Acoustic Cross Section Research Articles

Model Based Inversion of Acoustic Impedance from Seismic Trace for Lithofacies Differentiation: an Application in Xy Field Offshore Niger Delta

This study presents the result of a Model-based seismic inversion technique which was used to invert an acoustic impedance structure within a reservoir interval by intergrating well logs and 3D post stack seismic data obtained from XY field offshore Niger Delta. The purpose was to delineate lateral and vertical alternations in subsurface rock properties which is caused by difference in lithofacies within the reservoir interval. This would help to define hydrocarbon fairways better and constrain the range of hydrocarbon zones for field development. The inversion workflow used in this study includes forward modelling of reflection coefficients from a low frequency impedance model driven from well logs and convolution of the reflection coeffiecients with a source wavelet derived from the seismic data. Acoustic impedance cross section obtained from the inversioin algorithim showed impedance values increasing from 4112 to 7539 (m/sec*g/cm 3 ) from top to bottom of the reservoir with gas filled sand facies observed at the top of the reservoir within time window 1900-2100msec. Below time window 2100msec, there is variation in impedance values observed within the anticlinal structures seen at this interval which suggests porous sand facies containing little shale intercalations. This is characteristic of sandstone reservoirs within the Agbada formation in the Niger Delta. These sands were most likely deposited through distributaries channel deposits, distributaries mouth bars, barrier bars, alluvial fans and crevasse which characterize the reservoir rocks (sandstones) in the Niger Delta. At time window 2100-2200msec, anticlinal structures containing porous sand facies with little shale intercalations was observed again. At time window 2200msec, water bearing sand facies (clean sandstone) was observed and at the bottom of the reservoir within time window 2300- 2500msec, the impedance was dominantly high which suggests the presence of shale facies at the bottom of the reservoir. Gas-oil contact (GOC) was observed between time window 2100-2200msec of the acoustic impedance section. These variations in acoustic impedance amplitude is due to lateral changes in lithofacies within the reservoir. The results obtained gave enhanced structural disposition of the reservoir and are important for accurate stratigraphic imaging interpretation to lower the risk in drilling of exploratory and development wells. Keywords : Acoustic impedance, Seismic inversion, Model-based, Lithofacies

Intrinsic acoustical cross sections in the multiple scattering by a pair of rigid cylindrical particles in 2D

The multiple scattering effects occurring between two scatterers are described based upon the multipole expansion formalism as well as the addition theorem of cylindrical wave functions. An original approach is presented in which an effective incident acoustic field on a particular object, which includes both the primary and re-scattered waves from the other particle is determined first, and then used with the scattered field to derive closed-form analytical expressions for the inherent (i.e. intrinsic) cross-sections based on the far-field scattering. This method does not introduce any approximation in the calculation of the intrinsic cross-sections since the procedure is reduced to the one-body problem. The mathematical expressions for the intrinsic cross-sections are formulated in partial-wave series expansions (PWSEs) in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. Numerical examples illustrate the analysis for two rigid circular cylindrical cross-sections with different radii immersed in a non-viscous fluid. Computations for the dimensionless extrinsic and intrinsic extinction cross-section factors are evaluated with particular emphasis on varying the angle of incidence, the interparticle distance, as well as the sizes of the particles. A symmetric behavior is observed for the dimensionless extrinsic extinction cross-section, while asymmetry arises for the intrinsic extinction cross-section of each particle with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of the intrinsic (local) scattering, absorption and extinction cross-sections in the multiple acoustic scatterings of plane progressive waves of arbitrary incidence by a pair of scatterers. The results and computational analyses can be used as a priori information for future applications to guide the direct or inverse characterization of multiple scattering systems in acoustically-engineered metamaterials, cloaking devices, particle dynamics, levitation, manipulation and handling, and other areas.

A stochastic pseudospectral and T-matrix algorithm for acoustic scattering by a class of multiple particle configurations

We consider absorption and scattering of acoustic waves from uncertain configurations comprising multiple two dimensional bodies with various material properties (sound-soft, sound-hard, absorbing and penetrable) and develop tools to address the problem of quantifying uncertainties in the acoustic cross sections of the configurations. The uncertainty arises because the locations and orientations of the particles in the configurations are described through random variables, and statistical moments of the far-fields induced by the stochastic configurations facilitate quantification of the uncertainty. We develop an efficient algorithm, based on a hybrid of the stochastic pseudospectral discretization (to truncate the infinite dimensional stochastic process) and an efficient stable truncated version of Waterman's T-matrix approach (for cost effective realization at each multiple particle configuration corresponding to the pseudospectral quadrature points) to simulate the statistical properties of the stochastic model. We demonstrate the efficiency of the algorithm for configurations with non-smooth and non-convex bodies with distinct material properties, and random locations and orientations with normal and log-normal distributions.

Acoustic cross sections and resonance frequencies of large fish schools

A prerequisite for stable inversion of bioacoustic parameters of fish schools from large-scale broadband acoustic observations is a theoretical model that permits fast and accurate calculations of acoustic cross sections and school resonance frequencies based on realistic geometrical models of fish schools. The schools of commercially important species, such as sardines, anchovies, and herring, may be characterized by dense nuclei which contain tens of thousands of individuals (N) with separations (S) on the order of one fish length, and diffuse “fuzz” regions with fish at significantly larger separations. Numerical computations of cross sections and school resonances based on the fundamental equations of multiple scattering for point scatterers for these fish school geometries will be presented. Initial results indicate that bubble cloud frequencies of large schools depend primarily on the average spacing between fish in the nuclei and are essentially independent of school size and shape. It will be shown that theoretical calculations of bubble cloud frequencies (based on previously reported values of N and S of sardine schools) are consistent with Diachok's (1999) observations of the average resonance frequency of sardine schools which were derived from broadband transmission loss measurements. [Work is supported by the Office of Naval Research.]

Amplitude-Modulation Chirp Imaging for Contrast Detection

We propose an amplitude-modulation chirp imaging method for contrast detection with high-frequency ultrasound. Our proposed method detects microbubbles by extracting and then selectively compressing the component of the backscattered chirp signal modulated by changes in the radii of microbubbles at their resonance frequency. Microbubbles are sonicated simultaneously with a narrowband, low-frequency pumping signal at their resonance frequency and a wideband, high-frequency imaging chirp signal. Changes in the radii of the resonant microbubbles result in periodic changes in their acoustic cross section that modulate the amplitude of the backscattered imaging chirp signal, forming pumping and imaging frequency sum-and-difference chirp terms. The frequency-sum or -difference chirp component is then extracted by a bandpass filter (BPF). Because a long imaging pulse duration is required to obtain a sufficient modulation depth on the chirp for contrast detection and to facilitate frequency-sum-and-difference signal extraction with the BPF, a chirp with a longer-than-usual waveform is used so pulse compression of the extracted chirp signal can then be performed to maintain the axial resolution, and even further improve the signal-to-noise ratio and contrast-to-tissue ratio. Experiments performed on flow phantoms with and without a speckle-generating background were performed to demonstrate the efficacy of the proposed technique. These results indicate that our proposed method can potentially provide high-resolution contrast detection in the microvasculature. (E-mail: ckyeh@mx.nthu.edu.tw)

Human motion analyses using footstep ultrasound and Doppler ultrasound

Human footsteps generate periodic broadband frequency envelopes of sound due to dynamic friction forces. Also, human body motion when walking is a cyclic temporal process. The individual body parts have different acoustic cross sections and velocities that form unique human Doppler signatures. The paper introduces an approach to analyze this motion using passive and active ultrasound. The passive method employs a narrowband microphone that is sensitive to the sound from footsteps. The active method utilizes continuous-wave ultrasound to measure the Doppler shifted signal from the body appendages. These two methods show time synchronization between Doppler and ultrasonic human footstep signatures.

Bound and free surface waves in a large wind‐wave tank

Microwave and acoustic systems operated in the large wind‐wave tank in Luminy, Marseille, France, show that most small‐scale waves produced at large angles to the wind are products of breaking events bound to longer waves in the tank. These longer waves propagate at the dominant wave phase speed for fetches near 7 m but travel at speeds corresponding to the phase speed of a wave half as long as the dominant wave at fetches near 26 m. The microwave and acoustic systems operated at both 8 mm and 2 cm wavelengths. They were set to look at the same surface spot simultaneously at the same incidence and azimuth angles. Measurements were made at seven wind speeds, five incidence angles, seven azimuth angles, and two nominal fetches. Two peaks were found in either the microwave or acoustic Doppler spectrum when looking upwind or downwind but never in both. The low‐frequency peak is due to Bragg scattering from freely propagating short waves, while the high‐frequency peak is a result of Bragg scattering from short waves bound to longer waves. At azimuth angles not aligned with the wind direction the high‐frequency peak was found to move lower until it merged with the low‐frequency peak at azimuth angles around 60°. Fitting the first moments of these Doppler spectra along with the backscattering cross sections to a model of free wave/bound wave scattering showed that the intensity of bound and free short waves generally decreased with azimuth angle but that free wave spectral densities decreased more rapidly. Differences in microwave and acoustic cross sections confirmed that the bound waves were tilted by their parent waves. Spectral densities of bound and free waves were estimated individually by fitting the data to the model. The sum of these spectral densities, the total short‐wave spectral density, was similar to, but lower than, previous measurements. The nature of millimeter‐length bound waves was found to be different at long fetches than at short fetches, a feature not observed in centimeter‐length bound waves.

Energy: converting from acoustic to biological resource units.

Acoustic backscattering strength is often used as an index of biomass; however, the relationship between these variables has not been directly validated. Relationships were investigated between acoustic cross section at 200 kHz, measured as part of a previous study, and measured values of length, biovolume, dry weight, ash-free dry weight, and caloric content of the same individual specimens. Animals were part of the Hawaiian mesopelagic boundary community and included shrimps, squids, and myctophid fishes. The strong relationships found between all the variables measured make it possible to approximate any one variable from the measured values of others within a class of animals. The data show that for these midwater animals, acoustic scattering can be used as an index of biomass. Dorsal-aspect acoustic cross section at 200 kHz predicted dry weight and ash-free dry weight at least as well as did body length, a standard predictor. Dorsal-aspect acoustic cross section at 200 kHz was also a strong predictor of total caloric content. The relationship between dorsal-aspect acoustic cross section and caloric content of Hawaiian mesopelagic animals was linear and additive. Consequently, it is possible to directly convert acoustic energy from these animals to organic resource units without having knowledge of the size distribution of the populations being studied.

Project Artemis—A retrospective view

Approximately 45 years ago, the Underwater Acoustics Community of the U.S. undertook a massive research program called Project Artemis. The objective of this endeavor was to determine what were the necessary capabilities needed to build an active mono-static sonar that was capable of detecting a submerged submarine at ranges of about 1000 km. Although no operational capability ever resulted from this effort, the research undertaken by this project identified the limitations in existing technology and in the community’s knowledge of underwater water acoustics that precluded achievement of the original objective. In the area of technology, the most obvious limitation was the limited speed of available computers that forced the use of cumbersome analog devices for signal processing and for beam steering. Techniques for controlling the location of the source dynamically and for the construction and for the operation of large-scale acoustic high-powered phased arrays were developed successfully. Unresolved issues that formed the basis for future research efforts related to signal coherence time, low-frequency acoustic cross sections of submarines, the development of reliable computation models for propagation loss, low-frequency acoustic absorption processes in ocean, and the development of algorithms that accounted for source Doppler. Project Artemis terminated in the mid-1960s.

Surf zone bubble spectrometry: The role of the acoustic cross section

Fifty years ago, there were doubts as to whether microbubbles existed in the sea at all. Herman Medwin settled the issue in the 1960s by showing that they were indeed present, and in very large numbers. He interpreted in situ measurements of backscatter and attenuation using the concept of the acoustic cross section. In essence that procedure forms the basis of the most popular ways of measuring microbubbles today, the two favored experimental layouts (measurement of attenuation and sound speed along a propagation path, and the acoustical resonator) being based on techniques pioneered by Medwin. In recent years attempts have been made to take these open ocean techniques and deploy them in the surf zone. Here the assumptions inherent in the standard form of the cross section can be violated. Specifically, the conditions may not relate to plane wave insonification of isolated bubbles undergoing steady state single-frequency linear pulsations in the free field in an incompressible liquid. This paper describes the attempts that have been made to produce cross sections which are not restricted by these limitations, and how these are exploited in determining the evolution, anatomy, and effects of bubble clouds. [The support of The Royal Society Leverhulme Trust is acknowledged.]

Gas cavities in phytoplankton

Acoustical and related properties of phytoplankton suspensions were investigated in laboratory conditions and in situ. A review of studies is present. It was found that cells have gas cavities which allow them to keep a neutral buoyancy. Under sharp compression gas cavities dissolve and recover only under the light exposition. Such properties can explain an anomalous migration of some sound scattering layers. The use of the compression/decompression method allowed us to find gas cavities in blood erythrocites also. The 6.5-MHz acoustic backscattering from phytoplankton suspensions was applied for characterization of reverberation level under the natural condition and compression (up to 5 atm), which allowed us to evaluate a relative volume of gas cavities in cells. Gas cavities increase an acoustical cross section by 2–3 orders. A dispersion of sound velocity in phytoplankton suspensions with the phase and the resonance methods (from 200 Hz to 11 MHz) for six kinds of living cell suspensions was also studied. Both the increase and decrease of sound velocity dispersion with frequency was observed. The effect is different for cells of different kinds. [Work supported in part by RFBR, Russia.]

Airborne Insects as Potential Sources of Acoustic Reflectivity

Abstract Laboratory measurements of the acoustic backscattering cross sections of a variety of insects at 3.4 kHz are reported. The authors argue from these data, and from what is known (from radar studies) about insect concentrations in the lower atmosphere, that acoustic returns from insects may seriously contaminate sodar data. They suggest that this possibility should be carefully considered when interpreting backscatter coefficient data acquired in acoustic sounding experiments.

Gas bubbles in phytoplankton

Phytoplankton plays a very important role in gas exchange in the ocean. But until now it has not been considered as acoustically significant as zooplankton. The existence of gas cavities in phytoplankton cells was suggested a long time ago but has not been detected so far because of early methods of observation. The review of recent works on acoustical investigations of gas bubbles associated with phytoplankton cells is given in this paper. Acoustical and related properties of phytoplankton suspensions were studied under laboratory conditions and in situ by several methods including acoustic 6.5-MHz backscattering under ordinary conditions with additional compression up to 5 atm. It was observed that, under the sharp compression gas cavities dissolve and recover under the light exposition. The volume of gas cavity associated with a phytoplankton cell was found to be up to 0.3 of the volume of a cell for different alga species. Such a bubble may increase the acoustical cross section of a pure cell by 2–3 orders. Roles of phytoplankton bubbles for sound propagation, for anomalous migration of some sound scattering layers, and for hydrodynamic cavitation in the subsurface layer and in wakes of sea animals are discussed. Experimental examples are given. [Work was supported by RFBR (Grant No. 95-05-15632).]

On counting ocean bubbles acoustically

The earliest attempts to determine ocean bubble densities were optical, because everyone knows that ‘‘seeing is believing.’’ Unfortunately, bubbles smaller than 60-μm radius were not always recognized in photographs of the dirty, detritus-contaminated, bubbles. And bubbles greater than 150-μm radius were so infrequently observed that the average values were quite unreliable. Acoustical ‘‘counting’’ by inversion of the linear processes of backscatter, excess attenuation, and dispersion has great advantages over optical measurements. Primarily this is because the acoustic cross sections of a resonating bubble are orders of magnitude greater than optical values for the same radius. The ability to gather data rapidly, the ease of obtaining correlations with other oceanographic variables, and the simple inverse relation between sound frequency and resonant bubble radius have given acoustics great advantages over optical bubble-counting at sea. For 30 years, at several locations, under various ocean conditions, active in-situ pulse echo systems and resonators using broadband transducers have yielded a rich harvest of well-resolved data for bubble radii from 15 to 300 μm. More recently, by passively listening to newly created damped oscillating bubbles, acousticians have provided meteorologists and climatologists with accurate fundamental data of ocean surface gas transfer and hydrosol production due to breaking waves and rainfall. Techniques and results of active and passive linear acoustical monitoring are reviewed. [Research supported by ONR.]

Acoustical properties of interacting particles

Acoustical cross sections of random homogeneous dense systems of interacting Rayleigh particles are studied analytically. A model for the radial distribution function is proposed. The role of the far-field and the near-field effects on the acoustic characteristics is investigated. It is found that the near-field effect on the scattered sound is negligible compared to the far-field effect. The validity of some assumptions is investigated. It is found that interaction among particles may increase or decrease the attenuation effect depending on the volume fraction and the properties of the particulate system.

Effects of changing spatial scale on acoustic observations of patchiness in the Gulf Stream

We examine the influence of spatial scale on studies of nektonic patchiness at the north edge of the Gulf Stream by altering the grain size of acoustic cross sections and applying a patch-finding algorithm. From original ‘pictures’ of 180 pixels deep by 540–1260 pixels long, we averaged depth and length, to give 9 scales ranging from fine grain (1 m vertical × 25 m horizontal sized pixels) to coarse grain (12 m × 300 m sized pixels). Measures of overall echo intensity within patches were the most predictable and showed little change with scale. Measures of variability of the echo within patches showed simple negative trends with scale and were best measured at fine spatial scales. Patch size and shape related variables have a more complex relationship with scale with differences between day and night transects more pronounced at intermediate scales. This suggests behavioral patch forming mechanisms within the nekton occur at a specific grain size (4 m vertical × 100 m horizontal) within the Gulf Stream front.

A statistical approach for the scattering of sound from elastic objects

The scattering cross section of an extended elastic body is usually a very irregular function of frequency. This is partly due to the vibrational characteristics of the body and partly due to interference effects. The related problem of predicting the response of a body to localized excitation or a reverberent field has been analyzed using the statistical energy analysis and the mean value method with some success. In this paper, statistical methods are employed to predict aspects of the acoustic cross section of some relatively simple, extended objects.

Acoustical absorption and scattering cross sections of spherical bubble clouds

The present work investigates the acoustical absorption and scattering cross sections of spherical bubble clouds subject to harmonic farfield pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility, and relative motion of the two phases are included. The equations of motion for the average flow and for the bubble radius are linearized and a closed-form solution is obtained. Due to the presence of natural oscillatory modes and frequencies, the acoustical cross sections of the cloud are very different from those of each individual bubble in the cloud, as well as from the acoustical cross sections of a single large bubble with the same volume of vapor and gas. In general, the acoustical properties of any given volume of the dispersed phase depend strongly on the degree of dispersion because of the complex interactions of the dynamics of the bubbles with the whole flow.

A simple model for the acoustic cross section of sand grains

Previous work on determining the acoustic cross section of sand grains [Geophys. Res. Lett. 9(2), 175–178 (1982)] identified a problem with the application of the simple compressible sphere model for the cross section. Use of the complete elastic sphere model [J. Acoust. Soc. Am. 34, 1582–1592 (1962)] failed to remove the conflict with observation. Application of the bistatic cross-section theorem to the angle averaged cross section shows that the appropriate cross section is the total absorption cross section, not the backscatter cross section. The total absorption cross section for the fluid sphere model is found to be in semiquantitative agreement with scattering data for sand grains.

On the classification of underwater acoustic signals. II. Experimental applications involving fish

In a previous paper (Part I) a general approach to adaptive classification has been presented. That approach is applied here (Part II) to classification of waveforms obtained in a number of illustrative experiments. Experiments at 116 kHz (in the ARL Test Tank Facility) have provided backscattered waveforms (echoes) from known types of scatterers, randomly located and with random acoustic cross sections. Scatterers of primary interest here are a variety of small fish. Signals which form competing categories are scattering from seaweed (aquarium grass), surface reverberation, and artifacts (glass bottles). The data obtained are representative of three classification problems that have some practical significance in underwater acoustics. These three problems require distinguishing between the received signals which result from scattering by: (1) fish versus air–water surface, seaweed, and/or artifacts; (2) fish and air–water surface versus air–water surface only; and (3) ’’low density’’ versus ’’medium density’’ versus ’’high density’’ of fish. In each case the waveforms are analyzed and features appropriate to the classification task are extracted from a portion of the data. These features are then used to design a classification algorithm for the environmentally adaptive approach and for its conventional counterpart. These algorithms are then used on the remaining data to make classifications. The superiority and usefulness of the proposed environmentally adaptive approach is demonstrated here by the noticeable improvement in quantitative classification which results from the exploitation of environmental state data.