Numerical simulations of seismic wave propagation in fractured media are often performed in the framework of the linear slip theory (LST). Therein, fractures are represented as interfaces and their mechanical properties are characterized through a compliance matrix. This theory has been extended to account for energy dissipation due to viscous friction within fluid-filled fractures by using complex-valued frequency-dependent compliances. This is, however, not fully adequate for fractured porous rocks in which wave-induced fluid flow (WIFF) between fractures and host rock constitutes a predominant seismic attenuation mechanism. In this letter, we develop an approach to incorporate WIFF effects directly into the LST for a 1D system via a complex-valued, frequency-dependent fracture compliance. The methodology is validated for a medium permeated by regularly distributed planar fractures, for which an analytical expression for the complex-valued normal compliance is determined in the framework of quasistatic poroelasticity. There is good agreement between synthetic seismograms generated using the proposed recipe and those obtained from comprehensive, but computationally demanding, poroelastic simulations.

SUMMARY The presence of sets of open fractures is common in most reservoirs, and they exert important controls on the reservoir permeability as fractures act as preferential pathways for fluid flow. Therefore, the correct characterization of fracture sets in fluid-saturated rocks is of great practical importance. In this context, the inversion of fracture characteristics from seismic data is promising since their signatures are sensitive to a wide range of pertinent fracture parameters, such as density, orientation and fluid infill. The most commonly used inversion schemes are based on the classical linear slip theory (LST), in which the effects of the fractures are represented by a real-valued diagonal excess compliance matrix. To account for the effects of wave-induced fluid pressure diffusion (FPD) between fractures and their embedding background, several authors have shown that this matrix should be complex-valued and frequency-dependent. However, these approaches neglect the effects of FPD on the coupling between orthogonal deformations of the rock. With this motivation, we considered a fracture model based on a sequence of alternating poroelastic layers of finite thickness representing the background and the fractures, and derived analytical expressions for the corresponding excess compliance matrix. We evaluated this matrix for a wide range of background parameters to quantify the magnitude of its coefficients not accounted for by the classical LST and to determine how they are affected by FPD. We estimated the relative errors in the computation of anisotropic seismic velocity and attenuation associated with the LST approach. Our analysis showed that, in some cases, considering the simplified excess compliance matrix may lead to an incorrect representation of the anisotropic response of the probed fractured rock.

<p>The characterization of volcanic hydrothermal systems (VHS) is fundamental for the early detection of precursors to phreatic or magmatic eruptions and for understanding hazards related to slope instabilities. Since these phenomena can be related to pore-fluid dynamics within the volcanic edifice, monitoring the spatial distribution of the different fluid phases (water, air, vapor) is of great importance. Ambient noise seismic interferometry has been employed for this task, correlating temporal changes in seismic velocities with variations in the water table depth in volcanic areas. However, this technique usually considers that above this depth, the pore space within the rock is totally occupied by a gaseous phase. This, in turn, implies that the body wave velocities and the density of the unsaturated zone are constant values, which is expected to impact on the determination of the water table depth. In this work, we assess the influence of partial saturation in the unsaturated zone of a VHS on ambient seismic noise, by employing a comprehensive rock physics model based on a saturation profile given by the Van Genuchten model. We focus on the sensitivity of Rayleigh waves, which are usually considered to be the most important contribution to the ambient seismic noise.</p><p> </p><p>We consider an altered andesite layer overlying a half-space consisting of a relatively unaltered andesite representing the volcanic basement, which is representative of the VHS of La Soufrière de Guadeloupe volcano (Eastern Caribbean, France). We base our rock physics model on Gassmann’s equations to compute body wave velocities as a function of fluid saturation. We compute Rayleigh wave phase velocities for different positions of the water table and analyze their relative difference with respect to a reference scenario that corresponds to the mean value of the water table depth in this region. Our results suggest that the existence of a partial water saturation distribution could affect the Rayleigh wave velocities, and that this effect depends on the range of frequencies considered and the degree of hydrothermal alteration of the medium. For highly altered andesite, characterized by a higher porosity and a lower rock-mass stiffness, the relative variation in velocity obtained with a partial saturation distribution can be up to twice or down to half of the variation for the scenario corresponding to a constant saturation, depending on the frequency range considered. The depth sensitivity kernels of the Rayleigh wave phase velocities exhibit significant variations within regions with variable water content for frequencies between 4 and 6 Hz, which indicates that these seismic waves are able to distinguish the presence of a partial saturation distribution. These results indicate that relative velocity differences derived from ambient noise interferometry provide the possibility of inferring spatial distributions of water content and, therefore, density variations within VHS. This technique therefore emerges as a useful tool to inform on volcanic hazards related to hydrothermal activity, such as erratic explosions and partial flank collapses.</p>