Compressional Wave Attenuation Research Articles

Non-uniqueness of reflected and transmitted waves

Although many numerical and instrumental studies over the last decades have focused on studying the effects of subsurface geometry on seismic ground motion, it has not yet been feasible to incorporate such effects into regular engineering practice, seismic building codes, earthquake hazard assessment and risk mitigation policies. In the present work, extensive numerical analyses of the linear viscoelastic response of trapezoidal sedimentary basins are performed to investigate the sensitivity of their 2D seismic response attributes to parameters related to the geometry of the basin (width, thickness and inclination angles of lateral boundaries) and the dynamic soil properties (shear and compressional wave velocities, soil density and attenuation). Basin effects are quantified and discussed through a period-dependent “aggravation factor”, defined as the ratio between 2D and 1D acceleration response spectra at the basin surface. This aggravation factor expresses the additional effect of the 2D response at different locations along the basin with respect to the corresponding 1D response that is normally accounted for in building codes. In order to identify the maximum amplification of ground motion that can be attributed to the 2D response of the basin, the main focus is put on the maximum values of aggravation factors, as well as their spatial distribution. It is shown that above the sloping edge of the basin, maximum values of aggravation factors less than one may occur, meaning that 2D response is deamplified with respect to the corresponding 1D response, particularly for steep slopes. At the nearly constant-depth part of the basin, maximum aggravation factors strongly depend on the shape ratio of the basin, defined as the ratio of the maximum thickness of the basin to its half-width. A general increase is observed with the shape ratio and the increase is more pronounced at the central part of the basin, where for high shape ratio, i.e. deep and narrow valleys, the computed median values are as high as 1.8 and 84th percentiles around 2.3. Maximum aggravation factors are higher and exhibit a larger scattering for basins with higher values of fundamental period at the center T0,c.

Improved materials characterization by pressure-dependent ultrasonic attenuation in air-filled permeable solids

Recently developed airborne ultrasonic inspection techniques can supplement other methods routinely used for materials characterization of permeable solids. In particular, the velocity and attenuation of the slow compressional wave transmitted through thin plates of a few millimeter thickness can be used to assess the tortuosity and dynamic permeability of the specimen. The main advantage of the ultrasonic method over conventional flow resistivity, electrical conductivity, and other measurements is that it can be used to study the heterogeneity of the pore structure at scales comparable to the grain size. In the 100–500 kHz frequency range slow wave images can be obtained with resolution on the order of 1 mm or better. However, due to substantial viscous and scattering losses, the sensitivity of the method is relatively low therefore, the technique is limited to materials of at least 10% connected porosity and permeability higher than 200 mD. It is demonstrated in this letter that varying the air pressure significantly enhances the capabilities of slow wave inspection. Using high-pressure air saturation significantly reduces the absorption losses so that better resolution can be achieved by increasing the frequency. Alternatively, materials of lower permeability or specimens of higher thickness can be inspected at the same frequency. In addition, scattering losses can be eliminated by subtracting images taken at the same frequency but at different pressures.

Acoustic lance: New in situ seafloor velocity profiles

The acoustic lance is an instrument developed to obtain in situ compressional wave velocity and attenuation (Q−1) profiles for a sedimentary layer of several meters thickness at the sediment–seawater interface. The self-contained instrument consists of ten independent recording channels with a linear array of receivers embedded in the seafloor below a broadband acoustic source. It provides in situ recording of full waveforms to determine interval velocity and attenuation. The system can be attached to a gravity corer or to a specially designed probe. A comprehensive experiment was carried out in Mid-Atlantic Ridge sediment ponds where the lance made in situ measurements, and core samples were recovered. Core data agree well with in situ data in one location, but disagree in other locations. Lance data indicate that the sediment ponds have similar in situ velocity distributions, with an acoustic channel much thinner than that predicted by earlier investigators.

Geoacoustic profile estimation by inversion of head wave data

An approach is described for estimation of geoacoustic model parameters in shallow water based on inversion of head wave data obtained in experiments with vertical line arrays (VLA). Analysis of head waves obtained in seismic refraction surveys with horizontal arrays is a widespread practice in exploration seismology. However, in shallow water, there can be practical advantages in the use of VLAs. Inversion of head wave data obtained with a VLA provides estimates of the layer depths, and compressional wave speeds and attenuations. Three inversion techniques are compared: inversion of travel time versus range data for a single sensor, direct measurement of the critical angle using the VLA, and inversion of travel time versus hydrophone depth data for a specific range. The techniques are applied to data from an experiment on the continental shelf off Vancouver Island. Shallow explosive charges were used as sound sources out to ranges of 5 km. Strong head wave signals were recorded from two distinct layers, and the data were inverted using the travel time versus depth method. The estimated values of 1750 and 1900 m/s for the compressional wave speeds are consistent with results from conventional seismic surveys in the vicinity.

Recent developments in the in‐situ measurement of sediment geoacoustic properties

The latest version of the in‐situ sediment acoustic measurement system (ISSAMS) allows direct, in‐situ measurement of sediment geoacoustic properties. Geoacoustic probes, which are mounted on a rigid frame, are inserted into the sediment hydraulically. The entire operation is controlled and monitored in real‐time from the surface. Data is collected and processed by a wet‐side computer and transmitted to the surface for waveform display and analysis. Video cameras both monitor insertion of probes and provide preliminary indication of sediment type. A seabird CTD is used to measure bottom water temperature, salinity, and sound speed. Sediment compressional wave velocity and attenuation are measured over pathlengths of 40 to 110 cm and at depths of between 0 to 50 cm below the sediment–water interface. Pulsed sine waves are transmitted at 58‐kHz and time delays and voltages are used to determine values of velocity and attenuation between identical radial‐poled ceramic cylinders (two transmit and two receive). Shear wave velocity and attenuation are measured using a similar pulse technique. Bimorph bender elements mounted in flexible silicone rubber mounts and driven at 100 to 2000 Hz to generate shear waves. Values of sediment geoacoustic properties from muddy sediments of Eckernförde Bay, Baltic Sea and carbonate sediments of the Florida Keys presented used to illustrate the operation and utility of the new system.

High-frequency bottom backscattering: Volume scattering from gassy mud

Bottom backscattering data at 40 kHz were collected from a stationary tripod deployed in a muddy embayment characterized by subsurface methane gas. Near-surface sediment geoacoustic, physical, and roughness properties were measured concurrently with the acoustic data in order to compare model predictions with measured backscatter strength as a function of grazing angle. Insitu values for sediment compressional wave velocity and attenuation, sediment density values from diver-collected cores, and values for interface roughness parameters from underwater photogrammetry were used to calculate the parameters for the composite roughness model. The model prediction for scattering strength from the sediment–water interface fell well below the measured value, indicating that volume scattering from within the sediment was the dominant process. Data obtained by other investigators reveal a layer of free methane located approximately 1 m below the sediment–water interface. These gas bubbles were evidently responsible for the high level of backscattering observed. A fit of the volume scattering component of the composite-roughness model to the data provides a measure of the contribution of these bubbles to acoustic backscatter.

Acoustical properties of undisturbed sands from the West Florida sand sheet

Eight undisturbed large-diameter (10.1-cm) gravity cores, ranging in length from 13.5 to 50.5 cm, were collected at the CBBL-SRP study site southeast of Panama City, FL. The recovered sediments varied from coarse sand and shell fragments near the surface to fine/medium sand at depth. The Multi Sensor Core Logger was used to measure compressional wave velocity, density, and attenuation as a function of depth in each of the unsplit cores in two mutually perpendicular directions. Two spring-loaded compressional wave transducers operating at 500 kHz, mounted on the outside of the liner, were used to measure velocity and attenuation, and a Cs-137 gamma ray source with scintillation counter were used to measure bulk density. In the longest of the cores, PC-GC-623, compressional wave velocity varied between 1700 and 1730 m/s in the upper 10 cm and between 1650 and 1700 m/s below that depth. Attenuation decreased slightly with depth, with most values falling between 0.3 and 0.5 dB/kHz/m (with reference to core liner filled with water). Density was relatively depth-independent and ranged between 1.8 and 1.9 g/cm3.

The effects of free-methane bubbles on the propagation and scattering of compressional and shear wave energy in muddy sediments

Free-methane bubbles cause significant scattering of acoustic energy in the soft sediments of Eckernfoerde Bay, Baltic Sea. Insitu and laboratory measurement of sediment geoacoustic and physical properties were made in an attempt to understand the physical mechanisms responsible for this scattering. Insitu shear wave velocities (at 100–500 Hz) increased from 5–7 near the surface to 15–20 m s−1 at 2 m into the seafloor, whereas insitu compressional wave velocities (at 38 and 58 kHz) varied little (∼1425 m s−1) with depth. Methane bubbles apparently caused significant attenuation of compressional waves at depths below 1 m, whereas shear wave attenuation was unaffected by gas and decreased with depth. Compressional waves (at 400 kHz) in cores (1%–5% free gas) maintained at insitu pressures were highly attenuated but show little evidence of velocity dispersion. Comparison of geoacoustic data with theory suggest that primary control of the interaction of acoustic profilers with this gassy seafloor is by bubbles larger than about 1 mm diameter and that the observed high-frequency scattering can be described by models of the seafloor bubbles as individual scatters of acoustic energy. Response of the seafloor as a medium with modified bulk propagation properties would occur at lower frequencies than those used in the Eckernfoerde experiments.

Velocity and attenuation of compressional waves in nearly saturated soils : J.P. Bardet & H. Sayed, Soil Dynamics & Earthquake Engineering, 12(7), 1993, pp 391–401

Velocity and attenuation of compressional waves in nearly saturated soils : J.P. Bardet & H. Sayed, Soil Dynamics & Earthquake Engineering, 12(7), 1993, pp 391–401

A modified ultrasonic interferometer for sound velocity measurements in molten metals and alloys

An ultrasonic interferometer has been developed for measuring compressional wave velocity (VP) and attenuation (or conversely, quality factor QP) in molten Fe, Fe-Ni, Fe-Ni-S, and Fe-Ni-Si alloys. Results for pure molten Fe are presented. A radio frequency (rf) induction technique is used for heating that allows a ±1 K temperature stability at 1973 K. The effects of the electromagnetic field interaction with the molten conductive metal are discussed in terms of applicability to VP and QP measurements. Considerations of acoustic impedance and thermal absorption are presented to discuss the high-temperature use of polycrystalline Al2O3 buffer rods for velocity and attenuation measurements. Viscoelastic theories, when applied to pure molten Fe, predict an extremely small acoustic coefficient of attenuation. Suggestions are made to circumvent the experimental difficulties encountered in attenuation measurements.

The shallow attenuation structure of the fast‐spreading East Pacific Rise near 9°30′N

Direct measurements of Q values in the shallow crust are difficult to obtain due to the lack of energy turning in this region. We analyze a unique data set consisting of seven refraction experiments carried out with both the source and receiver near the seafloor. This experimental geometry allows us to resolve the shallow compressional wave attenuation structure of young crust at the East Pacific Rise. All models depict a low‐Q layer 2A (apparent Q=11–22), and several models resolve a layer 2B with a much higher Q (apparent Q > 70). This structure is consistent with a layer 2A composed of extrusives overlying a layer 2B composed of sheeted dikes.

Elastic wave scattering by an elliptical inclusion in a fluid‐saturated porous medium

The problem of the scattering of an elastic wave by a small (compared to the wavelength of the fast compressional wave) elliptical porous inclusion placed in another fluid‐saturated porous medium is studied using the Born approximation. The mechanical behavior of both host and inclusion materials is described by the low‐frequency version of Biot’s theory. Explicit formulas for the amplitudes of the scattered normal compressional and shear waves and of Biot’s slow compressional wave are obtained. The effectiveness of Biot’s slow wave generation depends essentially on the ratio of the wavelength of the slow compressional wave to the inhomogeneity size. For large values of this ratio the results agree with the earlier low‐frequency results [J. G. Berryman, J. Math. Phys. 26, 1408–1419 (1985)] derived for a spherical inclusion. In the opposite case new results are obtained. They are used to estimate the effective velocity and attenuation of the normal compressional wave in a porous medium containing randomly distributed inclusions. The frequency dependence of the attenuation is consistent with the results for randomly layered porous materials.

Low-frequency dispersion and attenuation in partially saturated rocks

A theory is developed for the attenuation and dispersion of compressional waves in inhomogeneous fluid-saturated materials. These effects are caused by material inhomogeneity on length scales of the order of centimeters and may be most significant at seismic wave frequencies, i.e., on the order of 100 Hz. The micromechanism involves diffusion of pore fluid between different regions, and is most effective in a partially saturated medium in which liquid can diffuse into regions occupied by gas. The local fluid flow effects can be replaced on the macroscopic scale by an effective viscoelastic medium, and the form of the viscoelastic creep function is illustrated for a compressional wave propagating normal to a layered medium. The wave speeds in the low- and high-frequency limits are associated with conditions of uniform pressure and of uniform ‘‘no-flow,’’ respectively. These correspond to the isothermal and isentropic wave speeds in a disordered thermoelastic medium.

Acoustic properties of fine-grained sediments from Emerald Basin: Toward an inversion for physical properties using the Biot–Stoll model

Acoustic data from two long cores, comprising marine clays and silts taken from Emerald Basin off Nova Scotia, are presented. High-resolution measurements of compressional wave velocity, attenuation, and power law exponent are made using ultrasonic frequencies between 100 to 1000 kHz. The observed values of the frequency dependence of attenuation suggest that a nonconstant Q mechanism is needed to explain these data, and Biot–Stoll theory is used to model the experimental results. An inversion scheme is used to constrain physical parameters in the Biot–Stoll dispersion relation. The inversion shows that there is a restricted range of permeability and grain size. By assigning reasonable values for grain size in the inversion, the Biot–Stoll model predicts unique values for the permeability and frame bulk modulus that agree well with estimates made by other means.

An issue (sediment volume fluctuations) and a nonissue (shear wave propagation) in shallow water acoustics

A two-way full-wave PE reverberation model has been developed that provides predictions of mean reverberation levels in shallow water to long ranges (hundreds of water depths) due to sediment volume fluctuations as well as bottom and basement interface roughnesses. Using T. Yamamoto’s tomographically measured sediment volume fluctuation spectra as one of the inputs, the PE reverberation model has been exercised at several locations on the shelf in the East China Sea over a broad range of frequencies. It has been found that predicted reverberation levels due to both mechanisms are generally comparable in magnitude, and that absolute levels are controlled mainly by total field ensonification of the sediment volume and boundaries, i.e., forward transmission losses. The question whether it is necessary to include shear wave propagation in shallow water acoustic models has been resolved: the answer is definitely negative, and this is no longer an issue. Measured shallow water transmission loss data over a broad range of frequencies with source and receiver in the water column has been successfully modeled using a full-wave range-dependent PE model that includes rough bottom forward scattering (necessary for good agreement), but treats shear wave effects as an equivalent fluid by augmenting the volume attenuation of compressional waves in the sediment layers. The conclusion that it is not necessary to include shear wave propagation when sources and receivers are in the water column has been further confirmed by inter-model and intra-model comparisons using realistic geoacoustic sediment properties as measured by T. Yamamoto’s BSMP system [J. Acoust. Soc. Am. 90, 441–456 (1991)]. [Work supported by ONR, 1125OA.]

Velocity and attenuation of compressional waves in nearly saturated soils

Based on the two-phase theory of Biot, we present exact and approximate expressions for the velocity and attenuation of compressional waves within nearly saturated poroelastic media. We use the approximate solutions to model the low-frequency compressional waves within nearly saturated soils. The model accounts for the effective stress, degree of saturation, and void ratio, and is capable of describing experimental results on Ottawa sand. The three-phase theory of Vardoulakis and Beskos and the two-phase theory of Biot similarly describe the velocity and attenuation of compressional waves in most soils. However, the former theory breaks down for nearly saturated gravels and dense sands.

Acoustic attenuation in oceanic gabbro

SUMMARY Compressional wave velocity and attenuation were measured in oceanic Layer 3 from nearly 0.5 km of recovered core at Ocean Drilling Program Site 735 in the southern Indian Ocean. High-frequency (400 kHz) acoustic transmission experiments were conducted on 117 water-saturated minicore samples under room conditions of temperature and pressure on board the drillship JOlDES Resolution. Although experimental errors were large in some deformed samples, the average of our measurements of attenuation, Qp', on these samples is 0.049 f 0.032. Agreement between 'spectral ratio and inversion estimates of Qp' indicates that acoustic noise in the data does not significantly reduce the measurement accuracy. Ultrasonic tests on a 1 per cent porosity sample at elevated effective pressures from 10 to 500MPa showed an increase in V, from 6.8 to 7.0kms-' and a decrease in Qp' from 0.026 to 0.023. The small pressure dependence of Qp' in this low-porosity gabbro suggests that it is possible to use measurements at room conditions for relative interpretation as a function of depth. The measurements of Qp' show (1) an overall decrease as a function of depth, (2) a decrease in the average variance in the measurement with depth, and (3) an inverse relationship between average V, and average Qp', although Qp' shows greater variation in these rocks than V,. Our explanation for these results is that rock fabric has a significant effect on V, and Qp'. A simple deduction from these results is that seismic data will be strongly influenced by the degree of alteration and tectonism in similar crustal rocks. Particularly in fracture zones, seismic reflections from lithologic contacts may be attenuated, and deep crustal reflectors, identified as faults or as the Mohorovic discontinuity, may result from V, and Qp' contrasts caused by alteration and tectonism within Layer 3, not from the lithologic contact itself.

INTEGRATED INTERPRETATION OF MARINE ENGINEERING GEOLOGICAL AND GEOPHYSICAL DATA ON THE PRINCIPLES OF EXPERT SYSTEM TECHNOLOGY1

We describe an approach to the construction of an engineering geological expert system for identification of sub-bottom soils in accordance with some predefined nomenclature. The following principles of integrated interpretation of engineering geophysical and geotechnical data are presented: Firstly, the transformation of physical data (compressional- and shear-wave velocities, compressional-wave attenuation coefficients, electrical conductivity, etc.) for each of the medium points into subjective probabilities for the soil belonging to each type listed in the nomenclature, and secondly, the extrapolation of local geotechnical data (primarily drilling data) to the surrounding space by means of diffusion of the initial membership function distribution, resulting in the same set of probabilities for soil types at each point in the medium under consideration. Aggregation of the fuzzy information obtained, sufficient for reaching a conclusion for most points in the medium, is carried out by means of Bayesian summation. An example is given of integrated interpretation of real data obtained from four different sources (compressional- and shear-wave velocity sections V p ( x, z ) and V s ( x, z ), and two boreholes) related to the same profile.

Estimation of the geoacoustic properties of the upper oceanic crust from bottom reflection loss measurements

Geoacoustic models have been estimated for the upper oceanic crust by inversion of bottom reflection loss versus angle data. The data were obtained in the PACIFIC ECHO experiments at thin-sediment sites in the North Pacific where the age of the crust increased from 40 to 64 million years. The measurements were carried out using a horizontal line array and small explosive charges, and the reflection loss was determined from beamformed array data in order to resolve the specular component. The geoacoustic models consist of profiles of the density, and the compressional (P) and shear (S) wave speeds and attenuations of both the sediment and basalt crust layers. The inversion assumes either a simple homogeneous half-space basement, or a layered model with constant sound-speed gradients in the upper crust overlying a homogeneous basement. The results indicate that the P-wave speed near the sea floor increases with increasing age of the oceanic crust from values of 2700 to about 3300 m/s. These values are significantly lower than those for the sound speed of basalt at thick sediment sites of similar crustal age. Also, there is evidence of a shear wave critical angle at the oldest site. The effects of seafloor scattering and sediment shear wave resonances are discussed.

The Born approximation in the problem of elastic wave scattering by a spherical inhomogeneity in a fluid-saturated porous medium

The Born approximation is applied to the problem of scattering of elastic waves by a small (compared to the wavelength of the fast compressional wave) spherical porous inclusion placed in another porous medium described by the low-frequency version of Biot’s theory. The results depend significantly on the ratio of the wavelength of slow compressional wave to the inhomogeneity size. For small values of this ratio results are in accordance with exact results of Berryman [J. Math. Phys. 26, 1408 (1985)]. In the opposite case new results are obtained and used to calculate compressional wave attenuation in a porous medium containing randomly distributed inclusions. The frequency dependence of attenuation is found to be in agreement with the results for randomly layered porous materials.