Scattering Attenuation Coefficients Research Articles

Depth and Spatial Variation of the Shear Wave Attenuation Parameters in the Shallow Crust and Lower Crust/Upper Mantle of Mt. Etna (Italy)

AbstractSeismic wave attenuation is a key feature of seismic wave propagation that provides constraints on the composition and physical state of the medium within the Earth. We separated intrinsic and scattering attenuation coefficients for the shallow crust and lower crust/upper mantle in the Mt. Etna area. For this purpose, the Multiple Lapse Time Window Analysis (MLTWA) was applied to two groups of earthquakes, well separated in depth. We also studied the spatial variation of the attenuation parameters by dividing the study area into four sectors around Etna. The results show an effective homogeneity of the propagation characteristics inside Etna and, in particular, some lateral variations and minor variations with depth. We observe that structural discontinuities and lithology control scattering losses at all frequencies, with higher scattering in the shallow crust. The intrinsic absorption shows no sensitivity to the presence of these main geological structures and is quite uniform for different depths. Furthermore, compared to the northern sector of the volcano, the southern one shows stronger scattering attenuation at low frequencies. This pattern correlates well with the high seismic activity along most of Etna’s active tectonic structures and ascending magmatic fluids that characterize this sector of the volcano. Although we only discuss the differences in the "average" scattering and inelastic properties of the investigated volumes, the results of this study are very informative about the characteristics of each region. Moreover, they suggest that a future study is necessary, providing a more detailed picture of the spatial distribution of seismic attenuation in the study area, through a 3D inversion of the attenuation parameters estimated along the single source-receiver paths.

Boundary effects of anisotropic medium on cloaking under shallow-water waves

The cloaking of offshore structures exposed to water waves can effectively protect them from hydrodynamics. In this study, an anisotropic medium designed by applying the space transformation method was used to cloak offshore structures exposed to shallow-water waves. By designing a theoretical cloaking space, the wave path could be controlled to bypass a certain area and cloak the structure within the wave field. Based on the form invariance of the shallow-water wave-governing equation, this unique wave path can be physically created using an anisotropic medium that includes water depth and gravity acceleration. First, an anisotropic medium was designed to cloak a single cylinder. The effects of the no-flux inner boundary conditions of the anisotropic medium on cloaking were investigated. The total- and scattered-wave distributions around the structure were calculated and analyzed. The scattering attenuation coefficient was used to measure the cloaking effect. In addition, a numerical truncation method for the medium parameters near the inner boundary was proposed and investigated to analyze the singularity of the medium parameters near the inner boundary. Moreover, an anisotropic medium was introduced to cloak multibody structures in water waves using simplified parameters. The results indicated that the inner area could also be protected without a no-flux boundary. Cloaking was effective in a simplified anisotropic medium. An anisotropic medium with simplified parameters can successfully cloak multibody structures exposed to shallow-water waves.

Measuring optical properties of clear and turbid media with broadband spectral interferometry.

The group index, n g, group velocity dispersion (GVD), and scattering attenuation coefficient, μ s, were measured for dilutions of glycerol, ethanol, and Intralipid 20% with water. Experiments were performed with a supercontinuum laser based Mach-Zehnder spectroscopic interferometry setup for wavelengths between 400 and 930nm. All optical properties could be retrieved from a single calibrated measurement of the interference spectrum. Scattering attenuation was determined from the envelope of the interference. The group index and GVD were retrieved from the unwrapped spectral phase. It was found that the group indices of glycerol and ethanol dilutions are in accordance with the Lorentz-Lorenz mixing formula. The scattering attenuation matches well to a semi-empirical model based on the Twerksy effective packing fraction.

Spectroscopic optical coherence tomography for classification of colorectal cancer in a mouse model.

Noninvasive diagnosis of the malignant potential of colon polyps can improve prevention of colorectal cancer without the need for time-consuming and expensive biopsies. This study examines the use of spectroscopic optical coherence tomography (OCT) to classify tissue from genetically engineered mouse models of early-stage adenoma (APC) and advanced adenocarcinoma (AKP) in which tumors are induced in the distal colon. The optical tissue properties of scattering power and scattering attenuation coefficient are evaluated by analyzing the imaging data collected from tissues. Classifications are generated using 2D linear discriminant analysis with high levels of discrimination obtained. The overall classification accuracy obtained was 91.5%, with 100% sensitivity and 96.7% specificity in separating tumors from benign tissue, and 77.8% sensitivity and 99.4% specificity in separating adenocarcinoma from nonmalignant tissue. Thus, this study demonstrates the clinical potential of using spectroscopic OCT for rapid detection of colon adenoma and colorectal cancer.

A MCNP simulation for a new dual-energy dual-beam X-ray inspection method using multi-angle compton scattering to determine the effective atomic number of explosives

This study suggests an improved X-ray inspection method to determine the effective atomic number to identify explosives during luggage inspection with high resolution of the effective atomic number (Zeff). To obtain high resolution in Zeff, the suggested inspection method uses the ratio of the total and Compton scattering attenuation coefficients between two different energies for decomposing the attenuation coefficients of the Rayleigh scattering and photoelectric absorption that are highly dependent on the atomic number. To acquire the total and Compton scattering coefficient ratio of two different energies, dual-energy X-ray beams and four detectors for the photons transmitted and scattered in three different angles were introduced. MCNP6 simulations were carried out for several materials with X-ray source spectra from a tungsten anode generator to show the effectiveness of the method. The estimated Zeff values with the line beam assumption showed good agreement with the reference values for explosive substances within a relative error of 3% while the additional simulation considering beam width showed increased errors that are acceptable for beam widths less than 1.5 mm.

Seismic scattering and absorption of oceanic lithosphericSwaves in the Eastern North Atlantic

SUMMARYThe scattering and absorption of high-frequency seismic waves in the oceanic lithosphere is to date only poorly constrained by observations. Such estimates would not only improve our understanding of the propagation of seismic waves, but also unravel the small-scale nature of the lithosphere and its variability. Our study benefits from two exceptional situations: (1) we deployed over 10 months a mid-aperture seismological array in the central part of the Eastern North Atlantic in 5 km water depth and (2) we could observe in total 340 high-frequency (up to 30 Hz) Po and So arrivals with tens to hundreds of seconds long seismic coda from local and regional earthquakes in a wide range of backazimuths and epicentral distances up to 850 km with a travel path in the oceanic lithosphere. Moreover, the array was located about 100 km north of the Gloria fault, defining the plate boundary between the Eurasian and African plates at this location which also allows an investigation of the influence of an abrupt change in lithospheric age (20 Ma in this case) on seismic waves. The waves travel with velocities indicating upper-mantle material. We use So waves and their coda of pre-selected earthquakes to estimate frequency-dependent seismic scattering and intrinsic attenuation parameters. The estimated scattering attenuation coefficients are between 10−4 and 4 × 10−5 m−1 and are typical for the lithosphere or the upper mantle. Furthermore, the total quality factors for So waves below 5 Hz are between 20 and 500 and are well below estimates from previous modelling for observations in the Pacific Ocean. This implies that the Atlantic Ocean is more attenuative for So waves compared to the Pacific Ocean, which is inline with the expected behaviour for the lithospheric structures resulting from the slower spreading rates in the Atlantic Ocean. The results for the analysed events indicate that for frequencies above 3 Hz, intrinsic attenuation is equal to or slightly stronger than scattering attenuation and that the So-wave coda is weakly influenced by the oceanic crust. Both observations are in agreement with the proposed propagation mechanism of scattering in the oceanic mantle lithosphere. Furthermore, we observe an age dependence which shows that an increase in lithospheric age is associated with a decrease in attenuation. However, we also observe a trade-off of this age-dependent effect with either a change in lithospheric thickness or thermal variations, for example due to small-scale upwellings in the upper mantle in the southeast close to Madeira and the Canaries. Moreover, the influence of the nearby Gloria fault is visible in a reduction of the intrinsic attenuation below 3 Hz for estimates across the fault. This is the first study to estimate seismic scattering and absorption parameters of So waves for an area with several hundreds of kilometres radius centred in the Eastern North Atlantic and using them to characterize the nature of the oceanic lithosphere.

Experimental and numerical studies on kV scattered x-ray imaging for real-time image guidance in radiation therapy

Motion management is a critical component of image guided radiotherapy for lung cancer. We previously proposed a scheme using kV scattered x-ray photons for marker-less real-time image guidance in lung cancer radiotherapy. This study reports our recent progress using the photon counting detection technique to demonstrate potential feasibility of this method and using Monte Carlo (MC) simulations and ray-tracing calculations to characterize the performance. In our scheme, a thin slice of x-ray beam was directed to the target and we measured the outgoing scattered photons using a photon counting detector with a parallel-hole collimator to establish the correspondence between detector pixels and scatter positions. Image corrections of geometry, beam attenuation and scattering angle were performed to convert the raw image to the actual image of Compton attenuation coefficient. We set up a MC simulation system using an in-house developed GPU-based MC package modeling the image formation process. We also performed ray-tracing calculations to investigate the impacts of imaging system geometry on resulting image resolution. The experiment demonstrated feasibility of using a photon counting detector to measure scattered x-ray photons and generate the proposed scattered x-ray image. After correction, x-ray scattering image intensity and Compton scattering attenuation coefficient were linearly related, with R 2 greater than 0.9. Contrast to noise ratios of different objects were improved and the values in experimental results and MC simulation results agreed with each other. Ray-tracing calculations revealed the dependence of image resolution on imaging geometry. The image resolution increases with reduced source to object distance and increased collimator height. The study demonstrated potential feasibility of using scattered x-ray imaging as a real-time image guidance method in radiation therapy.

Ultrasonic roughness measurement based on scattering attenuation

Surface roughness measurement is very critical for the functional performance evaluation of machined parts. At present, two most widely used methods for roughness measurement are stylus profiler and optical scattering methods with disadvantages of slow measuring speed and measurable range limit. In this research, an approach for characterizing surface roughness of machined parts using one ultrasonic transducer is put forward, which is an alternative non-contact and efficient in situ measuring method. A single scattering event of ultrasonic wave on the rough surface is firstly analyzed with the consideration of the influence of local incident angle. Then, the theoretical relationship between the scattering attenuation coefficient of ultrasonic pulse-echo and the roughness level is derived based on Kirchhoff Approximation and Phase Screen Approximation. At last, a series of experiments were performed on nickel alloy samples with different levels of roughness to validate the established theoretical model. The measurement results demonstrated the feasibility and applicability of the proposed ultrasonic roughness measurement method.

Effect of scattering and porosity on the apparent absorption in porous biphasic structures—Application to cortical bone

In this in-silico study, the attenuation coefficient in porous structures mimicking simplified cortical bone is calculated both in presence and absence of absorption, to isolate the effect of scattering on attenuation. Pore distributions with various pore concentrations (5–25 pore/mm2) and diameters (40–120 μm) are generated. The propagation of 8 MHz plane waves is simulated using a 2D FDTD package. The attenuation coefficient is measured by fitting the exponential decay of the signal amplitude in the frequency domain during propagation in the absence or presence of absorption (coefficient of 10 dB/cm/MHz to mimic bone tissue), for different pore concentrations and sizes. The difference between total attenuation and scattering attenuation coefficients (obtained with no absorption) is defined as the apparent absorption coefficient. For ka 1, increasing porosity leads to a higher apparent absorption, indicating a higher impact of absorption, even though the absorption coefficient and the overall volume fraction of absorbing material (solid phase) were kept constant. This suggests complex interactions between the wave and the structure, and could be attributed to longer propagation paths in the solid phase due to multiple scattering by the pores.In this in-silico study, the attenuation coefficient in porous structures mimicking simplified cortical bone is calculated both in presence and absence of absorption, to isolate the effect of scattering on attenuation. Pore distributions with various pore concentrations (5–25 pore/mm2) and diameters (40–120 μm) are generated. The propagation of 8 MHz plane waves is simulated using a 2D FDTD package. The attenuation coefficient is measured by fitting the exponential decay of the signal amplitude in the frequency domain during propagation in the absence or presence of absorption (coefficient of 10 dB/cm/MHz to mimic bone tissue), for different pore concentrations and sizes. The difference between total attenuation and scattering attenuation coefficients (obtained with no absorption) is defined as the apparent absorption coefficient. For ka 1, increasing porosity leads to a higher appa...

Scattering Attenuation of SH‐Waves in Fiber‐Reinforced Composites with Partial Imperfectly Bonded Interfaces

The influence of partial imperfectly bonded interfaces between each fiber and the matrix on the scattering attenuation of coherent SH‐waves in fiber‐reinforced composites is investigated. The imperfection of interfaces is modelled using the spring model, in which the level of imperfection is characterized by a parameter K, which is called the stiffness of the imperfect interfaces. First, the single scattering of SH‐waves by a cylindrical fiber with such a partial imperfectly bonded interface to the matrix is formulated and subsequently solved using the collocation point (CP) method. Later on, based on the analysis of the corresponding single scattering problem, effects of several parameters (i.e., frequency of the incident wave, level of imperfection of interfaces, and width of the imperfect interfaces) on the far‐field scattering magnitude, scattering cross section, and scattering attenuation coefficients of coherent SH‐waves are shown graphically. The potential application of the current results to nondestructive evaluation of interfaces in composites is also discussed.

Pore-scale modeling of pore structure effects on P-wave scattering attenuation in dry rocks.

Underground rocks usually have complex pore system with a variety of pore types and a wide range of pore size. The effects of pore structure on elastic wave attenuation cannot be neglected. We investigated the pore structure effects on P-wave scattering attenuation in dry rocks by pore-scale modeling based on the wave theory and the similarity principle. Our modeling results indicate that pore size, pore shape (such as aspect ratio), and pore density are important factors influencing P-wave scattering attenuation in porous rocks, and can explain the variation of scattering attenuation at the same porosity. From the perspective of scattering attenuation, porous rocks can safely suit to the long wavelength assumption when the ratio of wavelength to pore size is larger than 15. Under the long wavelength condition, the scattering attenuation coefficient increases as a power function as the pore density increases, and it increases exponentially with the increase in aspect ratio. For a certain porosity, rocks with smaller aspect ratio and/or larger pore size have stronger scattering attenuation. When the pore aspect ratio is larger than 0.5, the variation of scattering attenuation at the same porosity is dominantly caused by pore size and almost independent of the pore aspect ratio. These results lay a foundation for pore structure inversion from elastic wave responses in porous rocks.

Ultrasonic scattering from poroelastic materials using a mixed displacement-pressure formulation

In this work, a numerical technique suitable for evaluating the ultrasonic scattering from a three-dimensional poroelastic material is presented. Following Biot’s derivation of the macroscopic governing equations for a fluid saturated poroelastic material, the predicted two propagating wave equations are formulated in terms of displacement and pressure. Assuming that porosity variations on a microscopic scale have a cumulative effect in generating a scattered field, the scattering attenuation coefficient of a Biot medium can be determined. The scattered fields of the wave equations are numerically evaluated as Neumann series solutions of the Kirchhoff-Helmholtz integral equation. A Pade approximant technique is employed to extrapolate beyond the Neumann series’ radius of convergence (weak scattering regime). In the case of bovine trabecular bone, the relationship between the scattering attenuation coefficient and the structural and mechanical properties of the trabecular bone is of particular interest. The results demonstrate the validity of the linear frequency-dependent assumption of attenuation coefficient n the low frequency range. Further comparisons, between measured observations and the numerical results will be discussed.

A reappraisal of seismic Q evaluated at Mt. Etna volcano. Receipt for the application to risk analysis

A new approach in dealing with seismic risk in the volcanic areas of Italy, by taking into account the possible occurrence of damaging pre- or syn-eruptive seismic events, is exciting the scientific interest and is actually the topic developed in several research projects funded by the European Community (e.g., UPStrat-MAFA, www.upstrat-mafa.ov.ingv.it/UPstrat/) and the Civil Defense Department of Italy. To achieve this goal, it is necessary to have a detailed knowledge of the local attenuation-distance relations. In the present paper, we make a survey of the estimates of the seismic quality factor of the medium reported in literature for the Etna area. In the framework of a similar paper published for the Campi Flegrei zone in Southern Italy, we first review the results on seismic attenuation already obtained for Etna and then apply a standard technique to separately measure intrinsic and scattering attenuation coefficients from passive seismic data recorded by the Etna seismological network. Indications are then given for the correct utilization of the attenuation parameters to obtain the best candidate quality factor Q to be used in this area for seismic risk purposes.

Wave attenuation in a marginal ice zone due to the bottom roughness of ice floes

AbstractWave attenuation in a diffuse marginal ice zone (MIZ) is thought to be mainly a result of wave scattering. In a compact MIZ, additional physical factors are thought to be relevant. In this paper, we propose that viscous drag, form drag and energy lost to internal waves under the ice play a role in attenuating wave energy. We derive a relation for the wave attenuation due to drag. We combine the drag attenuation coefficient with the scattering attenuation coefficient and compare the result to experimental results for compact MIZs. We find that the combined scatter and drag (CSD) model improves the rate of decay of wave attenuation in compact ice fields, but fails to predict the ‘rollover’ seen at short periods.

Multiple and dependent scattering effects in Doppler optical coherence tomography

Doppler optical coherence tomography (OCT) is a technique to image tissue morphology and to measure flow in turbid media. In its most basic form, it is based on single (Mie) scattering. However, for highly scattering and dense media multiple and concentration dependent scattering can occur. For Intralipid solutions with varying scattering strength, the effect of multiple and dependent scattering on the OCT signal attenuation and Doppler flow is investigated. We observe a non-linear increase in the OCT signal attenuation rate and an increasingly more distorted Doppler OCT flow profile with increasing Intralipid concentration. The Doppler OCT attenuation and flow measurements are compared to Monte Carlo simulations and good agreement is observed. Based on this comparison, we determine that the single scattering attenuation coefficient micros is 15% higher than the measured OCT signal attenuation rate. This effect and the distortion of the measured flow profile are caused by multiple scattering. The non-linear behavior of the single scattering attenuation coefficient with Intralipid concentration is attributed to concentration dependent scattering.

Depth dependent seismic scattering attenuation in the Nuevo Cuyo region (southern central Andes)

In the present work we separated intrinsic from scattering attenuation coefficients both for the crust and the upper mantle in the tectonically highly active areas of the Southern‐Central Andes ‐ Nuevo Cuyo region, analyzing two groups of earthquakes, well separated in depth. This region is characterized by the presence of flat subduction. We apply MLTWA (Multiple Lapse Time Window Analysis), coda normalization and Q‐coda techniques to measure the scattering and intrinsic attenuation coefficient and the total Q for S waves. We find that intrinsic attenuation does not decrease with depth whereas scattering attenuation is higher in the crust than in the upper mantle, and that intrinsic attenuation predominates over scattering attenuation. We interpret this observation in terms of the release of water and other fluids into the overlying lithosphere due to the dynamics of the subduction process, in agreement with most of the prevalent geodynamic models.

Separation of depth-dependent intrinsic and scattering seismic attenuation in the northeastern sector of the Italian Peninsula

SUMMARY We investigated the intrinsic dissipation and scattering properties of the lithosphere under the Friuli region (northeastern Italy) using two hypotheses: (i) a uniform earth model and (ii) two ‘reasonable’ non-uniform, layered crustal models. For case (i) we measured the coda Q, and used the multiple-lapse time window analysis (MLTWA) technique to obtain separate estimates of intrinsic absorption and scattering attenuation. Results for the uniform earth model show that the lithosphere in northeastern Italy is characterized by a low-scattering attenuation (small scattering Q-inverse, Q −1 ), and by a relatively high intrinsic attenuation (high intrinsic Q-inverse, Q −1 ). A comparison between the investigated region and other areas around the world shows that both Q −1 and Q −1 for the Friuli region are among the lowest values ever measured, with the exception of the southern Apennines, which has the lowest measured Q −1 . For case (ii), numerical simulation of the energy envelopes was performed using two-layered earth models, where the values of the intrinsic and scattering attenuation coefficients are both within ‘reasonable ranges’ when compared with the geological information. The theoretical envelopes calculated for the homogeneous model give a good fit to the synthetic envelopes calculated for the layered models; the best fit is obtained for scattering attenuation coefficients of the uniform model always greater than those of the layered model. The main result is consequently that scattering Q −1 obtained using the MLTWA under the assumption of a uniform medium is overestimated, on average, by a factor 2. Finally, coda Q −1 appears to be closer to the total Q −1 than to the intrinsic Q −1 ,a spredicted

Effective elastic properties of randomly fractured soils: 3D numerical experiments

ABSTRACTThis paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so‐called rotated staggered finite‐difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non‐intersecting thin penny‐shaped dry cracks, the numerical simulations of P‐ and S‐wave velocities are in good agreement with the predictions of the self‐consistent approximation. We observe similar results for fluid‐filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non‐intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective‐medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results.

Separation of intrinsic and scattering seismic attenuation in the Southern Apennine zone, Italy

Scattered waves observed at the seismographs of the National Italy's seismic network have been used to investigate the intrinsic dissipation and scattering properties of the lithosphere under the Southern Apennines, Italy. First, we investigate the coda-Q properties, then we apply the MLTW analysis in the hypothesis of velocity and scattering coefficient constant with depth, and finally we interpret these results with the aid of numerical simulations in a medium with depth dependent velocity and scattering coefficient. Results obtained in the hypothesis of a uniform model show that a low scattering-Q−1 and a relatively higher intrinsic-Q−1 characterize the lithosphere of the Southern Apennines. Numerical simulations of the seismogram energy envelopes were performed hypothesizing a strongly scattering crust and trasparent upper mantle, both with reasonable intrinsic dissipation coefficients. In these symplifying assumptions the theoretical curves calculated for the homogeneous model fit to the synthetic envelopes with scattering attenuation coefficients always greater than the synthetic values. This results lead to the consideration that scattering-Q−1 obtained using MLTW analysis under the assumption of uniform medium are overestimated. The values of the scattering-Q−1 estimated for Apennines at low frequency (1–2 Hz) in the hypothesis of uniform medium are of the same order of those obtained in several areas around the world. The estimates obtained for frequencies ranging from 2 to 12 Hz are very low if compared with those obtained in the same hypothesis for other areas around the world. Coda Q−1 closely resembles intrinsic Q−1.

Scat-Cad: a Mathcad 2000 professional package to model the energy decay due to seismic attenuation

An important taskin seismology is the estimation of attenuation parameters for the earth medium, as they permit the reconstruction of the source spectral shape. Further, knowledge of the attenuation adds information on the constitution of the earth’s interior. In particular, it allows the modeling at small scale of site effects which contribute to seismic hazard studies. Several methods are frequently used to obtain this information from seismological data. Most of them are based on the estimation of the spectral decay coefficient with hypocentral distance, which is proportional to the inverse of the total quality factor of the earth medium. The attenuation parameter estimated in this way contains the combined effects of intrinsic and scattering attenuation. Scattering attenuation is produced by interaction of the primary waves with the elastic heterogeneity (which can be viewed as space fluctuations of the elastic parameters like velocity, for example). This interaction produces a secondary radiation, which comes to the receiver later than the primary. In this way, the apparent energy of the primary waves is lost. The intrinsic dissipation is the real energy loss produced by the transformation of the energy into heat. It is not always easy to interpret the (total) attenuation results in terms of geological structures: a medium which contains high heterogeneity may in fact produce a high-energy decay as a function of source–receiver distance, in apparently the same way in which a uniform, but highly dissipative medium (as a magmatic reservoir for example) can do. So, it is necessary to model the seismic propagation in terms of both scattering and dissipative attenuation. To perform this taska scattering model is necessary. Hoshiba (1993) modeled the propagation in an earth medium filled by randomly but uniformly distributed heterogeneity by means of numerical simulations. He hypothesized isotropic scattering and included multiple scattering, providing as output a set of energy–distance curves evaluated as a function of total attenuation and seismic albedo (L � 1 e and B0; respectively). These two parameters are defined as a combination of intrinsic and scattering attenuation coefficients, or what is the same, of the intrinsic and scattering quality factors. B0 ¼ QT =QS; where QT and QS are, respectively, the total and the scattering quality factors; L � 1