Roughness Statistics Research Articles

Temporal prediction of acoustic backscatter from sediments at 10–250 kHz

A temporal model of high-frequency (10–250 kHz) seafloor acoustic backscatter has been developed which simulates the average squared echo envelope from a monostatic echo sounder. Tests comparing the model to measured backscatter echoes from pelagic and terrigineous sediments are presented, and the diminishing contribution of the sediment volume with increasing acoustic frequency is demonstrated. The temporal model was developed to assist in the identification of sediments by statistically comparing its output to the echo amplitude time series measured with bottom mapping sonars. The model incorporates the sonar geometry, electroacoustic transfer function and transmitted signal characteristics, the ocean volume parameters, the statistical geoacoustic parameters which describe the water/bottom interface and the sediment volume, and the multiscale roughness statistics of the interface for the bottom types being investigated. [Work supported by ONR.]

Angular memory effect of millimeter‐wave scattering from two‐dimensional conducting random rough surfaces

An experimental study was conducted to investigate the angular memory effect of millimeter‐wave scattering from two‐dimensional conducting random rough surfaces. The surfaces under investigation were machine‐fabricated with known Gaussian roughness statistics, and the copolarized and cross‐polarized angular correlation functions (ACFs) of scattering amplitudes were measured. It was found that for the case of reference antenna positions located bistatically in a backward direction, the measured ACF exhibits broad response when single scattering dominates but two peaks when multiple scatteringdominates. These observations are in good agreement with the second‐order Kirchhoff approximation (KA2). Specifically, the observed broad and peak responses are analytically identified to be due to the first‐order and second‐order (ladder and cyclical) scattering components, respectively, in KA2.

Experimental studies of bistatic scattering from two-dimensional conducting random rough surfaces

Despite the recent development of analytical and numerical techniques for problems of scattering from two-dimensional rough surfaces, very few experimental studies were available for verification. The authors present the results of millimeter-wave experiments on scattering from two-dimensional conducting random rough surfaces with Gaussian surface roughness statistics. Machine-fabricated rough surfaces with controlled roughness statistics were examined. Special attention was paid to surfaces with large rms slopes (ranging from 0.35 to 1.00) for which enhanced backscattering is expected to take place. Experimentally, such enhancement was indeed observed in both the copolarized and cross-polarized returns. In addition, it was noticed that at moderate angles of incidence, the scattering profile as a function of observation angle is fairly independent of the incident polarization and operating frequency. This independence justifies the use of the geometric optics approximation embodied in the Kirchhoff formulation for surfaces with large surface radius of curvature. When compared with the experimental data, this analytical technique demonstrates good agreement with the experimental data.

Subcritical penetration of sandy sediments due to interface roughness.

Seafloor roughness can cause acoustic energy to propagate into sediments for ‘‘subcritical’’ incident grazing angles, that is, grazing angles smaller than the critical angle determined by the compressional wave speed. Such effects must be considered in interpreting experimental data on sound penetration into sediments. The sediment is modeled as a fluid supporting only compressional waves and a twofold theoretical approach is used. First, an exact integral equation is solved numerically to obtain the penetrating field in two dimensions. Physical insights are abstracted from these results which are also used to show that perturbation theory is valid for problems of interest. Using perturbation theory, a numerically tractable three-dimensional model is compared to some of the experimental data of Chotiros and colleagues [N. P. Chotiros, J. Acoust. Soc. Am. 97, 199–214 (1995)]. The model and data match well subject to plausible assumptions about roughness statistics. [Work supported by ONR.]

Experimental studies on the phase distribution of two copolarized signals scattered from two-dimensional rough surfaces

The experiment results of the phase distribution of millimeter-waves scattered from two-dimensional rough surfaces of controlled surface roughness statistics are presented. The statistics of /spl phi//sub vv/-/spl phi//sub hh/ were obtained for different surfaces, including very rough surfaces which are known to create backscattering enhancement. It is shown that the distribution of /spl phi//sub vv/-/spl phi//sub hh/ is strongly related to the surface roughness. In addition, the authors found that the standard deviation decreases as the incidence angle increases. This phenomena is contradictory to the reported data of radar scattering from soil.

Role of tape abrasivity on friction, wear, staining and signal degradation in audio tapes

Audio tapes with varying amounts of head cleaning agent (HCA), pigment volume concentration (PVC) and lubricant concentration were run against a mu-metal audio head in a linear tape drive. Surfaces were characterized with atomic force microscope (AFM). Head wear was measured using a Knoop indentation technique in which the change in the length of the indent diagonal corresponds to the wear depth. Any formation of head stains was optically observed. An electrical sine wave signal was recorded at different frequencies. Degradation in this signal was measured by measuring the changes in its RMS value. Coefficients of friction for each tape were measured using an off-line friction tester. Tests were also conducted on uncalendered tapes with various HCA contents. Tapes with different HCA contents, PVC and lubricant levels have the same average roughness statistics, within a given roughness matrix. Consequently, they exhibit similar friction characteristics. Increasing HCA and/or roughness reduces propensity of head stains, resulting in better signal reproduction at the expense of higher head wear. However, there seems to be a limit to improving signal quality by increasing HCA or roughness. Increase in PVC results in a slight decrease of head wear and better signal reproduction. Signal reproduction remains largely unaffected by varying lubricant level. Head wear however slightly increases with decreasing lubricant content. Abrasive wear is the dominant wear mechanism for the head in each case as evidenced by extensive scratches on the head surface. Adhesive transfer debris is also formed by each tape. The tape wear occurs mainly by burnishing, i.e. high asperities on the tape surface are knocked off during the wear process. This study provides a data base which is expected to be useful to design engineers in predicting behavior of new tape formulations and plant engineers in understanding the implications of their process variability.

Modeling of three-dimensional seismoacoustic reverberation from anisotropic roughness patches

A perturbation approach to narrow- and wideband modeling of scattering from roughness patches on an interface separating a fluid and an elastic half-space has previously been developed [LePage and Schmidt, J. Acoust. Soc. Am. 89, 1941(A) (1991)]. However, based on a 2-D Fourier transform formulation it allows for modeling of the scattered near-field only, and it prohibits incorporation of waveguide effects. Here, a coordinate transformation is presented, yielding a representation of the virtual seismic moment sources for the scattered field in cylindrical coordinates. This source representation is compatible with the 3-D version of the OASES/SAFARI code, which has consequently been modified to provide extremely efficient numerical simulation of seismoacoustic reverberation in shallow- and deep-water waveguides. This new model has been applied to model the reverberation from horizontal roughness patches in the ARSRP mid-Atlantic environment. The model’s efficiency has allowed for Monte Carlo estimation of the statistical properties of the reverberation from patches with anisotropic roughness statistics, including mean reverberation intensity and spatial correlation. The effects of roughness anisotropy, bottom elasticity and the waveguide physics are discussed. The principal result of this theoretical analysis is the conclusion that Lambert’s law is totally inadequate for representing bistatic bottom reverberation. This conclusion is consistent with the results of the analysis of the bistatic data from the ARSRP experiment, as discussed in the companion paper by Bondaryk etal. [Work supported by ONR.]

Trans-Arctic propagation effects of changes in ice morphology

The objective of the Trans-Arctic Propagation (TAP) experiment carried out in the spring of 1994 was to investigate the feasibility of using acoustic thermometry for inferring changes in the Arctic climate [P. Mikhalevsky, J. Acoust. Soc. Am. 94, 1760(A) (1993)]. An important issue is which acoustic property will provide the strongest climate change signature. The sensitivity of various properties of the acoustic field to changes in ice volume was investigated theoretically. A perturbation formulation for 3-D scattering from rough ice has been combined with the kraken normal-mode code to provide a model of the second-order statistics of the acoustic field. Such a hybrid model has been shown to provide excellent agreement with historical Arctic transmission loss data [LePage and Schmidt, J. Acoust. Soc. Am. 96, 1783–1795 (1994)]. We use this model to investigate the sensitivity of deterministic properties of the coherent field, such as modal loss, and modal phase and group velocity, to change in ice thickness and roughness statistics. In addition, the model has been use to investigate the sensitivity to changes in the ice cover of the higher-order statistics such as cross-modal correlation, and spatial correlation in general. Comparing these theoretical sensitivity measures, we discuss the potential performance of both deterministic and statistic acoustic thermometry in the Arctic.

Temporal model of high-frequency seafloor acoustic backscatter

A monostatic temporal model of seafloor acoustic backscatter has been developed to investigate the relative contributions of interface roughness and inhomogeneities in the sediment volume for measurements made at various angles of incidence. The model takes into account sonar parameters such as acoustic wavelength, beam pattern, pulse length, and angle of incidence, and it includes a theoretical angular dependence of seafloor scattering strength that is controlled by the roughness statistics of the surface insonified, by its refraction index, and by a volume reverberation term. Simulations have been carried over angles of incidence from 0° to 60°, and at acoustic frequencies ranging from 10 to 100 kHz for various types of substrates. The theoretical angular dependence predicts that the contribution from the sediment volume becomes noticeable for angles of incidence greater than about 6°; however, in the temporal model it is shown that this contribution can be detected closer to normal incidence for small beamwidths (e.g., 2°). When applied to a multi-narrow-beam sonar geometry this temporal model shows greater potential for bottom classification than the angular dependence function of acoustic backscatter obtained by integrating the returns received in each beam. [Work supported by ONR.]

Scanning tunneling microscopic roughness statistics on the electrochemical quartz microbalance

Morphological changes and reconstractions of metallic electrode surfaces can prevent direct monitoring of the molecular organization in the electrochemical double layer by means of the electrochemical quartz microbalance (EQMB). Roughness can feign mass charges by carrying electrolyte in surface pockets. There are contradictory results from EQMB, charge, and scanning electron microscopy morphology investigations. We resolved these problems by a statistical evaluation of scanning tunneling microscopic images at gold surfaces emersed at relevant potentials. No roughness was observed in the hyfroxide monolayer potential region because this is thermodynamically more favourable, especially in base, than growth of a three-dimensional hydroxide layer involving molecular place exchange connected with roughening.

Copolarized and cross‐polarized enhanced backscattering from two‐dimensional very rough surfaces at millimeter wave frequencies

Wideband millimeter wave experiments from 75–100 GHz on the scattering from two‐dimensional very rough conducting surfaces are presented. The two‐dimensional very rough surfaces are manufactured using a computer‐numerical‐controlled milling machine so that the surface statistics are precisely controlled. The surfaces have both Gaussian roughness statistics and Gaussian surface correlation functions. Bistatic scattering experiments on surfaces with either isotropic or anisotropic correlation functions are performed. Copolarized and cross‐polarized bistatic scattering cross sections are measured for both transverse electric and transverse magnetic incidence at 20°. For isotropic surfaces, backscattering enhancement exists for both copolarized and cross‐polarized returns and is found to be a function of the surface rms slope. In addition, a strong frequency dependence is observed across the 25‐GHz bandwidth in the cross‐polarized returns. To investigate the effect of surface correlation anisotropy, scattering experiments on anisotropic rough surfaces are also performed. It is found that the bistatic scattering cross section for an anisotropic surface is a function of the effective correlation length projected along the plane of scattering. Results on the bistatic scattering experiments presented here serve as a motivation to further pursue more elaborate and complete scattering experiments in order to advance research on scattering from very rough surfaces.

Source localization in an uncertain acoustic scattering environment

The sensitivity of conventional matched-field processing algorithms to uncertainty in ocean acoustic environmental parameters has prompted the design of more robust methods for source localization. In a recent study, Richardson and Nolte [J. Acoust. Soc. Am. 89, 2280–2284 (1991)] reported on the development of a new algorithm which incorporates prior knowledge of the environmental uncertainty into the design of the matched-field processing algorithm. The result was the optimum uncertain field processor (OUFP). The present study addresses the problem of source localization in an imperfectly known acoustic scattering environment. The propagation scenario of interest, the surface duct, is characterized by the property that the received pressure field consists primarily of rays which are scattered from the sea surface. The surface roughness statistics are presumed to be axisymmetric, parametrized by rms height and correlation length. Two approaches to modeling the scattered field will be considered (1) the Eckart reflection coefficient and (2) numerical evaluation of the Helmholtz–Kirchhoff integral for the quadrature components in the specular direction. In each case, simulation results demonstrate that the OUFP outperforms a conventional matched-field processor when surface statistics are imperfectly known. It is also noted that, in the context of source localization, the Eckart method is only suitable for modeling scatter from slightly rough surfaces. For rougher surfaces, it is seen that combining the Kirchhoff model with the OUFP algorithm results in robust localization performance for a propagation channel that is dominated by acoustic interaction with a nondeterministic boundary.

Near-normal incidence scattering from rough, finite surfaces: Kirchhoff theory and data comparison for arctic sea ice

The Kirchhoff theory is applied for the target strength of a rough, circular surface whose roughness is characterized by a two-dimensional, isotropic power-law wave number spectrum, W2(κ) = η2κ−p2. The reflection coefficient for ice and three nondimensional parameters are found to govern the target strength. These parameters are ζ=κ0a, η≡η2ap2−4, and p1=p2−1, where κ0 is the acoustic wave number, a is the radius of the surface, and p1 is the spectral exponent of the one-dimensional power-law wave-number spectrum from which W2(κ) is derived. The general influence of ζ, p1, and η on the target strength is discussed. Calculations of average target strength of the ice/water interface of a submerged cylindrical block of ice are shown, which are then compared with individual realizations of measured target strengths of ice blocks for ζ between 25 and 100, corresponding to frequencies between 20 and 80 kHz for a=0.29 m. Data and theory show that the (smooth surface) form function for a finite surface does not describe the observed diffraction pattern. Instead, the lobes of the pattern diminish and the nulls fill in—i.e., the total backscatter becomes more incoherent—as frequency increases or as the large wave-number components of the roughness spectrum contribute more to the total acoustic return. These comparisons also allowed us to infer the rough surface statistics of the ice surface and the compressional sound-speed structure within the skeletal zone of the ice.

Modeling and analysis of low‐angle ice canopy reverberation in the Arctic

Recent advances in modeling coherent loss in the Arctic have made it possible to attempt a constrained inversion of monostatic Arctic reverberation for the ice scattering matrix. An analysis is presented of low‐frequency active reverberation data collected in the Central Arctic in 1992 where such an inversion yields meaningful results and compare them to theoretical predictions. Historical and measured ice roughness statistics collected in tandem with the acoustic portion of the experiment were used to obtain elastic perturbation theory predictions of scattering loss and backscatter. These losses were integrated into the Kraken normal mode model to yield highly accurate predictions of the coherent signal structure to very long ranges in the Arctic waveguide, as verified by TL measurements. Based on these predictions, a significant portion of the time/frequency structure of the backscattered return received on a 256‐element hydrophone array was modeled. To construct a well‐conditioned inverse problem, prop...

Controlled millimeter‐wave experiments and numerical simulations on the enhanced backscattering from one‐dimensional very rough surfaces

We present experimental results on the scattering of electromagnetic waves at millimeter‐wave frequencies from one‐dimensional very rough conducting surfaces with controlled surface roughness statistics. Very rough surfaces are defined as surfaces with rms height and correlation length of the order of a wavelength such that the rms slope is at least unity. It is expected that scattering experiments using these surfaces can provide useful insights since their statistics lie outside the range of validity of the present theories, namely, the Kirchhoff and perturbation theories. Strong backscattering enhancement at different incident angles, both in the transverse electric and transverse magnetic polarizations, are observed experimentally. Numerical calculations based on the exact integral equation method for cylindrical beam wave illumination compare favorably with the experimental results. The agreement between measurements and numerical calculations is good over a wide range of incident angles and for all scattering angles. The close agreement between the experimental results and numerical simulations indicates that this controlled experimental setup can be used to study scattering phenomena from one‐dimensional very rough surfaces with different roughness statistics as well as from two‐dimensional rough surfaces.

The Effect of Two-Dimensional Surface Roughness on the Load-Carrying Capacity of a Thin Compressible Gas Film

The influence of two-dimensional surface roughness on a very low clearance gas bearing slider is analyzed for conditions typical of current and near term hard disk data storage products. A model lubrication equation including finite width effects, compressibility and molecular slip is first developed and expressed in terms of the product variable, Z = PH. The analytical solution is then obtained by a combined variation of parameters and perturbation expansion method. Results obtained show that the product variable, which is proportional to longitudinal mass flow per unit depth, is not influenced by the details of surface roughness but is instead influenced by the statistics of the roughness distribution. The gas film pressure, however, is found to be a function of both the roughness details and statistics. The bearing load support is increased by the surface roughness, with the roughness first influencing the load through a second order effect.

Ice canopy roughness inversion and Arctic propagation loss estimates via elastic perturbation theory

Low-frequency (f≪100 Hz) boundary interaction loss in the central Arctic has been observed to exceed the losses that may be predicted by free surface Kirchhoff or MSP scattering theories, 2-D boss scattering models, or large elastic feature scattering arguments. In addition, the measured frequency dependence of the scattering loss in the Arctic (∝f1.5) is lower than that which is predicted with either the boss or the large elastic feature scattering models. Here a self-consistent elastic perturbation theory is used to estimate coherent boundary interaction loss for the Arctic scenario. Using this theory it is found that the elasticity of the ice canopy can account for a substantial decrease in the local coherent reflection coefficient in comparison with a rough free surface interaction, while the frequency dependence of the loss remains proportional to f2. Using acoustics measurements obtained by a horizontal array under the Arctic ice, a ML inversion for the ice canopy roughness statistics is obtained using the perturbation theory, and these parameters are used to estimate the loss per interaction. This loss, when combined with a ray cycle distance taken from the relevant literature, yields an estimate of scattering propagation loss (dB/km), which closely matches the data in the low-frequency regime. When the canonical roughness parameters and cycle distances from the literature are used in the theory, the estimated loss is lower, but improvements are still obtained over the free surface results. [Work supported by ONR.]

Scattering cross sections for non-Gaussian rough surfaces: unified full wave approach

The unified wave approach is used to compute both the like- and the cross-polarized scattering cross sections for composite rough surfaces characterized by a family of gamma functions of order K ranging from K=1 to K=25. This family of joint height probability density functions properly decorrelates to the product of the marginals as the surface height autocorrelation function vanishes. These results are compared with the like and cross-polarized cross sections for the surface with Gaussian characteristics (K to infinity ). It is shown how radar could be used most effectively to remotely sense the rough surface statistics of non-Gaussian rough surfaces. >

Seismo-acoustic rough bottom scattering of ambient noise in a stratified ocean.

A previously developed formulation [J.-Y. Liu and H. Schmidt, J. Acoust. Soc. Am. 89, 2013 (1991)], based on a combination of theories for rough interface scattering in a stratifed medium [W. A. Kuperman and H. Schmidt, J. Acoust. Soc. Am. 86, 1511–1522 (1989)] and for the noise field produced by distributed random sources at the sea surface [W. A. Kuperman and F. Ingenito, J. Acoust. Soc. Am. 67, 1988–1996 (1980)], has been applied to a realistic ocean model to explore the noise field characteristics due to the rough bottom scattering of ambient noise. The scattering mechanism established in the previous study was able to account for the high noise levels in an otherwise ‘‘quiet’’ bottom of an upward refracting deep ocean environment. The intensity and spatial correlation of the overall noise field have been examined. It is demonstrated that the existence of the rough interfaces greatly affects the noise field; in particular, the rescattering of Scholte waves due to roughness accounts for the major scattering energy near the bottom of the ocean, and the rough surface statistics shows a dominant effect on the spatial characteristics of the noise field. [Work supported by NOARL.]

Three‐dimensional rough interface scattering of ambient noise

Based on the previously developed theory of perturbation approach to rough surface scattering [W. A. Kuperman and Henrik Schmidt, J. Acoust. Soc. Am. 86, 1511–1522 (1989)] and a model for the noise field generated by surface random sources in an occean waveguide [W. A. Kuperman and F. Ingenito, J. Acoust. Soc. Am. 67, 1988–1996 (1980)], a formulation for rough interface scattering of surface‐generated ambient noise in a horizontally stratified ocean is established. The result is then applied to study the three‐dimensional scattering in a shallow‐water waveguide environment bounded below by a viscoelastic medium. The three‐dimensional spatial correlation of the reverberated noise in the waveguide and the scattered noise in the elastic medium are examined in terms of the relation to frequency, water depth, and rough interface statistics. It is demonstrated that even in deep water, the scattering of surface generated noise into interface waves (Scholte waves) is important, showing these waves carriers of amb...