Attenuation Of Seismic Waves Research Articles

Modelling regional-scale attenuation across Italy and the Tyrrhenian Sea

Modelling regional-scale attenuation of seismic waves at ~1 Hz is challenging, especially when these waves propagate across both continental and oceanic crust. Recent developments in seismic imaging and modelling have provided us with the computational tools necessary to reconstruct these mixed settings using deterministic (coherent) and stochastic (coda) information. Here, we present new tomographic maps of coda-attenuation for both the Italian peninsula and the Tyrrhenian Sea. Kernel-based coda attenuation imaging in the diffusive approximation is tested in the oceanic environment, highlighting a non-diffusive behaviour across the Southern Tyrrhenian Sea. Joint deterministic and Radiative Transfer forward modelling of coherent and scattered waves (Radiative3D) is then performed for the portion of this area showing the lowest coda attenuation. The corresponding parametric study shows that coda attenuation is an efficient marker of variations of Moho depths and crustal reverberations, such as those we observe in a transitional area (characterized by continental crust and thicker Moho) between two oceanic basins (Vavilov and Marsili). Diffusive tomographic imaging informed by Radiative3D modelling reconstructs high-attenuation patterns along the Italian peninsula in agreement with the thick sediments cover across the Po Plain and the Adriatic coast and the magmatic systems in the Central Campanian province. A combined approach of coda-attenuation imaging and modelling can constrain Moho depth and spatial variations of seismic attenuation at regional scale and in mixed continental-oceanic settings.

Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media

Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation in attenuating media, where the real and imaginary parts of the eikonal function capture dispersion effects and amplitude attenuation of seismic waves, respectively. Conventionally, such a complex-valued eikonal is mainly computed either by tracing rays exactly in complex space or by tracing rays approximately in real space so that the resulting eikonal is distributed irregularly in real space. However, seismic data processing methods, such as prestack depth migration and tomography, usually require uniformly distributed complex-valued eikonals. Therefore, we have developed a unified framework to Eulerianize several popular approximate real-space ray-tracing methods for complex-valued eikonals so that the real and imaginary parts of the eikonal function satisfy the classic real-space eikonal equation and a novel real-space advection equation, respectively, and we dub the resulting method the Eulerian partial-differential-equation method. We further develop highly efficient high-order methods to solve these two equations by using the factorization idea and the Lax-Friedrichs weighted essentially nonoscillatory schemes. Numerical examples demonstrate that our method yields highly accurate complex-valued eikonals, analogous to those from ray-tracing methods. Our methods can be useful for migration and tomography in attenuating media.

Wave propagation in the poro-viscoelastic orthorhombic two-phase media: plane-wave theory and wavefield simulation

SUMMARY Most researches on the Biot-squirt (BISQ) model are limited to the poroelastic transverse isotropic (TI) media. Actually, the poro-viscoelasticity and the orthorhombic anisotropy are closer to the realistic properties of many reservoir media. Therefore, we expand the BISQ model theory to the poro-viscoelastic orthorhombic media and develop the corresponding constitutive relation and 3-D wave equations in the time domain. Here, the generalized Zener linear body model is introduced to describe the relaxation effect of the solid skeleton, and the pore fluid is assumed to be saturated. The expressions of the complex and phase velocities for two quasi-compressional waves qP fast (qP1) and qP slow (qP2), and two quasi-shear waves qS1 and qS2 are obtained from the homogeneous plane-wave analysis, respectively. While introducing the viscoelasticity to our model, the attenuation value predicted by the conventional quality factor is not accurate, and the group velocity representing the position of the wave front in the poroelastic model becomes meaningless. So we derive the novel quality factor and the energy velocity expression by invoking the energy balance equation and the Poynting theorem. Two examples are implemented. First, the 3-D multicomponent wavefield is simulated. The snapshots show the orthorhombic anisotropy and viscoelastic effects lead to significant changes in the wavefield. The comparison to the synthetic seismogram in the poroelastic model indicates that the relaxed skeleton can describe the strong attenuation of seismic waves in the seismic exploration band. Secondly, the variations in the velocities and the quality factor curves with propagation direction, frequency and porosity are analysed. Both examples present the characteristics of wave propagation in the poro-viscoelastic orthorhombic media and validate the correctness of the proposed theory and equations.

NUMERICAL ALGORITHM OF SEISMIC ATTENUATION ESTIMATION IN ANISOTROPIC FRACTURED POROUS FLUID-SATURATED MEDIA

In our work we investigate the effect of transport and elastic properties anisotropy on seismic attenuation due to fracture-to-fracture wave-induced fluid flow using numerical algorithm of estimation of seismic wave attenuation in anisotropic fractured porous fluid-saturated media. Algorithm is based on numerical solution of anisotropic Biot equations using finite-difference scheme on staggered grid. We perform a set of numerical experiments to model wave propagation in fractured media with anisotropic fractured-filling material providing wave-induced fluid flow within interconnected fractures. Recorded signals are used for numerical estimation of inverse quality factor. Results demonstrate the effect of fracture-filling material anisotropy on seismic wave attenuation.

Intraplate earthquakes in the Potiguar Basin, Brazil: Evidence for superposition of local and regional stresses and implications for moderate-size earthquake occurrence

The understanding of earthquake occurrence in intraplate areas has been one of the most challenging tasks in Seismology. The attenuation of seismic waves in these areas is lower compared to border plate regions. Therefore, even moderate magnitude earthquakes can represent a great hazard. In this case, assessing the stress field in the intraplate areas is important to better understanding the earthquake generating mechanisms. We analyzed 241 earthquakes of the 2017 seismic sequence in the NW part of the Potiguar Basin and estimated the stress regime. Seismically defined faults were determined for four high-precision relocated NW-SE- and NE-SW-trending clusters. Faulting intersection acting in one of these clusters was representative for suggesting an intersection model for intraplate earthquakes to explain why moderate size earthquakes occur in the study region. Another cluster presented a seismically defined fault vertically segmented with a clear spatiotemporal evolution and occurrence of almost entire activity in a very short period, which suggest energy build-up and rapid release between its fault segments. We calculated the composite focal mechanism for three clusters, with predominant strike-slip faulting with a sinistral movement. The inversion of focal mechanisms reinforces evidence for a superposition of local and regional stresses, with major compressional axis subparallel to the continental equatorial margin.

The method of fundamental solutions for the elastic wave scattering in a double-porosity dual-permeability medium

For materials that have a matrix porosity at the microscopic scale, and an interconnecting fracture system at the mesoscopic scale, the double-porosity dual-permeability model provides a better prediction of seismic wave attenuation than the single porosity model, due to the flow exchange mechanism between these different size pores. The current work offers for the first time a numerical solution tool based on the method of fundamental solutions for problems of 3-D wave scattering and dynamic stress concentration around scatterers, such as cavities and embedded inhomogeneous inclusions, in an infinite double-porosity dual-permeability medium. The method of fundamental solutions is based on the spherical wave potentials representing three compressional waves and one shear wave. The accuracy and stability of the method are tested against other available results, and are demonstrated to be excellent. Wave scattering and dynamic stress concentration problems due to spherical cavity and poroelastic inclusion are then investigated for incident plane P1 and SV waves in the frequency domain. The research shows that the seismic responses are sensitive to the incident frequency, the boundary drainage condition, and material properties such as porosity.

Pre-stack Q estimation based on inverse spectral decomposition

The quality factor can quantitatively measure the attenuation of seismic waves, and it can compensate for seismic wave amplitude attenuation and correct the phase distortion. The traditional Q extraction method uses the post-stack seismic data to extract the Q-factor. Due to the low-pass filtering effect of the stacked seismic data, the obtained quality factor may be inaccurate. A method of estimating the quality factor using pre-stack common midpoint (CMP) gather data is proposed in this paper. In this method, inversion spectrum decomposition (ISD) and shaping regularization are introduced to obtain the Q-factor. During the process, we obtained the average-Q through inversion and finally obtained the internal-Q by using the average-Q. The numerical simulation and field data application show that the Q obtained using this method can accurately identify the oil-bearing area. Then, the Q is applied to the inverse Q-filter and produces seismic data with a high resolution and a high signal-to-noise ratio.

Combined effects of permeability and fluid saturation on seismic wave dispersion and attenuation in partially-saturated sandstone

Knowledge of dispersion and attenuation is essential for better reservoir characterization and hydrocarbon identification. However, limited by reliable laboratory data at seismic frequency bands, the roles of rock and fluid properties in inducing dispersion and attenuation are still poorly understood. Here we perform a series of laboratory measurements on Bentheimer and Bandera sandstone under both vacuum-dry and partially water-saturated conditions at frequencies ranging from 2 to 600 Hz. At vacuum-dry conditions, the bulk dispersion and attenuation in Bandera sandstone with more clay contents are distinctly larger than those in Bentheimer sandstone, suggesting clay contents might contribute to the inelasticity of the rock frame. The partially water-saturated results show the combined effects of rock permeability and fluid saturation on bulk dispersion and attenuation. Even a few percent of gas can substantially dominate the pore-fluid relaxation by providing a quick and short communication path for pore pressure gradients. The consequent bulk dispersion and attenuation are negligible. Only as the samples are approaching fully water-saturated conditions, rock permeability begins to play an essential role in the pore-fluid relaxation. For Bandera sandstone with lower permeability, a partially relaxed status of pore fluids is achieved when the gas saturation is lower than 5%, accompanied by significant attenuation and dispersion. Cited as : Wei, Q., Wang, Y., Han, D., Sun, M., Huang, Q. Combined effects of permeability and fluid saturation on seismic wave dispersion and attenuation in partially-saturated sandstone. Advances in Geo-Energy Research, 2021, 5(2): 181-190, doi: 10.46690/ager.2021.02.07

Attenuation of Seismic Waves in Partially Saturated Berea Sandstone as a Function of Frequency and Confining Pressure

Frequency-dependent attenuation (1/Q) should be used as a seismic attribute to improve the accuracy of seismic methods and imaging of the subsurface. In rocks, 1/Q is highly sensitive to the presence of saturating fluids. Thus, 1/Q could be crucial to monitor volcanic and hydrothermal domains and to explore hydrocarbon and water reservoirs. The experimental determination of seismic and teleseismic attenuation (i.e., for frequencies < 100 Hz) is challenging, and as a consequence, 1/Q is still uncertain for a broad range of lithologies and experimental conditions. Moreover, the physics of elastic energy absorption (i.e., 1/Q) is often poorly constrained and understood. Here, we provide a series of measurements of seismic wave attenuation and dynamic Young’s modulus for dry and partially saturated Berea sandstone in the 1–100 Hz bandwidth and for confining pressure ranging between 0 and 20 MPa. We present systematic relationships between the frequency-dependent 1/Q and the liquid saturation, and the confining pressure. Data in the seismic bandwidth are compared to phenomenological models, ultrasonic elastic properties and theoretical models for wave-induced-fluid-flow (i.e., squirt-flow and patchy-saturation). The analysis suggests that the observed frequency-dependent attenuation is caused by wave-induced-fluid-flow but also that the physics behind this attenuation mechanism is not yet fully determined. We also show, that as predicted by wave-induced-fluid-flow theories, attenuation is strongly dependent on confining pressure. Our results can help to interpret data for near-surface geophysics to improve the imaging of the subsurface.

Porosity Estimation of a Porous Goaf Area Based on Seismic Wave Attenuation

In underground coalmines, the porosity of the goaf area is a significant indicator for evaluating the working face stability and subsidence of the ground surface. However, porosity is difficult to measure directly in a closed goaf. To overcome this, we investigated seismic wave attenuation and elastic velocity changes through porous rock by laboratory measurements using compressed porous rock and coal samples consisting of crushed coal and rock particles. The attenuation of seismic waves through porous rock is strongly influenced by porosity. However, for equal porosity, compressed porous media comprising large particles shows lower seismic attenuation than media with smaller particles. To evaluate seismic attenuation and elastic velocity changes in rock/coal with different porosities, we investigated the effect of particle size (D) and seismic wavelength (λ). We developed a new seismic attenuation model (the Revision model) based on the multi-fractured rock attenuation model by Boadu and Long (Geophysical Journal International 127(1):86–110, 1996). The Revision model accounts for (i) greater attenuation through fragmented rock due to increased contact points between the particles, and (ii) decreased attenuation caused by network propagating through the porous media. The Revision model was applied to the laboratory measurement results of ultrasonic wave attenuation using compressed porous rock and coal samples, and good agreement was found for various porosities, particle sizes and wavelength. Thus, the Revision model may be a useful tool for estimating the porosity in a goaf based on measurements of seismic attenuation and velocity change.

Investigation and Control of the Blasting-Induced Ground Vibration under Cold Condition

This paper focuses on the investigation and control of the blasting-induced ground vibration under cold condition. The mechanical performance and wave propagation characteristics of the frozen rock mass are quite different from that of the conventional condition. Laboratory tests were implemented to investigate the wave impedance of rock mass in the frozen, saturated, normal, and drying states. Results reveal the longitudinal wave velocity could be enlarged by 40 percent in the frozen state. Then long-term monitoring of blasting vibration was implemented based on the blasting excavation of the Fengman hydropower station reconstruction project in the north of China. Results demonstrate the PPV and frequency both attenuate much slower when the rock mass is frozen, and the obvious turning points of PPV could be found between different temperatures, where the change of the PPV relationship happens. At last, numerical simulation of the blasting seismic wave attenuation and the response in the protected structure was implemented. The equivalent freezing simulation method was proposed and verified with the site experiment data. Results demonstrate that the attenuation coefficient decreases obviously as the frozen depth of the rock mass increases. The dynamic degree response in structure is much stronger and the maximum charge weight per delay was limited more strictly under the frozen condition. A most adverse frozen depth was determined when the charge weight per delay gets the minimum value. With the above control approaches, a total of 676 blasting was completed in Fengman hydropower station reconstruction and no case of excessive measurement could be found.

Seismic Wave Attenuation and Dispersion Due to Partial Fluid Saturation: Direct Measurements and Numerical Simulations Based on X‐Ray CT

AbstractQuantitatively assessing seismic attenuation caused by fluid pressure diffusion (FPD) in partially saturated rocks is challenging because of its sensitivity to the spatial fluid distribution. To address this challenge we performed depressurization experiments to induce the exsolution of carbon dioxide from water in a Berea sandstone sample. In a first set of experiments we used medical X‐ray computed tomography (CT) to characterize the fluid distribution. At an equilibrium pressure of approximately 1 MPa and applying a fluid pressure decline rate of approximately 0.6 MPa per minute, we allowed a change in saturation of less than 1%. The gas was heterogeneously distributed along the length of the sample, with most of the gas exsolving near the sample outlet. In a second set of experiments, at the same pressure and temperature, following a very similar exsolution protocol, we measured the frequency dependent attenuation and modulus dispersion between 0.1 and 1,000 Hz using the forced oscillation method. We observed significant attenuation and dispersion in the extensional and bulk deformation modes, however, not in the shear mode. Lastly, we use the fluid distribution derived from the X‐ray CT as an input for numerical simulations of FPD to compute the attenuation and modulus dispersion. The numerical solutions are in close agreement with the attenuation and modulus dispersion measured in the laboratory. Our approach allows for accurately relating attenuation and dispersion to the fluid distribution, which can be applied to improving the seismic monitoring of the subsurface.

Estimation of Seismic Attenuation of the Greenland Ice Sheet Using 3‐D Waveform Modeling

AbstractWe estimated the seismic attenuation (Q factor) of the Greenland Ice Sheet (GrIS) by comparing observed and theoretical Rayleigh waveforms. Observed waveforms are obtained by interfering noise waveforms in vertical‐component seismograms between stations belonging to the latest broadband seismic network distributed throughout Greenland (GLISN network). Theoretical waveforms are calculated by parallel computation using the latest 3‐D seismic waveform modeling method. Comparing the observed waveforms with the theoretical waveforms at different Q factors reveals that the GrIS has a low Q of 10 ≤ QP, QS ≤ 50, indicating very high attenuation of seismic waves due to the ice. This study is the first to establish the low Q factor of ice sheets via ultra‐long‐distance propagation (350−1,000 km). The Q factors obtained in this study are indispensable for estimating the thermal state and density distribution of the GrIS, as well as for interpreting the characteristics of seismic waveform that propagates through the GrIS.

Seismic resolution enhancement by the Curvelet transform

Zone A in Nanpu Sag of Bohai Bay has the characteristics of multiple provenances, multiple sedimentary systems, fast phase transition, many faults, a short fault distance, thin reservoirs and rapid lateral changes. At present, due to the low resolution of seismic data and thin sand layer of the target formation, it is difficult to depict the channel sand body, and it is also difficult to meet the requirements of accurately implementing low amplitude structures, reservoir prediction and well location deployment. When a seismic wave propagates in the stratum, it has the characteristics of multi-scale, multi-resolution and multi-directionality, while the Curvelet transform has the advantage of expressing these characteristics. In this paper, according to the geological characteristics and seismic response characteristics of continental thin interbedded strata in zone A, the seismic data are first transformed to the Curvelet domain. Then, the formation absorption and seismic wave attenuation are compensated in the Curvelet domain. Lastly, the data mentioned above are inversely transformed into the time–space domain. This paper presents the method and process of using the Curvelet transform to enhance the resolution of seismic data in thin interbedded strata. The application of a theoretical model and field data show that this method can effectively enhance the resolution of seismic data while maintaining a high signal-to-noise ratio. The innovative use of this method in zone A lays the foundation for the follow-up work of this structure.

Attenuation of seismic waves in partially saturated Berea sandstone as a function of frequency and confining pressure

Attenuation of seismic waves in partially saturated Berea sandstone as a function of frequency and confining pressure

The Effect of Pressure on Grain‐Growth Kinetics in Olivine Aggregates With Some Geophysical Applications

AbstractThe effect of pressure on grain‐growth kinetics of olivine was investigated up to 10 GPa at 1773 K under relatively water‐poor conditions. The results are interpreted using a relation to obtain the activation volume = 5.0 ± 1.1 cm3/mol for n = 2 or = 5.2 ± 1.1 cm3/mol for n = 3. The small activation volume means that grain‐growth kinetics in pure olivine aggregates is fast even in the dry deep upper mantle, implying that grain‐size is controlled by the pinning by other phases or by dynamic recrystallization except for the early stage after the phase transformation from wadsleyite in upwelling materials. The present results are applied to seismic wave attenuation that is likely controlled by grain‐boundary processes. The inferred peak in attenuation just below the oceanic lithosphere‐asthenosphere boundary from the NoMelt array is difficult to be explained by the pressure effects assuming the absorption band behavior because such a model requires a much larger activation volume than determined in this work and it also fails to explain high attenuation in the deep asthenosphere. This suggests that either melt accumulation or other processes such as elastically accommodated grain‐boundary sliding (EAGBS) is responsible for the peak in attenuation. The present results are also applied to EAGBS. We suggest that the deep upper mantle is likely to be relaxed by EAGBS, which implies that the shear velocity of the deep upper mantle can be several percent smaller than that inferred from single crystal elasticity.

Seismic metamaterials with cross-like and square steel sections for low-frequency wide band gaps

This study investigates the propagation of Lamb waves in seismic metamaterials (SMs) assembled using periodically arranged cross-like and square steel sections in a soil medium to assess the feasibility of their use for seismic wave attenuation. Four types of SMs with different steel sections were considered. The finite element method was used to carry out numerical simulations to investigate the band gap characteristics, vibration modes, and the effects of various parameters of the SMs. The results show that SMs with three complete band gaps (CBGs) below 20 Hz are of particular interest for low-frequency vibration control. The SMs composed of square steel sections exhibit a more favorable performance as compared to the SMs composed of cross-like steel sections in terms of the formation of wider CBGs. The volume fraction of steel is beneficial for enlarging the CBGs by planarizing the upper and lower edges of a single CBG. Moreover, geometric and material parameters play important roles in the band gap distributions. A vibration simulation analysis was carried out to simulate the seismic wave propagation through the SMs to the buildings, and the results indicate that Bragg scattering is the formation mechanism for the first CBG of the four SMs. This study provides a new way to build SMs by designing the volume fraction and steel section shapes to provide ultra-low and broad-band frequency vibration isolation capabilities that will allow the shielding of seismic waves in specific frequency ranges.

Modelling viscoelastic wave phenomenon by homogenisation of the poroelasticity equations

Poroelastic effects have been of great interest in the seismic literature as they have been identified as a major cause of wave attenuation in heterogeneous porous media. The observed attenuation in the seismic wave can be explained in part by energy loss to fluid motion in the pores. On the other hand, it is known that the attenuation is particularly pronounced in stratified structures where the scale of spatial heterogeneity is much smaller than the seismic wavelength. Understanding of poroelastic effects on seismic wave attenuation in heterogeneous porous media has largely relied on numerical experiments. In this work, we present a homogenisation technique to obtain an upscaled viscoelastic model that captures seismic wave attenuation when the sub-seismic scale heterogeneity is periodic. The upscaled viscoelastic model directly relates seismic wave attenuation to the material properties of the heterogeneous structure. We verify our upscaled viscoelastic model against a full poroelastic model in numerical experiments. Our homogenisation technique suggests a new approach for solving coupled equations of motion.

Monitoring of seismic attenuation change associated with vapor-liquid phase transition using time-lapse reflection seismic data in Kakkonda geothermal field, Japan

Seismic wave attenuation can potentially be used for the investigation of the fluid phase and flow properties in a fractured reservoir. However, seismic attenuation estimation is easily affected by various factors, such as tuning effects, source and receiver coupling, and effects from near-surface weathering layers. Time-lapse seismic attenuation estimation can avoid these problems because the above factors are canceled between surveys. We conducted time-lapse attenuation estimation using three reflection seismic surveys with different timings acquired in the Kakkonda geothermal field during a 12-day period spanning a well shut-in period. To investigate geothermal fluid changes associated with increased pore pressure, we propose an approach for estimating attenuation changes between time-lapse seismic surveys. Firstly, three seismic reflection sections were obtained from the corresponding time-lapse seismic data using the modified prestack time migration method, which can handle the uncertainties of migration velocity estimation in a highly fractured and structurally very complex medium, for which accurate velocity estimation is difficult to achieve using conventional methods. Then, time-lapse attenuation was evaluated for two of the three seismic reflection sections using the spectral ratio and the centroid frequency shift methods. Numerical modeling was conducted to verify our proposed procedure. Careful preprocessing was carried out to enhance the repeatability of time-lapse seismic data, especially on the frequency content, which is indirectly related to seismic attenuation. Finally, we demonstrated an increase of attenuation associated with an increase of pore pressure in and around the known super-shallow vapor-dominated reservoir during a short period (7 days) spanning from one day before the shut-in of producing well to a week after that. A possible cause of this short-period attenuation increase could be the vapor-liquid phase transition in the reservoir.

Seismic Wave Attenuation: A Promising Seismic Attribute for Gas and Oil Industry

Seismic Wave Attenuation: A Promising Seismic Attribute for Gas and Oil Industry