resolve localized fractures (Fig. 8c), our proposed method provides crucial information in fluid injection experiments (e.g., CO_{2} storage), in which localized fractures that may leak fluids are undesirable. Our proposed method creates the potential to detect such localized fractures using conventional surface seismic data.

## Summary

To characterize subsurface heterogeneities, we proposed a method for estimating spatial variation in attenuation coefficients of surface waves from multichannel–multishot data. Like the CMPCC analysis proposed by Hayashi and Suzuki (2004), this method retains high lateral resolution while estimating attenuation coefficients at each CMP. In this method, multishot data can be easily combined because source amplitude of each shot is canceled out in estimating the local attenuation coefficients.

Our study demonstrated that the lateral variation of attenuation coefficients estimated by the proposed method can identify sharp lateral discontinuities such as lithological boundaries and fracture zones. Estimating attenuation coefficients separately from positive- and negative-offset data is effective in identifying lithological boundaries. We also demonstrated that attenuation coefficients are more sensitive to localized fractures than phase velocities, although both attenuation coefficients and phase velocities are sensitive to lithological boundaries. Therefore, simultaneous interpretation of lateral variation of attenuation coefficients and that of phase velocities has a potential to distinguish lithological boundaries from the localized lateral discontinuities (fractures associated with faults). This ability would be valuable in applications such as fluid injection studies, where it may allow localized fractures to be detected using conventional seismic data.

## Declarations

### Authors’ contributions

TI carried out the data analysis and drafted the manuscript. TT joined the methodological discussion and helped to draft the manuscript. Both authors read and approved the final manuscript.

### Acknowledgements

We thank Editor Hiroshi Takenaka and two anonymous reviewers for constructive comments that improved manuscript. We also thank Shikoku Electric Power Co., Inc., and Shikoku Research Institute Inc., for seismic data acquired across the MTL. This study was done in collaboration with Shikoku Research Institute Inc. We gratefully acknowledge the support provided by the International Institute for Carbon Neutral Energy Research, sponsored by the World Premier International Research Center Initiative, MEXT, Japan.

### Authors’ information

TI received a B.S. (2009) in Global Engineering, M.Sc. (2011) in Civil and Earth Resources Engineering, and a Ph.D. (2014) in Urban Management from Kyoto University, Japan. Since 2014, he has been a postdoctoral research associate at the CO_{2} Storage Division of the International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University. His research interests include surface wave analysis considering the effects of higher modes, lateral variation, attenuation, and anisotropy. TT received a B.S. (2002) in Resources Engineering from Waseda University, Japan, and an M.Sc. (2004) and a Ph.D. (2007) in Earth Science from the University of Tokyo, Japan. From 2007 to 2012, he was an assistant professor of Engineering Geology Group at Kyoto University. From 2010 to 2011, he stayed at Rock Physics Department of Stanford University. Since 2012, he has been an associate professor at Kyushu University. He is lead principal investigator at the CO_{2} Storage Division of the International Institute for Carbon-Neutral Energy Research (WPI-I2CNER). His research interests include seismic reflection and refraction analysis, surface wave analysis, seismic attributes analysis, rock physics, seismic anisotropy, seismic interferometry, and interferometric SAR.

### Competing interests

Both authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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