Abstract. We offer a first-principle-based effective medium model for elastic-wave velocity in unconsolidated, high porosity, ocean bottom sediments containing gas hydrate. The dry sediment frame elastic constants depend on porosity, elastic moduli of the solid phase, and effective pressure. Elastic moduli of saturated sediment are calculated from those of the dry frame using Gassmann's equation. To model the effect of gas hydrate on sediment elastic moduli we use two separate assumptions: (a) hydrate modifies the pore fluid elastic properties without affecting the frame; (b) hydrate becomes a component of the solid phase, modifying the elasticity of the frame. The goal of the modeling is to predict the amount of hydrate in sediments from sonic or seismic velocity data. We apply the model to sonic and VSP data from ODP Hole 995 and obtain hydrate concentration estimates from assumption (b) consistent with estimates obtained from resistivity, chlorinity and evolved gas data.

The ultrasonic compressional [Formula: see text] and shear [Formula: see text] velocities and first‐arrival peak amplitude [Formula: see text] were measured as functions of differential pressure to 50 MPa and to a state of saturation on 75 different sandstone samples, with porosities ϕ ranging from 2 to 30 percent and volume clay content C ranging from 0 to 50 percent, respectively. Both [Formula: see text] and [Formula: see text] were found to correlate linearly with porosity and clay content in shaly sandstones. At confining pressure of 40 MPa and pore pressure of 1.0 MPa, the best least‐squares fits to the velocity data are [Formula: see text] and [Formula: see text]. Deviations from these equations are less than 3 percent and 5 percent for [Formula: see text] and [Formula: see text], respectively. The velocities of clean sandstones are significantly higher than those predicted by the above linear fits (about 7 percent for [Formula: see text] and 11 percent for [Formula: see text]), which indicates that a very small amount of clay (1 or a few percent of volume fraction) significantly reduces the elastic moduli of sandstones. For shaly sandstones we conclude that, to first order, more sensitive to the porosity and clay content than is [Formula: see text]. Consequently, velocity ratios [Formula: see text] and their differences between fully saturated (s) and dry (d) samples also show clear correlation with the clay content and porosity. For shaly sandstones we conclude that, to first order, clay content is the next most important parameter to porosity in reducing velocities, with an effect which is about 0.31 for [Formula: see text] to 0.38 for [Formula: see text] that of the effect of porosity.

The exact expressions for the effective stress (•r•) and, in particular, pressure (P> that cause elastic strain of material with pore fluids are, assuming only that Hook's law is valid, (•r•) -o'• --aPO,• and (P) --Pc --aP• where a --I --(K/K.), Pc and P,are confining and pore pressures, and K and K. are the bulk moduli of the rock and grain, respectively. The equation for (P> was first suggested by Geertsma (1957) and by Skempton (1960) on empirical grounds. The expression does not depend directly on porosity, but when t•ores vanish the effective pressure (P> equals the confining pressure Pc, because then K --K.. Thus the strain of a porous solid with pore pressure can be completely determined from the elastic modulus of the solid without pore pressure, if the effective stress law in the equation for (•> is used.The exact expression for the effective stress describes quite accurately the measured strains in sandstone and granite samples at confining and pore pressures to 2.5 kb. The results are not applicable to inelastic processes, such as fracture, or elastic processes other than strain.The classical work by Terzaghi [1923] revealed that the application of pore pressure to porous elastic earth materials causes an apparent increase of volume similar in magnitude, but reversed in sign, to the volume change caused by a confining pressure. Similar results were obtained later by numerous investigators. However, there is a great deal of disagreement on the theoretical accuracy and validity of Terzaghi's relation. Part of the difficulty arises from occasionally vague definitions of strains and stresses in a porous aggregate. Following Biot [1941] we will define the strain in an aggregate as a local average over a small, but finite, area, such as measured with a strain gauge on rock samples in the laboratory. The area over which the strain is taken is large enough to average over a sufficient number of grains and pores. Using this definition, we do not consider the local deviations of strain from the local average. Similarly we also define the stress a acting on a porous solid in the way it is done in the laboratory, namely, by the ratio of force F to a small, but finite, area A, to which this force is applied; thus (r = F/A. Note that porosity V does not enter the expression for the stress when it is so defined. The stresses, like the strains, are therefore also local averages taken over a small, but finite, area. ELASTICITY OF PoRous MATERIALSWe now make the important assumption, following Terzaghi [1923], Blot [1941], and others, that the strains can be expressed as linear combinations of the stresses within the

We have analyzed two laboratory data sets obtained on high‐porosity rock samples from the North Sea. The velocities observed are unusual in that they seem to disagree with some simple models based on porosity. On the other hand, the rocks are unusually poorly‐cemented (for laboratory studies, at least), and we investigate the likelihood that this is the cause of the disagreement. One set of rocks, from the Oseberg Field, is made of slightly cemented quartz sands. We find that we can model their dry‐rock velocities using a cementation theory where the grains mechanically interact through cement at the grain boundaries. This model does not allow for pressure dependence. The other set of rocks, from the Troll Field, is almost completely uncemented. The grains are held together by the applied confining pressure. In this case, a lower bound for the velocities can be found by using the Hertz‐Mindlin contact theory (interaction of uncemented spheres) to predict velocities at a critical porosity, combined with the modified Hashin‐Strikman lower bound for other porosities. This model, which allows for pressure‐dependence, also predicts fairly large Poisson’s ratios for saturated rocks, such as those observed in the measurements. The usefulness of these theories may be in estimating the nature of cement in rocks from measurements such as sonic logs. The theories could help indicate sand strength in poorly consolidated formations and predict the likelihood of sand production. Both theoretical methods have analytical expressions and are ready for practical use.

Large shallow earthquakes can induce changes in the fluid pore pressure that are comparable to stress drops on faults. The subsequent redistribution of pore pressure as a result of fluid flow slowly decreases the strength of rock and may result in delayed fracture. The agreement between computed rates of decay and observed rates of aftershock activity suggests that this is an attractive mechanism for aftershockss.

The velocities and attenuation of seismic and acoustic waves in rocks with fluids are affected by the two most important modes of fluid/solid interaction: (1) the Biot mechanism where the fluid is forced to participate in the solid’s motion by viscous friction and inertial coupling, and (2) the squirt‐flow mechanism where the fluid is squeezed out of thin pores deformed by a passing wave. Traditionally, both modes have been modeled separately, with the Biot mechanism treated in a macroscopic framework, and the squirt flow examined at the individual pore level. We offer a model which treats both mechanisms as coupled processes and relates P‐velocity and attenuation to macroscopic parameters: the Biot poroelastic constants, porosity, permeability, fluid compressibility and viscosity, and a newly introduced microscale parameter—a characteristic squirt‐flow length. The latter is referred to as a fundamental rock property that can be determined experimentally. We show that the squirt‐flow mechanism dominates the Biot mechanism and is responsible for measured large velocity dispersion and attenuation values. The model directly relates P‐velocity and attenuation to measurable rock and fluid properties. Therefore, it allows one to realistically interpret velocity dispersion and/or attenuation in terms of fluid properties changes [e.g., viscosity during thermal enhanced oil recovery (EOR)], or to link seismic measurements to reservoir properties. As an example of the latter transformation, we relate permeability to attenuation and achieve good qualitative correlation with experimental data.

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Application of uniaxial stress to a sample of granite causes elastic wave velocity anisotropy. Compressional waves travel fastest in the direction of the applied stress. Two shear waves travel with generally different speeds in any direction, exhibiting acoustic double refraction which increases with increasing stress.