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SUMMARY: We consider surface-wave propagations at an interface separating a fluid layer and a double-porosity medium embedded with cracks. The theory is based on a generalization of the Biot-Rayleigh model from spherical cavities to penny-shaped cracks randomly embedded into a host medium, where mesoscopic local fluid flow (LFF) plays an important role. We derive closed-form dispersion equations of surface waves, based on potentials and suitable boundary conditions (BCs), to obtain the phase velocity and attenuation by using numerical iterations. Two special cases are considered by letting the thickness of the fluid (water) layer to be zero and infinity. We obtain pseudo-Rayleigh and pseudo-Stoneley waves for zero and infinite thickness and high-order surface modes for finite nonzero thickness. Numerical examples confirm that the LFF affects the propagation at low frequencies, causing strong attenuation, whereas the impact of BCs is mainly observed at high frequencies, due to the propagation of slow wave modes. The crack density mainly affects the level of attenuation, whereas the aspect ratio the location of the relaxation peak. The fundamental mode undergoes a significant velocity dispersion, whose location moves to low frequencies as the thickness increases. In all cases, there also exist two slower surface modes that resemble the two slow body waves, only present for sealed BCs. [ABSTRACT FROM AUTHOR]

We obtain the amplitude and energy reflection coefficients of seismic waves in porous media with penny-shaped inclusions, based on the generalized Biot-Rayleigh model that takes into account the attenuation due to mesoscopic local fluid flow (LFF). We consider two cases, including a contact between two porous media having either different fluids (gas–water contact) or crack density and aspect ratio, as well as a water half-space overlying a porous medium, and study the frequency-dependent reflection-transmission (scattering) coefficients for open- and sealed-pore boundary conditions. Our examples show that the LFF mechanism mainly reduces the reflection coefficients (amplitude and energy) at the gas–water contact and at a water–porous medium interface for frequencies less than 10 kHz, due to the fact that the velocity in the lower medium decreases. For the latter case, if the fluid is gas, the LFF effect becomes only important at frequencies between 0.0001 and 10 Hz for the open-pore case. This is due to the fact that the acoustic impedance contrast between water and gas is high. At frequencies less than 0.0001 Hz, the interface is equivalent to a water–elastic medium one, and hence the results are the same as those of the sealed-pore case. Moreover, the crack density and aspect ratio affect the mesoscopic attenuation and relaxation frequency, and therefore the reflection coefficients. [ABSTRACT FROM AUTHOR]

We analyse the reflection coefficient of an inhomogeneous plane wave incident on the thermally insulated surface of a thermo-poroelastic medium. The theory, which includes the classic Lord-Shulman (LS) and Green-Lindsay (GL) theories as well as a generalization of the LS model, predicts three inhomogeneous longitudinal waves and one transverse wave, described by potential functions specified by the propagation direction and inhomogeneity angle. The GL model can give a stronger P1-wave thermal attenuation and consequently a stronger velocity dispersion than the LS model. We investigate the influence of inhomogeneity angle, type of incident wave, frequency and surface boundary conditions. The generalized LS model exhibits increased P1-wave thermal attenuation with increasing Maxwell–Vernotte–Cattaneo relaxation time and consequently predicts more interference energy, irrespective if the surface is open or sealed. The inhomogeneity angle affects the energy partitions particularly near the grazing incidence, with a significant interference energy, which must be taken into account to satisfy the energy conservation. The thermal dispersion occurs at frequencies around the thermal relaxation peak, which moves to low frequencies when the conductivity increases. [ABSTRACT FROM AUTHOR]

We develop a numerical algorithm for simulation of wave propagation in linear nonisothermal poroelastic media, based on Biot theory and a generalized Fourier law of heat transport in analogy with Maxwell model of viscoelasticity. A plane wave analysis indicates the presence of the classical P and S waves and two slow waves, namely, the Biot and the thermal slow modes of propagation, which present diffusive behavior under certain conditions, depending on viscosity, frequency, and the thermoelastic constants. The wavefield is computed with a direct meshing method using the Fourier differential operator to calculate the spatial derivatives. We propose two alternative time‐stepping algorithms, namely, a first‐order explicit Crank‐Nicolson method and a second‐order splitting method. The Fourier differential operator provides spectral accuracy in the calculation of the spatial derivatives. Modeling the thermal diffusive mode is relevant for high‐temperature high‐pressure fields and since it leads to mesoscopic attenuation by mode conversion of the fast waves to the thermal waves. Key Points: The differential equations of dynamic thermoporoelasticity are solved with a direct grid methodThe solver is based on the Fourier pseudospectral method to compute the spatial derivativesThe simulation reveals the behavior of four wave modes, namely, the fast P, slow P, S, and the thermal wave-diffusion field [ABSTRACT FROM AUTHOR]

The correct simulation of wave propagation with direct grid methods at fluid–solid interfaces requires a proper implementation of the boundary condition, which involves continuity of the normal component of the particle velocity and traction. The horizontal component of the particle velocities can differ (slip) and the tangential traction vanishes. The challenge is to model the interface waves, which are relevant when the source and receiver are located close to the interface, in particular the Scholte and leaky (or pseudo, or generalized) Rayleigh waves. The explicit modelling is based on a domain-decomposition technique (one mesh for the fluid and another mesh for the solid) and the Fourier and Chebyshev differential operators along the horizontal and vertical directions, respectively. On the other hand, two implicit modelling algorithms are based on a single mesh and the fluid is described by setting to zero the shear wave velocity above the interface. The modelling is verified by comparisons with the analytical solution for a fluid–solid interface in lossless media, with source and receiver away from and at the interface. To our knowledge, the latter comparison, mainly involving the interface waves (Scholte and leaky-Rayleigh), has not been performed with other grid methods so far. It is shown that the implicit simulation yields erroneous results. [ABSTRACT FROM AUTHOR]

The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields. [ABSTRACT FROM AUTHOR]

The recently developed cross-rhombus stencil-based time–space domain finite-difference (FD) method for modeling two-dimensional acoustic equations, controls the temporal and spatial dispersions synchronously and outperforms cross-stencil-based FD (CS-FD). However, it is only applicable to modeling on equally spaced grids and extensive application is hindered. In this work, we extend it further and develop novel cross-rhombus stencil-based FD (CRS-FD) for modeling on arbitrarily rectangular grids. Two kinds of rhombus stencils involving grid points both on and off the axis are developed first to achieve fourth order and sixth order FD accuracies, respectively, for solving the second order temporal derivative on rectangular grids. The plane wave theory is then used to derive the time–space-domain dispersion relations, when the temporal and spatial derivatives are solved by the new rhombus-stencil-based temporal high order FD and the cross-stencil-based spatial high order FD, respectively. The extrapolation stencil is a mixture of rhombus and cross stencils, and the involved FD coefficients are determined by applying the Tayler expansion on the time–space domain dispersion relation. Our new CRS-FD is high-order accurate in both time and space, and applicable to modeling on arbitrarily rectangular grids. Dispersion analysis, stability analysis and modeling examples on rectangular grids show that the CRS-FD is more accurate and stable than the CS-FD. Meanwhile, we develop the variable-length schemes for CRS-FD to further increase efficiency and apply them to extrapolate wavefields in reverse time migration. The results validate that the CRS-FD is more efficient than the CS-FD because much larger time steps can be used while reaching a similar accuracy. The variable-length scheme further reduces the computational time in comparison with the fixed-length scheme. [ABSTRACT FROM AUTHOR]