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1.
M. Schulz 《Annales Geophysicae》1997,15(11):1379-1387
The source-surface method offers an alternative to full MHD simulation of the heliosphere. It entails specification of a surface from which the solar wind flows normally outward along straight lines. Compatibility with MHD results requires this (source) surface to be non-spherical in general and prolate (aligned with the solar dipole axis) in prototypical axisymmetric cases. Mid-latitude features on the source surface thus map to significantly lower latitudes in the heliosphere. The model is usually implemented by deriving the B field (in the region surrounded by the source surface) from a scalar potential formally expanded in spherical harmonics, with coefficients chosen so as to minimize the mean-square tangential component of B over this surface. In the simplified (scalar) version the quantity minimized is instead the variance of the scalar potential over the source surface. The scalar formulation greatly reduces the time required to compute required matrix elements, while imposing essentially the same physical boundary condition as the vector formulation (viz., that the coronal magnetic field be, as nearly as possible, normal to the source surface for continuity with the heliosphere). The source surface proposed for actual application is a surface of constant , where r is the heliocentric distance and B is the scalar magnitude of the B field produced by currents inside the Sun. Comparison with MHD simulations suggests that k 1.4 is a good choice for the adjustable exponent. This value has been shown to map the neutral line on the source surface during Carrington Rotation 1869 (May–June 1993) to a range of latitudes that would have just grazed the position of Ulysses during that month in which sector structure disappeared from Ulysses magnetometer observations.  相似文献   

2.
The scale invariant properties of fractal sets make them attractive models for topographic profiles because those profiles are the end product of a complex system of physical processes operating over many spatial scales. If topographic data sets are fractal, their power spectra will be well represented by lines in log-log space with slopess such that –3s<–1. The power spectra from a Digital Elevation Model (30 meter sample spacing) of the Sierra Nevada Batholith and from Seabeam center beam depths (425 meter sample spacing) along a flowline in the South Atlantic are curved. Straight sections in the spectra can be identified but the slopes of those sections are strongly dependent upon the particulars of the data analysis. Fractal geometry must be used with caution in the discussion of topographic data sets.  相似文献   

3.
This study aims at quantifying the effect of rheology on plan-view shapes of lava flows using fractal geometry. Plan-view shapes of lava flows are important because they reflect the processes governing flow emplacement and may provide insight into lava-flow rheology and dynamics. In our earlier investigation (Bruno et al. 1992), we reported that flow margins of basalts are fractal, having a characteristic shape regardless of scale. We also found we could use fractal dimension (D, a parameter which quantifies flow-margin convolution) to distinguish between the two endmember types of basalts: a a (D: 1.05–1.09) and pahoehoe (D: 1.13–1.23). In this work, we confirm those earlier results for basalts based on a larger database and over a wider range of scale (0.125 m–2.4 km). Additionally, we analyze ten silicic flows (SiO2: 52–74%) over a similar scale range (10 m–4.5 km). We note that silicic flows tend to exhibit scale-dependent, or non-fractal, behavior. We attribute this breakdown of fractal behavior at increased silica contents to the suppression of small-scale features in the flow margin, due to the higher viscosities and yield strengths of silicic flows. These results suggest we can use the fractal properties of flow margins as a remote-sensing tool to distinguish flow types. Our evaluation of the nonlinear aspects of flow dynamics indicates a tendency toward fractal behavior for basaltic lavas whose flow is controlled by internal fluid dynamic processes. For silicic flows, or basaltic flows whose flow is controlled by steep slopes, our evaluation indicates non-fractal behavior, consistent with our observations.  相似文献   

4.
R/S analysis of the oxygen isotope curve of Pacific core V28-239 yields a fractal dimension of 1.22. This value is considered to characterize global climatic change over the last 2 million years as expressed by changing O18 ratios and confirms that climatic variations are characterized by long-term persistence. The fractal dimension of 1.22 compares favorably with the approximate fractal dimension of 1.26 for annual precipitation records for nine major cities in the United States. Although the precipitation and oxygen isotope data are measured in different physical units and recorded at different time scales, fractal analysis allows for a mathematical comparison of the two phenomena. Additionally, since the fractal dimensions of the oxygen isotope and precipitation records are similar, it is implied that such fractal dimensions are characteristic of climate change over the spectral range of 10 to 106 years. Given this temperature curves based on fractal parameters of long-term O18 data could be constructed which would allow examination of characteristics of temperature variation over tens and hundreds of years. Such studies may allow the establishment of limits on natural temperature variation and document the persistence of temperature trends through time. If these trends and limits can be resolved, long-range climatic prediction is feasible.  相似文献   

5.
In order to study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge is a quantitative measure of flood potential. With scale invariance is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting.  相似文献   

6.
In order to study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge is a quantitative measure of flood potential. With scale invariance is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting.  相似文献   

7.
Regional and local characteristics of active fault patterns and elevation variation throughout Honshu, Japan are characterized in terms of their fractal dimensions; this allows variation in these complex variables to be compared directly to the scalar properties of net Quaternary vertical displacement, elevation and 10- and 110-year horizontal strains. The comparisons reveal that, throughout Honshu as a whole, there is significant correlation (r=0.75) between Quaternary vertical displacement, elevation, and its fractal properties. There is poor correlation, however, of elevation and its fractal properties to horizontal crustal strain, and also between Quaternary vertical displacement and horizontal crustal strain. A slight negative correlation is observed between the fractal properties of the active fault system and horizontal crustal strain measured over 10- and 110-year time periods (–0.43 and –0.26, respectively). The correlation between the 10-year (1985–1994) and 110-year (1883–1994) area strains, 0.48, reveals the occurrence of considerable change in the distribution of regional strain over these short time frames. Local computations of the correlation between data sets made for overlapping 160 km length windows of data spaced every 20 km along analysis lines reveal internal fluctuations in the correlation between variables. The local correlation between Quaternary vertical displacement and elevation is highest through central Japan and the Kinki Triangle. There is weak negative correlation between area strain and fractal dimensions of the active fault network. The local correlation between the fractal dimensions of active faults and horizontal area strain over the recent 10-year time period averages about –0.6 through central Japan in an area that extends across the Kinki Triangle through the northern part of central Honshu and northeast across the Itoigawa Shizuoka Tectonic Line. In general, regions of greatest complexity in the active fault network are associated with persistent negative area or compressional strain. Sparsely faulted areas in general coincide with areas of positive or roughly zero area strain. The presence of negative correlation through central Japan and the Kinki Triangle area in the recent 10-year period results from a decrease of area strain within an increasingly complex active fault system that reaches maximum negative values concentrated in the Kinki Triangle during the 1985–1994 time period.  相似文献   

8.
Fractals in geology and geophysics   总被引：21，自引：0，他引：21  
The definition of a fractal distribution is that the number of objectsN with a characteristic size greater thanr scales with the relationNr –D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. Fractals were originally introduced by Mandelbrot to relate the length of a coastline to the length of the measuring stick. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photographs of many geological features is one indication of the wide applicability of scale invariance to geological problems, scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.  相似文献   

9.
The particle size distributions of fault gouge from the San Andreas, the San Gabriel, and the Lopez Canyon faults in Southern California were measured using sieving and Coulter-Counter techniques over a range of particle sizes from 2 m to 16 mm. The distributions were found to be power law (fractal) for the smaller fragments and log-normal by mass for sizes near and above the peak size. The apparent fractal dimensionD of the smaller particles in gouge samples from the San Andreas fault, the San Gabriel fault and the Lopez Canyon gouge were 2.4–3.6, 2.6–2.9 and 2.4–3.0, respectively. The averageD for the Lopez Canyon gouge was 2.7±0.2, which is in agreement with earlier studies of this gouge using planar 2-D sections. The fractal dimension of the finer fragments from all three faults is observed to be correlated with the peak fragment size, with finer gouges tending to have a largerD. A computer automaton is used to show that this observation may be explained as resulting from a fragmentation process which has a grinding limit at which particle reduction stops.  相似文献   

10.
While seismic reflection amplitudes are generally determined by real acoustical impedance contrasts, there has been recent interest in reflections due to contrasts in seismic‐Q. Herein we compare theoretical and modelled seismic reflection amplitudes for two different cases of material contrasts. In case A, we examine reflections from material interfaces that have a large contrast in real‐valued impedance () with virtually no contrast in seismic‐Q. In case B, we examine reflections from material interfaces that have virtually no contrast in but that have very large seismic‐Q contrasts. The complex‐valued reflection coefficient formula predicts non‐zero seismic reflection amplitudes for both cases. We choose physical materials that typify the physics of both case A and case B. Physical modelling experiments show significantly large reflections for both cases – with the reflections in the two cases being phase shifted with respect to each other, as predicted theoretically. While these modelling experiments show the existence of reflections that are predicted by theory, there are still intriguing questions regarding the size of the Q‐contrast reflections, the existence of large Q‐contrast reflections in reservoir rocks and the possible application of Q‐reflection analysis to viscosity estimation in heavy oilfields.  相似文献   

11.
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12.
The physical parameters that affect the formation of Pele's hair and Pele's tears during lava fountaining are discussed. Experiments on ink jets produced from a nozzle under different Weber number (We) and Reynolds number (Re) show the following results: if (Re) is relatively large compared with (We), an ink droplet is produced. However, if (Re) is relatively small and (We) is large, the spurting ink becomes thread-like. I define the Pele number (Pe) as (We)/(Re), which is expressed as v/0, where v is the spuring velocity from an erupting vent, and are viscosity and interfacial tension of the erupting magma, and and 0 are density of air and magma. The experimental results from ink jets suggest that Pele's hair will be produced for larger (Pe), while Pele's tears are very likely produced for relatively small (Pe). I conclude that Pele's hair could be produced when the spurting velocity of erupting magmas is high, and Pele's tears when it is relatively low. As an additional point of interest, the similarity of SEM photographs of the characteristic shape of Pele's hair to those of the failed products of commercial glass fibre are shown.  相似文献   

13.
— The devastating intraplate earthquake of Mw 7.7 of 26 January, 2001 took place along the south-dipping reverse fault in the lower crust ( 23 km) of Kutch, Gujarat, India, obliterating some 14,000 people. The aftershock activity has ensued for three years. We analyzed 997 aftershocks of M 3.0 to study the b value and fractal correlation dimensions in time and space. The b value is found to be 0.8 ± 0.03 from the Gutenberg-Richter relation and 0.76 ± 0.02 from the maximum-likelihood, suggesting a typical value for the intraplate region. The spatial correlation is 1.71 ± 0.02, indicating that events are approaching a two-dimensional region. Further, the temporal correlation dimension is estimated to be 0.78 ± 0.02, confirming the structure is mono-fractal in time domain. The depth section of b value shows a peak at 15–35 km depth range coinciding with the maximum occurrence of aftershocks ( 47%), which is inferred as a fluid-filled highly fractured rock matrix with fractures of high density. It will be important to note that tomographic results also suggest a low Vp, low Vs and a large Poissons ratio for the same depth range, further confirming this inference. Additionally, we have studied the variation of D2s and b value with time. During the first two months of aftershock activity the results show a marked negative correlation between spatial correlation dimension D2 (large) and b value (low), indicating the predominance of large events associated with weak clustering. The negative correlation means the stress release along faults of a larger surface area. After two months the fractal dimension (D2s) and b value suggests a positive correlation implying more numerous smaller shocks with stress release along faults of a smaller surface area. This would indicate a reduced probability of large magnitude earthquakes due to fragmentation of the fault zone.Acknowledgement. The authors thank Dr. V.P. Dimri, Director, NGRI for his encouragement and kind permission to publish this work. The Department of Science and Technology, New Delhi supported this study.  相似文献   

14.
Multifractal measures,especially for the geophysicist   总被引：9，自引：0，他引：9  
This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function (), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity is called Hölder exponent. In terms of the alternative functionf() used in the approach of Frisch-Parisi and of Halseyet al., one has ()=f()–E for measures supported by the Euclidean space of dimensionE. Whenf()0,f() is a fractal dimension. However, one may havef()<0, in which case is called latent. One may even have <0, in which case is called virtual. These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD q, which is shown forq>1 to be a critical dimension for the cuts. An enhanced multifractal diagram is drawn, includingf(), a function called (q) andD q.This text incorporatesand supersedes Mandelbrot (1988). A more detailed treatment, in preparation, will incorporateMandelbrot (1989).  相似文献   

15.
The Aftershock sequence of Chamoli earthquake (M w 6.4) of 29 March 1999 is analyzed to study the fractal structure in space, time and magnitude distribution. The b value is found to be 0.63 less than which is usually observed worldwide and in the Himalayas. This indicates that the numbers of smaller earthquakes are relatively less than the larger ones. The spatial correlation is 1.64, indicating that events are approaching a two-dimensional region meaning that the aftershocks are uniformly distributed along the trend of the aftershock zone. Temporal correlation is 0.86 for aftershocks of M 1, indicating a nearly continuous aftershock activity. However, it is 0.5 for aftershocks of M 1.75, indicating a non continuous aftershock activity. From the assessment of slip on different faults it is inferred that 70% displacement is accommodated on the primary fault and the remainder on secondary faults.  相似文献   

16.
The response of the dayside ionospheric flow to a sharp change in the direction of the interplanetary magnetic field (IMF) measured by the WIND spacecraft from negative Bz and positive By, to positive Bz and small By, has been studied using SuperDARN radar, DMSP satellite, and ground magnetometer data. In response to the IMF change, the flow underwent a transition from a distorted twin-cell flow involving antisunward flow over the polar cap, to a multi-cell flow involving a region of sunward flow at high latitudes near noon. The radar data have been studied at the highest time resolution available (2 min) to determine how this transition took place. It is found that the dayside flow responded promptly to the change in the IMF, with changes in radar and magnetic data starting within a few minutes of the estimated time at which the effects could first have reached the dayside ionosphere. The data also indicate that sunward flows appeared promptly at the start of the flow change (within 2 min), localised initially in a small region near noon at the equatorward edge of the radar backscatter band. Subsequently the region occupied by these flows expanded rapidly east-west and poleward, over intervals of 7 and 14 min respectively, to cover a region at least 2 h wide in local time and 5° in latitude, before rapid evolution ceased in the noon sector. In the lower latitude dusk sector the evolution extended for a further 6 min before quasi-steady conditions again prevailed within the field-of-view. Overall, these observations are shown to be in close conformity with expectations based on prior theoretical discussion, except for the very prompt appearance of sunward flows after the onset of the flow change.  相似文献   

17.
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18.
Multifractal analysis of earthquakes   总被引：5，自引：0，他引：5  
Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculatedD q-q curves (the generalized dimension) indicate that the earthquake process is multifractal or heterogeneous in the fractal dimension. Japanese earthquakes are the most heterogeneous and Californian earthquakes are the least. Since the earthquake process is multifractal, a single value of the so-called fractal dimension is not sufficient to characterize the earthquake process. Studies of multifractal models of earthquakes are recommended. Temporal changes of theD q-q curve are also obtained for Californian and Japanese earthquakes. TheD q-q curve shows two distinctly different types in each region; the gentle type and the steep type. The steeptype corresponds to a strongly heterogeneous multifractal, which appears during seismically active periods when large earthquakes occur.D q for smallq or negativeq is considerably more sensitive to the change in fractal structure of earthquakes thanD q forq2. We recommend use ofD q at smallq to detect the seismicity change in a local area.  相似文献   

19.
Supposing that the distribution of scatterers in a three-dimensional medium is not uniform but fractally homogeneous with fractal dimensionD, we have made the dimensional analysis for the temporal decay of the multiple scattering energy density at the hypocenter.The number of scatters in a sphere of radiusR is assumed to be proportional toR D . Then, the energy density of thekth order scattering decays according to the [(D–2)k–3]th power of lapse time. A fractal dimension ofD=3 corresponds to the uniform distribution. If 2<D3, multiple scattering terms of orderk2 dominate over the single scattering term (k=1) at long lapse time. IfD=2, energy density of every order decays according to the — 3rd power of lapse time. The single scattering model survives on conditionD<2; the single scattering term dominates over the higher order multiple scattering terms even at long lapse time, since the negative power of lapse time fork=1 is the smallest of all.  相似文献   

20.
Summary The paper presents, in a condensed form, the fundamentals of global atmospheric energetics that have a bearing on the linear theory of compensation of non-equilibrium states in the Earth's atmosphere. The author introduces a new coordinate system with the vertical coordinate *=Z*/T*, which suits global atmospheric energetice.The relation between the energetics of the atmospheric system as a whole and the mean energetics level (MEL) is shown. Contrary to what has been assumed so far, it is proved that this level is neither an isopycnic level nor a physical surface, where */t=0 applies everywhere.List of Symbols Used x, y, z space coordinates in thez-system - x, y, space coordinates in the -system - t time - p, T, pressure, thermodynamic temperature and air density - p*, T*, pressure, temperature, density and geopotential on the mean energy level - g acceleration of the Earth's gravity - c p ,c v ,R specific temperature under constant pressure, volume and specific gas constant - = c p /c v Poisson's constant - E k ,E v ,E p kinetic, internal and potential energies of the atmospheric system - r'(x,y) correction function to inhomogeneous atmosphere - v, v n magnitude of motion velocity, magnitude of the normal component of velocity - O, S, S 0 volume of the whole atmospheric system, surface limiting volumeO and the Earth's surface - Z S height of surfaceS - arbitrary scalar quantity - H , horizontal differential operators in thez- andp-systems Dedicated to Corresponding Member Vojtch Vítek, Director of the Institute of Physics of the Atmosphere of the Czechoslovak Academy of Sciences, at the occasion of his sixtieth birthday.  相似文献   

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