Complicated Interference Pattern Research Articles

Theory of acoustic radiation over a 3-D hyperbolic ocean ridge

An analytic solution to a 3-D problem of ocean acoustics involving horizontal refraction is presented. An expression for the acoustic field due to a harmonic point source in an isovelocity ocean overlying a hyperbolic ridge with perfectly reflecting boundaries is given as a finite modal sum of integrals. The integrals are in terms of Mathieu functions, the eigenfunctions of the reduced wave equation in the elliptical coordinate system. These eigenfunctions are approximated away from the low-frequency limit by standard WKB techniques and the resulting integrals are then estimated by first- and second-order stationary-phase asymptotics. This gives an approximation in terms of elliptical functions for which standard numerical routines are available. The approximation is very accurate in the shallow depth and gentle slope limits appropriate to the physical situation of ridges in an isovelocity ocean. The solution includes the locations of the caustics and shadow zones and predicts a complicated intramodal interference pattern resulting from the intersection of up to three rays in a given mode. The intermodal interference from the finite modal sum is also evident in the full solution. The explicit representation of the features arising from horizontal refraction makes this model useful as a 3-D benchmark solution.

Seismic evidence for ultralow‐velocity zones beneath Africa and eastern Atlantic

SKS waveforms recorded at distances of about 110° are extremely useful to constrain seismic velocity structure at the base of the mantle. SKS waves near this distance develop a complicated interference pattern with the phases SPdKS and SKPdS. We report anomalous behavior of this interference in a number of recordings of deep earthquakes beneath South America from stations in Europe and Africa. We model these data with two‐dimensional dome‐like structures at the base of the mantle which extend laterally by a few hundred kilometers and in which the shear velocity is up to 30% lower than in the Preliminary Reference Earth Model (PREM). The spatial extent of these structures, their position with respect to the SKS core exit points, and their seismic characteristics can not be uniquely determined. However, the presence of a dipping or a concaved upper interface is a key attribute of successful models. Models that invoke flat layers are insufficiently complex to explain the most erratic waveform behavior. The most anomalous data correspond to sampling regions at the base of the mantle beneath the East African Rift and beneath the Iceland, where possibly, whole mantle upwellings form.

Magnetic field transforms with low sensitivity to the direction of source magnetization and high centricity

Magnetic data interpretation faces difficulties due to the various shapes of magnetic anomalies and the positions of their extrema with respect to the causative bodies for different directions of the source magnetization. The well‐known transforms — reduction to the pole, pseudogravity field, and analytic signal (total gradient) — help in reducing the problem. Another way to achieve the required effect is the transformation of magnetic data, ΔT or Z, into values of the anomalous magnetic intensity T. In this respect, we have found some transforms based on differential operators such as the gradient of T and its modulus R = |∇T|, the Laplacian L = ∇2T, the product T ∇2T and its square root Q, and the Laplacian ∇2(T2) and its square root E, to be useful. They are slightly sensitive to the magnetization orientation and their extrema occur above the sources.For a 2D anomaly of a homogeneous causative body, the proposed transforms do not depend on the inclination of magnetization. In the 3D case, such independence does not exist even for the elementary field of a point dipole. The influence of the magnetization direction is estimated by an integral coefficient of sensitivity. This coefficient takes values of up to 2.0 for ΔT or Z anomalies, while their transforms T, R, E, Q and L have values of less than 0.28, 0.29, 0.24, 0.16 and 0.07, respectively, i.e. on average, 10 times less. The estimation of the centricity is carried out using the relative deviation of the principal extremum of the anomaly or its transforms from the epicentre of the model body at a depth equal to 100 units. For a ΔT anomaly this deviation is up to 67%; for the L transform it is less than 8%; for Q, E, R and T it is less than 10%, 15%, 20% and 25%, respectively.The proposed transforms take only non‐negative values. With respect to their shape, the peripheral magnetic extrema are removed, the anomalous configuration is simplified and the resolution of complicated interference patterns is improved. Their calculation does not require additional data for the direction of magnetization, which is an essential advantage over the reduction‐to‐the‐pole and pseudogravity‐field transforms. A joint analysis of the measured field and its transforms T, E and L offers possibilities for more confident separation of the anomalous effects and direct correlation to their sources. The model tests performed and the 3D field applications to real magnetic data confirm the useful properties of the transforms suggested here.

Geología y topografía: el programa SUPERPOSICIÓN como recurso para su enseñanza

The computer program Superposición has been developed in Pascal and compiled with Borland Delphi 2.0, to simulate the relationships between topography and geology. The program allows to create very simple geologies, formed by horizontal layers, or very complicated interference patterns, formed by three fold system, faults and a discordance. The interference patterns and their topographic expression are generated by using matrix methods.Superposición permits its employ as a didactic resource for teaching. The program can be used to resolve field observations as a part of a research project subject to the validity of the simple shear deformation model.

Theory of acoustic radiation near a hyperbolic ridge

A solution to the acoustic field due to a harmonic point source near a hyperbolic ridge with perfectly reflecting boundaries in an isovelocity ocean is derived and developed. An exact expression for the field is given as a modal sum of integrals. The integrals are in terms of eigenfunctions of the reduced wave equation in the three-dimensional elliptical coordinate system. The eigenfunctions are approximated away from the low-frequency limit by standard WKB techniques. The resulting integrals are estimated by first and second order stationary phase asymptotics, which are matched in the vicinity of the caustics, yielding a complete representation of the field. The field is given in terms of standard elliptic functions for which fast numerical routines are available. The solution includes the locations of the caustics and shadow zones, as well as predicting a complicated intramodal interference pattern resulting from the intersection of up to three rays in a given mode. The explicit representation of these features arising from horizontal refraction makes this theoretical model useful as a new fully three-dimensional benchmark solution.

Electron angular distribution in above-threshold two-photon detachment of

We present angular-differential above-threshold two-photon detachment rates of below the second ionization threshold. They have been calculated using an close-coupling method with a B-spline basis. We have found that in the non-resonant region the angular distribution of photoelectrons is close to that obtained from a pure D partial wave. This is also the case in the vicinity of the lowest doubly excited state. In contrast, the angular distribution in the vicinity of the doubly excited states is the result of a complicated interference pattern between S and D waves. In the latter case, knowledge of the corresponding phase shifts is essential to interpret the actual results.

Features in the spectra of gamma-ray bursts

Gravitational lensing of cosmological gamma-ray bursts by objects in the mass range about 10 exp 17 to 10 exp 20 g (femtolensing) may introduce complicated interference patterns that might be interpreted as absorption or emission lines in the bursts' spectra. This phenomenon, if detected, may be used as a unique probe of dark matter in the universe. The BATSE spectral data should allow one to detect such spectral features or to put significant upper limits on the cosmic density of a dark matter component that may be in the femtolensing range. Software to generate theoretical spectra has been developed, and it is accessible over the computer network with anonymous ftp.

Inter-related plutonism and deformation in South Victoria Land, Antarctica

AbstractThe Lower Palaeozoic Bonney Pluton is a regionally extensive coarse-grained, variably megacrystic, monzodioritic to granitic body that crops out over 1000 km2 in South Victoria Land. It intruded upper amphibolite facies Koettlitz Group metasediments and interlayered orthogneisses. Magmatic fabrics are developed in the centre of the pluton by flow alignment of K-feldspars before the majority of phases had crystallized, whereas solid-state fabrics developed in the pluton margins by ductile–plastic deformation. Structures developed in the host-rocks vary around this elongate northwest–southeast-trending pluton. Upright, tight northwest–southeast-trending macroscopic folds are developed at the sides of the pluton, with axis-parallel stretching lineations and boudinage indicating strong northwest–southeast extension. Broad warps of tight macroscopic folds, and mesoscopic refolded folds, sheath folds and complicated interference patterns characterize areas at the ends of the pluton. Emplacement of the pluton involved radial expansion in a regional northeast–southwest compression, and growth predominantly in the northwest–southeast direction. Superposition of the radial expansion and regional compression resulted in an inhomogeneous strain field at a regional scale, with coaxial strain at the sides of the pluton and non-coaxial strain at the ends. Upright folds developed at the pluton's sides, and became tighter with continued coaxial deformation. Non-coaxial structures developed at the ends of the pluton and were pushed aside by the growing pluton into areas of coaxial deformation, resulting in complex folding, re-folding and sheath folds. Metamorphism of the host-rocks and migmatite development was more intense at the sides of the pluton than near the ends, possibly due to different P-T-t paths of host-rocks around syntectonic plutons.

Investigations of the polarity of the photo-induced electrical signal of chloroplast suspensions

This paper reports data and considerations relevant to the question of what determines the polarity of the voltages induced between electrodes in a suspension of chloroplasts when irradiated with a flash of light from a laser or flash-lamp. We found positive polarity (electrode nearest the light source positive) with excitation by ns pulses at 694, 539 and 530 nm wavelength. This and the earlier finding (Meszéna et al. (1988) Studia Biophysica 126:77-86), confirmed in this work, of negative polarity at 420 nm confirm, in part, the action spectrum reported by Gräber and Trissl (1981 FEBS Let 123:95-99) using 50 μs flashes. Gräber and Trissl also showed that swelling the chloroplasts can reverse the polarity.Negative polarity is expected on the basis of a simple light-gradient in the sample together with what is known about photosynthetic charge movements. The cause of positive polarities has eluded explanation. Duration of flash was suspected. We tried a random series of short flashes averaging about 10 μs apart and found that all simply duplicated the first flash. If there is any effect of light following the first flash it must occur in less than about 10 μs.We suggest that the polarity is determined by a complicated interference pattern of the light in the chloroplast which can focus it onto different parts, front or back, depending upon the wavelength of the light and the structure of the chloroplast.

Acoustic Microscopy at Low Frequency

A new design of the acoustic microscopy experimental set up is proposed and analyzed in this paper. The proposed microscope can operate at low frequency (0.1 to 3 MHz) and can be efficiently used in fracture mechanics, structural, and geomechanics applications. In the new design there is no buffer rod and the transducer is proposed to have a shape of a cylindrical shell to produce a line focus beam which is necessary to measure material anisotropy. A line receiver is introduced instead of standard transducer-cum-receiver arrangements. A line receiver can receive only one specularly reflected ray and a few critically reflected rays and thus produces less complicated interference pattern or acoustic material signature (AMS) which is easier to analyze. The shape of the generated AMS depends on the exact location of the receiver strip. Finally, theoretically synthesized AMS of an aluminum plate for different receiver locations are presented.

HREM images and atom positions

How accurately may atomic positions (in projection, at least) be deduced from high resolution electron images? If your experience begins before the last ten to fifteen years, when ‘lattice’ and ‘atomic’ images have become almost commonplace, you are likely to regard a micrograph as at least as much a complicated interference pattern as an image, and be much less sanguine than younger microscopists about the accuracy with which dark spots in images may be expected to correspond to actual atomic sites. The ‘simulation’ approach to image intepretation, in which atomic positions are deduced via a comparison of experimental and calculated images whether or not these bear any direct interpretation, is born of this caution; however, atomic sites are increasingly being inferred directly from micrographs, and this paper is concerned with the two principal ways in which digital processing can be used to make the process more reliable.

Spphases from the transition zone between the upper and lower mantle

abstractPrecursors to S and SKS were observed in long-period SRO and WWSSN seismograms of the Romanian earthquake of March 4, 1977, recorded in the United States at distances from 68° to 93°. According to the fault-plane solution, the stations were close to a nodal plane and SV radiation was optimum in their direction. Particle-motion diagrams, constructed from the digital data of the SRO station ANMO (distance 89.1°), show the P-wave character of the precursors. Several interpretations are discussed; the most plausible is that the precursors are Sp phases generated by conversion from S to P below the station. The travel-time differences between S or SKS and Sp are about 60 sec and indicate conversion in the transition zone between the upper and lower mantle. Sp conversions were also observed at long-period WWSSN stations in the western United States for 2 Tonga-Fiji deep-focus earthquakes (distances from 82° to 96°).Special emphasis is given in this paper to the calculation of theoretical seismograms, both for Sp precursors and the P-wave coda, including high-order multiples such as sP4 which may arrive simultaneously with Sp. The Sp calculations show: (1) the conversions produced by S, ScS, and SKS at interfaces or transition zones between the upper and lower mantle form a complicated interference pattern, and (2) conversion at transition zones is less effective than at first-order discontinuities only if their thickness is greater than about half a wavelength of S waves. As a consequence, details of the velocity structure between the upper and lower mantle can only be determined within these limits from long-period Sp observations. Our observations are compatible with velocity models having pronounced transition zones at depths of 400 and 670 km as have been proposed for the western United States, and they exclude much smoother structures. Our study suggests that long-period Sp precursors from pure thrust or normal-fault earthquakes, observed at distances from 70° to 95° close to a nodal plane and at azimuths roughly perpendicular to its strike, offer a simple means for qualitative mapping of the sharpness of the transition zones between the upper and lower mantle.

Toroidal Free Oscillations of the Laterally Heterogeneous Earth

Summary The splitting of the eigenfrequencies of the Earth due to lateral heterogeneities is studied by means of the theory of perturbation of the degenerate eigenfrequencies of the spherically symmetric average earth. The eigen-functions numl(r) associated with a degenerate frequency lead asymptotically (for large l) to surface waves propagating along great circle paths determined by l and m. The lateral heterogeneities couple these eigenfunctions and produce a complicated interference pattern on the surface of the Earth. The perturbation expansion leads, to first order, to a matrix eigenvalue problem for a Hermitian matrix. The elements of the matrix express the coupling between different eigenvectors of the degenerate problem. We expand the lateral heterogeneities in a series of spherical harmonics (δρts(r) Yts(θ, φ), δμts(r) Yts(θ, φ)). Every term in this expansion couples the eigenfunctions selectively. These selection rules can all be deduced from a simple vector diagram. If there is no strong coupling with overtones or spheroidal-toroidal coupling, the odd terms in the spherical harmonics expansion of the heterogeneities do not affect the eigenfrequencies. For instance, there would be no splitting if the Earth had a continental hemisphere and an oceanic hemisphere. Also, terms such that s > 2l do not affect the eigenfrequencies of modes of order l.

Amplitude curves of seismic body waves between 5° and 25°

abstract Amplitude-distance curves of seismic body waves in the distance range between 5° and 25° derived for the region of Southeastern Europe and the northern part of Asia Minor are presented. The shape of the amplitude curves indicates the complex character of wave groups denoted as P and S. It appears that these wave groups are composed of many wave types which arrive in comparable travel times and produce a complicated interference pattern of the P- and S-wave groups. At different epicentral distances different wave types predominate, thus forming the maximum of the wave group in question.

Outline of Chinese Geology

The structural framework of Greater China consists of three positive areas and the geosynclines that separate and enclose them. These are compared with analogous features of eastern North America. A thick succession of Paleozoic formations accumulated in a great trough which extended northeast and southwest across China proper. At the end of Ordovician time this trough was restricted on the north and Silurian, Devonian and Mississippian strata are unrepresented in north China. The Pennsylvanian and Permian seas, however, again extended into that area. Eastern Asia was uplifted at the end of Triassic time and subsequent sedimentation was almost entirely non-marine. Mountain-forming movements, which began in mid-Pennsylvanian time and have continued with modifications to the present, produced a series of shifting sedimentary basins in which all later formations accumulated. The structure of central Asia is dominated by curving east-west mountain arcs but the coastal region is characterized by northeast-southwest trending structures. Throughout much of China proper these two systems have produced a complicated interference pattern. Diastrophism that affected central and eastern Asia since the Paleozoic era was so profound that most parts of China are intensely folded and faulted. Five large sedimentary basins are present, however, two in Chinese Turkistan, one in Tibet, and two in western and northern China proper.