Wave Attenuation Model Research Articles

Seismic tomography of compressional wave attenuation structure for Kı̄lauea Volcano, Hawai‘i

AbstractWe present a frequency‐independent three‐dimensional (3‐D) compressional wave attenuation model (indicated by the reciprocal of quality factor Qp) for Kı̄lauea Volcano in Hawai‘i. We apply the simul2000 tomographic algorithm to the attenuation operator t* values for the inversion of Qp perturbations through a recent 3‐D seismic velocity model and earthquake location catalog. The t* values are measured from amplitude spectra of 26708 P wave arrivals of 1036 events recorded by 61 seismic stations at the Hawaiian Volcanology Observatory. The 3‐D Qp model has a uniform horizontal grid spacing of 3 km, and the vertical node intervals range between 2 and 10 km down to 35 km depth. In general, the resolved Qp values increase with depth, and there is a correlation between seismic activity and low‐Qp values. The area beneath the summit caldera is dominated by low‐Qp anomalies throughout the entire resolved depth range. The Southwest Rift Zone and the East Rift Zone exhibit very high Qp values at about 9 km depth, whereas the shallow depths are characterized with low‐Qp anomalies comparable with those in the summit area. The seismic zones and fault systems generally display relatively high Qp values relative to the summit. The newly developed Qp model provides an important complement to the existing velocity models for exploring the magmatic system and evaluating and interpreting intrinsic physical properties of the rocks in the study area.

Comparison of P‐wave attenuation models of wave‐induced flow

ABSTRACTWave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for P‐wave dispersion and attenuation at seismic frequencies. Hence, the P‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with White's and Johnson's models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.

Shear wave attenuation and micro-fluidics in water-saturated sand and glass beads.

An improvement in the modeling of shear wave attenuation and speed in water-saturated sand and glass beads is introduced. Some dry and water-saturated materials are known to follow a constant-Q model in which the attenuation, expressed as Q(-1), is independent of frequency. The associated loss mechanism is thought to lie within the solid frame. A second loss mechanism in fluid-saturated porous materials is the viscous loss due to relative motion between pore fluid and solid frame predicted by the Biot-Stoll model. It contains a relaxation process that makes the Q(-1) change with frequency, reaching a peak at a characteristic frequency. Examination of the published measurements above 1 kHz, particularly those of Brunson (Ph.D. thesis, Oregon State University, Corvalis, 1983), shows another peak, which is explained in terms of a relaxation process associated with the squirt flow process at the grain-grain contact. In the process of deriving a model for this phenomenon, it is necessary to consider the micro-fluidic effects associated with the flow within a thin film of water confined in the gap at the grain-grain contact and the resulting increase in the effective viscosity of water. The result is an extended Biot model that is applicable over a broad band of frequencies.

Three‐dimensional compressional wave attenuation tomography for the crust and uppermost mantle of Northern and central California

AbstractI present a frequency‐independent three‐dimensional (3‐D) compressional wave attenuation model (indicated by quality factor Qp) for the crust and uppermost mantle of Northern and central California. The tomographic inversion used t∗ values measured from amplitude spectra of 80,988 P wave arrivals of 3247 events recorded by 463 network stations through a 3‐D seismic velocity model. The model has a uniform horizontal grid spacing of 15 km, and the vertical node intervals range between 2 and 10 km down to 45 km depth. In general, the resulting Qp values increase with depth and agree with the surface geology at shallow depth layers. The most significant features observed in the Qp model are the high Qp values in the Sierra Nevada mountains and low Qp anomalies in the western fault zones. Low Qp values are also imaged in Owens Valley and Long Valley at shallow depths and the Cape Mendocino region in the lower crust (∼25 km depth). An overall contrast of Qp values across the fault is observed in the creeping, Parkfield and Cholame‐Carrizo sections of the San Andreas Fault. The new 3‐D Qp model provides an important complement to the existing regional‐scale velocity models for interpreting structural heterogeneity and fluid saturation of rocks in the study area.

Seismic attenuation tomography of the Northeast Japan arc: Insight into the 2011 Tohoku earthquake (Mw9.0) and subduction dynamics

Detailed three-dimensional (3-D) P and S wave attenuation (Qp and Qs) models of the crust and upper mantle under the entire Northeast Japan (Tohoku) arc from the Japan Trench to the Japan Sea coast are determined, for the first time, using a large number of high-quality t* data measured precisely from P and S wave spectra of local earthquakes. The suboceanic earthquakes used in this work are relocated precisely using sP depth phases. Our results reveal a prominent landward dipping high-Q zone representing the subducting Pacific slab, a landward dipping intermediate- to high-Q zone in the mantle wedge between the Pacific coast and the volcanic front, and significant low-Q anomalies in the crust and mantle wedge between the volcanic front and the Japan Sea coast. Prominent high-Q patches surrounded by low-Q anomalies are revealed in the interplate megathrust zone under the Tohoku fore arc where the great 2011 Tohoku-oki earthquake (Mw 9.0) occurred. The high-Q patches in the megathrust zone generally exhibit large coseismic slips of megathrust earthquakes and large slip deficit on the plate interface. We think that these high-Q patches represent asperities in the megathrust zone, whereas the low-Q anomalies reflect weakly coupled areas. We also find that the hypocenters of the 2011 Tohoku-oki interplate earthquakes (Mw > 7.0) are located in areas where Qp, Qs, and Qp/Qs change abruptly. These results suggest that structural heterogeneities in the megathrust zone control the interplate seismic coupling and the nucleation of megathrust earthquakes.

The Influence of Marine Environment to the Electromagnetic Field on the Wireless Network Communication

It is one of the important technologies to realize the wireless network communication in the special marine environment. The fog that contains salt and water above the surface of the sea has certain influence on the attenuation of electromagnetic field in the wireless communication. The attenuation coefficient of electromagnetic wave in such medium is discussed in this paper, by replacing the permittivity of the salty fog with that of the NaCl solution. And then such attenuation coefficient will be introduced to the electromagnetic fading model with the sight considered. Finally, this paper designs a electromagnetic wave attenuation model of the sea, which could provide some suggestions for establishing wireless communication network on the sea.

Experimental Studies of Sound Attenuation in Seabed Sediments on Column Sample Length Scale

Seabed sediment microstructure has an influence on its acousto-physical properties, and the properties in a length of the sediment column reflect an aspect of the macroscopic behavior of the microstructure. An original measurement method of the sound attenuation within small distance cross sections in a sediment column, and the corresponding approach in data processing to attain an attenuation factor are detailed in the paper. This method was used to measure the compressional wave in series of points with a small distance in the sediment column, and it is shown that exponential attenuation is a type of compressional wave attenuation model for a sediment column in its full length. It indicates that there are various models of compressional wave attenuation in seabed sediments in the South China Sea after comparison of data from other literature. The method of measuring sound attenuation satisfies the sampling space interval in the acoustical forward and inverse problems in seabed sediments, and the original method provides a new approach for finding out sound attenuation mechanism in seabed sediments on small length scale.

Field observations and modeling of wave attenuation over colonized beachrocks

Beachrocks are common coastal formations, constructed through the lithification of beach sediments by carbonate cements. The objectives of the present contribution were to (a) assess the impacts of beachrock benthic communities on nearshore wave dynamics; (b) present a numerical model, developed to simulate wave propagation over shallow nearshore waters characterized by both loose sediment beds and colonized/non-colonized beachrocks; and (c) discuss the structure and dynamics of beachrock macro-benthic communities in an E. Mediterranean micro-tidal beach (Vatera, Lesbos Island, NE Aegean Sea), as well as their interactions with the wave forcing. Field measurements of wave height and flow velocity were processed to assess shoaling wave energy dissipation due to bottom friction from the colonized beachrock outcrops. The equivalent Nikuradse hydraulic roughness of the beachrock surface, estimated through spectral wave attenuation calculations, was found to be around kN=0.13m. The corresponding wave friction factors were incorporated into a wave propagation model to obtain estimates of the wave-induced bed shear stress τw acting on the beachrock benthic communities. Information about the structure and characteristics of the latter was obtained through the collection and analysis of samples from 15 stations along a beach transect, during two months of the year (April and September) and the results showed that benthic communities at the beachrock habitat were very similar to the ones typically found at NE Mediterranean hard substrates. Wave-induced bed shear stress τw values were able to explain cross-shore variations in population density and biomass, both decreasing significantly above water depths of about h=1.8–2m. The latter values corresponded, for the studied conditions, to shear stresses of about τw=2.2Nt/m2. The present findings clearly show that nearshore wave patterns not only control to a certain extent the spatial structure of the beachrock habitats, but can be also influenced by them. Thus, hydrodynamics and beachrocks habitats constitute a complex system which remains very little understood and demands for further investigation.

Wave attenuation by submerged vegetation: combining the effect of organism traits and tidal current

Accurate wave height prediction along the shore plays an important role in coastal protection and management. To account for the effect of submerged vegetation in wave-attenuation models, it is important to understand how the interaction between vegetation characteristics and hydrodynamic forcing affects wave attenuation. To determine the effect of vegetation characteristics, we used seagrass mimics that varied in (1) blade stiffness, (2) shoot density and (3) leaf length; to investigate the effect of hydrodynamic forcing, we studied wave attenuation in the absence and presence of a tidal current. Results show that wave attenuation is positively correlated with blade stiffness and for a given wave in shallow water, attenuation is dependent on a combination of shoot density and leaf length, which can be described by the leaf area index. The presence of a tidal current strongly reduced the wave-attenuating capacity of seagrass mimics, and this reduction was most pronounced at high shoot densities. Thus, most studies that have been carried out under waves only will structurally overestimate wave attenuation for tidal environments, emphasising that tidal currents need to be taken into account in future studies on wave attenuation by vegetation.

Attenuation of elastic waves due to wave-induced vorticity diffusion in porous media

A theory for attenuation of elastic waves due to wave-induced vorticity diffusion in the presence of randomly correlated pore-scale heterogeneities in porous media is developed. It is shown that the vorticity field is associated with a viscous wave in the pore space, the so-called slow shear wave. The latter is linked to the porous medium acoustics through incorporation of the fluid strain rate tensor of a Newtonian fluid in the poroelastic constitutive relations. The method of statistical smoothing in random media is used to derive dynamic-equivalent elastic wave numbers accounting for the conversion scattering process into the slow shear wave. The result is a model for wave attenuation and dispersion associated with the transition from viscosity- to inertia-dominated flow regime in porous media. It is also shown that the momentum flux transfer from the slow compressional into the slow shear wave is a proxy for the dynamic permeability in porous media. A dynamic permeability model is constructed that consists of an integral over the covariance function of the random pore-scale heterogeneities modulated by the slow shear wave. In a smooth pore-throat limit, the results reproduce the dynamic permeability model proposed by Johnson etal. [J. Fluid Mech. 176, 379 (1987).]

Seismic Noise by Wind Farms: A Case Study from the Virgo Gravitational Wave Observatory, Italy

Abstract We present analyses of the noise wave field in the vicinity of Virgo, the Italian–French gravitational wave observatory located close to Pisa, Italy, with special reference to the vibrations induced by a nearby wind farm. The spectral contribution of the wind turbines is investigated using (1) onsite measurements, (2) correlation of spectral amplitudes with wind speed, (3) directional properties determined via multichannel measurements, and (4) attenuation of signal amplitude with distance. Among the different spectral peaks thus discriminated, the one at frequency 1.7 Hz is associated with the greatest power, and under particular conditions it can be observed at distances as large as 11 km from the wind farm. The spatial decay of amplitudes exhibits a complicated pattern, which we interpret in terms of the combination of direct surface waves and body waves refracted at a deep (≈800 m) interface between the Plio-Pleistocenic marine, fluvial, and lacustrine sediments and the Miocene carbonate basement. We develop a model for wave attenuation that allows determining the amplitude of the radiation from individual turbines, which is estimated on the order of for wind speeds over the 8–14 m/s range. On the basis of this model, we then develop a predictive relationship for assessing the possible impact of future wind farm projects.

A poroelastic model for ultrasonic wave attenuation in partially frozen brines

Although there are many possible mechanisms for the intrinsic seismic attenuation in composite materials that include fluids, relative motion between solids and fluids during seismic wave propagation is one of the most important attenuation mechanisms. In our previous study, we conducted ultrasonic wave transmission measurements on an ice-brine coexisting system to examine the influence on ultrasonic waves of the unfrozen brine in the pore microstructure of ice. In order to elucidate the physical mechanism responsible for ultrasonic wave attenuation in the frequency range of 350–600 kHz, measured at different temperatures in partially frozen brines, we employed a poroelastic model based on the Biot theory to describe the propagation of ultrasonic waves through partially frozen brines. By assuming that the solid phase is ice and the liquid phase is the unfrozen brine, fluid properties measured by a pulsed nuclear magnetic resonance technique were used to calculate porosities at different temperatures. The computed intrinsic attenuation at 500 kHz cannot completely predict the measured attenuation results from the experimental study in an ice-brine coexisting system, which suggests that other attenuation mechanisms such as the squirt-flow mechanism and wave scattering effect should be taken into account.

Porous medium acoustics of wave-induced vorticity diffusion

A theory for attenuation and dispersion of elastic waves due to wave-induced generation of vorticity at pore-scale heterogeneities in a macroscopically homogeneous porous medium is developed. The diffusive part of the vorticity field associated with a viscous wave in the pore space—the so-called slow shear wave—is linked to the porous medium acoustics through incorporation of the fluid strain rate tensor of a Newtonian fluid in the poroelastic constitutive relations. The method of statistical smoothing is then used to derive dynamic-equivalent elastic wave velocities accounting for the conversion scattering process into the diffusive slow shear wave in the presence of randomly distributed pore-scale heterogeneities. The result is a simple model for wave attenuation and dispersion associated with the transition from viscosity- to inertia-dominated flow regime.

A three‐dimensional model of wave attenuation in the marginal ice zone

A three‐dimensional model of wave scattering by a large array of floating thin elastic plates is used to predict the rate of ocean wave attenuation in the marginal ice zone in terms of the properties of the ice cover and the incoming wavefield. This is regarded as a small step toward assimilating interactions of ocean waves with areas of sea ice into oceanic general circulation models. Numerical results confirm previous findings that attenuation is predominantly affected by wave period and by the average thickness of the ice cover. It is found that the shape and distribution of the floes and the inclusion of an Archimedean draft has little impact on the attenuation produced. The model demonstrates a linear relationship between ice cover concentration and attenuation. An additional study is conducted into the directional evolvement of the wavefield, where collimation and spreading can both occur, depending on the physical circumstances. Finally, the attenuation predicted by the new three‐dimensional model is compared with an existing two‐dimensional model and with two sets of experimental data, with the latter producing convincing agreement.

Anisotropic dispersion and attenuation due to wave‐induced fluid flow: Quasi‐static finite element modeling in poroelastic solids

Heterogeneous porous media such as hydrocarbon reservoir rocks are effectively described as anisotropic viscoelastic solids. They show characteristic velocity dispersion and attenuation of seismic waves within a broad frequency band, and an explanation for this observation is the mechanism of wave‐induced pore fluid flow. Various theoretical models quantify dispersion and attenuation of normal incident compressional waves in finely layered porous media. Similar models of shear wave attenuation are not known, nor do general theories exist to predict wave‐induced fluid flow effects in media with a more complex distribution of medium heterogeneities. By using finite element simulations of poroelastic relaxation, the total frequency‐dependent complex stiffness tensor can be computed for a porous medium with arbitrary internal heterogeneity. From the stiffness tensor, velocity dispersion and frequency‐dependent attenuation are derived for compressional and shear waves as a function of the angle of incidence. We apply our approach to the case of layered media and to that of an ellipsoidal poroelastic inclusion. In the case of the ellipsoidal inclusion, compressional and shear wave modes show significant attenuation, and the characteristic frequency dependence of the effect is governed by the spatiotemporal scale of the pore fluid pressure relaxation. In our anisotropic examples, the angle dependence of the attenuation is stronger than that of the velocity dispersion. It becomes clear that the spatial attenuation patterns show specific characteristics of wave‐induced fluid flow, implying that anisotropic attenuation measurements may contribute to the inversion of fluid transport properties in heterogeneous porous media.

Three-dimensionalQp- andQs-tomography beneath Taiwan orogenic belt: implications for tectonic and thermal structure

SUMMARY We determined the 3-D Qp- and Qs- structure of the Taiwan orogenic belt to enhance understanding of the related tectonic and thermal structure beneath the collision zone. The inversion used t* values measured from the spectra of P and S waves from the dense Taiwan strong motion network for moderate size earthquakes (ML 4.5–5.5) to avoid source complexity. The time period, 1991–2007, includes the aftershock sequence of the 1999 Chi-Chi earthquake that provides good ray coverage in central Taiwan. Over 18 000 velocity spectra from 883 earthquakes were analysed. A non-linear least square technique is applied to the spectra for t* determination by assuming a ω−2 source model for the frequency band of 1–30 Hz. A frequency-independent Q was assumed in this study. The corner frequency of a specific event was fixed for the corresponding stations, and a quality index was defined to assure good quality data for the inversion. The results reveal the sharp variation of Qp and Qs across the recently ruptured Chelungpu Fault, and the Kaoping and Chaochou Faults in Pingtung Plain. The Q values in the hangingwall are smaller by about 85 and 110 for Qp and Qs, respectively, relative to the footwall. The fault geometry is distinctly delineated by the contour of Qp/Qs of 1.2 that extends to the depth of the geologically identified decollement structure. Beneath the Central Range, the low Qp, low Qs and high Qp/Qs features coincide well with the aseismic zone. Comparison to the recent thermomechanical numerical models of Taiwan shows that the low Q zone corresponds to the exhumation of the lower crust. The low Qs regime (high attenuation) beneath the Central Ranges at the depth of 5–22 km coincides with predicted temperatures of 400–600 °C. The Qs comparison with the major tectonic and thermal mechanical models of Taiwan reveals that the shear wave attenuation model contains comprehensive rheological and thermal information of relevance to understanding mountain building processes. This technique appears particularly useful for distinguishing strong and weak crustal regions in the absence of other constraints.

A Simultaneous Multiphase Approach to Determine P-Wave and S-Wave Attenuation of the Crust and Upper Mantle

Abstract We have generalized the methodology of our regional amplitude tomography from the Lg phase to the four primary regional phases ( Pn , Pg , Sn , Lg ). Differences in the geometrical spreading, source term, site term, and travel paths are accounted for, while event source parameters such as seismic moment are consistent among phases. In the process, we have developed the first comprehensive regional P -wave and S -wave attenuation model of the crust and upper mantle by simultaneously using the amplitudes of four regional phases. When applied to an area encompassing the Middle East, eastern Europe, western Asia, south Asia, and northeast Africa for the 1–2 Hz passband, we find large differences in the attenuation of the lithosphere across the region. The tectonic Tethys collision zone has high attenuation, while stable outlying regions have low attenuation. While crust and mantle Q variations are often consistent, we do find several notable areas where they differ considerably but are appropriate given the region’s tectonic history. Lastly, the relative values of Qp and Qs indicate that scattering Q is likely the dominant source of attenuation in the crust at these frequencies.

On the estimation of ice thickness from scattering observations

This paper is inspired by the proposition that it may be possible to extract descriptive physical parameters – in particular the ice thickness, of a sea-ice field from ocean wave information. The motivation is that mathematical theory describing wave propagation in such media has reached a point where the inherent heterogeneity, expressed as pressure ridge keels and sails, leads, thickness variations and changes of material property and draught, can be fully assimilated exactly or through approximations whose limitations are understood. On the basis that leads have the major wave scattering effect for most sea-ice [Williams, T.D., Squire, V.A., 2004. Oblique scattering of plane flexural-gravity waves by heterogeneities in sea ice. Proc. R. Soc. Lon. Ser.-A 460 (2052), 3469–3497], a model two dimensional sea-ice sheet composed of a large number of such features, randomly dispersed, is constructed. The wide spacing approximation is used to predict how wave trains of different period will be affected, after first establishing that this produces results that are very close to the exact solution. Like Kohout and Meylan [Kohout, A.L., Meylan, M.H., 2008. An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone. J. Geophys. Res. 113, C09016, doi:10.1029/2007JC004434], we find that on average the magnitude of a wave transmitted by a field of leads decays exponentially with the number of leads. Then, by fitting a curve based on this assumption to the data, the thickness of the ice sheet is obtained. The attenuation coefficient can always be calculated numerically by ensemble averaging but in some cases more rapidly computed approximations work extremely well. Moreover, it is found that the underlying thickness can be determined to good accuracy by the method as long as Archimedean draught is correctly provided for, suggesting that waves can indeed be effective as a remote sensing agent to measure ice thickness in areas where pressure ridges are not sizeable, i.e. away from coastal regions of high deformation.

Anelastic Earth structure from the coherency of the ambient seismic field

Cross correlation of the ambient seismic field is now routinely used to measure seismic wave travel times; however, relatively little attention has been paid to other information that could be extracted from these signals. In this paper we demonstrate the relationship between the spatial coherency of the ambient field and the elastodynamic Green's function in both time and frequency domains. Through measurement of the frequency domain coherency as a function of distance, we sequentially recover phase velocities and attenuation coefficients. From these measurements we generate 1‐D shear wave velocity and attenuation models for southern California. The ambient field measurements of attenuation and the exceptional path coverage that results from the many possible interstation measurements allow us to extend Q estimates over a range of frequencies that has previously been difficult to analyze using earthquake data. Measurements from paths that cross major sedimentary basins show both lower wave speeds and lower‐quality factors than other paths, as expected. Our results indicate that there is a wealth of information available in the spatial coherency of the ambient seismic field.

An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone

We present a model for wave attenuation in the marginal ice zone (MIZ) based on a two‐dimensional (one horizontal and one vertical dimension) multiple floating elastic plate solution in the frequency domain, which is solved exactly using a matched eigenfunction expansion. The only physical parameters that enter the model are length, mass, and elastic stiffness (of which, the latter two depend primarily on thickness) of the ice floes. The model neglects all nonlinear effects as well as floe collisions or ice creep and is therefore most applicable to floes which are large compared to the thickness and to wave conditions which are not extreme. The solution for a given arrangement of floes is fully coherent, and the results are therefore dependent on the exact geometry. We firstly show that this dependence can be removed by averaging over a distribution of floe lengths (we choose the Rayleigh distribution). We then show that after this averaging, the attenuation coefficient is a function of floe number and independent of floe length, provided the floe lengths are sufficiently large. The model predicts an exponential decay of energy, just as is shown experimentally. This enables us to provide explicit values for the attenuation coefficient, as a function of the average floe thickness and wave period. We compare our theoretical predictions of the wave attenuation with measured data and other scattering models. The limited data allows us to conclude that our model is applicable to large floes for short to medium wave periods (6 to 15 seconds). We also derive a floe breaking model, based on our wave attenuation model, which indicates that we are under‐predicting the attenuation coefficients at long periods.