Both types of body waves, compressional (P-) and shear (S-) waves, are useful in probing hydrate deposits. Shear waves transmit a particle motion that is perpendicular (transverse) to their travel direction. Their speed is controlled by the shear modulus (or "rigidity") and density. Compressional waves have a particle motion parallel to the propagation direction and always travel at a faster speed than S-waves. Their velocity is determined by both compressional and shear modulus, as well as density. Fluids and gases have no "rigidity" (i.e., shear modulus = 0), so they cannot transmit S-waves.
Predicting the P- and S-wave velocities of hydrate- and gas-bearing sediments is not straightforward, since those sediments consist of multi-phase aggregations of minerals (commonly clay, quartz, and calcite), pore fluid (typically saline water), and hydrate or gas. Sediment Vp and Vs are commonly estimated from the properties of the mineral components, pore fill, and the sediment frame (which accounts for the geometry how the grains packed together). Two kinds of approaches have been used to estimate the properties of hydrate- and gas-bearing sediments: empirical approaches, which rely on versions of the Wyllie time-average or Wood equations calibrated to laboratory data [Lee et al., 1996], or physics-based approaches, which use versions of Biot-Gassmann theory [Helgerud et al., 1999]. Uncertainties in both of these approaches arise primarily from the current lack of understanding as to whether hydrates behave as a "cement" between the mineral grains and significantly stiffen the sediment frame, whether they behave as mineral grains as part of the sediment frame, or whether they modify the properties of the pore fill [Helgerud et al., 1999].
With those caveats in mind, several generalizations can be drawn. Because of the low P-wave velocity of gases, sediment Vp is particularly sensitive to even small amounts of gas in the pore space (e.g., (Domenico, 1976)). Sediment Vs, however, is controlled only by grain and frame properties; since the pore fill (gas or fluids) will not transmit shear energy, sediment Vs is relatively unaffected by gas (a small change is predicted due to lower density of gas). Vs is particularly sensitive to changes in the frame "stiffness" due to adding gas hydrates into the frame as additional grains or as cement between the sediment grains. Mathematically, however, the effect of gas hydrates on sediment Vs (and Vp) depends largely on the microscopic details of gas hydrate distribution within the sediments (also see Chapter 20).
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