Fluid-saturated Rocks Research Articles

Analytical model for laser cutting in porous media

Laser cutting in porous media presents both challenges and opportunities for various applications. Laser cutting requires a deep understanding of heat transfer, materials, and laser physics, and can involve nonlinear and transient effects. There is a lack of literature regarding modelling laser cutting in porous media. Using conservation of energy principle, an analytical model has been developed to calculate the total laser power required to cut a porous media without the need for complex numerical simulations.The model incorporates a new correlation for calculating waste power due to heat transfer into the surrounding during laser cutting as well as modifications to the energy balance equation to incorporate the effect of porosity and fluid saturation.The model has been validated with experimental data of cutting porous media (carbonate rock) and corroborated well. Model validation showed around 10 % accuracy for fluid saturated rock samples and around 17 % accuracy for dry rock samples. Also it has been observed that the level of accuracy improves with lower Peclet number (i.e. lower cutting speed).The proposed analytical model has been used to examine the effect of Peclet number, porosity, fluid saturation, rock type and material thickness on laser cutting performance. The methodology described in this article can be used as a guideline to calculate laser power requirements and size the laser equipment at an early stage prior to the manufacturing process.

Stress–strain hysteresis during hydrostatic loading of porous rocks

A micro-mechanical model is proposed to predict the stress–strain hysteresis during the cyclic hydrostatic loading of fluid-saturated rocks under drained or undrained conditions. A spherical pore is surrounded by a multi-cracked shell where local deviatoric stress develops despite the remote hydrostatic loading. The effective properties of the material composing the shell are constructed assuming an isotropic distribution of cracks with no interaction, and the overall properties thanks to the spherical assemblage approach. The fluid pressure in drained and undrained conditions is assumed to be uniform throughout the assemblage. A new analytical solution is proposed, assuming all cracks are closed and slipping either forwardly or reversely. It is shown with numerical simulations for drained conditions that this assumption is indeed respected for sufficiently small values of the crack friction angle. However, for reasonable values, the closed cracks during the unloading phase could slip in either direction: reversely close to the pore and still forwardly away from the pore. Moreover, at critical radii, the slip could occur in either direction depending on the crack orientation. A similar micro-structural response is observed for undrained conditions, although the remote confining stress required to close the cracks is much larger. The model’s predictions compare favourably with recent experimental data on dry sandstones and carbonates, which were presented in a study on the influence of strain amplitude on the transition between static and dynamic properties. The crack density and matrix elasticity modulus are sufficient fitting parameters to accurately predict the hysteresis loops, especially for porosity levels above 10%.

Theoretical model for the elastic properties of cracked fluid-saturated rocks considering the crack connectivity

SUMMARY Cracks are a common rock microstructure and have a large effect on elastic properties during wave propagation. The fluid flow between a crack and its adjacent pore space can cause wave attenuation and dispersion. In this work, we introduce a crack connectivity parameter which is meant to improve the expression of local flow by weighting the contributions of fully connected and isolated cracks. We then update the analytical expression for frequency-dependent moduli by modifying the boundary conditions of the linearized Navier–Stokes equation and mass conservation equation. The proposed model contains the effect of cracks and stiff pores, in which the attenuation and dispersion are determined by squirt-flow and stiff-pore relaxations. The resulting model shows the squirt-flow relaxation frequency depends on not only the crack aspect ratio but also the crack connectivity. However, their contributions are different. The crack connectivity has little effect on the attenuation amplitude of shear modulus, but affects the attenuation amplitude of bulk modulus when multiple sets of cracks exist in the rock. The attenuation frequency band is also affected by the crack connectivity. As the crack connectivity deteriorates, the attenuation peak moves to low frequencies. In addition, by comparing the crack connectivity with the fluid viscosity coefficient, it is observed that the crack connectivity only affects the attenuation frequency band of cracks, whereas the fluid viscosity coefficient affects the attenuation frequency bands of cracks and stiff pores simultaneously. Thus, the introduction of crack connectivity is a supplement to the theoretical model of cracked fluid-saturated rocks. It helps understand the local fluid flow induced by seismic waves and provides a reasonable variation analysis of moduli and attenuation, especially for tight reservoirs.

Effects of background elastic and permeability anisotropy on dynamic seismic signatures of a fluid-saturated porous rock with aligned fractures

Seismic dispersion, attenuation, and frequency-dependent anisotropy due to wave-induced fluid flow (WIFF) in fluid-saturated porous and fractured rocks have been widely studied. However, most of these studies do not consider the effects of background elastic and permeability anisotropy. In this work, we study such effects by considering a fluid-saturated porous rock with penny-shaped fractures embedded in the isotropic plane of a transversely isotropic (TI) background. Starting with P-waves propagating perpendicularly to the fracture plane, we obtain the wavefields in the fluid-saturated porous TI background scattered from a single fracture. This allows for the calculation of effective P-wavenumber through the Foldy approximation and the derivation of a frequency-dependent fracture compliance matrix. The angle-dependent seismic dispersion and attenuation, as well as frequency-dependent anisotropy, can thus be calculated. Using this model, we study a fractured tight sandstone with a TI background. The results show that the background elastic anisotropy primarily affects the seismic frequency-dependent anisotropy, while the background permeability anisotropy not only affects seismic frequency-dependent anisotropy but also influences seismic dispersion and attenuation. In particular, the background permeability anisotropy alters the rate of change in seismic velocities and velocity anisotropy parameters with frequencies and the peaks of seismic attenuation and attenuation anisotropy parameters. By comparing the theoretical predictions of our model to other theories and also to two sets of experimental data, our model is validated. Our model can be applied to characterize the fractured, layered earth.

Joint Inversion Method of Nuclear Magnetic Resonance Logging Multiwait Time and Multiecho Time Activation Data and Fluid Identification

Summary Nuclear magnetic resonance (NMR) logging is effective for reservoir evaluation; at present, NMR logging data acquisition parameters are primarily divided into dual wait time (TW) and dual echo time (TE) and then are analyzed, respectively. However, the interpretation results of the two activations are often inconsistent and confuse the identification and quantitative evaluation of reservoir fluids. Based on the principle of multi-TW and -TE activations of NMR logging, the relaxation mechanism is analyzed, and the relationship between the amplitude of the echo train and the pore structure, fluid types, and content of different activations is established. The joint system of the amplitude of echo trains in multiactivations is constructed. Then, the difference spectrum and the oil porosity of the flushed zone can be calculated by the least squares algorithm (LSQR). The fluid-saturated rock model is set, and the numerical simulation of NMR is used to verify the data joint inversion is correct and that the calculation result is more accurate than the previous time domain analysis (TDA) processing method. Moreover, the oil porosity of the flushed zone-deep induction resistivity crossplot is constructed and is also proposed to identify fluid. The above method was applied to the Yanchang Formation in the western Ordos Basin. Based on the joint inversion of NMR multi-TW and -TE logging data in the study area, the methodology yields more precise calculations of fluid volume and saturation compared with conventional approaches. The crossplots derived from these calculations demonstrate high efficacy in identifying fluid types; therefore, the method for fluid identification exhibits potential for practical application and holds considerable value for widespread adoption in the field.

Simulating squirt flow in realistic rock models using graphical processing units (GPUs)

SUMMARY Understanding the underlying mechanisms of seismic attenuation and moduli dispersion in fluid-saturated cracked porous rocks is of great importance for the development of non-invasive methods to characterize the subsurface. Wave-induced fluid flow at the pore scale, so-called squirt flow, is responsible for seismic attenuation and moduli dispersion at sonic and ultra-sonic frequencies and may be relevant at seismic frequencies. The squirt flow associated attenuation is usually quantified using analytical models. However, numerical experiments suggest that the squirt flow related dissipation is sensitive to fine details of the pore geometry, which can only be modelled numerically. Most of the existing numerical studies explore this phenomenon using simplified models, and there is a lack of numerical studies that model the physics in realistic pore geometries with sufficient numerical resolution. As a result, the impact of wave-induced fluid flow on the effective static and time-dependent mechanical characteristics in realistic settings is still poorly understood. I address these issues by developing a numerical method to model the effective mechanical properties of a hydromechanically coupled system at the pore scale suitable for graphical processing units. A numerical evaluation of attenuation and modulus dispersion due to squirt flow in models based on 3-D microtomography images of cracked Carrara marble is presented. It is shown that the local hydraulic conductivity can be quantitatively estimated from the numerically evaluated effective properties. The accuracy of the numerical results is carefully analysed. This study improves the understanding of the underlying mechanisms of attenuation and moduli dispersion in fluid-saturated cracked rocks. The new method can be applied to model squirt flow for entire laboratory samples in the centimetre scale which was not possible a decade ago.

Seismic wave modeling of fluid-saturated fractured porous rock: including fluid pressure diffusion effects of discretely distributed large-scale fractures

Abstract. The scattered seismic waves of fractured porous rock are strongly affected by the wave-induced fluid pressure diffusion effects between the compliant fractures and the stiffer embedding background. To include these poroelastic effects in seismic modeling, we develop a numerical scheme for discretely distributed large-scale fractures embedded in fluid-saturated porous rock. Using Coates and Schoenberg's local-effective-medium theory and Barbosa's dynamic linear slip model characterized by complex-valued and frequency-dependent fracture compliances, we derive the effective viscoelastic compliances in each spatial discretized cell by superimposing the compliances of the background and the fractures. The effective governing equations for fractured porous rocks are viscoelastic anisotropic and numerically solved by the mixed-grid-stencil frequency-domain finite-difference method. The main advantage of our proposed modeling scheme over poroelastic modeling schemes is that the fractured domain can be modeled using a viscoelastic solid, while the rest of the domain can be modeled using an elastic solid. We have tested the modeling scheme in a single fracture model, a fractured model, and a modified Marmousi model. The good consistency between the scattered waves off a single horizontal fracture calculated using our proposed scheme and the poroelastic modeling validates that our modeling scheme can properly capture the fluid pressure diffusion (FPD) effects. In the case of a set of aligned fractures, the scattered waves from the top and bottom of the fractured reservoir are strongly influenced by the FPD effects, and the reflected waves from the underlying formation can retain the relevant attenuation and dispersion information. The proposed numerical modeling scheme can also be used to improve migration quality and the estimation of fracture mechanical characteristics in inversion.

An extended continuum-mechanics standard linear solid rheology for fluid-saturated porous rock

SUMMARY In a large body of rock-physics research, seismic wave velocity dispersion and attenuation in fluid-saturated porous rock are studied by constructing analytical or numerical models for time- or frequency-dependent dynamic (effective, or viscoelastic) moduli. A key and broadly used model of such kind is the Zener's, or the standard linear solid (SLS). This model is qualitatively successful in explaining many field and laboratory observations and serves as the key element of many generalizations such as the Burgers model for plastic deformations or the generalized SLS explaining band-limited or near-constant seismic attenuation. However, as a physical model of fluid-saturated porous rock, the SLS has several major limitations: disregard of inertial effects, absence of secondary wave modes and lack of key physical parameters such as porosity and Skempton coefficients. Grainy and porous rock is an unconsolidated material in which the effective density is frequency-dependent, and its effects on wave velocities may exceed those of the dynamic modulus. To overcome these limitations of the empirical SLS, we propose a rigorous rheologic model based on classical continuum mechanics and called the extended SLS, or eSLS. This rheology explains the available attenuation and dispersion observations equally well, but it is also close to Biot's model, honours all poroelastic relations, includes inertial effects, and reveals several new physical properties of the material. Detailed comparison of the eSLS and Biot's models gives a physical-mechanism-based classification of wave-induced fluid flow (WIFF) phenomena. In this classification, the so-called ‘global-scale’ flows occur in Biot's type structures within the material, whereas the ‘local-scale’ WIFF occurs in eSLS-type structures. Combining Biot's and eSLS models gives a broad class of rheologies for linear anelastic phenomena within rock with a single type of porosity. The model can be readily generalized to multiple porosities and different types of internal variables, such as describing squirt flows, wetting or thermoelastic effects. Modelling is conducted with relatively little effort, using a single matrix equation similar to a mechanical form of the standard SLS. By combining the eSLS and Biot's models, observations of dynamic-modulus dispersion and attenuation can be inverted for macroscopic mechanical properties of porous materials.

Dispersion and attenuation characteristics of an obliquely incident SV wave in a fluid-saturated porous rock containing aligned penny-shaped fractures

Owing to the complex structural characteristics of aligned fractured rocks with a fluid-saturated porous background, many existing single-wave attenuation mechanism models cannot accurately characterize measuring multiband shear vertical (SV) wave data. Moreover, the coupled effect of wave-induced fluid flow between fractures and the background (FB-WIFF) and elastic scattering (ES) from the fractures leads to ambiguity in the elastic response of the SV wave. Using Biot’s theory and mixed boundary constraints, the exact solutions of the scattering problem for a single penny-shaped fracture with an obliquely incident SV wave are derived. Furthermore, a theoretical model for a set of aligned fractures is developed by using Foldy’s scheme. The numerical results indicated that the FB-WIFF, ES of fractures, and their coupling effects were mainly responsible for wave dispersion and attenuation. The FB-WIFF occurs primarily in the low-frequency seismic exploration frequency band, whereas the ES of the fracture surface depends on the relationship between the wavelength and fracture size. In addition, by comparing our model with an existing interpolation approximation model and previous experimental measurements, the accuracy and effectiveness of the model was validated. The results of this work can explain the acoustic response of SV-wave experimental data in different frequency bands and theoretically support fracture detection and characterization.

Identifying the fracture characteristics that control deformation localization and catastrophic failure in fluid-saturated crystalline rocks in upper crustal conditions

Previous studies show that the total volume of fractures increases non-linearly during loading as rocks approach failure in triaxial compression at stress and temperature conditions representative of the upper crust. However, the factors that control the critical volume of fractures or the critical spatial organization of the fracture network that trigger macroscopic failure remain unclear. To identify the fracture characteristics that determine the timing of macroscopic failure and localization of the fracture networks, we analyze data from six X-ray tomography experiments on Westerly granite with varying confining stress, fluid pressure, and amounts of preexisting damage. We develop machine learning models to predict 1) the timing of failure, 2) the localization of the fracture networks as measured with the Gini coefficient of the fracture volume, and 3) the change in localization from one differential stress step to the next. When the models only have access to individual fracture characteristics, the fracture length produces the best predictions of the distance to failure. When the models have access to the fracture length and sets of other characteristics, the fracture volume, aperture, and distance between fractures produce the best predictions of the distance to failure. The characteristics that describe the time or loading in the experiment, the axial strain and differential stress, produce some of the best predictions of the Gini coefficient. The results are generally consistent among the different experiments, suggesting that the fracture characteristics that determine the timing of macroscopic failure, and the localization of the fracture network, are independent of the range of confining stress, fluid pressure, and amount of preexisting damage tested here. Our results are consistent with the idea that monitoring the spatial distribution of deformation and changes in the seismic wave properties indicative of fracture growth may improve forecasting efforts of failure in the crust.

Frequency-dependent velocities and attenuations in fluid-saturated rocks: Fractures aligned in isotropic medium with random pore shape

The modeling of seismic wave velocity and attenuation is crucial for the interpretation of seismic data. In fluid-saturated rocks, the presence of fractures causes dispersion and attenuation of seismic waves due to fluid flow between cracks and pores. Meanwhile, the parallel distribution of cracks is an important reason for the anisotropy of rocks. Combined with poroelasticity theory, we extend Chapman’s model to media with penny-shaped fractures and an isotropic porous matrix, for which no restrictions are placed on the pore shape of the matrix. We conduct simulations at different frequencies to indicate the predicted anisotropy of velocity and attenuation. The variation of velocities and attenuations with orientation angle is consistent with Chapman’s model. Because a typical porous matrix is used in the new model, predicted velocities are lower than those under assumption of spherical matrix pores. Then, we analyze the effect of pore compressibility of the matrix on the velocity and attenuation. We also conduct discussions about the effect of different porosities on velocity and attenuation. The analysis indicates that the predictions of the new model are more closely related to the modulus of the porous matrix than Chapman’s model. The strength of fluid flow in the new model also will change with the matrix pores. The comparison of the new model and Chapman’s model with experimental data indicates that the new model is in better agreement with the experimental results.

A simple and accurate model for attenuation and dispersion caused by squirt flow in isotropic porous rocks

Seismic waves propagating in fluid-saturated porous rocks exhibit attenuation and velocity dispersion in a broad range of frequencies. At sonic and ultrasonic frequencies, the attenuation is predominantly caused by fluid flow in cracks and grain contacts, so-called squirt flow. This physical mechanism for attenuation also may be relevant at seismic frequencies. We develop a simple and accurate analytical model for attenuation and dispersion caused by squirt flow in isotropic porous rocks. The input material properties for a specific rock model can be directly measured in a laboratory or calculated using analytical and numerical approaches. The results from our squirt flow model are compared with inherently accurate 3D numerical solutions for the same pore geometries. The analytical and numerical results are in good agreement. Furthermore, we observe that our analytical model is more accurate than the currently available analytical solution for squirt flow in isotropic porous rocks. MATLAB routines to reproduce the presented results are made available.

A seismic elastic moduli module for the measurements of low-frequency wave dispersion and attenuation of fluid-saturated rocks under different pressures

Knowledge about the seismic elastic modulus dispersion, and associated attenuation, in fluid-saturated rocks is essential for better interpretation of seismic observations taken as part of hydrocarbon identification and time-lapse seismic surveillance of both conventional and unconventional reservoir and overburden performances. A Seismic Elastic Moduli Module has been developed, based on the forced-oscillations method, to experimentally investigate the frequency dependence of Young's modulus and Poisson's ratio, as well as the inferred attenuation, of cylindrical samples under different confining pressure conditions. Calibration with three standard samples showed that the measured elastic moduli were consistent with the published data, indicating that the new apparatus can operate reliably over a wide frequency range of f∈[1–2000, 106] Hz. The Young's modulus and Poisson's ratio of the shale and the tight sandstone samples were measured under axial stress oscillations to assess the frequency- and pressure-dependent effects. Under dry condition, both samples appear to be nearly frequency independent, with weak pressure dependence for the shale and significant pressure dependence for the sandstone. In particular, it was found that the tight sandstone with complex pore microstructure exhibited apparent dispersion and attenuation under brine or glycerin saturation conditions, the levels of which were strongly influenced by the increased effective pressure. In addition, the measured Young's moduli results were compared with the theoretical predictions from a scaled poroelastic model with a reasonably good agreement, revealing that the combined fluid flow mechanisms at both mesoscopic and microscopic scales possibly responsible for the measured dispersion.

Determination of the Effective Electrical Conductivity of a Fluid–Saturated Core from Computed Tomography Data

Abstract—This paper proposes a technique for determining the effective specific electrical conductivity of rock samples when their digital models are used. A modified algorithm for reconstructing the internal structure of the sample from the core’s nondestructive imaging data can be used to construct a relevant discrete model that approximates the pore space with a high degree of accuracy. Unlike existing approaches, the reconstructed discrete geometric model of a heterogeneous medium sample is hierarchical and oriented to the application of parallel computational schemes of multiscale finite element methods for a forward mathematical simulation of electromagnetic processes. The paper presents the results of solving the problem of determining the effective specific electrical conductivity of fluid–saturated rock samples and compares them with the data from laboratory experiments.

Research on the forward-modeling method of viscoelastic Chapman extension in partially saturated rocks

The propagation of seismic waves in fractured rocks is greatly influenced by the fracture system and fluid content. Seismic anisotropy varies with frequency and fluid saturation. Previous theories on frequency-dependent anisotropy (FDA) are mostly limited to the assumption of single-phase fluid, whereas almost all reservoirs are usually partially or fully saturated with one or more fluids. The inelasticity, heterogeneity, and anisotropy exhibited by real earth media seriously challenge the traditional theory of uniform fully elastic media. Therefore, based on the Chapman elastic theory, we consider the viscoelastic model, the relative mobility of saturated fluids, and the coupled effects of commonly independently considered squirt flow and patch effects on the frequency-dependent anisotropic seismic wave propagation in viscoelastic media. By calculating the frequency-dependent anisotropic elastic coefficients of two-phase immiscible fluid-saturated fractured rocks, a new viscoelastic Chapman extension model for FDA in partially saturated rocks, which includes the unified seismic wave propagation effects of squirt flow and patch effects, is constructed. The effect of relative permeability is significant, and compared to the case of complete saturation, the effective fluid mobility in partially saturated rocks may be lower, which may lead to nonmonotonic changes in elastic modulus and water saturation. Numerical experiments are conducted on our viscoelastic Chapman extension model to discuss the coupling effects of squirt flow and patch effects on the FDA of viscoelastic media in cracked rocks with partially saturated reservoirs, under the conditions of no fractures and the existence of fractures. The simulation results of the P-wave modulus, P-wave velocity, and anisotropy parameters confirm the validity of our method and model. We link the anisotropy of viscoelastic media with fluid flow parameters in fractures, which is conducive to improving the understanding of frequency-dependent seismic anisotropy in partially saturated rocks with fractures and the combination of seismology and reservoir engineering.

A theoretical approach for water saturation estimation in shaly sandstones

The process of quantitative reservoir characterization is a crucial component spanning from the initial estimation of in-place reserves to the optimization of production design. Water saturation is a critical parameter in quantitative reservoir characterization that directly impacts the in-place reserve estimates. In the case of shale-free sandstones, the computation of water saturation using Archie's equation yields fairly accurate results. However, in shaly sandstone reservoirs, the presence of multiple conductive entities in the rock poses additional complexities. Currently, various empirical, semi-empirical and theoretical equations are available in literature to estimate water saturation; nevertheless, none of these models is such that it is both theoretically sound and practically applicable.In this study, we present a novel approach that is both theoretically sound and practically applicable in computing water saturation in shaly sandstones. The fluid-saturated rocks are treated as a system consisting of two interlocked lattice-like structures, namely grains and fluid in the interconnected pores. The composite fluid comprising water and hydrocarbon is modeled using the general mixture rule, while the Hanai-Bruggeman equation is employed to model the electrical conductivity of this system. The resulting electrical conductivity equation is then utilized to compute water saturation in shaly sandstones.The proposed equation was effectively validated using the published core data. Furthermore, we compare the new model with other grain conductivity-based models such as Mixing model and Berg's model. Our findings show that while describing core data the proposed equation gives a lower average Relative Root Mean Squared Error (RRMSE) of 2.05% as compared to 7.56% and 5.58% for the Mixing and Berg's model available in literature, respectively. Moreover, the range of porosity and water conductivity for which the proposed model is applicable, surpasses that of the current models. We also suggest that this equation can be extended to other systems with a similar two interlocked lattice-like structure, such as carbonates.

Elastic waves in fluid-saturated rocks with randomly orientated slit cracks

Elastic waves in fluid-saturated rocks with randomly orientated slit cracks

Tectonic Structure of Northern Sumatra Region Based on Seismic Tomography of P and S Wave Velocity

The tectonic setting of Sumatra Island is strongly influenced by the oblique subduction of the Indo-Australian Plate, which subducts the Eurasian Plate at a speed of 52–60 mm/year. The movement of these plates resulted in the Northern Sumatra region having seismic sources from tectonic and volcanic activity. The data used in this study is in the form of seismic wave travel-time recorded by numerous seismic stations in the research area from January 2012 to December 2020. The data comes from 5,003 earthquakes recorded by the BMKG seismic network. The inversion is a simultaneous inversion between seismic velocity models (Vp and Vs) and hypocenter parameters by applying a double-difference seismic tomography algorithm. Tomogram results in parts of Aceh (Singkil and Subulussalam) and North Sumatra (Pakpak Bharat and Dairi) at a depth of 0 km show negative perturbations in Vp and Vs values and high Vp/Vs values. The anomaly is most likely related to cracks in fluid-saturated rocks. The tomograms in the south of Lake Toba at depths of 30 km and 40 km have high Vp and Vs perturbation values and low Vp/Vs values. This anomaly indicates a magma supply line that is no longer active or has cooled for a long time. Based on the seismic tomography modeling results, the subducted Indo-Australian Plate to the Eurasian Plate is visible in the study area.

Thermo-poro-viscoelastic response of a disc-shaped inclusion

SUMMARY The study of deformation sources in volcanic and geothermal fields is a topic of great importance that generates a large debate in the scientific literature. A correct interpretation of the deformation sources acting in a volcanic context is crucial to distinguish between the mechanical effects due to the tectonic of the area, the intrusion of new magma and/or the mechanical response of rocks to temperature or pore pressure changes. In the recent literature, thermo-poro-elastic (TPE) inclusions were proposed as possible deformation sources that can explain seismicity and displacements even in absence of the emplacement of new magma. In fact, TPE inclusions allow us to compute the mechanical effects due to temperature and pore-pressure changes brought by the arrival of hot and pressurized fluids permeating a closed volume. In the present work, we improve the modellization of such deformation sources to include the effects of viscoelasticity, which should be expected in high temperature and fluid saturated rocks due to thermally activated and pressure-solution creep. The analytical thermo-poro-viscoelastic (TPVE) solutions for a disc-shaped inclusion embedded in a uniform viscoelastic medium are obtained through the correspondence principle. Our results can be useful to represent transient effects of both deformation and stress fields that can occur in both volcanic and geothermal areas, which would be difficult to explain otherwise. In fact, TPE inclusion models predict that an increase of uplift occurs simultaneously with an increase of stress, and vice versa. Instead, we shall see that a TPVE inclusion can provide an increase of uplift even in presence of a strongly decreasing deviatoric stress. For this reason, a TPVE inclusion can be suitable to represent a decrease in seismicity rate accompanied by an increase in surface uplift, as observed, for example, during the ’82–’84 unrest phase of Campi Flegrei in Italy.

Time-domain Green’s function in poroelastic mediums and its application to 3-D spontaneous rupture simulation

SUMMARY Plenty of studies have suggested that pore fluid may play an important role in earthquake rupture processes. Establishing numerical models can provide great insight into how pore fluid may affect earthquake rupture processes. However, numerical simulation of 3-D spontaneous ruptures in poroelastic mediums is still a challenging task. In this paper, it is found that a closed-form time-domain Green’s function of Biot’s poroelastodynamic model can be constructed when the source frequency and source-field distance are within a certain range. The time-domain Green’s function is validated by being transformed into the frequency domain and comparing with the frequency-domain Green’s functions obtained by former papers. Poroelastic wave propagation phase diagrams for various two-phase poroelastic mediums are then plotted to show the applicable range of frequency and source-field distance for the new time-domain Green’s function. It is shown that the applicable range not only include the frequency and spatial range of concern in seismology but also overlap that in acoustics. Based on the time-domain Green’s function, the boundary integral equations (BIEs) for modelling dynamic ruptures in elastic mediums are extended to fluid-saturated mediums. In the meantime, a functional relationship between the effective stress tensor and the total stress tensor in fluid-saturated mediums is also obtained, which allows us to directly obtain the effective stress by BIEs. The spontaneous rupture processes controlled by the slip-weakening friction law on faults in elastic mediums and in fluid-saturated mediums are compared. It is found that under the same conditions, fluid-saturated rocks are more prone to supershear rupture than dry rocks. This result suggests that pore fluid may promote the excitation of supershear rupture. The poroelastic wave propagation phase diagrams also suggest that simulating a coseismic phase in the real scale requires a certain sample length in laboratories. They also suggest that an undrained governing equation is suitable for seismic wave propagation simulation in poroelastic media.