SummaryA fracture within a porous background is modeled as a thin porous layer with increased compliance and finite permeability. For small layer thickness, a set of boundary conditions can be derived that relate particle velocity and stress across a fracture, induced by incident poroelastic waves. These boundary conditions are given via phenomenological parameters that can be used to examine and characterize the seismic response of a fracture. One of these parameters, here it is called membrane permeability, is shown through several examples to control the scattering amplitude of the slow P waves for very low-permeability fractures, which in turn controls the intrinsic attenuation of the waves.

For better understanding of frequency dependence (dispersion) of seismic wave velocities caused by stress-induced fluid flow, broadband laboratory measurements were performed on a suite of synthetic glass media containing both equant pores and thermal cracks. Complementary forced oscillation, resonant bar, and ultrasonic techniques provided access to millihertz-hertz frequencies,~1 kHz frequency, and~1 MHz frequency, respectively. The wave speeds or effective elastic moduli and associated dissipation were measured on samples under dry, argon-or nitrogen-saturated, and water-saturated conditions in sequence. The elastic moduli, in situ permeability, and crack porosity inferred from in situ X-ray computed tomography all attest to strong pressure-induced crack closure for differential (confining-minus-pore) pressures <30 MPa, consistent with zero-pressure crack aspect ratios <4 × 10 À4 . The low permeabilities of these materials allow access to undrained conditions, even at subhertz frequencies. The ultrasonically measured elastic moduli reveal consistently higher shear and bulk moduli upon fluid saturation-diagnostic of the saturated-isolated regime. For a glass rod specimen, containing cracks but no pores, saturated-isolated conditions apparently persist to subhertz frequencies-requiring in situ aspect ratios (minimum/maximum dimension) <10 À5 . In marked contrast, the shear modulus measured at subhertz frequencies on a cracked glass bead specimen of 5% porosity, is insensitive to fluid saturation, consistent with the Biot-Gassmann model for the saturated-isobaric regime. The measured dispersion of the shear modulus approaches 10% over the millihertz-megahertz frequency range for the cracked and fluid-saturated media-implying that laboratory ultrasonic data should be used with care in the interpretation of field data. Gurevich et al. (2010) incorporated the influence of "squirt" flow, as originally proposed by Mavko and Nur (1975), for a unified model of Biot and squirt-flow dispersion. In contrast, in effective medium theory, individual inclusions with assigned geometries are embedded within a solid to estimate the overall elastic properties of the composite from the elastic properties of individual constituents (Eshelby, 1957;Kachanov, 1993;Kuster & Toksöz, 1974;Wu, 1966;Zimmerman, 1991). Consideration of frequency-dependent fluid communication between the isolated fluid phases of conventional effective medium models provides insight into the dispersion of fluid-saturated medium and the influence of microstructure on dispersion (Adelinet et al.

A B S T R A C TAccurate estimation of CO 2 saturation in a saline aquifer is essential for the monitoring of supercritical CO 2 injected for geological sequestration. Because of strong contrasts in density and elastic properties between brine and CO 2 at reservoir conditions, seismic methods are among the most commonly employed techniques for this purpose. However the relationship between seismic (P-wave) velocity and CO 2 saturation is not unique because the velocity depends on both wave frequency and the CO 2 distribution in rock. In the laboratory, we conducted measurements of seismic properties of sandstones during supercritical CO 2 injection. Seismic responses of small sandstone cores were measured at frequencies near 1 kHz, using a modified resonant bar technique (Split Hopkinson Resonant Bar method). Concurrently, saturation and distribution of supercritical CO 2 in the rock cores were determined via x-ray CT scans. Changes in the determined velocities generally agreed with the Gassmann model. However, both the velocity and attenuation of the extension wave (Young's modulus or 'bar' wave) for the same CO 2 saturation exhibited differences between the CO 2 injection test and the subsequent brine re-injection test, which was consistent with the differences in the CO 2 distribution within the cores. Also, a comparison to ultrasonic velocity measurements on a bedded reservoir rock sample revealed that both compressional and shear velocities (and moduli) were strongly dispersive when the rock was saturated with brine. Further, large decreases in the velocities of saturated samples indicated strong sensitivity of the rock's frame stiffness to pore fluid.

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To better understand the relationship between P-wave velocities and ice content in saturated, unconsolidated saline permafrost, we constructed an effective-medium model based upon ultrasonic P-wave data that were obtained from earlier laboratory studies. The model uses a two-end-member mixing approach in which an ice-filled, fully frozen end member and a water-filled, fully unfrozen end member are mixed together to form the effective medium of partially frozen sediments. This mixing approach has two key advantages: (1) It does not require parameter tuning of the mixing ratios, and (2) it inherently assumes mixed pore-scale distributions of ice that consist of frame-strengthening (i.e., cementing and/or load-bearing) ice and pore-filling ice. The model-predicted P-wave velocities agree well with our laboratory data, demonstrating the effectiveness of the model for quantitatively inferring ice content from P-wave velocities. The modeling workflow is simple and is largely free of calibration parameters — attributes that ease its application in interpreting field data sets.