Important mechanisms of wave attenuation in fluid-saturated porous media from seismic to ultrasonic frequencies, include friction between grain boundaries (Winkler and Nur, 1982), global flow or Biot's mechanism (Biot, 1962), and wave-induced fluid flow at mesoscopic and microscopic scales (e.g., Müller et al., 2010). At the mesoscopic scale, patchy saturation and fractures are the most prominent causes of wave-induced fluid flow (White, 1975; White et al., 1975; Brajanovski et al., 2005; Tisato and Quintal, 2013; Quintal et al., 2014). At the microscopic scale, wave-induced fluid flow is commonly referred to as squirt flow and typically occurs between interconnected microcracks or between grain contacts and stiffer pores (O'Connell and Budiansky, 1977; Murphy et al., 1986; Mavko and Jizba, 1991; Sams et al., 1997; Adelinet et al., 2010; Gurevich et al., 2010). The attenuation caused by global flow as well as that caused by wave-induced fluid flow at microscopic or mesoscopic scales are frequency dependent. While the latter can have a strong effect at seismic frequencies (Pimienta et al., 2015; Subramaniyan et al., 2015; Chapman et al., 2016), global flow will only cause significant attenuation in reservoir rocks at ultrasonic frequencies or higher (e.g., Bourbie et al., 1987). The attenuation caused by friction between grain boundaries is, however, frequency independent and basically depends on the confining pressure and the strain imposed by the propagating wave (Winkler and Nur, 1982). Its effect is expected to be small for the correspondingly small strains caused by seismic waves used in exploration and reservoir geophysics. Furthermore, the attenuation caused by wave-induced fluid flow tends to be linearly superposed to that due to friction between grain boundaries, as shown by Tisato and Quintal (2014).

Gas hydrates (GH) are ice-like structures comprised of gas molecules entrapped by water molecules (Sloan and Koh, 2008). The widespread global occurrence of GH and the fact that 1 m3 of GH contains up to 164 m3 of natural gas (CH4 and CO2 at standard conditions) draws attention to the idea of using GH as a potential future energy resource (Schicks et al., 2011). Nevertheless, GH-bearing sediments have been discussed not only as a relatively clean hydrocarbon reservoir (Collett and Ladd, 2000), but also as a geohazard that could potentially contribute to global warming associated with hydrate dissociation and the subsequent destabilization of GH-cemented deep sea sediments at continental margins (Kvenvolden, 1993; Nixon and Grozic, 2007). Occurrences of GH are restricted to locations providing the required amount of gas and water and the preferred pressure-temperature (p/T) conditions, which are commonly referred to as gas hydrate stability zones. Usually, GH reservoirs are mainly limited to marine continental margins, deep lakes and permafrost regions (Bohrmann and Torres, 2006).

In the search for GH reservoirs, the attenuation of seismic waves caused by the pore fluids might be an important survey tool (e.g., Bellefleur et al., 2007). However, little effort has been directed toward studying its effects for unconsolidated sediments hosting GH in a rather dispersed manner. GH forming in the pore space of unconsolidated sediments at given p/T conditions alters the effective elastic and effective transport properties of the hosting sediment. It is known that the presence of GH in the sediment not only reduces the porosity and causes significant changes in its permeability, but also results in higher P and S wave velocities due to stiffening of the hosting matrix (Dvorkin et al., 2003; Guerin and Goldberg, 2005; Yun et al., 2005; Priest et al., 2006; Waite et al., 2009). In other words, the bulk and shear moduli increase due to the GH matrix-supporting effect within the sedimentary frame (Ecker et al., 1998). Additionally, the presence of GH causes higher attenuation of the seismic waves (Bellefleur et al., 2007; Dewangan et al., 2014) which was in particularly observed for sediments containing dispersed GH in the pore space (Guerin and Goldberg, 2002; Dvorkin and Uden, 2004). This anomalous seismic behavior in terms of increased attenuation and velocities (Guerin and Goldberg, 2002; Dvorkin and Uden, 2004) cannot be fully explained, although wave-induced fluid flow at the microscopic and mesoscopic scales has been speculated to cause them (Priest et al., 2006; Gerner et al., 2007). Gerner et al. (2007) conducted numerical P wave velocity simulations in highly permeable sedimentary layers, similar to hydrate-bearing sediments, and identified interlayer flow at the mesoscopic scale (White et al., 1975) as a potential mechanism of attenuation. Other authors have considered classical squirt flow models (O'Connell and Budiansky, 1977; Murphy et al., 1986) as the main source of attenuation in hydrate-bearing sediments (Dvorkin and Uden, 2004; Guerin and Goldberg, 2005; Priest et al., 2006; Waite et al., 2009; Marin-Moreno et al., 2017).

Quantifying GH saturation levels through geophysical exploration techniques is, however, not straightforward as there are still open questions on GH formation, its microstructure, and its distribution in the natural settings. Additionally, the recovery of unaltered natural GH samples is hampered due to their fast decomposition under ambient conditions. Therefore, various researchers have attempted to mimic the natural environment of GH-bearing sedimentary matrices in laboratory experiments (Berge et al., 1999; Ecker et al., 2000; Dvorkin et al., 2003; Yun et al., 2005; Spangenberg and Kulenkampff, 2006; Priest et al., 2006, 2009; Best et al., 2010, 2013; Hu et al., 2010; Li et al., 2011; Zhang et al., 2011; Dai et al., 2012; Schicks et al., 2013). The results of this collective effort established a number of conceptual models for the role of GH embedded in its sedimentary matrix (Fig. 1). Nevertheless, these approximations are currently unsatisfactory. Although it has been suggested that all hydrate habits known from laboratory investigations involving synthetic samples also occur in nature (Spangenberg et al., 2015), none of those simplified models can yield accurate predictions of GH saturations from field electric resistivity or seismic data alone (Waite et al., 2009; Dai et al., 2012).

Chaouachi et al. (2015) performed in situ experiments based on different formation mechanisms, including the “water in excess” and the “gas in excess” methods, to form gas hydrates in various sedimentary matrices. The in situ experiments coupled with high-resolution synchrotron-based X-ray micro-tomography (SRXCT) yielded 3-D images of sub-micrometer spatial resolution. Using the “gas in excess” method, the water present in the samples weds the grain surfaces and transforms into GH at the required p/T conditions. When hydrate is formed with the “water in excess method” the grains will also be water wet, but these very thin (sub-micron) hydrate films between the grains and the hydrate structure will only occur at very high GH saturations. The resulting 3-D micro-tomography data revealed the systematic presence of interfacial water films between the pore-filling GH and the grains, independent of which formation method was used (“gas in excess” or “water in excess”). The observed interfacial water films are occasionally interconnected via water bridges but water pockets are also embedded in the GH.

For this study, the SRXCT data presented by Chaouachi et al. (2015) underwent an image processing workflow in order to quantify the thicknesses of the thin interfacial water films. Based on the obtained results, we introduce a conceptual model for GH-bearing sediments to numerically study squirt flow. Our numerical simulations allow for the dispersion of the P wave modulus and the frequency-dependent P wave attenuation. The results demonstrate the high levels of seismic attenuation/dispersion that a range of variations of our conceptual model can cause. Additionally, our results support the suggestions that the estimation of GH saturation for GH occurring in a rather dispersed manner could be accomplished by using seismic wave attenuation as a tool for indirect geophysical quantification (Guerin and Goldberg, 2002; Priest et al., 2006; Best et al., 2013; Marin-Moreno et al., 2017).

Chaouachi et al. (2015) conducted various in situ experiments coupled with synchrotron-based tomography at the TOMCAT beamline of the Paul Scherrer Institute in Villigen, Switzerland. The aim was to study the formation process and distribution of gas hydrates in various matrices, such as pure quartz sand and glass beads, as well as mixtures of quartz sand with clay minerals. These in situ experiments were conducted using an experimental setup that allowed for high pressures and low temperatures. Further details are given by Chaouachi et al. (2015), Falenty et al. (2015), and Sell et al. (2016).

For this study, the SRXCT data obtained from the abovementioned in situ experiments focused on samples containing pure natural quartz sand sieved at a 200–300 µm grain size. Chuvilin et al. (2011) provides details on the sedimentology and mineralogy of the host sediment. We use a reconstruction process (Marone and Stampanoni, 2012) that yields an image matrix of 2560×2560×2160 voxels, with isometric voxel sizes of 0.74 and 0.38 µm at 10 fold and 20 fold optical magnification, respectively. The reconstructed tomograms revealed discernible grey value differences between the three relevant phases of the sample: solid grains, hydrate, and water (Fig. 2). To reduce image artifacts, such as inhomogeneity in grey scale values, streaks and edge enhancement, we apply a systematic image enhancement workflow comprising different image filter combinations in 2-D and 3-D (Sell et al., 2016). Chaouachi et al. (2015) observed the systematic appearance of an interfacial water film separating the quartz grains from the GH phase in samples where GH was formed directly from the juvenile state not involving GH dissociation, as well as where GH was formed from the “gas in excess method”. This observation is in accordance with the publication from Tohidi et al. (2001). Additionally several molecular numerical simulations showed that water layers prefer the interface of GH and quartz grains (Bagherzadeh et al., 2012; Bai et al., 2011; Liang et al., 2011). Identifying the water films and quantifying their thickness was one scope of this study to adapt our conceptual model.

The broad range of grey scale values of the filtered images were classified using watershed segmentation combined with region growing tools from the Avizo Fire 7 (FEI, France) and Fiji software packages. In the present study, we determined the thickness variation and geometry of the water film (Fig. 3). Following the image enhancement and segmentation process described by Sell et al. (2016), the segmented data illustrate the characteristics and appearance of the phases distributed in the samples (Fig. 4). Moreover, the high resolution of the data enables us to obtain 3-D images in which particular details, such as water bridges connecting two interfacial water films, are detectable (Fig. 5). With information collected from the 3-D data, our proposed conceptual model involves spherical grains covered by a homogenous water film which is, in turn, embedded in non-porous hydrate. The conceptual model can be adjusted to include water bridges connecting the water films (Fig. 6) and/or isolated water pockets within the hydrate and separated from the water films.

Many sources of squirt flow might coexist in unconsolidated sediments hosting GH, such as those resembling the conventional squirt flow models introduced by O'Connell and Budiansky (1977) for interconnected microcracks and by Murphy et al. (1986) for microcracks or grain contacts connected to spherical pores. Marin-Moreno et al. (2017) describes an integrated approach that combines the effects of some squirt flow models and other attenuation mechanisms. Here our objective diverges from that. We instead aim at studying the squirt flow phenomenon and the resulting frequency-dependent attenuation associated with a specific model, which is geometrically different from the previously mentioned conventional squirt flow models and is based on the thin interfacial water films. We thus neglect all other potential sources of attenuation.

Interfacial water films between sediment grains and the embedding GH matrix were recently observed in GH-bearing sediments through synchrotron-based micro-tomography at a spatial resolution down to 0.38 µm. Based on these data, we have determined the appearance and thicknesses of such films. With this knowledge, a new conceptual squirt flow model, which refers to a spherical water film coating the solid grains, was introduced for GH-bearing sediments. This geometry differs from the classical squirt flow models involving microcracks, interconnected or connected to spherical pores. Numerical simulations were performed to calculate the energy dissipation in the proposed model, considering a range of scenarios. Our results show that squirt flow in spherical interfacial water films can cause large and frequency-dependent P wave attenuation in a broad frequency range including seismic frequencies.

The numerical scheme is based on a set of coupled equations that reduce to Hooke's law in the subdomains of the model corresponding to the elastic solid materials (grains and GH) and to the quasi-static, linearized Navier–Stokes equations in the subdomains corresponding to the fluid (water). The results for our conceptual model show that the P wave attenuation peak is shifted to lower frequencies with decreasing thickness of the interfacial water film and with increasing grain size (or the length of the film), as analogously known for the microcrack aperture and length in classical squirt flow models. Furthermore, we tested the effect of inserting water pockets in an embedding GH matrix and the effect of connecting two neighboring interfacial water films through a water bridge. In general, the water bridges have a stronger effect on energy dissipation than the water pockets. Introducing such connections between neighboring interfacial water films causes a broadening of the P wave attenuation spectrum towards higher frequencies. Conversely, the presence of water pockets in the GH background only causes a slight overall increase in P wave attenuation. Although the majority of our simulations were performed for 2-D models, results of a 3-D simulation showed that 3-D effects are small for the basic 2-D models that we have considered.

Our results represent a strong base to explain fundamental processes in GH-bearing sediments and support previous speculations (Guerin and Goldberg, 2002; Dvorkin and Uden, 2004; Priest et al., 2006) that squirt flow is an important attenuation mechanism in such media, even at frequencies as low as those in the seismic range. This strengthens the perception that P wave attenuation may be used as an indirect geophysical attribute to estimate GH saturation. Nevertheless, further studies considering more realistic geometries for the microstructure of GH bearing sediments are necessary for the development of a successful strategy to estimate GH saturations, where hydrate is distributed in a dispersed manner instead of massive layers. This study represents the first attempt at understanding P wave attenuation in unconsolidated sediments which have large GH saturations. Following work will be aimed at implementing the segmented 3-D images obtained from synchrotron-based micro-tomography as a direct model input for numerical investigations, whereby realistic grain-to-grain contacts will be taken into account. The step towards more realistic structures as a model input is challenging due to the corresponding large computational demand. Furthermore, such model input requires additional segmentation steps for the 3-D images that allow for a smoothing of the stair-like resolution artifacts at the boundaries of the interfacial water films.