Attenuation Of Seismic Waves Research Articles

Three methods of visco‐acoustic migration based on the De Wolf approximation and comparison of their migration images

AbstractThe viscosity of a medium affects the amplitude attenuation and velocity dispersion of seismic waves. Therefore, it is necessary to consider these factors during migration. First, to eliminate the viscous effect of a medium, we combine the Futterman model with the integral equation of the De Wolf approximation to construct a compensation operator of the De Wolf approximation for a visco‐acoustic medium. Next, we use the visco‐acoustic screen approximation method to realize the continuation operator then establish a prestack depth migration algorithm. Finally, an error analysis, impulse response test and model test are performed. The results show that three different generalized visco‐acoustic screen methods (phase screen method, generalized screen method and extended local Born Fourier method) can satisfactorily compensate for the attenuation of deep interface amplitude. Among these methods, the visco‐acoustic extended local Born Fourier method has the highest accuracy and the best compensation effect.

Attenuation of seismic waves using resonant metasurfaces: A field study on an array of rubber oscillators

Resonant metasurfaces (RMS) have garnered increasing attention as a type of seismic metamaterial for attenuating seismic waves. To date, most research has been limited to numerical simulations with few experimental studies. Here, we first used Comsol Multiphysics to simulate and identify an RMS structure, which is a periodic array of rubber column oscillators, and then conducted a field experiment on a granular layer. The results indicate that our RMS can effectively attenuate seismic waves in both horizontal and vertical directions across an ultra-wide bandgap. Additionally, the RMS demonstrates greater efficiency in attenuating Love waves compared to Rayleigh waves. This observation is well-accounted for by the resonator model we developed. This work demonstrates that even a simple and cost-effective ground-based RMS is capable of mitigating seismic wave-induced vibrations.

Seismic Isolation via I-Shaped and T-Shaped Large-Scale Phononic Metamaterials

In this work, the attenuation of surface seismic waves from large-scale phononic metamaterials is numerically studied. The proposed metamaterials consist of rectangular trenches that form either I-shaped or T-shaped cavities embedded at the ground surface. The numerical investigation includes the study of the response of the proposed structures for different values of their geometric parameters. In addition, modifications of the proposed structures where heavy cores coated with a soft material were considered in the cavities were also numerically studied. For a more realistic numerical approach, the transmission spectrum of a selected large-scale phononic metamaterial was also investigated in a suitable half-space numerical scheme. The results of the present research showed that the studied large-scale metastructures could be a very promising potential candidate for seismic shielding applications for the protection of existing urban or countryside structures. The proposed metamaterials are low in cost and easy to construct for the protection of existing buildings, critical infrastructures, or even entire urban areas without need for any kind of intervention at them, therefore providing an effective solution in the field of seismic isolation.

Adaptive-coefficient finite difference frequency domain method for time fractional diffusive-viscous wave equation arising in geophysics

The diffusive-viscous wave (DVW) equation is a widely used model to describe frequency dependent attenuation of seismic wave in fluid-saturated porous medium. In this paper taking power law frequency dependent attenuation into account, we first introduce a modified DVW equation (time fractional DVW equation) in which the first order temporal derivative of viscous term is replaced with a fractional order temporal derivative. In consideration of that most of the existing numerical simulations for seismic wave equations are based on time domain methods and truncation with some specific boundary conditions, we incorporate the absorbing boundary condition as complex-frequency-shifted (CFS) perfectly matched layer (PML) into the time fractional DVW equation, and then develop an adaptive-coefficient (AC) finite difference frequency domain (FDFD) method for numerical simulation. The corresponding analytical solution for homogeneous time fractional DVW equation is provided for model validation, and the effectiveness of the developed AC FDFD method is verified by some numerical examples including the homogeneous model and the layered model. Numerical results show that AC FDFD method is more accurate than the traditional 2nd-order FDFD method for numerical modeling of time fractional DVW equation with CFS PML absorbing boundary condition, while requiring similar computational costs.

Separation of Intrinsic and Scattering Seismic Wave Attenuation in the Crust of Central and South-Central Alaska

ABSTRACT Seismic hazard analysis is essential for evaluating the potential consequences and dangers linked to earthquakes, particularly in areas with regular seismic activity such as central and south-central Alaska. A detailed study of attenuation can help in better defining the wave behavior and so refine the ground-motion prediction. Here, we examined the scattering (Qs−1), intrinsic (Qi−1), and coda-wave (Qc−1) attenuation in central and south-central Alaska. To do so, we performed the multiple lapse time-window analysis (MLTWA) techniques and estimated the coda energy decay. We considered earthquakes that occurred between December 2014 and December 2020, with magnitudes between 2.0 and 6.5. We observed significant spatial variations in scattering loss (Qs−1) up to 3 Hz, which diminish at 6 and 12 Hz. The Wrangell block exhibits the most significant scattering loss at a frequency of 1.5 Hz. Another area of marked scattering loss was identified north of the Alaska Range (AR), where it was pronounced up to 6 Hz. The area around Anchorage registered the lowest intrinsic absorption across all the central frequencies, whereas the highest values were detected north of the AR, particularly at 3 and 6 Hz. The seismic albedo (B0) in central and south-central Alaska varies spatially and is mainly dominated by scattering loss up to 3 Hz. Both the Chugach mountains and Yakutat block (YB) area exhibit lower B0 values at all central frequencies showing the dominance of intrinsic absorption. Low values of Qc (high attenuation) are focused almost on all the frequencies along the Denali fault and YB, showing a strong influence of these structures on the attenuation. The results yield a comprehensive understanding of the unique attenuation characteristics of each region, underscoring the significance of investigating the behavior of seismic wave attenuation for seismic risk purposes.

Water-tank metabarrier for seismic Rayleigh wave attenuation.

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Hydrous Melting and its Seismic Signature

Hydrogen is known to affect elastic and anelastic properties of mantle rocks and minerals. Hydrogen dissolution in minerals notably alters the properties of transition zone phases, which may accommodate very high water contents. Moreover, even small amounts of water can induce partial melting in certain mantle regions and modify seismic wave velocities and attenuation. Progress in seismic imaging of the mantle—particularly the mapping of seismic attenuation and velocities—has improved constraints on local hydrous melt content in the upper mantle, and evidence exists for partial melt–bearing layers above and below the transition zone owing to dehydration reactions induced by upward or downward flow of mantle material. Further observational and modeling studies are needed to more fully understand the influence of hydrous melting on the global water cycle, mantle viscosity, and large-scale geodynamics.

Novel small-size seismic metamaterial with ultra-low frequency bandgap for Lamb waves

Seismic metamaterials (SMs) possess bandgap characteristics, enabling effective attenuation of seismic waves within a specific frequency range. However, small-sized SMs typically struggle to achieve a wide low-frequency bandgap. This paper proposes four types of SMs. The dispersion curves of these models were analyzed, and their vibration modes were studied to elucidate the bandgap mechanism. To investigate the influence of structural parameters on the bandgap, geometric variables are analyzed. Subsequently, the spectrum and acceleration time history curves of Lamb waves in a finite SM system are analyzed to verify the bandgap's authenticity. The designed structure exhibits a bandgap ranging from 1.24 Hz to 16.86 Hz, with a relative bandwidth as high as 172.6% and over 96% maximum vibration displacement attenuation of the El Centro seismic wave. The designed SMs effectively cover the 2 Hz seismic peak spectrum that leads to structural damage. They possess ideal relative bandwidth and excellent isolation performance, further advancing the engineering application of SMs.

Novel Frame-Type Seismic Surface Wave Barrier with Ultra-Low-Frequency Bandgaps for Rayleigh Waves

Seismic surface waves carry significant energy that poses a major threat to structures and may trigger damage to buildings. To address this issue, the implementation of periodic barriers around structures has proven effective in attenuating seismic waves and minimizing structural dynamic response. This paper introduces a framework for seismic surface wave barriers designed to generate multiple ultra-low-frequency band gaps. The framework employs the finite-element method to compute the frequency band gap of the barrier, enabling a deeper understanding of the generation mechanism of the frequency band gap based on vibrational modes. Subsequently, the transmission rates of elastic waves through a ten-period barrier were evaluated through frequency–domain analysis. The attentional effects of the barriers were investigated by the time history analysis using site seismic waves. Moreover, the influence of the soil damping and material damping are separately discussed, further enhancing the assessment. The results demonstrate the present barrier can generate low-frequency band gaps and effectively attenuate seismic surface waves. These band gaps cover the primary frequencies of seismic surface waves, showing notable attenuation capabilities. In addition, the soil damping significantly contributes to the attenuation of seismic surface waves, resulting in an attenuation rate of 50%. There is promising potential for the application of this novel isolation technology in seismic engineering practice.

Split-type seismic metamaterials with pseudo-surface wave weakening mechanism

Pseudo surface waves, as a type of propagating wave, are detrimental to the attenuation of seismic Rayleigh waves. A split seismic metamaterial (SSM) that can weaken pseudo surface wave modes and generate ultra wideband gaps of 12.92Hz is proposed. The split configuration of SSM can be obtained by separating the modes of different waves within the energy band curve, which can cause the surface waves inside the sound cone to move outward and weaken the pseudo surface wave modes inside the band gap. Combined with the frequency response curve, it is further demonstrated that the attenuation amplitude of SSM is larger than that of monolithic seismic metamaterials (MSM) within the same bandgap range. Afterwards, by studying the changes in bandgap through structural parameters, the method of a gradient array was used to fuse the characteristic frequency that can generate larger attenuation with the weakened pseudo surface wave mode frequency, resulting in greater attenuation. Finally, it is verified by experiments that SSM can provide ultra-wide low-frequency band gaps while also generating large attenuation accuracy, which provides a practical solution for the application of seismic metamaterials.

Dynamic Component of the Asthenosphere: Lateral Viscosity Variations Due To Dislocation Creep at the Base of Oceanic Plates

AbstractThe asthenosphere is commonly defined as an upper mantle zone with low velocities and high attenuation of seismic waves, and high electrical conductivity. These observations are usually explained by the presence of partial melt, or by a sharp contrast in the water content of the upper mantle. Low viscosity asthenosphere is an essential ingredient of functioning plate tectonics. We argue that a substantial component of asthenospheric weakening is dynamic, caused by dislocation creep at the base of tectonic plates. Numerical simulations of subduction show that dynamic weakening scales with the surface velocity both below the subducting and the overriding plate, and that the viscosity decrease reaches up to two orders of magnitude. The resulting scaling law is employed in an apriori estimate of the lateral viscosity variations (LVV) below Earth's oceans. The obtained LVV help in explaining some of the long‐standing as well as recent problems in mantle viscosity inversions.

Direct Estimation of the Source Corner Frequency of Minor to Moderate Earthquakes from Fourier Phase Spectra Fitting

ABSTRACT Estimating the corner frequency (fc) of an earthquake is of fundamental importance to improving our knowledge of the physics of the rupture that gives rise to a seismic event, while also having important implications by providing information on the high-frequency radiation for seismic hazard studies. However, the estimation of fc through spectral-fitting methods suffers from trade-offs with the estimation of seismic wave attenuation, making the obtained values precise but not necessarily accurate. For this reason, after a review of the source model proposed by Brune (1970), a new method of estimating fc, based on the phase fitting of Fourier spectra of the Brune’s seismic pulse related to S-waves, called Fourier phase spectra fitting (FPS), is proposed and evaluated in this study. The method can be applied in cases in which Brune’s model may be appropriate, while also considering the effects of propagation on impulse deformation, for which the synthetic tests have been conducted. The results, obtained first using synthetic seismograms generated under controlled conditions and then on a data set of recordings of real seismic events collected at the Groningen gas field in the Netherlands, showed the method to be promising (being accurate and precise) and at the same time pointed out its limitations, with its applicability being restricted to short hypocentral distances of <20 km.

Attenuation of High-Frequency Seismic Waves in NW Iran

Attenuation of High-Frequency Seismic Waves in NW Iran

Large-scale engineered meta-barriers for attenuation of seismic surface waves

This study evaluates the performance of large-scale meta-barriers in attenuating seismic surface waves and transportation-induced vibrations in the most disastrous frequency range of 0–30 Hz. By developing analytical and three-dimensional numerical models, it evaluates the properties of the proposed meta-barrier and presents their effects on the attenuation range. Moreover, it discusses a simplified mass-spring-mass model of the meta-barrier, demonstrating that the attenuation range of a unit cell can be approximated using this model. The proposed design consists of three-dimensional two-layers (3D-2C) unit cells arranged periodically with different configurations to be placed between the wave source and structure. Specifically, the meta-barriers can be arranged gradually (periodic spacing along the length), widening the attenuation range to block nearly 85% of the most devastating waves using typically arranged stacked unit cells and triangular-like arrangement (double wedge). The results show that a typical stacked unit cells reflect the incoming waves towards the source, while using the double wedge design, the surface wave can be converted to bulk wave, thereby reducing the risk to the surroundings. Moreover, the study validates the attenuation range using three-dimensional time history analysis subjected to an artificial wavelet (Ormsby wavelet) and three actual seismic records (1975 Oroville, 1984 Bishop, and 2001 Anza time histories).

Acoustic wave propagation and scattering in visco-acoustic medium: Integral equation representation and De Wolf approximation

A visco-acoustic medium is an approximate representation of the absorption and attenuation characteristics of the actual earth medium, which will cause energy attenuation and velocity dispersion of seismic waves. The propagation law of scattered waves in viscoelastic media can be revealed through seismic wave forward simulation. However, the numerical simulation of scattered waves in a visco-acoustic medium using the De Wolf approximation method based on the Lippmann-Schwingr (L-S) equation has not been studied. Therefore, based on the Futterman dispersion relation, the mathematical expression of the integral equation of acoustic wave propagation and scattering in the visco-acoustic medium is derived. We combine the De Wolf approximation with the quality factor Q. The thin slab approximation and screen approximation methods are two realizations of the De Wolf approximation. The thin slab approximation and the screen approximation continuation operator in the viscous-acoustic medium are constructed and applied to the numerical simulation of the scattered wave field. The research results of the concave model and complex model indicate that due to the influence of medium viscosity, the energy of the deep reflected waves is weaker in the forward modeling records of the thin slab approximation method and screen approximation method, and the dominant frequency of seismic waves moves towards the low-frequency direction; Compared with the finite difference results, they only calculate one reflection, and there are no multiple wave signals in the seismic records. Finally, We discuss the thin slab approximation and the screen approximation method for detail around the division of the thickness of the thin slab, the selection of the reference frequency, and the non-uniformity of the medium.

Machine learning prediction of the mass and the velocity of controlled single-block rockfalls from the seismic waves they generate

Abstract. Understanding the dynamics of slope instabilities is critical to mitigate the associated hazards, but their direct observation is often difficult due to their remote locations and their spontaneous nature. Seismology allows us to get unique information on these events, including on their dynamics. However, the link between the properties of these events (mass and kinematics) and the seismic signals generated is still poorly understood. We conducted a controlled rockfall experiment in the Riou Bourdoux torrent (southern French Alps) to try to better decipher those links. We deployed a dense seismic network and inferred the dynamics of the block from the reconstruction of the 3D trajectory from terrestrial and airborne high-resolution stereophotogrammetry. We propose a new approach based on machine learning to predict the mass and the velocity of each block. Our results show that we can predict those quantities with average errors of approximately 10 % for the velocity and 25 % for the mass. These accuracies are as good as or better than those obtained by other approaches, but our approach has the advantage in that it does not require the source to be localised, nor does it require a high-resolution velocity model or a strong assumption on the seismic wave attenuation model. Finally, the machine learning approach allows us to explore more widely the correlations between the features of the seismic signal generated by the rockfalls and their physical properties, and it might eventually lead to better constraints on the physical models in the future.

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.

Effect of Melt on Polycrystal Anelasticity

AbstractThis study provides the quantitative assessment of the effect of melt on the polycrystal anelasticity by grain boundary sliding, which is necessary to evaluate the effect of melt on seismic wave velocity and attenuation. We measured elasticity, anelasticity, and viscosity of rock analog samples by changing temperature continuously from subsolidus to supersolidus. Our previous studies have shown that when homologous temperature exceeds 0.9, anelastic relaxation by grain boundary sliding is significantly enhanced, probably due to the increase in grain boundary disorder called pre‐melting. In this study, we found that when homologous temperature exceeds 1, grain boundary sliding is further enhanced by melt and that the viscoelastic property at supersolidus temperatures shows the combined total effect of disordered grain boundaries and melt. The relaxation strength due to melt depends on melt fraction, while that due to disordered grain boundaries does not. When melt fraction is very small (≪1%), the melt effect is negligibly small and the effect of disordered grain boundaries is dominant. Based on these experimental results, we present a new viscoelasticity model seamlessly applicable for a broad temperature range from subsolidus to supersolidus temperatures and for a broad frequency range from seismic waves to geodetic deformation. The new model covers an upper mantle region where a moderate amount of melt exists (e.g., near subduction zones). We further compare our data with those of rock samples and infer that a common physical mechanism, subsolidus and supersolidus enhancements on grain boundary sliding, may be dominant in these two data sets.

An Application of 3D Cross-Well Elastic Reverse Time Migration Imaging Based on the Multi-Wave and Multi-Component Technique in Coastal Engineering Exploration

Precise surveys are indispensable in coastal engineering projects. The extensive presence of sand in the coastal area leads to significant attenuation of seismic waves within unsaturated loose sediments. As a result, it becomes challenging for seismic waves to penetrate the weathered zone and reach the desired depth with significant amount of energy. In this study, the application of three-dimensional (3D) cross-well elastic reverse time migration (RTM) imaging based on multi-wave and multi-component techniques in coastal engineering exploration is explored. Accurate decomposition of vector compressional (P) and shear (S) waves is achieved through two wavefield decoupling algorithms without any amplitude and phase distortion. Additionally, compressional wave pressure components are obtained, which facilitates subsequent independent imaging. This study discusses and analyzes the imaging results of four imaging strategies under cross-correlation imaging conditions in RTM imaging. The analysis leads to the conclusion that scalarizing vector wavefields imaging yields superior imaging of P- and S-waves. Furthermore, the imaging results obtained through this approach are of great physical significance. In order to validate the efficacy of this method in 3D geological structure imaging in coastal areas, RTM imaging experiments were performed on two representative models. The results indicate that the proposed 3D elastic wave imaging method effectively generates accurate 3D cross-well imaging of P- and S-waves. This method utilizes the multi-wave and multi-component elastic wave RTM imaging technique to effectively leverage the Earth’s elastic medium without increasing costs. It provides valuable information about the distribution of subsurface rock layers, interfaces, and other structures in coastal engineering projects. Importantly, this can be achieved without resorting to extensive excavation or drilling operations. This method addresses the limitations of current cross-well imaging techniques, thereby providing abundant and accurate geological and geophysical information for the analysis and interpretation of 3D geological structures in coastal engineering projects. It has important theoretical and practical significance in real-world production, as well as for the study of geological structures in coastal engineering.

Improved numerical solution of anisotropic poroelastic wave equation in microseismicity: Graphic process unit acceleration and moment tensor implementation

AbstractThe accuracy and computational efficiency of full waveform forward modelling in poroelastic media are crucial for microseismic monitoring. It enables intuitive, precise and efficient simulation of subsurface responses, thereby improving the reliability of moment tensor inversion and seismic source mechanism interpretation. Additionally, it reflects the role of fluid effects in waveform evolution. In this paper, based on the Biot mechanism, we derived the first‐order velocity–stress equation of poroelastic media and discretized the model using a rotated staggered grid. The rotated staggered grid can well adapt to anisotropic media with high contrast parameters. We provide the finite difference formula based on graphic process unit–acceleration and moment tensor and also provide the graphic process unit workflow for forward modelling of anisotropic poroelastic media. First, two models with different grid sizes were run based on single graphic process unit, 1‐thread Central Processing Unit (CPU) and 16‐thread CPU. The results show that the speedup factors are approximately 14.3 and 3.7, respectively, compared with the running time of 1‐thread CPU and 16‐thread CPU. Then, we compare and evaluate the response of three basic source mechanisms (isotropic expansion, double couple and compensated linear vector dipole) in the model. The comparison of analytical and numerical results verifies the effectiveness of the method. Furthermore, wavefield snapshots of two typical anisotropic media (vertical transversely isotropic and horizontal transversely isotropic) are analysed to correspond to different moment tensor sources. The results showed that the source mechanism does not change the isotropic and anisotropic plane and the wave travel time, but it does change the polarization amplitude of the velocity component. The attenuation of slow qP‐wave increases along with the increase of the value of viscosity. The effect of permeability on wavefield appears with the opposite effect of viscosity. Finally, the seismic waveform differences between multi‐layer elastic media and poroelastic media are compared and analysed. The results showed that the seismic wavefield and waveform of poroelastic media are more complex, the propagation speed of seismic waves is faster, but the attenuation of seismic waves is stronger.