Large Depth Variations Research Articles

Robust Regression for the Detection of Independent 3D Motion by a Binocular Observer

A method is proposed for the visual detection of objects that move independently of the observer in a 3D dynamic environment. Many of the existing techniques for solving this problem are based on 2D motion models, which is equivalent to assuming that all the objects in a scene are at a constant depth from the observer. Although such methods perform well if this assumption holds, they may give erroneous results when applied to scenes with large depth variations. Additionally, many of the existing techniques rely on the computation of optical flow, which amounts to solving the ill-posed correspondence problem. In this paper, independent 3D motion detection is formulated using 3D models and is approached as a problem of robust regression applied to visual input acquired by a binocular, rigidly moving observer. Similar analysis is applied both to the stereoscopic data taken by a non-calibrated stereoscopic system and to the motion data obtained from successive frames in time. Least Median of Squares (LMedS) estimation is applied to stereoscopic data to produce maps of image regions characterized by a dominant depth. LMedS is also applied to the motion data that are related to the points at the dominant depth, to segment the latter with respect to 3D motion. In contrast to the methods that rely on 2D models, the proposed method performs accurately, even in the case of scenes with large depth variations. Both stereo and motion processing is based on the normal flow field, which (in contrast to the optical flow field) can be robustly computed from the spatiotemporal derivatives of the image intensity function. Although parts of the proposed scheme have non-trivial computational requirements, computations can be expedited by various ways which are discussed in detail. This is also demonstrated by an on-board implementation of the method on a mobile robotic platform. The method has been evaluated using synthetic as well as real data. Sample results show the effectiveness and robustness of the proposed scheme.

Bathymetric roughness of the Southeast Indian Ridge: Implications for crustal accretion at intermediate spreading rate mid‐ocean ridges

The nature of the transition from axial highs to axial valleys at mid‐ocean ridges and the physical processes involved in the transition are important for understanding how axial morphology changes with spreading rate, mantle temperature, and lithospheric strength at mid‐ocean ridges. In order to provide observational constraints on the nature of the changes in axial morphology, we examined the regional‐ and segment‐scale variations in axial and flank morphology at the intermediate spreading Southeast Indian Ridge (SEIR) using newly collected geophysical data. An empirical orthogonal function analysis was used to separate regional and local components of the topography field and to estimate bathymetric roughness. Three distinct types of axial morphology were identified from the regional component of ridge topography in our area: axial highs, shallow axial valleys, and “Mid‐Atlantic Ridge‐type” deep axial valleys. Axial depth increases by ∼2100 m from 88°E and 118°E, while off‐axis depth only increases by ∼500 m. In addition, except for one segment with a deep axial valley, there is little change in off‐axis depth within segments, in contrast to the large intrasegment variations in axial depth. These observations indicate that the overall and intrasegment variations in crustal thickness are much smaller than would be predicted from the variations in axial depth and that the major portion of the variations in ridge axis depth are dynamically supported. There are step‐like increases in bathymetric roughness as axial morphology changes from an axial high to a shallow axial valley and from a shallow axial valley to a deep axial valley. The step changes in roughness imply that the change from one mode of axial morphology to another is accompanied by an abrupt change in the strength of the lithosphere. The abrupt changes in lithospheric strength may be due to the existence of a “threshold” mantle temperature or crustal thickness about which the lithospheric strength is very sensitive to small fluctuations. Systematic intrasegment variations in roughness are also observed. Roughness shows V‐shaped patterns within segments with axial highs but no clear pattern within segments with axial valleys. The different patterns in roughness at axial highs and axial valleys on the SEIR may result from the presence or absence of a magma chamber. The presence of a magma chamber at a ridge segment with an axial high implies weaker axial lithosphere and hence lower roughness near the center of segments relative to the segment ends.

Resolving Redshifted Molecular Absorption toward the Gravitational Lens PKS 1830−211

Using the high-resolution configuration of the BIMA array, we have spatially resolved molecular absorption at z = 0.89 toward the gravitational lens PKS 1830-211. Two continuum sources are detected at λ3 mm separated by 098 at the known positions of the doubly lensed radio core. Broad molecular absorption of width 40 km s-1 is found toward the southwest component only, where surprisingly it does not reach the base of the continuum, despite the large optical depth inferred from the molecular transitions (Wiklind & Combes). This implies incomplete coverage of the southwest component, ~70%, by the molecular gas, despite the small projected size of the source, less than 8 h-1 pc at the absorption redshift. Similar saturated but unfilled columns of low-density molecular gas are found in absorption through the spiral arms of the Milky Way, with large variations in column depth on parsec scales, indicating that the southwest component of PKS 1830-211 may be occulted by an ordinary spiral arm. At spectral resolution better than 5 km s-1, we might expect the broad molecular absorption of PKS 1830-211 to resolve into multiple narrow lines.

Depth variation of the mid‐mantle seismic discontinuity

Short‐period array seismograms of deep events that occurred in the Indonesia, Japan and Izu‐Bonin arcs are stacked and beam‐formed to identify the near‐source S‐P converted waves that result from the mantle transition discontinuities. Most of the resulting images reveal the existence of a mid‐mantle seismic discontinuity (“920 km discontinuity”) in these regions. Of the 15 events analyzed, three that occurred at the western end of the Indonesia arc show clear S‐P arrivals observable even in individual seismograms. The mid‐mantle discontinuity is characterized by large depth variation (900 ∼ 1080 km) and velocity contrast variation in different subduction zones. Especially, the depth variation of the mid‐mantle discontinuity beneath the Indonesia arc, where the discontinuity deepens from 940 km at the eastern end to 1080 km at the western end, appears to be well correlated with the location of the high‐velocity anomalies in recent tomographic models. However, the mid‐mantle discontinuity cannot be simply coincided with the bottom of the high‐velocity anomalies, because a velocity increase at the discontinuity is observed from the waveform analysis.

Educational Psychology: What Do We Teach, What Should We Teach?

Teacher education students sometimes question the value of educational psychology courses even though educational psychology textbooks are primarily concerned with understanding and improving classroom teaching and learning. A survey of current educational psychology textbooks and instructors reveals that (a) most texts cover a wide variety of topics, (b) instructors rate most of these topics as important, (c) there are large variations in depth of coverage among texts, and (d) all texts contain numerous classroom applications. The questionable reputation of the educational psychology course may stem from its broad coverage. A dozen or more topics in one semester may decrease the probability that most students will achieve a solid grasp of any one topic, leaving students uncertain about the course's meaning and applicability. A proposed solution is to offer the introductory course as a two-semester sequence, with the second course offered as an elective.

Validation of Satellite Retrievals of Cloud Microphysics and Liquid Water Path Using Observations from FIRE

Cloud effective radii (re) and cloud liquid water path (LWP) are derived from ISCCP spatially sampled satellite data and validated with ground-based pyranometer and microwave radiometer measurements taken on San Nicolas Island during the 1987 FIRE IFO. Values of re derived from the ISCCP data are also compared to values retrieved by a hybrid method that uses the combination of LWP derived from microwave measurement and optical thickness derived from GOES data. The results show that there is significant variability in cloud properties over a 100 km×80 km area and that the values at San Nicolas Island are not necessarily representative of the surrounding cloud field. On the other hand, even though there were large spatial variations in optical depth, the re values remained relatively constant (with σ≤2–3 µm in most cases) in the marine stratocumulus. Furthermore, values of re derived from the upper portion of the cloud generally are representative of the entire stratiform cloud. When LWP values are less than 100 g m−2 then LWP values derived from ISCCP data agree well with those values estimated from ground-based microwave measurements. In most cases LWP differences were less than 20 g m−2. However, when LWP values become large (e.g., ≥200 g m−2), then relative differences may be as large as 50%–100%. There are two reasons for this discrepancy in the large LWP clouds: 1) larger vertical inhomogeneities in precipitating clouds and 2) sampling errors on days of high spatial variability of cloud optical thicknesses. Variations of re in stratiform clouds may indicate drizzle: clouds with droplet sizes larger than 15 µm appear to be associated with drizzling, while those less than 10 µm are indicative of nonprecipitating clouds. Differences in re values between the GOES and ISCCP datasets are found to be 0.16±0.98 µm.

Impact of waste from titanium mining on benthic fauna

The Jøssingfjord area, Norway has been used since 1960 for sea disposal of finely ground, inert tailings from a titanium mine. The discharged quantity was about 2 million tonnes · year −1 in the 1980s. The submarine outfall was in 1984 relocated from the shallow Jøssingfjord to a deep basin outside the fjord entrance. Results reported here are from yearly monitoring surveys in the period 1983–1988. The aim of the study was to examine the structure of the soft bottom communities, and describe effects of mine tailings disposal after relocation. The spreading of mine tailings has generally remained constant after 1984. The relocation resulted in increased accumulation within 2–3 km from the new outfall. The accumulated material decreases rapidly with distance, from several metres · year −1 in the outfall basin, to 4–5 cm · year −1 within 1 km from the outfall site, and is in the order of 1 mm · year −1 at distances > 2–3 km from the outfall. Changes in the benthic fauna at varying distances from the outfall were followed. Despite complicated bottom topography and large variations in depth and sediment types it has been possible to identify the biological impact of mine tailings. For example, one year after relocation a clear increase in numbers of the typical opportunistic species Heteromastus filiformis, Chaetozone setosa and Cossura longocirrata was found. In the following years a significant reduction in diversity was observed at sites most disturbed by sedimentation, while diversity at sites > 2–3 km from the outlet remained unaltered. Multivariate analysis of the faunal data (classification, MDS and DCA ordination) revealed clear site-group differences, and two site-groups were related to tailings content in the sediment. Multivariate methods combining fauna and environmental variables identified depth and sediment content of tailings and organic matter as the most important factors influencing the structure of the benthic communities in the area. A sedimentation of 4–5 cm of tailings · year −1 resulted in changes in fauna composition, while at rate of 1 mm · year −1 no impact was observed on the fauna. Recolonization on the old tailings deposits inside Jøssingfjord commenced within one year after cessation of discharge, and within 4 years all the main macrobenthic phyla were represented.

A split-step Padé solution for the parabolic equation method

A split-step Padé solution is derived for the parabolic equation (PE) method. Higher-order Padé approximations are used to reduce both numerical errors and asymptotic errors (e.g., phase errors due to wide-angle propagation). This approach is approximately two orders of magnitude faster than solutions based on Padé approximations that account for asymptotic errors but not numerical errors. In contrast to the split-step Fourier solution, which achieves similar efficiency for some problems, the split-step Padé solution is valid for problems involving very wide propagation angles, large depth variations in the properties of the waveguide, and elastic ocean bottoms. The split-step Padé solution is practical for global-scale problems.

Light sectioning with large depth of focus by means of Fresnel diffraction of an edge

We propose the use of Fresnel diffraction from an edge to produce a fringe pattern illumination with large depth of focus. The line separating dark and bright areas of the fringe pattern is used for light sectioning of the object, and the height profile is obtained through triangulation. The properties and advantages of this illumination approach are discussed. Experimental 3-D measurements are shown for various objects having large depth variations and are obtained with a height resolution of 1 mm at a distance of 500 mm, within a field of view of 25 deg.

A self-starter for the parabolic equation method

An efficient method is developed for generating accurate starting fields for the parabolic equation (PE) method for both fluid and solid media. The self-starter, which is constructed by solving a one-dimensional boundary-value problem (BVP) involving the PE operator, is more efficient than the normal-mode starter, which requires the solution of a large number of similar BVPs. The self-starter depends on the depth-dependent properties of the medium and satisfies all interface and boundary conditions. Since the self-starter is based on higher-order parabolic approximations, it is accurate for problems involving wide propagation angles, large depth variations in the properties of the medium, low frequencies, interface waves, and the continuous spectrum.

Time domain inversion of two-dimensional velocity fields using simulated annealing

Inversion of scattered sound fields caused by horizontal and lateral velocity variations can be done using an efficient Monte Carlo method called simulated annealing. The subsurface contains large velocity variations in both depth and range and thus, for inversion of transient signals, at least a two-dimensional (2-D) representation of the velocity field is required. This 2-D description requires that the nonlinear inversion is carried out in a huge parameter space. Standard local optimization methods will be trapped in local minima and a search throughout is computationally prohibitive. Thus the simulated annealing method is used. The present implementation is here based on an ensemble approach whereby several copies are annealed simultaneously. By using several copies it is possible to obtain statistical information about the optimal cooling rate. In order to make the method converge in acceptable time, both optimization and the forward modeling method of the inversion have to be fast. Thus geometrically flexible but computationally exhaustive methods such as finite difference are not yet used. At present, the forward modeling is done by either the one-dimensional convolution model or ray tracing. The 2-D effect of the one-dimensional convolution is obtained by geometrically requiring the structure to be stratified with a weak variation in range. For the ray tracing, the substructure shall also be stratified but here the wave propagation is in a real 2-D environment.

Higher-order Padé approximations for accurate and stable elastic parabolic equations with application to interface wave propagation

Higher-order Padé approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover. Accuracy is achieved by placing constraints on the derivatives of the Padé approximations at the point corresponding to the reference wave number. Stability is achieved by requiring that the Padé approximations map part of the lower-left quadrant of the complex plane into the upper half of the complex plane. Elastic parabolic equations based on these Padé series can handle problems involving compressional, shear, and interface waves, very wide propagation angles, and large depth variations and weak range variations in the seismoacoustic parameters. A finite-difference spectral solution is developed for generating reference solutions and starting fields. The rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range-dependent problems.

A higher-order energy-conserving parabolic equqation for range-dependent ocean depth, sound speed, and density

Outgoing solutions of the wave equation, including parabolic equation (PE) and normal-mode solutions, are usually formulated so that pressure is continuous with range for range-dependent problems. The accuracy of normal-mode solutions has been improved by conserving energy rather than maintaining continuity of pressure [Porter et al., “The problem of energy conservation in one-way equations,” J. Acoust. Soc. Am. 89, 1058–1067 (1991)]. This approach is applied to derive a higher-order energy-conserving PE that provides improved accuracy for problems involving large ocean bottom slopes and large range and depth variations in sound speed and density. A special numerical approach and complex Padé coefficients are applied to suppress Gibbs’ oscillations. The back-propagated half-space field, an improved PE starter, is applied to handle wide propagation angles. Reference solutions generated with a complex ray model and with the rotated PE are used for comparison.

VLA observations of the 6 centimeter and 2 centimeter lines of H2CO in the direction of W49

Formaldehyde absorption at 6 cm and 2 cm toward the radio continuum source W49 has been mapped with the VLA, and Gaussian components have been fitted to the H{sub 2}CO profiles obtained in the direction of the embedded ultracompact H II regions. The densities of H{sub 2} and column densities of ortho-H{sub 2}CO are derived for the Gaussian range - 2 km/s and + 20 km/s. Large variations in optical depth are observed across the region. The structure and dynamics within the molecular core of W49 are determined. The main features of the results can be explained if the absorption occurs within the dense core of the molecular cloud and arises close to the embedded ultracompact H II regions UC H II. 57 refs.

Weather Forecasts as a Control Input for Water Table Management in Coastal Areas

ABSTRACT FOUR water table management methods were compared in computer simulations of a controlled-drainage and subirrigation system using soils and climate conditions of the Mississippi Delta region. No significant difference in the predicted relative corn yield was obtained among the four management methods when the operation for each method was adjusted to maximize yield. However, stopping subirrigation pumping whenever the rainfall probability index (RPI) exceeded 55% reduced pumping requirements for three of the methods 12 to 21% compared to the continuous subirrigation method. The optimal management of soil-water for agricultural cropland in humid, coastal areas of the U.S. often involves complex daily control of the water table because of the erratic spatial and temporal distribution of rainfall. Periods of excess and deficit soil-water conditions are common within the same growing season. Thus, water management requires both controllable drainage and irrigation facilities. A water table management system popular in the humid region, especially in the southern coastal plains, uses a subsurface draintube system for both controlled-drainage and subirrigation. Controlled-drainage permits storage of rainfall and irrigation water in the soil profile below the depth of an overflow pipe at the drain outlet. Free'' drainage to the full depth of the drainline is often needed during periods of extended or heavy rainfall to reduce the duration of excess water in root zone. During subirrigation, the water level at the drain outlet is maintained just below the overflow pipe by pumping from an external source. A sump-type structure for controlling the water level at the drain outlet for a water table management system is illustrated in Fig. 1. The check-valve, activated by a double-float, allows fast subsurface drainage during peak flow events, functioning like the two-stage weir described by Fouss, et al. (1987b). It is often necessary to pump from a sump in level and low lying topography of the coastal plains, where subsurface drainage by gravity flow is not possible. Water table management with this type of system has a high potential for achieving maximum crop production and water use efficiency if properly controlled to compensate for changes in weather conditions. The timing of changes needed in controlled-drainage and subirrigation to manage optimally the water table depth is a major problem for farmers, especially in coastal areas with fine textured soils. In the Mississippi Delta frequent occurrences of rainfall can cause large variations in water table depth because of the small, 3 to 8%, drainable soil porosity. Results from computer simulation of four management methods for water table control are presented for soils and climate conditions of the Mississippi Delta. The primary research objective was to determine the best operational parameters that efficiently utilized rainfall during the growing season without creating periods of severe excess soil-water conditions, and which minimized the need for pumping drainage and subirrigation water. Special attention was given to the potential use of rainfall probability information from the daily weather forecast as a system control input to minimize subirrigation pumping.

Mesoscale Variability of Boundary Layer Properties in the Los Angeles Basin

Abstract We employ daytime radiosonde data to analyze boundary layer (BL) variability within the Los Angeles Basin for a case study day. The predominantly mesoscale forcing in the region produces large spatial and temporal variations in BL depth and vertically averaged BL virtual potential temperature and wind velocity. Particularly notable are the shallowing of BL depth—beginning in midmorning at the coast and in the early afternoon inland—and the afternoon decrease in BL potential temperature. The relative importance of terms in the BL continuity, thermodynamics, and momentum equations is evaluated; values for area-averaged entrainment velocity, surface heat flux, and mean BL pressure gradient force (PGF) are derived as residuals. Our budget equations are vertically integrated to the variable BL top and are thus more appropriate to investigations of BL variables than are equations integrated to a fixed height. Advection and divergence are shown to affect BL depth, heating, and acceleration significantly...

Diffusion models for gas production from coals: Application to methane content determination

Experimental studies of methane diffusion from coal cuttings have been analysed with both a unipore diffusion model and a bi-disperse pore structure diffusion model to determine the time range of each model's validity. Initial desorption, during the first 50% of volume desorbed, can be adequately described by the unipore model. For Fruitland coals of the San Juan Basin, the unipore diffusion coefficient varied by less than a factor of 2 from a value of 1 × 10 −5 s −1 despite large variations in sample depth and location. The unipore diffusion model has been successfully incorporated into a lost-gas-correction-factor determination as part of a new technique to delineate coal-bed methane. To describe methane diffusion over the full timescale of desorption, a more complex model which more accurately represents the observed bi-disperse pore structure of coal is required. Using that model the observed desorption rate is described over all the desorption. This model is especially applicable as a source term in describing overall well production.

On the Low-Frequency Fluctuations in the Eastern Skagerrak and in Gullmaren

An analysis is presented of the fluctuations with periods exceeding approximately one day in the coastal zone of the eastern Skagerrak and in the fjord Gullmaren based primarily on data from a three-month field experiment during the spring of 1979. Mean flow in the coastal zone consisted of a strong, persistent northward flow in a wedge of brackish water near the coast—the Baltic current-superimposed on a weaker general barotropic northward flow. Three distinct low-frequency bands characterized by high degrees of organized motion and different spatial structure are identified in the coastal zone by coherence and phase analysis. For a two day or more band, alongshore flow appears to be driven locally by the wind. Topographic vortex modes in the Skagerrak may explain highly-organized 56 h fluctuations. For the 5–6 day band the fluctuations are related more to the wind stress over the northern North Sea than to the local one. Topographic waves propagating eastward along the Norwegian Trench may communicate this remote forcing to the eastern Skagerrak. Our results and some additional analyses of historical data imply that as they reach the eastern Skagerrak these waves may be scattered into internal Kelvin waves and general topographic waves, the latter of which exhibit seaward as well as northward energy propagation. Also, large observed alongshore momentum flux divergences in this band may act as forcing functions for the mean circulation. Baroclinic instabilities do not seem to be an important source of low-frequency fluctuations in the study region. For the two week or more band the first Empirical Orthogonal Function (EOF) current mode was again more coherent with the northern North Sea than local wind stress and was highly coherent with the first adjusted sea level EOF mode from four stations around the Skagerrak-Norwegian trench region. These and other results suggest a topographic gyre model for the very low-frequency barotropic circulation in this region. The fluctuations in Gullmaren with periods less than ∼4 days appeared to be driven directly by the wind over the fjord and not by its interaction with the coastal zone. Coherence and phase relationships between EOF current and salinity modes and comparisons with expected phase speeds and vertical structures of “dynamical” modes there show the existence of internal seiches around periods of 27 and 56 h. At periods exceeding ∼4 days, fluctuations in Gullmaren are mainly coupled to those in the coastal zone. Large halocline depth and surface salinity variations at periods exceeding two weeks may be related to slow changes in the Baltic current (Kattegat-Baltic Sea estuary system) as well as to conditions in the Skagerrak. The relaxation of a downwelling event was studied in detail. It is shown that such coast-parallel wind events, although infrequent in the study area, have a profound effect on nearshore current structure and the exchange between Gullmaren and the coastal zone.

Nonlinear optical interferometer

The interferometer described, based on the second harmonic generation of light, is useful in the contouring of refractive objects with large variations in optical depth. The device is a real-time common-path self-referencing interferometer that yields interferograms in the visible with an equivalent wavelength of the order of 50 microm. We describe experiments that show that it can serve as a useful device. The key to the device is the use of Y-cut LiNbO(3) configured for surface acoustooptic applications rather than for conventional second harmonic applications. The crystals are noncritically phase matched by temperature control and are used with a repetitively pulsed Nd:YAG laser operating at 1.06 microm.

Contour Interaction in Visual Space

Virtually all the extensive research on inhibitory interactions among adjacent visual stimuli seen in such phenomena as simultaneous contrast and visual masking have employed situations in which the interacting stimulus elements occupy the same depth plane, i.e., the z-axis values are the same, in deference to the implicit assumption that processing of depth information occurs only after the visual processing of contour information is completed. But there are theoretical reasons and some data suggesting that the interactions among contours depend critically upon their relative positions in depth—interactions may not occur if the stimulus elements occupy different depth positions. The extent to which the metacontrast form of visual masking is dependent upon depth position was investigated in a series of experiments that used stereoscopic contours formed from random-element stereograms as test and mask stimuli. The random-element stereogram generation system permitted large variations in depth to be made without introducing confounding changes in proximal stimulation. The main results are 1) separation of test and mask stimuli in depth substantially reduces masking, and 2) when more than one stimulus is in visual space the stimulus that either appears first or appears closer to the observer receives preferential processing by the visual system.