Compressional Wave Attenuation Research Articles

Seismic Attenuation in Partially Saturated Dime-shaped Cracks

—We have examined the effect of surface contamination on the attenuation and stiffness of compressional seismic waves in artificial cylindrical glass cracks that are partially saturated with water. The compression of the gap perpendicularly to its plane reduces the gap volume and forces the water to redistribute within the gap (conservation of volume of an incompressible liquid). On clean surfaces, the water can flow without significant resistance across the glass. This leads to a very low and almost constant attenuation over a wide frequency range (approx. 3 mHz to 10 Hz), while the sample stiffness is constant. In the case of propanol contaminated surfaces, both the attenuation and the stiffness are considerably higher than in the clean case, and display a considerable frequency dependence. Both effects can be explained with the Restricted Meniscus Motion Model. In this model, the redistribution of the liquid in the gap first leads to a change (increase) of the contact angle. The change of the meniscus curvature results in an increase of the pressure in the liquid and thus to a stiffening of the sample. When the resistive force, that prevents the contact line from sliding along the surface, is finally overcome, the contact line starts moving across the contaminated surface. The motion against the resistive force dissipates energy and increases the attenuation. The calculated data are in good agreement for both the clean and the contaminated case; the model parameters fall in the range that was established by independent experiments (e.g. ).

An acoustic study of soils that model seabed sediments containing gas bubbles

The acoustic response of gassy seabed sediment is unique. It is a dispersive and extraordinarily attenuative natural material at frequencies which cause gas bubble resonance. It conceals the structure of the seabed from seismic profiling and it dampens acoustic signals that, for example, trigger acoustic mines. In the past, theoretical studies have formulated the probable cause of this response and crude experimental work has partially corroborated theory. This study measures compressional wave velocity and attenuation in a laboratory soil simulating natural gassy soil, and it investigates the structural properties that cause the unique acoustic response. It was confirmed that below the frequencies which cause resonance the soil behaves as a compressible material (containing gas), and above as a relatively incompressible material (containing no gas). Over the frequency range producing bubble resonance it is suggested that the soil should be modeled as a biphasic material of gas and a relatively incompressible saturated soil matrix (particles and fluid). Velocities for gassy soil were found to be as low as 220 m/s at frequencies below resonance and 1500 m/s above resonance; attenuations were found to be as high as 60 dB/cm for moderately gassy soil and as low as 1 dB/cm for soil with almost no gas.

Head wave data inversion for geoacoustic parameters of the ocean bottom off Vancouver Island

Head wave signals from small explosive charges have been analyzed to determine a geoacoustic profile for a shallow water site off the West coast of Vancouver Island. The experimental design contained a vertical aperture, provided by a vertical line array, and a synthetic horizontal aperture from shots at different ranges from the vertical line array. The simultaneous use of travel time and amplitude data for both apertures provided improved accuracy and vertical resolution of the estimated geoacoustic profile. Travel time vs range data from head waves from three distinct sub-bottom interfaces were used to measure compressional speeds in the layers below the interfaces and estimate the layers’ thicknesses. Spatial filtering of the vertical line array data was necessary to resolve the head wave arrival from the shallowest layers. Analysis of the interference structure of the head wave power spectra at the vertical line array provided the means to measure the travel time of the head wave from the deepest layer. In addition, the head wave power spectra were used to estimate the compressional wave attenuation, using a method based on the variation with range of the logarithmic derivative with respect to frequency of the head wave spectrum.

1D waves in a random poroelastic medium with large fluctuations

We examine the problem of wave propagation in a random poroelastic medium. The porous medium is modelled as a Biot poroelastic solid whose constitutive parameters fluctuate substantially over finite distances. Our main results are asymptotic analytical expressions for the mean velocity-stress wave; this solution incorporates two distinct length scales. The effect of the fluctuations appears on the regular depth coordinate while the parameters of the effective medium arise on a shorter scale of distance. Thus the method that we apply, the theory of averaging, allows us to give a rigorous derivation of the effective medium parameters. It also provides the correction terms which are caused by the fluctuations in the random medium; we find that the relative effect of the latter increases in proportion to ω1/2 where ω denotes the wave frequency. We also show that the fluctuations introduce significant attenuation of the fast Biot compressional wave and dispersion of the slow Biot wave. These results are illustrated by numerical examples using real oilfield data.

Seabed sediment attenuation profiles from a movable sub-bottom acoustic vertical array

The acoustic lance [S. S. Fu, M.Sc. Thesis, University of Hawaii at Manoa (1994); Fu et al., J. Acoust Soc. Am. 99, 234–241 (1996)] consists of a linear array of acoustic receivers below an acoustic source, all mounted on the outside of a core barrel or independent probe which is embedded in the seafloor. In earlier studies lance travel time data were processed to give in situ compressional wave sound speed as a function of depth. In this study lance waveforms are processed to extract compressional wave attenuation A=Q−1 as a function of depth. The processing technique is unusual because the L1 norm is used instead of the usual L2 norm, the model space of attenuation profiles is exhaustively searched within the limits of discretization, and the marginal posterior probability density function of attenuation is computed explicitly at each depth. The technique is described in terms of Bayesian inverse theory using the notation of Tarantola.

Effects of pore pressure on compressional wave attenuation in a young oceanic basalt

Laboratory data are reported for ultrasonic compressional wave attenuation (αp) as a function of pore pressure in a Juan de Fuca Ridge dredge basalt. Four experiments have been made to determine the relationships between attenuation and quality factor (Qp) and confining and pore pressures in the shallow ocean crust. Attenuation was measured at 1) a constant differential pressure of 40 MPa; 2) confining pressures to 120 MPa and atmospheric pore pressures; 3) a constant confining pressure of 50 MPa while varying pore pressures; 4) a constant confining pressure of 100 MPa while varying pore pressures. For atmospheric pore pressures, αp ranges from 1.64 dB/cm to 7.08 dB/cm (Qp = 24 to 10). In addition, attenuation increases systematically with increasing pore pressure and decreasing differential pressure (confining pressure ‐ pore pressure). Results from DSDP and ODP downhole packer experiments suggest that the hydrostatic pore pressure regime may best approximate in situ conditions for young oceanic crust. Hydrostatic pore pressures (@ 5000 meters depth) reduce Qp as much as 35% from normal atmospheric pressure conditions; therefore, pore pressures generated in the upper oceanic crust may be responsible in part for the observed low seismic Qp within layer 2A. Qp measurements at elevated pore pressures agree well with seismic Qp data.

Recent advances in acoustic sediment classification

Most acoustic techniques used to classify seafloor sediments rely on operator experience and require extensive ground-truth data to calibrate system predictions. Recent developments in transducer design, inversion and deconvolution techniques, and sensor motion composition should improve the reliability and accuracy of normal-incidence, seafloor classification techniques. This presentation provides an introduction to papers that describe the application of these techniques to normal-incidence acoustic returns collected from a variety of siliciclastic and carbonate sediments in coastal waters surrounding Florida and the Bahamas. Site locations and descriptions, sediment characteristics based on in situ and laboratory measurements, and a description of the acoustic measurement techniques are given. In addition, 3-D visualization techniques that provide near real-time presentation of results are described. Profiles of sediment acoustic impedance, compressional wave attenuation, seafloor roughness, and volume heterogeneity are directly determined from acoustic returns and physical constraints. Other properties such as sediment type, grain size, porosity, and shear strength are predicted on the basis of empirical relationships relating acoustic impedance and/or attenuation to sediment physical properties. Comparisons of predicted and measured sediment properties are given and the ping-to-ping variability inherent in acoustic returns is discussed. [Work supported by ONR.]

The influence of gas bubbles on sediment acoustic properties: in situ, laboratory, and theoretical results from Eckernförde Bay, Baltic sea

Acoustic turbidity caused by the presence of gas bubbles in seafloor sediments is a common occurrence worldwide,but is as yet poorly understood. The Coastal Benthic Boundary Layer experiment in the Baltic off northern Germany was planned to better characterize the acoustic response of a bubbly sediment horizon. In this context, in situ measurements of compressional wave speed and attenuation were made over the frequency range of 5–400 kHz in gassy sediments of Eckernförde Bay. Dispersion of compressional speed data was used to determine the upper limit of the frequency of methane bubble resonance at between 20 and 25 kHz. These data, combined with bubble size distributions determined from CT scans of sediments in cores retained at ambient pressure, yield estimates of effective bubble sizes of 0.3–5.0 mm equivalent radius. The highly variable spatial distribution of bubble volume and bubble size distribution is used to reconcile the otherwise contradictory frequency-dependent speed and attenuation data with theory. At acoustic frequencies above resonance (>25 kHz) compressional speed is unaffected by bubbles and scattering from bubbles dominates attenuation. At frequencies below resonance (<1 kHz) ‘compressibility effects’ dominate, speed is much lower (250 m s -1) than bubble-free sediments, and attenuation is dominated by scattering from impedance contrasts. Between 1.5 and 25 kHz bubble resonance greatly affects speed and attenuation. Compressional speed in gassy sediments (1100–1200 m s -1) determined at 5–15 kHz is variable and higher than predicted by theory (<250 m s -1). These higher measured speeds result from two factors: speeds are an average of lower speeds in gassy sediments and higher speeds in bubble-free sediments; and the volume of smaller-sized bubbles which contribute to the lower observed speeds is much lower than total gas volume. The frequency-dependent acoustic propagation is further complicated as the mixture of bubble sizes selectively strips energy near bubble resonance frequencies (very high attenuation) allowing lower and higher frequency energy to propagate. It was also demonstrated that acoustic characterization of gassy sediments can be used to define bubble size distribution and fractional volume.

Velocity structure, composition and discrimination of crustal provinces in the former Soviet Union

Significant progress had been made over the last two decades in seismic refraction/wide-angle reflection investigations of continental Russia. Highlights of this progress include the determination of crustal thickness, lithospheric body-wave velocities, compressional and shear wave attenuation, and existence of deeply penetrating dipping reflectors. These new multiwave Deep Seismic Sounding (DSS) data, recorded along geotraverses crossing Precambrian cratons (PC), provinces of Cenozoic basin deposition (CB), and Palaeozoic fold belts (PB), provide a basis for the study of Eurasian continental structure and tectonics. Interpretation of DSS data has shown that geological provinces of different age and tectonic history can be distinguished by the relationship between V p/ V s and the crystalline crustal thickness ( h). There are two primary relationships in the V p/ V s vs. h function. In the first (characteristics of PC), V p/ V s is directly proportional to crustal thickness. In the second relationship, observed in CB and PB, V p/ V s is inversely proportional to crustal thickness. Province boundaries are imaged as dipping reflectors through analysis of the wave field of three component records using special velocity filtering. Dynamic features of these reflections suggest that these boundaries are detachment faults separating relatively thin layers with complicated fine structure. The composition of the crystalline crust, determined from body wave velocities, varies significantly over the transition zone from one geological province to another. Mapping of regions according to the V p/ V s vs. h function, shows a correlation of the known mineral, oil, and gas deposits with province boundaries.

Spatial heterogeneity of acoustic bottom backscattering model parameters and predicted results

Sediment geoacoustic and roughness measurements were made during a mine burial experiment in the North Sea in November 1997. The experiment site was a sand ridge (20.5–32-m water depth) influenced by strong tidal currents and wave action. Stereo photographs indicated that the sediment roughness was characterized by cross-rippled fine sand that transitioned to straight- and sinuous-rippled mixtures of fine quartz sand and mollusk shell fragments. Box core samples were subsampled with core tubes from which measurements of sediment compressional wave velocity and attenuation, density, and grain size distribution were made. Values for sediment velocity ratio, density ratio, slope of the roughness power spectrum, roughness spectral strength, and other measured and calculated parameters were used as input parameters for the composite roughness model to predict bottom backscattering strengths from various regions within the experiment site. Horizontal and vertical variability in sediment properties is high relative to other shallow sites under the influence of strong hydrodynamic forcing. There is a marked interdependence among sediment geoacoustic properties, water depth and bottom roughness features. The influence of hydrodynamic conditions and sediment type on the acoustic model predictions is demonstrated by the spatial variability in predicted scattering of high-frequency sound from the site.

High-frequency bottom backscattering from a homogeneous seabed

High-frequency acoustic backscattering was measured from a sandy site located in very shallow water (8 m) off Tirrenia, Italy, at a range of frequencies and grazing angles. Concomitant measurements of the seabed indicated that the very fine sand was well sorted, relatively uniform with respect to vertical and horizontal distribution of compressional wave velocity and attenuation, and depleted with respect to biological activity. Bottom scattering strengths were very low and variability of sediment parameters was exceptionally low. Coefficients of variation determined for sediment compressional wave velocity and attenuation were 0.29% and 7.2%, respectively. These data compare with previously recorded minima of 0.30% and 14.8% for the same respective parameters, in nearshore, mobile fine sands from the Gulf of Mexico and the Pacific Ocean. Lack of variability in sediment sound velocity and density concurrent with low acoustic bottom scattering strength measurements would endorse recent modeling approaches that predict scattering from sediment impedance fluctuations. Acoustic data are compared with predictions from the composite roughness model (modified for inclusion of sediment volume scattering parameters) at various frequencies and grazing angles in order to test the model’s response at minimal perturbation of seabed properties.

Head wave data inversion for geoacoustic parameters of the ocean bottom off Vancouver Island

As a part of the Pacific Shelf-93 experiment, small explosive charges were used as underwater sound sources on the continental shelf off Vancouver Island. Broadband acoustic signals received by a vertical line array show the rich structure of precursors arriving prior to the direct water wave. Kinematic properties of the precursors are found to be consistent with those of head waves with different numbers of reflections at the ocean surface and bottom. Power spectra of the precursors reveal complicated interference structure, including deep nulls at relatively low frequencies. Positions of the nulls in the frequency domain and their depth dependence are shown to be sensitive to the variation of compressional wave speed in the bottom. A combination of beamforming, spectral analysis, and travel-time considerations is applied to separate and identify individual head wave arrivals in the sequence of precursor signals. Range- and depth-dependence of the travel times for individual head waves are inverted to determine compressional wave speeds in two distinct subbottom layers and to estimate the thickness of the sediment layers. The frequency- and range-dependence of the head waves amplitudes are analyzed to estimate the compressional wave attenuation. [Work supported by NSERC.]

Scattering of a compressional wave in a poroelastic medium by an ellipsoidal inclusion

SUMMARY We study the interaction of a plane elastic wave in a poroelastic medium with an elliptical heterogeneity of another porous material. The behaviour of both the inclusion and the host medium is described by Biot’s equations of poroelasticity with the standard interface conditions of Deresiewicz and Skalak at the inclusion’s surface. The scattering problem is studied in the Born approximation, which is valid for low contrast of the inclusion’s properties with respect to the host medium. The resulting scattered wavefield consists of the scattered normal compressional and shear waves and a Biot slow wave, which attenuates rapidly with distance from the inclusion. The Born approximation also allows us to derive explicit analytical formulae for the amplitudes of these scattered waves and to compute the amount of energy scattered by the inclusion into these waves. The amplitude and scattering cross-section for the Biot slow wave depend on the relationship between the dimensions of the inclusion and the wavelength of the Biot slow wave. The analytical results for a single inclusion are used to estimate the eVective attenuation of a normal compressional wave in a poroelastic medium with randomly distributed ellipsoidal inclusions. The eVective attenuation due to the elastic scattering of energy by the inclusions is compounded by an additional attenuation caused by poroelasticity, i.e. by the scattering of the incident normal compressional wave into the Biot slow wave. The frequency dependence of this so-called mode conversion attenuation has the form of a relaxation peak, with the maximum of the dimensionless attenuation (inverse quality factor) at a frequency at which the wavelength of the Biot slow wave is approximately equal to the characteristic size of the inclusion. The width and the precise shape of this relaxation peak depend on the aspect ratio of the ellipsoidal inclusion. Physically, the mode conversion attenuation is associated with the wave-induced flow of the pore fluid across the interfaces between the host medium and the inclusions. The results of our study demonstrate how the local flow (or squirt) attenuation can be eVectively modelled within the context of the Biot theory of poroelasticity.

From geology to geoacoustics—Evaluation of Biot–Stoll sound speed and attenuation for shallow water acoustics

A procedure for estimating acoustic wave velocity and attenuation in ocean sediment using a minimum amount of geological and geotechnical data is demonstrated. First, the Biot–Stoll theory is presented. Next, various asymptotic formulae for the attenuation coefficient are derived for high, low, and intermediate frequencies. These expressions clearly isolate the effects of intergranular Coulomb friction and fluid viscous dissipation on the attenuation of shear and compressional waves. Under the constraint of a minimum amount of geological and geotechnical information, a sequence of empirical equations is compiled to convert basic data, such as blow count number from a Standard Penetration Test or shipboard density, into sediment geoacoustic properties. As a demonstration, two well-known field cases, the Atlantic Generating Station (AGS) site and the Atlantic Margin Coring (AMCOR 6010) site, are examined. By incorporating the uncertainty involved in the data collection, the estimated geoacoustical parameters are provided with a standard deviation.

Geoacoustic and physical properties of carbonate sediments of the Lower Florida Keys

Near-surface sediment geoacoustic and physical properties were measured from a variety of unconsolidated carbonate sediments in the Lower Florida Keys. Surficial values of compressional and shear speed correlate with sediment physical properties and near-surface acoustic reflectivity. Highest speeds (shear 125–150 m s-1; compressional 1670–1725 m s-1) are from sandy sediments near Rebecca Shoal and lowest speeds (shear 40–65 m s-1; compressional 1520–1570 m s-1) are found in soft, silty sediments which collect in sediment ponds in the Southeast Channel of the Dry Tortugas. High compressional wave attenuation is attributed to scattering of acoustic waves from heterogeneity caused by accumulation of abundant shell material and other impedance discontinuities rather than high intrinsic attenuation. Compared to siliciclastic sediments, carbonate sediment shear wave speed is high for comparable values of sediment physical properties. Sediment fabric, rather than changes due to the effects of biogeochemical processes, is responsible for these differences.

Evaluation of Biot–Stoll theory for conversion of geology to geoacoustic data in shallow water

A procedure for estimating acoustic-wave velocity and attenuation in ocean sediment using a minimum amount of geological and geotechnical data is demonstrated. First, the Biot–Stoll theory is presented. Next, various asymptotic formulas for the attenuation coefficient are derived for high, low, and intermediate frequencies. These expressions clearly isolate the effects of the intergranular Coulomb friction and fluid viscous dissipation on the attenuation of shear and compressional waves. Under the constraint of a minimum amount of geological and geotechnical information, a sequence of empirical equations is compiled to convert basic data, such as the blow count number from a standard penetration test or shipboard density, into sediment geoacoustic properties. As a demonstration, two well-known field cases, the Atlantic Generating Station (AGS) site and the Atlantic Margin Coring (AMCOR 6010) site, are examined. By incorporating the uncertainty involved in the data collection, the estimated geoacoustical parameters are provided with a standard deviation.

The measurement of velocity dispersion and frequency‐dependent intrinsic attenuation in sedimentary rocks

A series of experiments to determine the elastic properties of a sequence of saturated sedimentary rocks over as wide a frequency range as possible was carried out at the Imperial College borehole test site. These experiments fall into four categories: vertical seismic profiles (VSPs) within the frequency range 30–280 Hz, crosshole surveys (0.2–2.3 kHz), sonic logging (8–24 kHz), and laboratory measurements (300–900 kHz). The intrinsic attenuation and velocity of compressional and shear waves were measured whenever possible. Velocity dispersion is observed for both compressional and shear waves. The intrinsic attenuation of compressional waves is frequency dependent with a peak in the attenuation in the sonic frequency band. The data were modeled assuming the attenuation is caused by local fluid flow in pores of small aspect ratio. The modeling indicates that the intrinsic attenuation may be dominated by cracks with aspect ratios of around [Formula: see text] to [Formula: see text].

Attenuation in fine‐grained marine sediments: Extension of the Biot‐Stoll model by the “effective grain model” (EGM)

It is postulated that the presence of swelling clay minerals in unconsolidated fine‐grained saturated marine sediments leads to deviations from the normally assumed ideal elasticity of the solid phase. In the proposed “effective grain model” (EGM), the elastic grain material is consequently replaced by an effective medium made up of a homogeneous elastic mineral phase that is isotropically interspersed with cylindrical, “penny‐shaped” inclusions of low aspect ratio representing the intracrystalline water layers in the swelling clay minerals. The two‐phase nature of the grain material thus specified results in a wave‐energy consuming squirt‐flow process from the inclusions into the pore space. Introducing the EGM into the Biot‐Stoll model (BSM) via the complex bulk modulus of the dissipative grain material leads to a better fit to literature data on the attenuation of compressional waves than does the original BSM alone. Since swelling clay minerals occur in nearly all clay‐bearing sediments, it is concluded that the attenuation mechanism of the EGM may represent a universal contribution to the overall intrinsic anelasticity of unconsolidated fine‐grained saturated marine sediments in the frequency range from a few kilohertz to about 1 MHz.

Observations on attenuation and shear-wave velocity in fine-grained, marine sediments

Compressional(P)-wave attenuation, shear(S)-wave attenuation, and shear(S)-wave velocity measurements, compiled for fine-grained, unconsolidated sediments, show trends that do not support empirical relationships [Hamilton, J. Acoust. Soc. Am. 68, 1313–1340 (1980); in Acoustics and Ocean Bottom (F. A. S. E. Specialize Conf., Madrid, 1987)] commonly used for geoacoustic modeling. The exception is compressional-wave attenuation data, from 10 Hz to 500 kHz, that essentially follow a frequency dependence of f1 (±2 standard deviations). P-wave attenuation with depth is difficult, if not impossible, to predict given the variability in the data. Examination of several attenuation/depth profiles indicates that those of Mitchell and Focke [J. Acoust. Soc. Am. 67, 1582–1589 (1980)] may be the best choice for predicting P-wave attenuation with depth at the present time. The assumption that S-wave and P-wave attenuations are proportional [Hamilton, J. Acoust. Soc. Am. 60, 334–338 (1976c); in Acoustics and Ocean Bottom (F. A. S. E. Specialize Conf., Madrid, 1987)] is not supported by the data. S-wave attenuations calculated from effective stress mimmick the data, however, suggesting this as a better method for predicting S-wave attenuation with depth. S-wave velocity/depth profiles fall into high- and low-velocity groups that (1) reflect gross differences in sediment texture, and (2) demonstrate the importance of sediment characterization in order to select an appropriate velocity/depth function.

Compressional wave velocity and attenuation at ultrasonic and sonic frequencies in near‐surface sedimentary rocks

Laboratory ultrasonic measurements of compressional wave velocity and attenuation were made as a function of effective pressure on samples of limestone, sandstone and siltstone taken from a shallow borehole test site. The results indicate that the sandstones are pervaded by grain contact microcracks which dramatically affect their compressional wave attenuations. Clean sandstone shows a compressional wave quality factor (Q{sub p}) of 24 {+-} 2 at 5 MPa effective pressure (close to the estimated in situ burial pressure) and a Q{sub p} of 83 {+-} 29 at 60 MPa. The Q{sub p} of limestones and siltstones at the site show negligible and small increases with pressure in the laboratory, respectively. The strong pressure dependence of Q{sub p} in clean sandstone was used to infer the presence of in situ microcracks. Sediment velocities measured in the laboratory at about 1 MHz were compared with those from the full waveform sonic log at about 10 kHz implies that they must also be highly attenuating over a significant part of the frequency range 10 kHz to 1 MHz, to account for the magnitude of the observed velocity dispersion. Assuming the laboratory Q{sub p} values measured at 5 MPa remain constant down to 10 kHzmore » predicts the observed dispersion quite well. Furthermore, the sonic log velocities of sandstones, limestones and siltstones (after normalizing each lithology for porosity and clay content) were found to reflect the same pressure (depth) trends observed in the laboratory. The results provide evidence for the existence of in situ microcracks in near-surface sediments.« less