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Accurately characterizing seismic attenuation effects on wave propagations is crucially important for structure interpretation and reservoir evaluation. The conventional fractional viscoelastic wave equation is not satisfactory on accuracy for small Q values. To solve this issue, we derive a novel fractional viscoelastic wave equation by combining an accurate relationship between angular frequency and complex wavenumber. The dissipation- and dispersion-dominated wave equations are also derived to simulate the amplitude-dissipation and phase-dispersion characteristics. The truncated Taylor-series expansion (TE) algorithm is developed to approximate the mixed-domain operators. After that, the generalized pseudospectral approach can be directly used to solve the new wave equation. In addition, an accurate viscoelastic wave equation constructed by the fractional time derivatives is used to calculate reference solutions to evaluate the accuracy of the new expression. Modelling results indicate that the newly proposed viscoelastic wave equation using the new fractional Laplacians is more accurate than the conventional one, especially in a small Q medium (i.e. QP = QS = 5). Furthermore, we also examine the accuracy of the TE approximation with a series of Q values. A homogeneous model and the modified BP2004 viscoelastic model are used to investigate the accuracy of viscoelastic wave propagations using the TE algorithm. All modelling results fully demonstrate the performance of the newly proposed viscoelastic wave equation and numerical algorithm. [ABSTRACT FROM AUTHOR]

Ray theory gives a high‐frequency asymptotic solution of the wave equation, which has been widely used in the seismic study because of its high computational efficiency and good physical insights for elementary waves. However, the fundamental high‐frequency assumption makes it difficult to accurately simulate the finite‐frequency effect of wave propagations. On the other hand, the Gaussian beam, as one of the advanced ray‐based methods, overcomes the amplitude singularity problem near the caustics by introducing a complex‐valued paraxial approximation. But Gaussian beams only use the velocity and up to second‐order velocity derivative of central rays and thus does not accurately simulate the response of heterogeneity away from the rays. To bridge the gap between the ray theory and wave‐equation methods, we present a two‐way beam wave method and apply it to seismic imaging. A fan of central rays are first shot to extract local ray‐centered model parameters in the global Cartesian coordinates. Then, a finite‐difference method is used to solve the acoustic wave equation in the ray‐centered coordinates to simulate wave propagations near the central rays. The beam wave method can accurately simulate the response of the velocity heterogeneities in the ray tubes and therefore produces more accurate wavefields. In addition, we discretize the ray‐centered wave equation onto a non‐orthogonal grid, which considerably reduces the computational cost. We apply the two‐way beam wave method in seismic imaging and develop a beam wave reverse‐time migration. It inherits the advantages of both ray‐based and wave equation migrations, and produces clear images for complicated structures with fewer artifacts than traditional imaging methods. Plain Language Summary: Seismic ray theory has evolved from classical asymptotic ray theory, through paraxial ray theory and Maslov's method, and then to the Gaussian beam method. Although the computational accuracy of the ray‐based methods for seismic modeling and imaging have been greatly improved, the fundamental high‐frequency approximation still prevents them from accurately describing finite‐frequency wave propagations in complex structures. We introduce the idea of reverse‐time migration into the beam method and develop a two‐way beam wave scheme for seismic modeling and imaging. Local velocities in the vicinity of central rays are first extracted and then the finite‐difference approach is used to solve the wave equation in the ray‐centered coordinate. Accurate wavefield simulation and beam‐to‐beam imaging condition enables us to achieve clear migrated images with fewer artifacts than traditional Gaussian beam migration and reverse‐time migration. Numerical examples for benchmark models and field data demonstrate the feasibility and adaptability of the proposed two‐way beam wave method. Key Points: It is difficult for ray theory to accurately simulate seismic wave phenomena in areas with strong velocity variationsA two‐way beam wave method is proposed to bridge the gap between ray‐based and wave equation approachesA beam wave reverse‐time migration approach is developed to improve the image quality for complicated subsurface environments [ABSTRACT FROM AUTHOR]

Several hypotheses have been proposed to explain intriguing circular shear wave splitting patterns in the Pacific Northwest, invoking either 2‐D entrained flows or 3‐D return flows. Here, we present some hitherto unidentified, depth‐dependent anisotropic signatures to reconcile different conceptual models. At depths shallower than 200 km, the fast propagation directions of seismic waves to the west of the Rocky Mountain are aligned sub‐parallel to the subduction direction of the Juan de Fuca and Gorda Plates. This pattern is consistent with previous onshore/offshore shear wave splitting measurements and indicates that 2‐D entrained flows dominate at shallower depths. From 300 to 500 km, two large‐scale return flows are revealed, one circulating around Nevada and Colorado and the other running around the edge of the descending Juan de Fuca slab. These observations suggest the development of toroidal‐mode mantle flows, driven by the fast rollback of the narrow, fragmented Juan de Fuca and Gorda slabs. Key Points: The fast directions are aligned sub‐parallel to the subduction direction of the Juan de Fuca Plates at depths shallower than 200 kmTwo large‐scale return flows are revealed, circulating around the edges of the descending Juan de Fuca and Gorda slabsThe uppermost lower mantle beneath the Cascadian Subduction Zone is dominated by a NE‐SW oriented flow field [ABSTRACT FROM AUTHOR]

Locating and monitoring passive seismic sources provides us important information for studying subsurface rock deformation, injected fluid migration, regional stress conditions as well as fault rupture mechanism. In this paper, we present a novel passive-source monitoring approach using vector-based elastic time-reversal imaging. By solving the elastic wave equation using observed multicomponent records as boundary conditions, we first compute back-propagated elastic wavefields in the subsurface. Then, we separate the extrapolated wavefields into compressional (P -wave) and shear (S -wave) modes using the vector Helmholtz decomposition. A zero-lag cross-correlation imaging condition is applied to the separated pure-mode vector wavefields to produce passive-source images. We compare imaging results using three implementations, that is dot-product, energy and power. Numerical experiments demonstrate that the power imaging condition gives us the highest resolution and is less sensitive to the presence of random noises. To capture the propagation of microseismic fracture and earthquake rupture, we modify the traditional zero-lag cross-correlation imaging condition by summing the multiplication of the separated P and S wavefields within local time windows, which enables us to capture the temporal and spatial evolution of earthquake rupture. 2-D and 3-D numerical examples demonstrate that the proposed method is capable of accurately locating point sources, as well as delineating dynamic propagation of hydraulic fracture and earthquake rupture. [ABSTRACT FROM AUTHOR]

SUMMARY: It has been widely recognized that seismic attenuation and dispersion can be induced by various mechanisms. Wave induced fluid flow (WIFF) is one of the popular mechanisms to interpret seismic wave attenuation and dispersion, especially at microscopic scale. In this study, we focus on the local flow induced by different compliances of adjacent pores and develop a unified model called BISSQ (Biot-spherical squirt) model based upon the Biot and spherical squirt flow theories. The proposed model is an extension of BISQ (Biot-squirt) model. The P -wave velocity and attenuation of BISSQ model are influenced by two mechanisms: the Biot and spherical squirt-flow mechanisms. To evaluate the impact of these two mechanisms on seismic wave propagation, we use different parameters (e.g. squirt flow length, fluid viscosity, permeability, saturation and so on) to simulate wave attenuation and dispersion. We then apply the proposed model to Fox Hills Sandstone, which shows that the model can realistically predict P -wave velocity dispersion. To sum up, our proposed model offers an alternative squirt flow attenuation mechanism, which can describe fluid state of squirt flow reasonably and help us to assess the effect of different parameters on seismic wave attenuation. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that anelasticity has significant effects on the propagation of seismic waves, as manifested by physical dispersion and dissipation. Investigations of anelasticity provide complementary constraints on the physical properties of Earth materials, but — contrary to imaging with elastic waves — progress in mapping Earthʼs anelasticity has been relatively slow, and there is only limited agreement between different studies or methodologies. Here, within the framework of adjoint tomography, we use frequency-dependent phase and amplitude anomalies between observed and simulated seismograms to simultaneously constrain upper mantle wavespeeds and attenuation beneath the European continent and the North Atlantic Ocean. In the sea-floor spreading environment beneath the North Atlantic, we find enhanced attenuation in the asthenosphere and within the mantle transition zone (MTZ). In subduction zone settings, for example beneath the Hellenic arc, elevated attenuation is observed along the top of the subducting slab down to the MTZ. No prominent reductions in wavespeeds are correlated with these distinct attenuation features, suggesting that non-thermal effects may play an important role in these environments. A plausible explanation invokes the transport of water into the deep Earth by relatively cold subducting slabs, leading to a hydrated MTZ, as previously suggested by mineral physics and geodynamics studies. [Copyright &y& Elsevier]

The acoustic behavior in fluid attenuating media can be effectively simulated using a fractional Zener model (FZM). Because of the fractional time derivatives of both stress and strain in the constitutive relationship, this mechanism is very realistic and flexible in describing seismic attenuation. However, using conventional FZM wave equations to propagate seismic waves requires storing large amounts of previous wavefield information to calculate the fractional time derivatives, which is unacceptable in practice. In this paper, we derive a new time-domain viscoacoustic wave equation in the framework of the FZM. This new equation does not contain any fractional time derivatives; thus, it is more economical in computational costs. Furthermore, the amplitude attenuation and phase dispersion effects are separated in the newly proposed equation, which is very favorable to compensate for energy loss and correct phase dispersion in reverse-time migration. To improve the accuracy, we incorporate a wave number (k)-space operator into the decoupled FZM wave equation to compensate for temporal dispersion errors caused by the second-order finite-difference discretization. Therefore, a high-temporal-accuracy viscoacoustic wave equation is derived to simulate nearly constant-Q wavefields in attenuating media. In the implementation, a low-rank decomposition method is introduced to solve the mixed-domain operators. Numerical analysis and modeling results demonstrate the effectiveness and applicability of the proposed method for simulating the decoupled viscoacoustic wavefield with high accuracy. [ABSTRACT FROM AUTHOR]