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At least 91 records · Page 5

Correlation of data on strain accumulation adjacent to the San Andreas Fault with available models

Theoretical and numerical studies of deformation on strike slip faults were performed and the results applied to geodetic observations performed in the vicinity of the San Andreas Fault in California. The initial efforts were devoted to an extensive series of finite element calculations of the deformation associated with cyclic displacements on a strike-slip fault. Measurements of strain accumulation adjacent to the San Andreas Fault indicate that the zone of strain accumulation extends only a few tens of kilometers away from the fault. There is a concern about the tendency to make geodetic observations along the line to the source. This technique has serious problems for strike slip faults since the vector velocity is also along the fault. Use of a series of stations lying perpendicular to the fault whose positions are measured relative to a reference station are suggested to correct the problem. The complexity of faulting adjacent to the San Andreas Fault indicated that the homogeneous elastic and viscoelastic approach to deformation had serious limitations. These limitation led to the proposal of an approach that assumes a fault is composed of a distribution of asperities and barriers on all scales. Thus, an earthquake on a fault is treated as a failure of a fractal tree. Work continued on the development of a fractal based model for deformation in the western United States. In order to better understand the distribution of seismicity on the San Andreas Fault system a fractal analog was developed. The fractal concept also provides a means of testing whether clustering in time or space is a scale-invariant process.

Turcotte, Donald L.↗

Two dimensional convolute integers for machine vision and image recognition

Machine vision and image recognition require sophisticated image processing prior to the application of Artificial Intelligence. Two Dimensional Convolute Integer Technology is an innovative mathematical approach for addressing machine vision and image recognition. This new technology generates a family of digital operators for addressing optical images and related two dimensional data sets. The operators are regression generated, integer valued, zero phase shifting, convoluting, frequency sensitive, two dimensional low pass, high pass and band pass filters that are mathematically equivalent to surface fitted partial derivatives. These operators are applied non-recursively either as classical convolutions (replacement point values), interstitial point generators (bandwidth broadening or resolution enhancement), or as missing value calculators (compensation for dead array element values). These operators show frequency sensitive feature selection scale invariant properties. Such tasks as boundary/edge enhancement and noise or small size pixel disturbance removal can readily be accomplished. For feature selection tight band pass operators are essential. Results from test cases are given.

Edwards, Thomas R.↗

On hierarchical solutions to the BBGKY hierarchy

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

Hamilton, A. J. S.↗

Pyramid image codes

All vision systems, both human and machine, transform the spatial image into a coded representation. Particular codes may be optimized for efficiency or to extract useful image features. Researchers explored image codes based on primary visual cortex in man and other primates. Understanding these codes will advance the art in image coding, autonomous vision, and computational human factors. In cortex, imagery is coded by features that vary in size, orientation, and position. Researchers have devised a mathematical model of this transformation, called the Hexagonal oriented Orthogonal quadrature Pyramid (HOP). In a pyramid code, features are segregated by size into layers, with fewer features in the layers devoted to large features. Pyramid schemes provide scale invariance, and are useful for coarse-to-fine searching and for progressive transmission of images. The HOP Pyramid is novel in three respects: (1) it uses a hexagonal pixel lattice, (2) it uses oriented features, and (3) it accurately models most of the prominent aspects of primary visual cortex. The transform uses seven basic features (kernels), which may be regarded as three oriented edges, three oriented bars, and one non-oriented blob. Application of these kernels to non-overlapping seven-pixel neighborhoods yields six oriented, high-pass pyramid layers, and one low-pass (blob) layer.

Watson, Andrew B.↗

A fractal approach to probabilistic seismic hazard assessment

The definition of a fractal distribution is that the number of objects (events) N with a characteristic size greater than r satisfies the relation N proportional to r exp - D is the fractal dimension. The applicability of a fractal relation implies that the underlying physical process is scale-invariant over the range of applicability of the relation. The empirical frequency-magnitude relation for earthquakes defining a b-value is a fractal relation with D = 2b. Accepting the fractal distribution, the level of regional seismicity can be related to the rate of regional strain and the magnitude of the largest characteristic earthquake. High levels of seismic activity indicate either a large regional strain or a low-magnitude maximum characteristic earthquake (or both). If the regional seismicity has a weak time dependence, the approach can be used to make probabilistic seismic hazard assessments.

Turcotte, D. L.↗

Ginga observations of quasi-periodic oscillations in type II bursts from the Rapid Burster

During Ginga observations of the 'Rapid Burster' in August 1988, strong quasi-periodic oscillations (QPOs) were detected in its X-ray intensity. The QPOs had centroid frequencies of 5 and 2 Hz during type II X-ray bursts which lasted for 10 and 30 s, respectively. The presence of the QPOs is correlated with the time scale-invariant burst profile. They are very strong during the initial peak in the burst, absent in the second peak, and strong again at the onset of the third peak. From an analysis of the X-ray spectrum as observed during the maxima and minima of the oscillations, it is found that the oscillations can be described by changes of the temperature of a blackbody emitter of constant apparent area.

Dotani, T.↗

Structures observed on the spot radiance fields during the FIRE experiment

Three Spot images taken during the FIRE experiment on stratocumulus are analyzed. From this high resolution data detailed observations of the true cloud radiance field may be made. The structure and inhomogeneity of these radiance fields hold important implications for the radiation budget, while the fine scale structure in radiance field provides information on cloud dynamics. Wieliki and Welsh, and Parker et al., have quantified the inhomogeneities of the cumulus clouds through a careful examination of the distribution of cloud (and hole) size as functions of an effective cloud diameter and radiance threshold. Cahalan (1988) has compared for different cloud types of (stratocumulus, fair weather cumulus, convective clouds in the ITCZ) the distributions of clouds (and holes) sizes, the relation between the size and the perimeter of these clouds (and holes), and examining the possibility of scale invariance. These results are extended from LANDSAT resolution (57 m and 30 m) to the Spot resolution (10 m) resolution in the case of boundary layer clouds. Particular emphasis is placed on the statistics of zones of high and low reflectivity as a function of a threshold reflectivity.

Seze, Genevieve↗

Non-Gaussian microwave background fluctuations from nonlinear gravitational effects

Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.

Salopek, D. S.↗

Fractal applications to complex crustal problems

Complex scale-invariant problems obey fractal statistics. The basic definition of a fractal distribution is that the number of objects with a characteristic linear dimension greater than r satisfies the relation N = about r exp -D where D is the fractal dimension. Fragmentation often satisfies this relation. The distribution of earthquakes satisfies this relation. The classic relationship between the length of a rocky coast line and the step length can be derived from this relation. Power law relations for spectra can also be related to fractal dimensions. Topography and gravity are examples. Spectral techniques can be used to obtain maps of fractal dimension and roughness amplitude. These provide a quantitative measure of texture analysis. It is argued that the distribution of stress and strength in a complex crustal region, such as the Alps, is fractal. Based on this assumption, the observed frequency-magnitude relation for the seismicity in the region can be derived.

Turcotte, Donald L.↗

Slope variations on the surface of Phobos

It has been suggested that slope fluctuations on the scale of pixel dimensions could be determined by statistical photoclinometry. A closer study of the surface of Phobos reveals variations in the scattering properties of single particles and microstructures formed by the particles. In the present context, the photoclinometric method of brightness moments is extended to account for these variations by allowing statistical fluctuations in the phase function of the assumed Lommel-Seeliger scattering law. The mean slope on the investigated regions of Phobos has been found to vary from about 12 deg on a 61 m scale to about 7 deg on a 216 - 272 m scale. On the same scales, a value of the order of 2 percent has been obtained for the standard deviation of the scattering phase function. Hints of a fractal-like scale-invariance have been noticed in the covariance function of brightness.

Muinonen, Karri↗

Cosmic rays from primordial black holes

The quark and gluon emission from primordial black holes (PBHs) which may have formed from initial density perturbations or phase transitions in the early universe are investigated. If the PBHs formed from scale-invariant initial density perturbations in the radiation dominated era, it is found that the emission can explain or contribute significantly to the extragalactic photon and interstellar cosmic-ray electron, positron, and antiproton spectra around 0.1-1 GeV. In particular, the PBH emission strongly resembles the cosmic-ray gamma-ray spectrum between 50 and 170 MeV. The upper limits on the PBH density today from the gamma-ray, e(+), e(-), and antiproton data are comparable, provided that the PBHs cluster to the same degree as the other matter in the Galactic halo.

Macgibbon, Jane H.↗

Recognizing Patterns In Log-Polar Coordinates

Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.

Weiman, Carl F. R.↗

Edge detection algorithm for SST images

An algorithm to detect fronts in satellite-derived sea surface temperature fields is presented. Although edge detection is the main focus, the problem of cloud detection is also addressed since unidentified clouds can lead to erroneous edge detection. The algorithm relies on a combination of methods and it operates at the picture, the window, and the local level. The resulting edge detection is not based on the absolute strength of the front, but on the relative strength depending on the context, thus, making the edge detection temperature-scale invariant. The performance of this algorithm is shown to be superior to that of simpler algorithms commonly used to locate edges in satellite-derived SST images. This evaluation was performed through a careful comparison between the location of the fronts obtained by applying the various methods to the SST images and the in situ measures of the Gulf Stream position.

Cayula, Jean-Francois↗

Lava flows are fractals

Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.

Bruno, B. C.↗

Limits of Gaussian fluctuations in the cosmic microwave background at 19.2 GHz

The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power-law spectra for n values between -2 and 1. An upper bound is placed on the quadrupole anisotropy of Delta T/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of the modeling of the Galaxy could yield a significant reduction of these upper bounds.

Boughn, S. P.↗

Structure in the COBE differential microwave radiometer first-year maps

Results of the first year of data from the differential microwave radiometers on the Cosmic Background Explorer are presented. Statistically significant structure that is well described as scale-invariant fluctuations with a Gaussian distribution is shown. The rms sky variation, smoothed to a total 10-deg FWHM Gaussian, is 30 +/-5 micro-K for Galactic latitude greater than 20-deg data with the dipole anisotropy removed. The rms cosmic quadrupole amplitude is 13 +/-4 micro-K. The angular autocorrelation of the signal in each radiometer channel and cross-correlation between channels are consistent and give a primordial fluctuation power-law spectrum with index of 1.1 +/-0.5, and an rms-quadrupole-normalized amplitude of 16 +/-4 micro-K. These features are in accord with the Harrison-Zel'dovich spectrum predicted by models of inflationary cosmology.

Smoot, G. F.↗

Minimum entropy deconvolution and blind equalisation

Relationships between minimum entropy deconvolution, developed primarily for geophysics applications, and blind equalization are pointed out. It is seen that a large class of existing blind equalization algorithms are directly related to the scale-invariant cost functions used in minimum entropy deconvolution. Thus the extensive analyses of these cost functions can be directly applied to blind equalization, including the important asymptotic results of Donoho.

Satorius, E. H.↗

The x ray variability of AGN and the anomalous behavior of NGC6814

The power spectra of the X-ray variable AGN are typically scale invariant with no characteristic timescale. The one strong exception to this is NGC6814, where the EXOSAT data showed evidence for a periodic component at 12200 plus or minus 100 seconds. The power spectra of a GINGA lightcurve from this source, found using simulation techniques to account for the uneven sampling, also cannot be well fit by a single power law. A folded light curve analysis of the GINGA data shows a strong peak in the variance, indicative of a periodic component, at 12130.9 plus or minus 0.6 seconds. A second GINGA observation of this source taken one year later is consistent with the periodicity maintaining phase coherence for 7 periods in the range of 12110-12145 seconds. Including the limits from the folding selects a period of 12130.39 plus or minus 0.05 seconds. Phase coherence is not maintained between this and the EXOSAT observations, as the structure of the folded light curves is very different. Thus the periodicity is long lived and stable, but phase coherence is only maintained on timescales of approximately 1 year.

Done, C.↗