Rock Physics Modeling of Acoustic Properties in Gas Hydrate-Bearing Sediment

Abstract

Gas hydrates (GH) are well known to have an influential effect on the velocity and attenuation of gas hydrate-bearing sediments (GHBS). Based on rock physics modeling, sediment velocity has been extensively used to characterize the distribution of gas hydrate. However, the results obtained from different models show a significant variation. In this study, we firstly review and compare the existing rock physics modeling for velocity and attenuation. The assumption, characteristics, theoretical basis, and workflow of the modeling are briefly introduced. The feasibility and limitations of the published models are then discussed and compared. This study provides insight into how to select a suitable rock physics model and how to conduct modeling in the application of the rock physics model to field data. Then, we introduce how to predict hydrate saturation, hydrate morphology, the dip angle of fracture, sediment permeability, and attenuation mechanisms from the comparison between the modeled and measured acoustic properties. The most important application of rock physics modeling is predicting the hydrate saturation and we discuss the uncertainties of the predicted saturation caused by the errors related to the velocity measurements or rock physics modeling. Finally, we discuss the current challenges in rock physics modeling related to optimizing the input parameters, choice of a suitable model, and upscaling problems from ultrasonic to seismic and well log frequencies.

1. Introduction

GH is a crystalline compound consisting of water and guest molecules that forms under high pressure and low temperature [1]. Great effort has been devoted to analyzing the potential of GH as a main alternative energy resource, and its important effects on global climate change and sub-marine geohazards [2,3,4,5,6]. Moreover, GH poses great challenges to the flow assurance in deepwater oil and gas exploitation and transportation because of the possible aggregation and flocculation caused by the coexistence of GH, asphaltenes, and resins in the pipelines [7,8,9]. The presence of GH indicates a finely balanced system in equilibrium, and the reduction in pressure and increase in temperature will cause the decomposition of GH [10,11].

The occurrence of GH accumulations under permafrost in polar continental shelves and the sediments beneath the ocean floor has triggered our interest in GH as an unconventional energy resource for the next few decades [3,12,13,14,15,16,17]. Although there still is disagreement over the concentration of GH within GHBS and the total amount of methane stored in GH accumulations, the estimated amount of methane in GH accumulations worldwide is considered to contain more potential energy than conventional oil, gas, and coal deposits [18,19,20,21]. The enormous amount of methane within GH accumulations and the widespread distribution of GHBS have been confirmed by previous studies [22]. Previous estimates of the available amount of methane in GH are highly varied over a wide range because direct sampling and analysis of GH in the natural state are an almost impossible task. It is challenging to retrieve intact GH samples during the coring process because of the unstable temperature and pressure conditions. Therefore, partially frozen systems are used as an analog for understanding GH occurrence because of their similar physical properties. The coexistence of hydrate, ice, and unfrozen water complicates the characterization of wave propagation in partially frozen sediments. Several rock physics approaches are applied to predict their acoustic properties [23,24,25,26,27]. Previous rock physical modeling indicated that the amount and pore-scale distribution of coexisting hydrate, ice, and unfrozen water significantly affect the acoustic properties of the partially frozen systems [26,27].

Collett (2002) indicated that whether the estimation of GH is accurate or not is dependent on the following reservoir parameters: coverage of the GH occurrence, reservoir conditions, reservoir thickness, sediment porosity, water, and GH saturation [28]. Some reservoir parameters can be estimated by the acoustic properties of GHBS which can be obtained from the field measurements such as the remote seismic method and the down-hole logging method [22]. Theoretical rock physics modeling can bridge the abovementioned reservoir parameters with the acoustic properties of GHBS. Moreover, rock physics modeling can provide a method to estimate the hydrate saturation from the acoustic properties in GHBS (P- and S-wave velocities and attenuations) [29,30,31,32,33,34]. However, previous studies indicated that the estimation based on different rock physics models varies significantly even for the same GHBS. Therefore, the choice of a rock physics model is crucial for the accurate estimation of GH in sediments. The main objective of this study is to review the existing rock physics models for GHBS and provide further insight into selecting a suitable model for a specific GHBS. Moreover, combing sediment velocity with attenuation will provide a method to accurately quantify the GH occurrence. This study also reviews how GH occurrence affects sediment attenuation by the rock physics method.

A series of recent field expeditions have provided new insights into the nature of GH occurrence. The confirmed GHBS occur in a wide variety of geologic settings, and the field data have indicated that the coarse-grained and fine-grained sands are superior GHBS due to their higher permeability [35]. Recently, the GH-filled fractures in clay-dominated reservoirs also became potential energy production targets [19,35]. Existing rock physics models generally assume the isotropic nature for sand-dominated sediment and the anisotropy nature for clay-dominated sediment. This study classifies the existing models into isotropic and anisotropic models to facilitate the application of these models to field data. The existing rock physics models also can characterize the acoustic properties of other reservoir types, such as the carbonate reservoir type, by introducing the mineral compositions in these reservoirs. Taking no account of the lithology type of GHBS, rock physics modeling will yield misleading hydrate saturation results. In this paper, we firstly review the acoustic properties of GHBS, including velocity and attenuation at various field investigation frequencies. According to the abovementioned classification of rock physics models, the commonly used rock physics models for GHBS are further introduced and compared. Finally, the application and challenges of rock physics models to field data will be discussed.

2. Acoustic Properties of GHBS at Various Frequency Domains

2.1. Gas Hydrate Morphology

It has been recognized that GH morphology combined with hydrate saturation significantly affects the acoustic properties of GHBS [36,37,38]. GH morphology provides information on the hydrate distribution and formation pattern in GHBS, and there seems to be no consensus on hydrate morphology even for the same geological environment because GH morphology is speculated to depend on the sediment lithology, pore structure, and GH saturation [37,39,40]. However, GH morphology is required information for most rock physics models in the prediction of velocity, attenuation, and hydrate saturation [41,42]. In coarse-grained sediment, GH usually grows with the following patterns: (1) free growth in the pores and without contact with sediment particles (pore-filling morphology) (Figure 1a); (2) intergranular growth at the contact between neighboring grains (contact cementing morphology) (Figure 1b); (3) growth as a sediment framework bridging neighboring sediment particles (load-bearing morphology) (Figure 1c); and (4) uniform growth coating the surface of sediment particles (envelope cementing morphology) (Figure 1d) [37,38,43]. In mature coarse-grained sediments, patchy hydrate morphology with pore space fully saturated by 100% hydrate can occur due to the Ostwald ripening in pore-filling conditions [40]. When the saturation of pore-filling hydrate is high enough to fill the connecting two or more pores, then the hydrate will become interpore-bridging patchy hydrate morphology (Figure 1e) [40,44,45]. GH in clay-dominated sediment usually forms with a larger size than the original fracture pores and then moves apart from the neighboring sediment particles, generating grain displacement hydrate (Figure 1f) [43,46,47,48]. Figure 1g,h,j,k shows the field hydrate morphology in the coarse-grained sediments in the Mallik, Nankai Trough, and Mt. Elbert [43]. The hydrates distributed in the pores of coarse-grained GHBS are not readily visible [43]. The GH morphology in fine-grained sediments was recognized as hydrate lenses, nodules, and veins by the nature hydrate cores in the South China Sea and Gulf of Mexico (Figure 1i,l) [43,48].

2.2. Acoustic Properties of GHBS

The presence of GH essentially affects the physical properties of GHBS including shear strength, porosity, permeability, and geophysical properties including resistivity, velocity, and attenuation [22,37]. Among these geophysical anomalies, the velocity and attenuation of P- and S-waves have been extensively used to characterize the occurrence and distribution of hydrate and assess the hydrate saturation of GHBS [37]. This study mainly focuses on how the presence of GH affects the P- and S-wave velocities and attenuations. In this section, hydrate morphologies and attenuation mechanisms associated with GH proposed in previous studies are reviewed.

2.2.1. Wave Velocity

It is generally considered that the pore space in GHBS is occupied by GH, whereas free gas is commonly trapped beneath the GHBS [49,50,51]. The presence of GH makes the sediments stiffer, and it might cement the grains together, and then cause the bulk and shear moduli to significantly increase, thus increasing both P- and S-wave velocities. However, the degree of increase in velocity is dependent on the hydrate saturation and hydrate morphology [38,52]. In addition, it is believed that a small amount of free gas will dramatically decrease the P-wave velocity because of the significant reduction in sediment bulk modulus, and the fact that the P-wave velocity of free gas-bearing sediment is strongly dependent on the distribution type of free gas and gas bubble size [49]. There is no effect of free gas on the S-wave velocity because S-waves cannot travel through fluid phases [29,53].

The rock physics model can provide a tool to relate P- and S-wave velocities to hydrate saturation, hydrate morphology, porosity, and physical properties of sediment mineral, pore fluid, and hydrate. Previous rock physics modeling has taken into account the effect of hydrate morphology on velocity [54,55,56,57]. The disseminated hydrate tends to form pore-filling hydrate at low hydrate saturation, while it tends to become load-bearing sediments as hydrate saturation exceeds 25–40% [38,52]. The velocities of P- and S- waves for cementing hydrate sharply increase even at a low hydrate saturation (< 3%), conversely those are insensitive to hydrate saturation until hydrate saturation exceeds 40% for load-bearing and pore-filling hydrate [58,59,60] (Figure 2a–d). Previous ultrasonic measurements indicated that for hydrate saturation above 15%, the hydrate morphology will transform from pore-filling hydrate morphology into patchy hydrate morphology, and the corresponding P-wave velocity will increase more steeply [44,45] (Figure 2e). The distribution of free gas in sediments is commonly assumed to be either uniform type, water and gas being evenly distributed in the pores, or patchy type, pores fully saturated with water and dry pores only filled with gas [55,61,62,63] (Figure 2f,g). The P-wave velocity of free gas-bearing sediment strongly depends on the distribution type of free gas in the sediment pores, and this issue is beyond the scope of this study.

2.2.2. Wave Attenuation

Previous studies have thoroughly elaborated on the effect of GH on sediment velocity, while there has been a very limited comprehensive investigation of the effect of GH on sediment attenuation. Attenuation is a measure of energy loss when the elastic wave travels through a rock [29]. The intrinsic sediment attenuations are generally dependent on sediment lithology, fluid saturation, frequency, and strain amplitude [64]. Several important attenuation mechanisms are provided including matrix anelasticity, friction dissipation due to relative motions between grains and crack surfaces [65,66], squeezing gas pockets for the case of partial saturation [67,68], global Biot flow [69,70], local squirt flow [71,72,73,74,75], and wave-induced flow due to mesoscopic scale patches [76,77,78,79]. It is believed that intrinsic attenuation for fluid-saturated rocks is frequency-dependent over a broadband frequency range through a series of experimental data [73,75,80,81,82].

The presence of GH makes the attenuation mechanism more complicated. The attenuation of GHBS is affected by hydrate saturation and interaction between the hydrate and matrix grains [29,83,84]. The proposed attenuation mechanisms associated with GHBS include the effect of hydrate morphology on attenuation (Figure 2a–d) [83,84,85], gas bubble damping (Figure 2f) [84], global Biot flow (Figure 2h), local squirt flow (Figure 2i) [29,83,84], and cementation and frictional loss between the hydrate and solid grain (Figure 2j) [29]. A thin bound water film was observed between hydrate and grain surface by X-ray microtomography [45,86]. The presence of water film will increase the sediment velocities such as pore-filling hydrate morphology and cause significant seismic attenuation [45,85,87,88] (Figure 2k). When the methane gas moves upward into the sediment and reaches the hydrate stability zone, hydrate film can occur between the gas bubble and the surrounding pore water (Figure 2l) [89,90]. The gas bubble trapping within the hydrate film results in the coexisting hydrate and gas bubble and a subsequent significant effect on sediment velocity and attenuation [42,90].

2.3. Acoustic Properties of GHBS at Various Investigation Frequencies

A tremendous number of geophysical exploration expeditions and deep-drilling expeditions were conducted to investigate the occurrence of GHBS in Japan [91], the United States [35], Canada [92], China [93,94], India [95], and Korea [96]. Geophysical exploration is one of the important approaches to identify and characterize GHBS such as hydrate saturation, lithology, permeability, porosity, and the extent and thickness of GHBS [35]. GH behaves at a higher P-wave velocity and a lower density than water, and has an elastic modulus comparable with ice [97]. All these changes in the sediment properties caused by the presence of GH or free gas will result in corresponding geophysical anomalies, allowing us to employ a corresponding geophysical method to characterize GHBS.

2.3.1. Seismic Technique and VSP Technique

The most commonly used geophysical technique for detecting GH is the seismic method. The bottom-simulating reflector (BSR) in the seismic reflection profile is often used to identify the base of GHBS in the marine environment [98]. However, it is not possible to use the BSR alone to infer the hydrate saturation. Moreover, it should be noted that hydrate can also be present in areas without BSR [41,99,100], and the BSR is considered to be related only to the top of free gas, and not necessarily the base of GHBS [101].

Using rock physics modeling, seismic velocity estimated from seismic data can be related to hydrate saturation. Thus, the evaluation of GHBS (structure, thickness, lateral extent) can be complemented [40]. It should be noted that the determination of hydrate saturation from the measuring P- and S-wave velocities of GHBS is still difficult because the velocity is also strongly dependent on sediment composition, porosity, and hydrate morphology.

The vertical seismic profiling (VSP) method can also be employed to help identify hydrate occurrence in the subsurface. VSP is a kind of measurement conducted inside the well hole and can obtain higher resolution than the seismic method but lower resolution than the well logging method. It allows us to measure the in-situ wave velocity and amplitude in GHBS at seismic frequencies [53,98]. The combined use of the surface seismic technique and VSP enables us to identify the lateral and vertical seismic velocity and amplitude in GHBS.

2.3.2. Well Logging Technique

Logging techniques are beneficial for the characterization of GHBS. The physical properties of GHBS can be measured in situ by well logging techniques including caliper, gamma-ray, resistivity, the amplitude of the waveform, sonic velocity, density, and neutron porosity. Sonic velocity logs of P- and S-waves have been used to identify GHBS [97]. The resistivity of GHBS is larger than that of non-hydrate bearing sediments, and resistivity logs are commonly used to estimate hydrate saturation by using Archie’s equation [102]. Other parameters (gamma-ray, porosity, and density) are also very important for the evaluation of GHBS. In the last decade, the sonic amplitude of P- and S-waves has become critical information to assess GH by using acoustic attenuation analysis [29,53,92,103].

2.3.3. Laboratory Measurements

It is challenging to retrieve intact GH samples during the coring process because of the unstable temperature and pressure conditions; therefore, laboratory analysis of artificial GH becomes important for understanding the GH occurrence. There are several autoclave systems for laboratory measurements, which are developed to measure the physical properties (P- and S-wave velocity, porosity, permeability, and electrical resistivity) of samples [104]. Priest et al. [58,59] and Best et al. [83] proposed a method based on a resonant column technique and measured the acoustic properties (P- and S-wave velocities and attenuations) over a much lower frequency domain (<550 Hz), while the common laboratory measurements are conducted in the ultrasonic frequencies (several hundred kHz). The tetrahydrofuran (THF) hydrate system is proposed to be an alternate methodology [105]. Although there are some differences between THF hydrate and methane hydrate, quite similar mechanical properties between them have been observed at a hydrate saturation lower than 40% [105].

There are two main challenges for laboratory measurements of natural or artificial GH samples. The formation method of GH samples affects the hydrate morphology, thus, in turn, affecting the physical properties of GH samples. The previous studies regarding the natural GH exhibit a specific pore-filling or load-bearing hydrate morphology, while laboratory synthetic samples formed from free gas generally result in cementing hydrate morphology at lower hydrate saturation [1,37,58,85]. However, Best et al. [83] also indicated that using the “excess water” method tends to result in pore-filling hydrate morphology. These discrepancies allow us to investigate the effects of hydrate morphology on the physical properties of GH sediment samples in laboratory measurements. In addition, when the measured physical properties of small hydrate samples in the laboratory are applied to the data obtained from the well logging or seismic method, there will be a problem of scale difference [37,97].

2.4. Rock Physics Modeling for Acoustic Properties of GHBS

The formation of hydrate in pore space will reduce the porosity and permeability of the sediment. The presence of GH is known to affect the physical properties of GHBS, and the sediment velocity increases with the increasing hydrate saturation. However, apart from hydrate saturation, the degree of increase is also strongly dependent on hydrate morphology, and this dependency will become more complicated [106,107]. By using rock physics modeling, the effect of hydrate saturation, hydrate morphology, and porosity on sediment velocity can be investigated (Figure 3).

It is generally accepted that both the P- and S-wave velocities increase with increasing hydrate saturation. However, significantly high attenuation has been widely observed along with the increase in velocity for both P- and S-waves in GHBS in the sonic logging frequency range [29,92,103,108,109,110]. This is contrary to our intuition that higher velocity corresponds to lower attenuation. In contrast to high attenuation at sonic frequencies in GHBS, attenuation at seismic frequencies (typically 10 to 150 Hz) is more contentious in existing studies [83,85,111,112,113,114,115]. There are extremely limited numbers of rock physical modeling focusing on elucidating the ultrasonic attenuation of GHBS. Pohl et al. [116] suggested that the high ultrasonic P-wave attenuation in THF hydrates might be related to the presence of liquid water between hydrate grains. Sahoo et al. [44] speculated that the ultrasonic P-wave attenuation changes might be caused by a decrease in coexisting gas bubble radius, and the creation of different aspect ratio pores during hydrate formation. Furthermore, Sahoo and Best [45] found that the ultrasonic S-wave velocity and attenuation can be explained by the decreasing permeability associated with the transition of hydrate morphology from pore-filling to load-bearing, and further to interpore hydrate framework morphology. Rock physics modeling for GHBS can consider the coupled effect of hydrate morphology, hydrate saturation, sediment porosity, permeability, anisotropic, and various attenuation mechanisms (Figure 3). The attenuation in the frequency range from seismic to sonic, and further to ultrasonic frequencies can be modeled (Figure 3).

3. Rock Physics Models for GHBS

3.1. Classification of Rock Physics Models

If GH occurs within the pores of coarse-grained sediments, the sediment velocity exhibits isotropic nature, whereas if GH occurs within fractures of fine-grained sediments, the sediment velocity exhibits an anisotropic nature [117]. Therefore, this study classifies the existing rock physics models into isotropic and anisotropic rock physics models. The existing isotropic rock physics models for GHBS are including the three-phase weighted model [118,119], three-phase Biot extension model [108,120], and effective medium model [84,121]. The existing anisotropic rock physics models for GHBS include the layered anisotropic model [100,122,123,124,125,126,127] and the effective medium anisotropic model [54,128,129,130,131]. The main characteristics, assumptions, workflows, attenuation mechanisms, and crucial input parameters for these models are provided as follows.

3.2. Isotropic Rock Physics Models

3.2.1. Three-Phase Weighted Model

Based on the assumption of pore-filling hydrate morphology, the Wood model is applicable in GHBS with high porosity, while using the time average equation associated with load-bearing hydrate morphology assumption, the Wyllie model is valid for GHBS with low porosity. As Figure 4 shows, using the P-wave velocities predicted from the Wood model and the Wyllie model, the P-wave velocity of composite sediment with any porosity can be obtained based on three-phase weighted equations. The calculation equations of this model are provided in Appendix A. In this model, the most crucial parameter is the arbitrary weighting factor when averaging the two types of velocities. The choice of weighting factor is dependent on the consolidation state of real GHBS and it can be predicted by fitting the P-wave velocity of non-hydrate sediment obtained from the sonic logging data to the velocity calculated from the three-phase weighted equations. The ratio of P-wave and S-wave velocities of GHBS is commonly associated with the velocity ratio of sediment matrix and porosity, and this ratio can be obtained by the Biot-Gassmann theory [132,133,134]. Consequently, the P- and S-wave velocities of GHBS can be calculated by using the three-phase weighted model and Biot-Gassmann equation, and this model is applicable for the sediment with high and low porosities.

Previous studies suggested that the main uncertainty of this method stems from the selection of the weighting factor, and the choice of weighting factor is dependent on the consolidation state of GHBS. The weighted factor of 1.27 and 1.29 are used by Shankar and Riedel [135] and Arun et al. [136], respectively, and they suggested that this value yields a best-fit P-wave velocity at the NGHP sites in the clay-dominated Mahanadi offshore, India. Chen et al. [137] proposed a calibration constant similar to the weighting factor and adjusted the calibration constant by fitting the experimental acoustic data to the modeling data. The results obtained show that the calibration of −0.6 allows a more accurate prediction of hydrate saturation for their synthetic sand-dominated sediment.

3.2.2. Three-Phase Biot Extension Model

The common three-phase Biot extension theory is based on the theory proposed by Leclaire et al. [48,49,119]. By using the percolation theory, the Leclaire theory incorporates the Biot flow in sand grains and ice, and describes the transition from a continuous to a discontinuous state during the freezing process. However, the Leclaire theory makes an important assumption that there is no contact between the ice and solid grains [70]. Therefore, as shown in Figure 5, the rigidity coefficient, mass density coefficient, friction coefficient, and shear modulus between sand grains and hydrate are equal to 0. The Leclaire theory includes the attenuation mechanisms due to energy dissipation caused by inertial coupling among three different phases, and global Biot flow (Figure 5). The Leclaire theory assumes no contact between ice and sand grains; however, Carcione and Tinivella [63] considered this contact (Figure 5). In addition, Carcione and Tinivella [63] added the apparent mass density between sand and hydrate grains (Figure 5), which was neglected in the Leclaire theory. Carcione and Tinivella [63] also introduced the viscous Biot dissipation of shear waves between a solid (sand and hydrate) and a fluid. Gei and Carcione [138] include the attenuation mechanisms due to energy dissipation caused by inertial coupling among three different phases, cementation between sand grains and hydrate, and global Biot flow (Figure 5). Concerning the inertial coupling coefficients among sand grains, hydrate, and fluid, Carcione and Tinivella [63] set the coupling coefficients to 0, and Guerin and Goldberg [29] showed that the coupling coefficients as 0 (which indicates the absence of inertial coupling between hydrate and fluid) significantly increase attenuation. Furthermore, Guerin and Goldberg [29] introduced squirt flow in sand grains and hydrate grains and the friction between sand grains and the hydrate (Figure 5). They consider the attenuation caused by the Biot and squirt flow in sand grains and hydrate grains, respectively. They also employ cementation between hydrate and solid grain, and friction between hydrate and solid grains. In addition, the effect of inertial coupling among hydrate, sand grains, and fluid has been taken into account in their model [29] (Figure 5). The calculation equations of this model are briefly introduced in Appendix B.

Although the intrinsic sediment attenuation is generally considered to be more sensitive to hydrate saturation and can better characterize the wave propagation in GHBS than sediment velocity [36,44,84], the sediment velocity is widely applied to model and predict the hydrate occurrence because of its flexible applicability. The grains cementation and the interaction between sediment grain and hydrate are considered to significantly affect sediment velocity [63]. Unlike the previous simple velocity average model, the main characteristic of the three-phase Biot extension model introduces the grain–hydrate interaction to model the hydrate occurrence in porous sediment [63]. Assuming a load-bearing GH morphology, a simplified three-phase Biot-type model is proposed to relate the P- and S-wave velocities of GHBS to hydrate saturation, porosity, and other physical properties such as the density, bulk modulus, and shear modulus of matrix components and pore water [41,113,114]. Due to the simple calculation procedure, this model has been successfully applied in marine sediments with high porosity, e.g., Alaska North Slope [57,117], Hydrate Ridge in the Cascadia margin [57,133], Blake Ridge in the Gulf of Mexico [57], Hikurangi margin of New Zealand [119], Shenhu area of the South China Sea [139], Krishna-Godavari Basin in the eastern Indian margin [120,140], South Shetland margin in the Antarctic peninsula [141,142], Nankai Trough in offshore Japan [143], Ulleung Basin offshore South Korea [144], etc. In the application of the three-phase Biot extension model, the selection of the consolidation parameter is crucial for the accurate prediction of velocity and hydrate saturation, which can be obtained by fitting the predicted velocities of non-hydrate sediment from rock physics modeling to the measured ones from field data [145]. The three-phase Biot extension model is usually suitable for the sand-dominated and unconsolidated GHBS with high hydrate saturation [94]. Note that the three-phase Biot extension theory usually fails to describe the hydrate occurrence of clay-dominated sediment because of abundant pore water bounded by clay particles and the basic Biot theory assumes that the pore water is not bound to sediment particles [119].

3.2.3. Effective Medium Model

The three-phase weighted model and three-phase Biot extension model approximate the hydrate occurrence as a part of the sediment matrix and assume the sequent alteration in sediment porosity and elastic moduli. The effective medium model considers the hydrate as pore fluid (pore-filling morphology), cement at the dry sediment frame (envelope and contact cementing morphologies), and sediment frame (load-bearing morphology) [55,146,147]. Different hydrate habits in pores alter the porosity, permeability, and elastic properties of the sediment in a different manner. The envelope and contact cementing morphologies reinforce the sediment frame and increase the sediment stiffness, the pore-filling hydrate morphology does not influence the sediment stiffness at all, and the load-bearing hydrate morphology weakly influences the sediment stiffness at high hydrate saturation [41,55]. Using the Voigt–Reuss–Hill average and assuming the hydrate as fluid or solid phases, the sediment porosity, and the bulk and shear moduli of solid and fluid phases in the sediment pores containing hydrate and water can be obtained. Introducing various hydrate morphologies, the bulk and shear moduli of the dry skeleton of GHBS can be calculated by the hydrate contact model proposed by Dvorkin et al. [146]. Then, the bulk and shear moduli of the dry sediment skeleton, solid phase, and fluid phase are substituted into Gassmann’s equation, and the effective elastic moduli of water-saturated sediment can be predicted. Finally, using the elastic moduli and density of water-saturated sediment, the P- and S-wave velocities of GHBS can be obtained. The detailed calculation equations of this model are introduced in Appendix C. This velocity-derived effective medium model has been widely applied to model the hydrate occurrence and to predict hydrate saturation in a pockmark offshore Norway [128], Mallik site in the Cascadia margin [148], Blake Ridge in the Gulf of Mexico [41,55,147,149,150], Hikurangi margin of New Zealand [151], Shenhu area of the South China Sea [93], Krishna-Godavari Basin in the eastern Indian margin [49,152], and Nankai Trough in offshore Japan [153]. In the application of the effective medium model, the assumption of hydrate morphology is the most critical problem, which will be discussed later.

Unlike the sediment velocity, the modeling of sediment attenuation based on the effective medium model is more complicated. This is because not only the hydrate morphology, but also fluid flow in the pores with different structures affects the sediment attenuation and these mechanisms should be included in the modeling. In addition to the effect of hydrate morphology on sediment attenuation, the introduction of porous hydrate in the effective model enables us to consider the geometrical shape of micropores and various attenuation mechanisms related to pore fluid in the micropores [154]. The squirt flow due to fluid inclusion in the porous hydrate is incorporated when calculating the bulk and shear moduli of fluid inclusion based on the correspondence principle proposed by Johnston et al. [64] (Figure 6). Then, the porous hydrate becomes an effective grain composed of homogeneous and isotropic elastic hydrate and interspersed ellipsoidal fluid inclusions [155]. The effective bulk and shear moduli of the effective hydrate with fluid inclusion become complex numbers as well as being frequency-dependent [83,84,155]. Then the real bulk and shear moduli of hydrate in the hydrate contact model can be replaced with the abovementioned complex bulk and shear moduli of the effective hydrate [41,147] (Figure 6). Subsequently, similar to the aforementioned calculation procedure of velocity, the effect of four modes of hydrate morphologies on attenuation is introduced by applying the hydrate contact model to calculate the effective bulk and shear moduli of the dry skeleton of GHBS [83,84] (Figure 6). Note that the contact cementing hydrate forms part of the solid frame, and the effective elastic moduli for the solid phase containing the contact cementing hydrate also become complex numbers, while the pore-filling hydrate is part of the fluid, and the effective elastic moduli of the fluid phase also becomes a complex number (Figure 6). Finally, the abovementioned effective and complex moduli of solid and fluid phases are then introduced into the Biot–Stoll model [156], and then the frequency-dependent P- and S-wave velocities and attenuations can be calculated [36,84]. In summary, the effective medium model considers the attenuation caused by the flow of fluid inclusions between micropores in hydrate and pore, the global Biot flow between sand grain and pore fluid, and energy loss due to the inelasticity of the hydrate frame, as shown in Figure 6.

3.3. Anisotropic Rock Physics Models

3.3.1. Layered Anisotropic Model

The abovementioned three-phase weighted model, three-phase Biot extension model, and effective medium model are usually suitable in sand-dominated isotropic GHBS. However, the acoustic properties of clay-dominated sediments commonly exhibit anisotropic characteristics when GH occurs in the fracture developed in fine-grained sediments [117,120]. The transverse isotropic medium is the simplest anisotropic medium and this anisotropy may be caused by clay particles or fracture-filled hydrate [100,130]. Pecher et al. [100] show that the observed transverse isotropy may be due to the directional alignment of clay grains rather than hydrate veins. In our description of anisotropic rock physics models, we assume that the anisotropy is caused by the high-velocity fracture-filled hydrate.

As Figure 7 shows, fracture-filled fine-grained GHBS can be modeled by laminated layers including the component of the pure hydrate layer and the isotropic water-saturated fine-grained sediment. The pure hydrate layer means the 100% hydrate-filled fracture and the P- and S-wave velocities, density, and volume fraction of this layer will be used in the modeling. The P- and S-wave velocities and density of water-saturated clay sediment can be computed by the aforementioned three-phase weighted equation or three-phase Biot extension equation without consideration of the hydrate. Using Lame constants of the two components, the anisotropic P-wave velocity and horizontally and vertically polarized S-wave velocities can be modeled by the Backus average. For a vertical borehole, the dip angle of a horizontal fracture is 0°, while the angle of a vertical fracture is 90° [126]. The dip angle of fracture is an important characteristic and the hydrate-filled fracture with a dip angle varying from 0° to 90° can be incorporated into this model using the anisotropy analysis of the Thomsen parameters [124,157]. Finally, P- and S-wave velocities and density of the transversely isotropic medium with an arbitrary dip angle of hydrate-filled fracture can be calculated. The detailed calculation equations of this model are provided in Appendix D.

Few studies have characterized the rock properties of fine-grained GHBS containing fracture-filled fracture. Anisotropic resistivity and velocity are two primary properties that can be obtained from resistivity logs and sonic logs [125]. Assuming the isotropic resistivity in fine-grained sediment with hydrate-filled fracture, the hydrate saturation estimated from resistivity logs is significantly higher than that calculated from core samples, which is possibly attributed to the anisotropy characteristic of this type of sediment [125]. In addition to the pronounced effect of anisotropy on sediment resistivity, the significant effect of anisotropy on P- and S-wave velocities has also been observed by previous modeling and field investigation [125]. The predicted velocity for anisotropic fine-grained sediment based on a layered anisotropic model shows that the anisotropy nature has a more significant effect on S-wave than P-wave [125]. Furthermore, except at high hydrate saturation, the P-wave velocity of anisotropic fine-grained sediment is insensitive to the dip angle of fracture [124]. Moreover, the orientation of the logging tool is required for the accurate estimation of dip angles using sonic logging data; however, this information is difficult to obtain [125]. A comparison of the velocities predicted from the layered anisotropic model and those measured from the field sonic logging data indicates the presence of high-angle fracture in clay-dominated GHBS such as the K-G Basin, eastern margin of India [125,126,130], the Ulleung Basin, East Sea of Korea [124], and the Shenhu area, South China Sea [158].

3.3.2. Effective Medium Anisotropic Model

Although the layered anisotropic model is widely used to model the hydrate-filled fracture in the clay-dominated sediment, the assumption of the laminated layers is unusual in filed investigations. Based on a theoretical framework combining the self-consistent approximation and differential effective medium approximation, several studies have successfully examined the intricate anisotropic microstructure caused by percolating clay and hydrate particles [54,128,129,130,131]. As Figure 8 shows, this model firstly creates a two-phase host composite consisting of aligned biconnected hydrate particles and water-saturated pores. The biconnected pore water is assumed as ellipsoidal inclusion and the biconnected hydrate particle is also ellipsoid with the same aspect ratio as the water-aurated pore. Using the self-consistent approximation theory, the effective stiffnesses of the hydrate–water host composite at the critical porosity (from 40% to 60%) are estimated as a function of the inclusion aspect ratio [159,160]. The stiffness at other porosities can be computed by the successive reduction in biconnected hydrate particles or water-saturated pores and the replacement of one component with the other component through differential effective medium approximation (Figure 8) [131]. Then, a new scheme composed of the host composite and clay particles is constructed, and the procedure of combining the self-consistent approximation and differential effective medium is repeated to predict the stiffnesses of the three-phase anisotropic effective medium composed of hydrate grain, pore water, and clay particles [130], as shown in Figure 8. The orientation of aligned clay particles is required for the accurate prediction based on the effective medium anisotropic model, and it can be provided by the measurement of core samples from scanning electron microphotographs [161] or the X-ray diffraction method [128], and the method of smoothing [54,129]. Therefore, the distribution of clay particles is employed in the host composite with different orientations consisting of hydrate–water. The calculation equations of this model are briefly introduced in Appendix E. The final model scheme incorporates the microstructure of biconnected solid and fluid phases, anisotropy caused by the alignment of clay particles, and grain displacement morphology due to the aligned hydrate inclusion. Consequently, the model successfully predicts the P- and S-wave velocities as a function of porosity and hydrate saturation [129,130].

3.4. Comparison of Rock Physics Models

In principle, all the rock physics models for the GHBS depict how the hydrate interacts with sediment components and how the presence of hydrate alters the acoustic properties and microstructure of the sediment. The acoustic properties predicted by various rock physics models may vary significantly due to the sediment mineral composition, sediment porosity, degree of consolidation, fracturing, hydrate morphology, hydrate saturation, and fluid type. One model may not be valid for all cases and even in the same drilling site, the rock physics model may be valid for some sediment layers, and invalid for other sediment layers. Therefore, the uppermost issue for rock physics modeling is deciding which model should be used to interpret the acoustic properties. Here, we try to make a general comparison of the commonly used rock physics models and assess the applicability and limitation of these models.

Different rock physics models are usually applied to the same data set to evaluate which model provides the best result for one certain reservoir type. Here, we provide the existing comparison examples of the application of different models to the GHBS in the Shenhu area, South China Sea, and the K-G basin, offshore eastern India. Wang et al. [94] introduced the three-phase Biot extension model and effective medium model to estimate hydrate saturation in the Shenhu area, South China Sea. GH saturation is predicted by the three-phase extension model with a maximum of 41.0%, which is slightly higher than those predicted by the effective medium model with a maximum of 38.5% [94]. Their results showed similar performance and they concluded that these two models are valid in the unconsolidated porous GHBS. However, Qian et al. [158] used the effective medium model and layered anisotropy model to examine the possible anisotropic effect due to the fracture developed in the same area. GH saturation predicted by the layered anisotropic model in the upper and lower facture-dominated layer shows a maximum of 25.0% and 85.0%, respectively, while GH saturation predicted by the isotropic model in the middle carbonate layer is lower than 20.0% [158]. They suggested that the anisotropic model provides a reliable result in the upper and lower hydrate layers, whereas the isotropic model gives a better estimate in the middle hydrate layer. In the K-G basin, offshore eastern India, various rock physics models have been used extensively to model the hydrate occurrence. Arun et al. [118] obtained an average GH saturation of 7.0% and 10.0% by the effective medium model and three-phase weighted model, respectively. They showed that the effective medium model with uncemented hydrate morphology provides a more accurate result in this area [118]. Joshi et al. [126] used the three-phase Biot extension model and layered anisotropic model to conduct velocity analysis. The obtained GH saturation by the isotropic model at two drilling sites shows an average of 45.8% and 33.8%, which are comparable with the saturation measured from nature cores. They suggested that the isotropic model yields the most accurate result [126]. Yadav et al. [145] suggested that the three-phase Biot extension model shows a very good correlation with the pressure core, and they also showed that this model generally overestimates the hydrate saturation in the fracture-filled GHBS. Shankar et al. [140] obtained the GH saturation with a maximum of 13.0% and 12.0% using the three-phase weighted equation at two drilling sites, while GH saturation predicted by the effective medium model shows a maximum of 16.0% and 22.0% at the same two sites. They found that the three-phase weighed equation predicted a better hydrate saturation [140]. They also suggested that the effective medium model is more accurate compared to the three-phase weighted equation because the latter model requires additional data to set the weighting factor. Ghosh and Ojha [130] compared the effective medium anisotropic model with the Wood average model, and they suggested that the former model yields a better agreement because of inherent anisotropy in the K-G basin, offshore eastern India.

Among the proposed rock physics models, the effective medium model, the three-phase Biot extension equation, and the three-phase weighted equation are generally suitable for the isotropic and unconsolidated coarse-grained sediment. The effective medium model is the only method to consider how the different hydrate morphologies affect the acoustic properties of GHBS. A knowledge of hydrate morphology is required for the accurate estimation of permeability, resistivity, and acoustic properties of the sediment. However, this model usually overestimates the S-wave velocity because of the introduction of friction at the grain contacts which does not exist for the unconsolidated GHBS [133,153]. This overestimation can be calibrated by the smooth contact model without consideration of the friction between grain contacts [148,153]. The three-phase Biot extension model generally holds true for the unconsolidated and coarse-grained marine sediment with high porosity. Existing applications of this model in various field investigations have indicated the broad applicability for GHBS when hydrates grow away from grain contacts. The model is widely used due to its ease of use and high efficiency; however, setting the consolidation factor will induce uncertainty in the estimation of sediment velocities and hydrate saturation. The three-phase weighted equation has been proved to be suitable for unconsolidated marine sediments with high or low porosity. This model can essentially be viewed as an empirical velocity–porosity equation and without consideration of hydrate–grains interaction except for the porosity reduction caused by hydrate growth. This model also requires supplementary data to constrain the weighting factor.

The abovementioned three models fail to handle the anisotropy caused by hydrate-filled fractures or the aligned orientation of clay particles. The layered anisotropic model simply considers the transversely isotropic nature by employing the laminated layer model [130]. The dip angle of fracture can be briefly estimated by this model [100,126,158]. This parameter is critical for characterizing the sediment anisotropy and interpreting the obtained seismic and sonic response in fracture-dominated sediment. However, the purely laminated medium concept does not hold true for the real GHBS. Among the aforementioned models, the effective medium anisotropic model is the only method to consider the microstructure characteristics of pore inclusion and grain displacement hydrate morphology [130,131,150]. The grain displacement hydrate morphology is the dominant distribution habit in fine-grained sediment. Adjusting the procedure of effective medium anisotropic modeling, the anisotropy in the clay-dominated GHBS caused by hydrate-filled fracture or aligned clay particles can be characterized [54]. However, the effective pressure is not considered and the model considers the greater compliance at the edges of different particle alignments [129]. In summary, the feasibility and limitations of the abovementioned models are compared in

Table 1. Feasibility and limitation of the various rock physics models.

Model		Feasibility	Limitation
Isotropic	Effective medium model	Various hydrate morphologies.	Unreasonably higher S-wave velocity at high porosities.
	Three-phase Biot extension model	Flexible application in high-porosity marine sediment.	Load-bearing morphology. Setting the consolidation factor
	Three-phase weighted model	Flexible application to the sediment with any porosity.	Pore-filling hydrate morphology. Setting the weighting factor.
Anisotropic	Layered anisotropic model	Transversely isotropic feature. Dip angle of fracture.	Laminated layer is unusual in field investigations.
	Effective medium anisotropic model	Grain displacement morphology. Microstructure of biconnected solid and fluid phases.	Weaker bonding and greater compliance at the edges of different particle alignments. Effective pressure is not considered.

.

4. Application of Rock Physics Modeling to Field Data

4.1. Rock Physics Modeling for Acoustic Properties of GHBS

The measured P- and S-wave velocities and attenuations from seismic data, sonic logging data, and ultrasonic measurements are the product of wave characteristics possibly caused by hydrate–mineral interaction, pore structure change, and fluid flow in the sediment. The rock physics model can transform these measurable acoustic properties into meaningful physical properties which are difficult to measure. Here, we briefly describe the calculation procedure (Figure 9). Inputting a set of parameters into the selected rock physics model, the P- and S-wave velocities and attenuations for the sediment or experimental material can be predicted as a function of hydrate saturation or frequency. These values are further compared with the measured ones from the field investigations or laboratory measurements, revealing the desired information on the hydrate, fluid, or pore structure. Whether the input parameters are reasonable is critical for successful rock physics modeling. As mentioned above, the crucial parameters for the three-phase weighted model, the three-phase Biot extension model, and the effective medium model are the weighting factor, consolidation factor, inclusion aspect ratio, inclusion concentration, and hydrate morphology, respectively. The crucial parameters for the layered anisotropic model and effective medium anisotropic model are the dip angle and inclusion aspect ratio, respectively. The supplementary data, such as measurement results of nature cores and artificial samples, are generally used to validate the selection of input parameters and part of the input parameters are directly taken from the existing studies. Appendix F provides the moduli, densities, and velocities of sand, clay, hydrate, and water borrowed from the existing studies. According to the comparison between the modeled and measured acoustic properties, several important parameters including hydrate morphology, the dip angle of fracture, sediment permeability, fluid viscosity, and attenuation mechanisms can be inferred, as introduced as follows.

The effective medium model is the only method to relate various hydrate morphologies to sediment velocities; therefore, hydrate morphology at a specific site can be determined from the measured velocities. The load-bearing and pore-filling hydrate morphologies are generally interpreted as natural morphologies from the sonic velocities using the effective medium model at the Blake Ridge site, the Mallik site, and the Nankai Trough [57,106,130]. In addition to the single homogenous hydrate morphology widely determined by the field velocities, hydrate morphology transition and multiple hydrate morphologies have also been inferred by previous studies based on rock physics modeling. Hu et al. [162] suggested that hydrate may be viewed as load-bearing morphology at hydrate saturation higher than 30% and pore-filling hydrate morphology at hydrate saturation lower than 30% based on the comparison of P-wave velocities predicted from two rock physics models and measured from consolidated sand samples. Zhang et al. [163] measured the ultrasonic P- and S-wave velocities in unconsolidated sediment and compared them with the modeled velocities using the effective medium model, and indicated that the hydrate morphology changes from the load-bearing morphology to pore-filling hydrate morphology at hydrate saturation of 25%. Sahoo et al. [44,45] interpreted their ultrasonic P- and S-wave velocities of consolidated sands as the morphology transition from the initial pore-filling to the patchy hydrates by using the effective medium model. Dai et al. [40] suggested that heterogeneous patchy hydrate morphology rather than homogenous hydrate morphologies captures the observed P-wave velocity in nature sands. Pan et al. [164,165] introduced an improved effective medium model to calculate the ratio of pore-filling and load-bearing hydrate morphologies in the Mallik field, the Nankai Trough, and the Hikurangi margin. In the Shenhu area, based on the effective medium modeling for the sonic velocities, the fraction of pore-filling hydrate in the multiple morphologies was determined as 60% by Liu et al. [166] and 80% by Zhan et al. [42].

Varying the dip angle of fracture in the layered anisotropic model from 0° to 90°, sediment velocities are estimated and then compared with those predicted by field investigations. Consequently, the dominated dip angle of fracture in the sediment can be determined by the comparison. Anisotropic modeling for the sonic P-wave velocities in the Ulleung Basin of the East Sea of Korea shows the presence of hydrate-filled fracture with a dip angle of 7° at the upper layer and high-angle fracture at the lower layer [124]. Lee and Collett [125] suggested the P-wave velocity predicted by the layered anisotropic model is insensitive to fracture angle, whereas S-wave velocity is sensitive to fracture orientation. They indicated that the assumption of high-angle fracture yields the best agreement between modeled velocity and measured velocity from the cores [125]. Using the anisotropic modeling of P-wave velocity, Joshi et al. [126] indicated the presence of vertical fracture at the lower layer in the K-G Basin on the eastern margin of India.

Rock physics modeling for the sediment attenuation is more related to fluid properties such as sediment permeability and fluid viscosity as compared to sediment velocity. Zhan and Matsushima [36] have modeled the P- and S-wave attenuations of GHBS by using the three-phase Biot extension equations and provided the estimate of sediment permeability through the comparison of the modeled attenuations and the measured attenuations from sonic and VSP data at Nankai Trough, Japan. Recently, Sahoo and Best [88] provided a first inversion method from the measured S-wave velocity and attenuation into the in situ sediment permeability based on the two-phase and three-phase Biot extension models, and their estimates have been proved to agree well with the permeability obtained from resistivity measurements.

Knowledge about attenuation mechanisms is required for quantifying the hydrate saturation based on geophysical methods at various investigation frequencies. Different rock physics models introduce different attenuation mechanisms, and the combined modeling for the P- and S-wave attenuations at seismic, sonic, and ultrasonic frequencies by employing various models may provide the dominant attenuation mechanism responsible for the measured attenuations. Effective medium modeling for P- and S-wave attenuations at seismic (50–550 Hz) and ultrasonic (448–782 kHz) frequencies shows a complex dependence of attenuation on hydrate morphology and the modeling indicates that a squirt flow in porous hydrate and low aspect ratio pores may be responsible for the observed attenuations at these frequencies [44,83]. Three-phase Biot extension modeling for P- and S-wave attenuation at sonic frequencies (0.5–20 kHz) suggests that viscous friction between hydrate and sediment grain and squirt flow caused by hydrate formation may dominate the P- and S-wave attentions at the sonic frequencies [29]. Sahoo and Best [88] suggested that the observed S-wave attenuation at the ultrasonic frequencies (448–782 kHz) varies with the permeability change related to hydrate morphology transition from pore-filling to patchy. Combining the effective medium model and three-phase medium model, Zhan and Matsushima [36] explained the frequency-dependent P-wave attenuation at seismic (30–110 Hz) and sonic (0.5–20 kHz) frequencies as the squirt flow between sand grains and hydrate grains, and/or the squirt flow caused by fluid inclusions with different aspect ratios.

4.2. Hydrate Saturation Prediction Based on Rock Physics Modeling

Based on rock physics modeling, hydrate saturation can be obtained from the measured velocity from filed investigations or laboratory measurements. As Figure 10 shows, porosity, density, and volume fractions as well as elastic moduli of sediment components (calcite, illite, and quartz) are input into the selected rock physics model to predict P- and S-wave velocities of GHBS. Hydrate saturation varies from 0 to 100% and is repeatedly input to the model. Then, the predicted P- and S-wave velocities are compared with those extracted from the field investigations or laboratory measurements. The final hydrate saturation will be output until the difference between the predicted and measured velocities is within the predefined error range.

Uncertainties of the predicted hydrate saturation are generally from errors related to the velocity measurements or rock physics modeling. Whether the P- and S-wave velocities are measured from field data or laboratory data, both of them rely on the quality of the collected data [167]. The first arrivals of P- and S-waves are always difficult to extract due to the strong attenuation caused by the presence of gas hydrate [42]. The bad borehole condition and coupling effect between the measurement tools and sediment may also result in a poor signal-to-noise ratio [168]. Moreover, uncertainties of saturation prediction strongly depend on the selection of the rock physics model. Application of the models proposed for the coarse-grained sediments to the fine-grained sediments may yield misleading results because they ignore the anisotropy caused by the aligned hydrate-filled fracture in the sediment. The uncertainties associated with rock physics modeling mainly stem from the mineral composition fraction, porosity, permeability, and density used in the model. To reduce these uncertainties, the aforementioned input parameters for the model should be similar to the physical properties of real sediment or materials [94,140]. The mineral composition fractions, density, and porosity can be calculated from the well logs and permeability can be estimated from the in situ measurement for the core samples. Few free parameters are unavailable for any kind of rock physics model. We will provide examples of how to set these parameters. The critical parameters for the three-phase weighted equation and three-phase Biot extension equation are the weighting factor and consolidation factor, respectively, which can be obtained by fitting the predicted velocities to the measured velocities from the non-hydrate sediment [135,136]. The assumptions of hydrate morphology, inclusion concentration, and inclusion aspect ratio are critical for the effective medium model [83,84]. In the prediction of hydrate saturation using the rock physics method, the effect of inclusion aspect ratio and inclusion concentration can be ignored because they have been proven to significantly affect attenuation rather than velocity [36,84]. However, the assumption of hydrate morphology affects the accuracy of the predicted saturation and it can be obtained by fitting the modeled velocity to the measured velocity in GHBS [42,164].

5. Challenges

Even with the extraordinary progress in this area, some challenges limit the further application of rock physics modeling.

• Optimizing the input parameters of models is crucial for successful modeling. Although the sonic logging data directly reflecting the porosity, density, and mineral composition of GHBS are widely used to improve the input parameters, more geological information is still required to constrain the set of free parameters. The integration of rock physics modeling with measurements for core samples by technologies such as X-ray computed tomography, nuclear magnetic resonance, and X-ray diffraction enables us to investigate the microstructure, rock properties, and hydrate distribution of GHBS, and this integration can reduce the uncertainties in the modeling.
• How should we choose a suitable rock physics model for a specific question? Although the existing rock physics models are mainly proposed to deal with a specific problem, a certain model is not always valid in practical application. For example, confirming the dominated attenuation mechanism associated with gas hydrate and free gas from the measured attenuations. A combination of various models allows us to introduce as many mechanisms as possible and is further beneficial to explaining the observed attenuations.
• The final goal of rock physics modeling is quantifying the gas hydrate occurrence and distribution of GHBS from seismic and well log investigations. Because of the difficulties posed by taking in situ measurements for the drilling core, the calibration of the rock physics model is mainly conducted by ultrasonic measurements for the synthetic hydrate samples. Are the observations at the ultrasonic frequency domain still valid at the seismic and well log frequency domains? Combining the sonic logging data and cross-well seismic data with ultrasonic measurements for the core samples at the same well location can provide an insight into the P- and S-wave velocities and attenuations at various frequency domains. Rock physics modeling for these acoustic properties can further constrain the model and better explain these observations.

6. Conclusions

Theoretical rock physics modeling provides a tool to link the hydrate occurrence of GHBS to the measurable acoustic properties at different investigation frequency domains. Based on the different theoretical basis, assumptions, and different propagating mechanisms, the published rock physics models are proposed for the modeling of velocity and attenuation of GHBS. Some important conclusions can be drawn as follows.

• P- and S-wave velocities are comprehensively affected by the hydrate saturation combined with the hydrate morphologies. Attenuation mechanisms associated with GHBS include the effect of hydrate morphology on attenuation, gas bubble damping, global Biot flow, local squirt flow, cementation and frictional loss between hydrate and solid grain, thin bound water film between hydrate and grain surface, and hydrate film between the gas bubble and the surrounding pore water.
• This study classifies the existing rock physics models into isotropic models for coarse-grained sediment including three-phase weighted equations, three-phase Biot extension equations, effective medium model, and anisotropic rock physics models for fine-grained sediment including layered anisotropic model and effective medium anisotropic model. We briefly introduce the assumption, characteristics, theoretical basis, and workflow of the aforementioned modeling. In particular, methods of introducing the attenuation caused by gas hydrate in the three-phase Biot extension model and effective medium model have also been reviewed. Then, the feasibility and limitations of these models are discussed and compared. This study provides insight into how to select a suitable rock physics model and how to conduct modeling in the application of the rock physics model to field data.
• Several important parameters, including hydrate morphology, the dip angle of fracture, sediment permeability, and attenuation mechanisms, can be inferred from the comparison between the modeled and measured acoustic properties. Based on the modeling examples using the abovementioned models, we investigated how to define these parameters. The most important application of rock physics modeling is predicting the hydrate saturation from the measured velocity from field investigations or laboratory measurements. We discussed the uncertainties of the predicted saturation caused by the errors related to the velocity measurements or rock physics modeling.
• We finally discussed the current challenges in rock physics modeling related to optimizing the input parameters, choice of a suitable model, and upscaling problems from ultrasonic to seismic and well log frequencies.