Falloff Rate Research Articles

Scalar wave falloff in topological black hole backgrounds

We investigate the behavior of conformal scalar waves in topological black hole spacetimes. These spacetimes are all asymptotically anti--de Sitter spacetimes, and have black hole event horizons which are compact two-surfaces of arbitrary genus. We solve numerically the conformal scalar wave equation and show that its late time behavior is the same near or far from the event horizon. This behavior is strongly dependent upon the genus $g$ of the black hole, with higher genus black holes exhibiting a less rapid exponential falloff rate with a lower frequency of oscillation. In general, waves respecting Dirichlet boundary conditions decay more rapidly than those obeying Neumann conditions. We consider also negative mass black holes (allowed solutions only for higher genus), and find that the behavior of the wave is considerably different from the positive mass cases, undergoing a transition from falloff to amplification.

Site attenuation and source parameters on the North Anatolian Fault zone, eastern Turkey estimated from the aftershocks of 13 March 1992 Erzincan earthquake

Site attenuation and source characteristics of 45 aftershocks of the 13 March 1992 Erzincan, eastern Turkey earthquake have been determined from SH-wave spectra using a least-squares best-fit method. Although the most of the seismograms were recorded on the ophiolitic rock sites and the average regional attenuation correction of Q(f) = 35 f0.83 was applied, the high fall-off rates γ ranging between 3.0 and 4.5 beyond the corner frequencies of 8–13 Hz were observed on the SH spectra. The site attenuation value, κ, has been calculated from the slope of the high frequency part of the SH spectra. It was found that κ varied in the range of 0.0124–0.0364 s and the average was 0.0246 s with a standard deviation of 0.0047 s. The high fall-off rates of observed spectra have decreased considerably as a result of site attenuation corrections and converged to an average value of 2.3. We concluded that the high fall-off rates of SH wave spectra are mainly controlled by highly deformed Miocene ophiolitic formations which covers a wide area in the North Anatolian Fault zone in the vicinity of Erzincan region. Using the spectra that were corrected for regional and site attenuation, and assuming a Brune's source model; seismic moment, source radius, and stress-drops of the aftershocks were computed. We found that stress-drops for some of the aftershocks in Erzincan area have slightly decreased after removal of site attenuation over SH wave observed spectra.

Stability analysis and improvement of structural index estimation in Euler deconvolution

Euler deconvolution has been widely used in automatic aeromagnetic interpretations because it requires no prior knowledge of the source magnetization direction and assumes no particular interpretation model, provided the structural index defining the anomaly falloff rate related to the nature of the magnetic source, is determined in advance. Estimating the correct structural index and electing optimum criteria for selecting candidate solutions are two fundamental requirements for a successful application of this method. We present a new criterion for determining the structural index. This criterion is based on the correlation between the total‐field anomaly and the estimates of an unknown base level. These estimates are obtained for each position of a moving data window along the observed profile and for several tentative values for the structural index. The tentative value for the structural index producing the smallest correlation is the best estimate of the correct structural index. We also propose a new criterion to select the best solutions from a set of previously computed candidate solutions, each one associated with a particular position of the moving data window. A current criterion is to select only those candidates producing a standard deviation for the vertical position of the source smaller than a threshold value. We propose that in addition to this criterion, only those candidates producing the best fit to the known quantities (combinations of anomaly and its gradients) be selected. The proposed modifications to Euler deconvolution can be implemented easily in an automated algorithm for locating the source position. The above results are grounded on a theoretical uniqueness and stability analysis, also presented in this paper, for the joint estimation of the source position, the base level, and the structural index in Euler deconvolution. This analysis also reveals that the vertical position and the structural index of the source cannot be estimated simultaneously because they are linearly dependent; the horizontal position and the structural index, on the other hand, are linearly independent. For a known structural index, estimates of both horizontal and vertical positions are unique and stable regardless of the value of the structural index. If this value is not too small, estimates of the base level for the total field are stable as well. The proposed modifications to Euler deconvolution were tested both on synthetic and real magnetic data. In the case of synthetic data, the proposed criterion always detected the correct structural index and good estimates of the source position were obtained, suggesting the present theoretical analysis may lead to a substantial enhancement in practical applications of Euler deconvolution. In the case of practical data (vertical component anomaly over an iron deposit in the Kursk district, Russia), the estimated structural index (corresponding to a vertical prism) was in accordance with the known geology of the deposit, and the estimates of the depth and horizontal position of the source compared favorably with results reported in the literature.

Timelike infinity and asymptotic symmetry

By extending Ashtekar and Romano’s definition of spacelike infinity to the timelike direction, a new definition of asymptotic flatness at timelike infinity for an isolated system with a source is proposed. The treatment provides unit spacelike three-hyperboloid timelike infinity and avoids the introduction of the troublesome differentiability conditions which were necessary in the previous works on asymptotically flat space–times at timelike infinity. Asymptotic flatness is characterized by the falloff rate of the energy-momentum tensor at timelike infinity, which makes it easier to understand physically what space–times are investigated. The notion of the order of the asymptotic flatness is naturally introduced from the rate. The definition gives a systematized picture of hierarchy in the asymptotic structure, which was not clear in the previous works. It is found that if the energy-momentum tensor falls off at a rate faster than ∼t−2, the space–time is asymptotically flat and asymptotically stationary in the sense that the Lie derivative of the metric with respect to ∂t falls off at the rate ∼t−2. It also admits an asymptotic symmetry group similar to the Poincaré group. If the energy-momentum tensor falls off at a rate faster than ∼t−3, the four-momentum of a space–time may be defined. On the other hand, angular momentum is defined only for space–times in which the energy-momentum tensor falls off at a rate faster than ∼t−4.

A Case for Exponential Cloud Fields?

Abstract In a large number of satellite infrared images the proportion of randomly spaced intervals of length p satellite pixels (width, one pixel) that are registered as completely cloudy falls exponentially with increasing interval length. This is exactly to be expected for a one-dimensional exponential cloud field. Further, for rectangular intervals there is also an exponential falloff, as the size of the rectangle increases, in the proportion of completely cloudy intervals. However, the rate of falloff is dependent on the perimeter of the rectangle rather than its area. It is suggested that this can be explained if the length and width of clouds are both exponentially distributed and independent. If this is the case, then the mean horizontal aspect ratio for clouds, defined as the ratio of its semimajor to semiminor axis, is undefined (infinite) even though the ratio of semiminor to semimajor axis has mean 2 ln(2) (≈0.38).

High-frequency

—Investigations of the spectral characteristics of teleseismic body waves revealed that the spectral falloff rate between 1 Hz and 10 Hz is primarily controlled by anelastic attenuation along the path. In addition, the amount of high-frequency energy in teleseismic body waves is far above the level expected on the basis of Q estimates at low frequencies, thus leading to the idea of frequency dependence in Q. Q variations in the earth’s mantle can be investigated by mapping out the variations of high frequency (4 - 10 Hz) energy relative to the low frequency (1 - 3 Hz) energy in teleseismic P waves, and similar ratios at lower frequencies in teleseismic S waves. Because of the extreme sensitivity of spectral content of short-period body waves to Q variations, large uncertainties in other factors affecting spectral content can be tolerated in such studies. With the increasing number and density of broadband seismic stations recording at high sampling rates, tomographic studies of Q at high frequencies become possible.

The paradox of the expected time until the next earthquake

AbstractWe show analytically that the answer to the question, (can it be that) “The longer it has been since the last earthquake, the longer the expected time till the next?” depends crucially on the statistics of the fluctuations in the interval times between earthquakes. The periodic, uniform, semi-Gaussian, Rayleigh, and truncated statistical distributions of interval times, as well as the Weibull distributions with exponent greater than 1, all have decreasing expected time to the next earthquake with increasing time since the last one, for long times since the last earthquake; the lognormal and power-law distributions and the Weibull distributions with exponents smaller than 1 have increasing times to the next earthquake as the elapsed time since the last increases, for long elapsed times. There is an identifiable crossover between these models, which is gauged by the rate of fall-off of the long-term tail of the distribution in comparison with an exponential fall-off. The response to the question for short elapsed times is also evaluated. The lognormal and power-law distributions give one response for short elapsed times and the opposite for long elapsed times. Even the sampling of a finite number of intervals from a Poisson distribution will lead to an increasing estimate of time to the next earthquake for increasing elapsed time since the last one.

The tetrad and hexad: Maximum beam separation as a starting point for noncoplanar 3D treatment planning: Prostate cancer as a test case

Purpose : In contrast to computer optimized three-dimensional (3D) treatment planning, we have used maximally separated, noncoplanar beams as the starting point for 3D treatment planning of prostate cancer to maximize the rate of dose fall off from the target volume and minimize dose to surrounding tissues. Materials and Methods : A planar four-field plan, a planar six-field plan, a tetrad plan, and a hexad plan are analyzed using a 3D treatment planning system which is capable of displaying real-time 3D dose distributions within volume reconstructed data sets (VISTAnet—an extension of the virtual simulator). The tetrad plan is based on the methane molecule and the hexad plan has a minimum separation of 58° on beam entrance. All fields are conformal. The irradiated volume equals the clinical target volume plus a 1 cm margin. Competing plans are compared using cumulative dose-volume histograms and normal tissue complication probabilities. Results : The crossover point, the isodose surface that conforms more to the beams than the target, is introduced and described. The hexad and tetrad plans result in tighter dose distributions when compared to the planar plans with the same number of beams. The tetrad plan treats a volume less than or equal to the planar six-field plan at isodose surfaces above 18% except between 37% and 44% where the tetrad volume is slightly larger. As expected from integral dose considerations, the amount of normal tissue receiving some radiation increases, but the amount receiving clinically significant amounts of radiation decreases as the number of beams increase. The plan involving the largest number of noncoplanar beams results in the tightest isodose distribution. Analysis of rectal and bladder cumulative dose volume histograms does not reveal a clearly superior plan based on normal tissue complication probabilities. Conclusions : Using basic principles of solid geometry, maximally separated beams without significant overlap on exit or entrance can be designed which minimize clinically significant dose to surrounding tissues and tighten the isodose distribution around the target volume. The emphasis of this treatment plan optimization is geometric in contrast to methods using computer optimization or artificial intelligence.

Bromine‐containing source gases during EASOE

Vertical profiles of CBrClF2 (Halon‐1211), CBrF3 (Halon‐1301) and methyl bromide (CH3Br) were measured during EASOE by means of cryogenic sampling and subsequent GC‐analyses. Three flights of the MPAE balloon‐borne sampler were carried out on January 18, February 6 and March 20, 1992, from Kiruna/Sweden. Stratospheric falloff rates of these substances, which constitute the dominant source of organically bound bromine in the atmosphere, were found, like those of other source gases measured during EASOE, to be considerably larger than those observed at midlatitudes. Total BrOx released from the three source gases was found to increase from about zero at 8 km to 11.4 pptV at 19 km altitude.

Windows with rapidly decaying sidelobes and steerable sidelobe dips

A window in the form of a sum of cosine terms is considered and the temporal weights are evaluated analytically so that it can have rapidly decaying sidelobes as well as steerable sidelobe dips. An analytic expression is derived so that the window designer can exploit the trade-off between a high sidelobe falloff rate (SLFOR) and many steerable sidelobe dips (SSLD). The treatment is based on using the L degrees of freedom inherent in the L temporal weights of the L+1 term window in partially achieving the goals of a high SLFOR and many SSLD. In the extreme case where all degrees of freedom are used in achieving the maximum SLFOR a simple closed-form expression is derived for the temporal weights thus formalizing and generalizing the results of Nuttall (1981). The other extreme case where all degrees of freedom are used in creating many SSLD has been recently treated by Zhong et al. (see ibid. vol.40, no.6, p.1452-1459, 1992) combining both desired features in one unified mathematical framework is the main objective of this paper. Simulation results demonstrate the superior performance of a window having both features to that of a window having only one feature in extracting a weak sinusoidal signal dominated by a leakage from another stronger signal.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fault growth and fault scaling laws: Preliminary results

We report progress made in the last few years on the general problem of the mechanism of fault growth and the scaling laws that result. Results are now conclusive that fault growth is a self‐similar process in which fault displacement d scales linearly with fault length L. Both this result and the overall nature of along‐strike fault displacement profiles are consistent with the Dugdale‐Barenblatt elastic‐plastic fracture mechanics model. In this model there is a region of inelastic deformation near the crack tip in which there is a breakdown from the yield strength of the unfractured rock to the residual frictional strength of the fault over a breakdown length S and displacement d0. Limited data also indicate that S and d0 also scale linearly with L, which implies that fracture energy G increases linearly with L. The scaling parameters in these relationships depend on rock properties and are therefore not universal. In our prime field locality, the Volcanic Tableland of eastern California, we have collected data over 2 orders of magnitude in scale range that show that faults obey a power law size distribution in which the exponent C in the cumulative distribution is ∼1.3. If the fault is growing within the brittle field, the zone of inelastic deformation consists of a brittle process zone which leaves a wake of fractured rock adjacent to the fault. Preliminary results of modeling the process zone are consistent with observations now in hand both in predicting the preferred orientation of cracks in the process zone wake and the rate of falloff of crack density as a function of distance from the fault. The preferred orientation of these cracks may be used to infer the mode and direction of propagation of the fault tip past the point in question. According to the model, the width of the process zone wake may be used to infer the length of the fault at the time its tip passed the measurement point, but data have not yet been collected to verify this prediction. If the fault displacement has been accumulated by repeated seismic slips, each of these will sweep the fault with a crack tip stress field of a smaller spatial extent than that of the fault tip stress field, producing an inner, more intensely fractured, process zone wake. This may be the mechanism that creates the cataclasite zone, rather than simple frictional wear, as has been previously supposed.

Estimated ground motions in Los Angeles due to MW = 7 earthquake on the Elysian thrust fault

Abstract The Elysian thrust fault has been identified as a blind thrust fault (Davis et al., 1989; Hauksson and Jones, 1989) representing a potentially serious seismic hazard to the metropolitan Los Angeles and its neighboring areas. We have simulated time histories, peak ground accelerations and their uncertainties using a semi-empirical method for a M W = 7.0 earthquake on the Elysian thrust fault using a flat-layered crustal structure. The accelerograms from the 4 October 1987 Whittier-Narrows aftershock (10h:50m; M L = 5.3) are used to represent the source functions of each subfault on the fault surface. To account for the velocity variation in the surface sediments, we compared simulated ground motions using two separate shearwave velocities, 0.6 km/sec and 0.9 km/sec, respectively, in the top layer of the crustal model. The use of such a simple crustal model is validated by modeling the accelerograms recorded during the 1 October 1987 Whittier-Narrows mainshock ( M L = 6.0). The duration and the relative frequency content observed on these accelerograms are successfully modeled. At some stations, the simulated peak accelerations agree well with the observed values; however, at some sites, the simulated and observed values differ by a factor of 2 to 3. The variation is attributed to a laterally varying crustal structure that is significant for small earthquakes. Additional site specific study is needed for an improved prediction of the observed peak accelerations. For large magnitude earthquakes, the near-source peak ground acceleration appears to be controlled by the source-receiver geometry relative to the fault, as well as the location of asperities on the fault surface. This is validated by simulating the peak acceleration data of the 1989 Loma Prieta earthquake recorded within 30 km of the source. For our simulations on the Elysian thrust fault, an additional component is added to the uncertainty by analyzing several asperity models. Finally, an analytical representation is given to the simulated average peak horizontal ground accelerations, Y ( R ), which is expressed by ln ( Y ( R ) ) = ( 5.38 ± 0.085 ) + ( − 2.09 ± 0.0268 ) ln ( R + 8.0 ) ± 0.343 in the range of 7.5 ≤ R ≤ 35 km ( R is the closest distance to the seismogenic rupture zone). This functional form predicts a rapid fall-off rate for the simulated ground motions compared with the fall-off rate predicted by the other published empirical attenuation relations. We use the finite-difference method to investigate the effects of irregular structure on ground motions resulting from point sources on the Elysian Park fault. The response computed at several depths beneath the basin suggests that the response is dominated by the initial direct arrivals for sources located interior to the basin. When the receivers are located at one end of the basin, and the seismic sources are located at the opposite edge, the characteristic features on the seismograms are the long durations caused by the trapped energy within the basin. The level of trapped energy decreases as the depth of the source increases. Thus, the fault model becomes important in determining the level of peak ground motions and shaking duration.

Design of windows with steerable sidelobe dips

Based on the frequency sampling method, a novel and simple window design technique was established upon three theorems. The technique produces a set of windows which have simple expressions and the steerable sidelobe-dip (SSLD) property. By steering the dips in the sidelobes, it is easy to reduce the edge of the mainlobe, or to minimize the height of sidelobes, or to create a 'hole' in the sidelobes if its desired to reduce spectral leakage at a particular frequency. It is found that windows constructed as a weighted sum of cosines over a finite support and with a -6 dB/OCT sidelobe falloff rate can all be simulated by appropriate SSLD distributions. In this sense, many good windows such as Hamming, Blackman, Blackman-Harris, and minimum sidelobe behaviors can be created with a minor constraint. This renders design flexibility for various applications. Finally, the new technique can be easily incorporated with other techniques to produce windows with hybrid merits.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Causality in local quantum field theory: Some general results

General asymptotic causality properties of chronologicalN-point functions and, in massive theories, ofN-particle collision amplitudes, are derived from locality and the spectral condition. Results include specified rates of exponential fall-off, with simple and direct physical content, for large non-causal separations of points or particles in Minkowski space-time depending on values of the energy-momenta and on the mass spectrum. Relevant mathematical results on rates of exponential fall-off of generalized Fourier transforms outside their microsupports are given.

Self-aligned, emitter-edge-passivated AlGaAs/GaAs heterojunction bipolar transistors with extrapolated maximum oscillation frequency of 350-GHz

Summary form only given. The authors present self-aligned, emitter-edge-passivated AlGaAs/GaAs heterojunction bipolar transistors (HBTs) with extrapolated maximum oscillation frequency of 350 GHz. To the authors' knowledge, this is the highest f/sub max/ ever reported for an HBT. The self-aligned, emitter-edge-passivated dual-liftoff process reported here enhances the device RF performance and DC current gain. The current gain of a typical HBT with 2 emitter fingers each 2 mu m*10 mu m was measured to be more than 20 at current density of 5*10/sup 4/ cm/sup 2/. A record high maximum oscillation frequency of 350 GHz was extrapolated by assuming 6-dB/octave falloff rate from the unilateral gains obtained from the s-parameters measured up to 40 GHz. >

Q for short-periodP-waves: is it frequency dependent?

SUMMARY Two types of anelastic attenuation model have been derived for short-period P-waves for teleseismic ray paths out of the Shagan River Test Site (STS), USSR and the Nevada Test Site (NTS) USA. One type assumes that the specific quality factor Q and hence t* (the ratio of traveltime to Q) is independent of frequency and the other that Q increases (and hence t* decreases) with frequency in the SP band. Evidence for the frequency-independent t* comes from the observed rate of fall-off of explosion spectra to high frequencies, whereas a frequency-dependent t* is required to bring the amplitudes at 1 Hz predicted from widely accepted source models, such as the Muellar-Murphy (M-M) model derived from close-in observations at the NTS, into agreement with observed amplitudes. It has also been claimed that the P spectra for STS explosions show evidence of the frequency-dependence of t*. In this paper results are presented derived by deconvolving observed P seismograms using each of the two types of attenuation model, in an attempt to determine which best describes the attenuation. Evidence from spectra for frequency-dependent f * models is also reassessed. The results of the deconvolution of STS seismograms show that neither the frequency-dependent nor the frequency-independent models produce deconvolved seismograms that can be interpreted as a series of pulses of the M-M type. Such M-M pulses should show a positive initial motion followed by a negative overshoot with amplitude less than about a third of that of the positive motion; the leading edge of the main pulse being sharper than the trailing edge. Use of the frequency-dependent t* leads to pulses apparently with overshoot. The amplitude of the overshoot however, is larger than predicted by the theoretical source model and appears to be an artefact of the processing rather than a property of the source pulse itself. With t* independent of frequency the estimated pulses have the form of symmetrical trapezia. Reassessment of the evidence from observed P spectra for frequency-dependent t* is shown to be at best inconclusive and it turns out that the spectra of symmetrical trapezia have a fall-off that can account for those features of explosion spectra that have been attributed to the effects of frequency-dependent t*. It is concluded that the frequency-independent t* model is the better attenuation model for paths from the STS. The results obtained from deconvolution of the P seismograms of NTS explosions are similar to those obtained for STS explosions and again suggest that t* is independent of frequency. As with the STS results, use of frequency-dependent t* sometimes leads to pulses with overshoots that appear to be artefacts of the processing and not part of the source pulse. Further, deconvolution using the frequency-independent t* leads to a more systematic variation of pulse duration with depth (and hence presumably yield) than is found using the frequency-dependent models. Use of the frequency-independent f* again leads to pulses which have the rough form of symmetrical trapezia.

Modeling and computer simulation of wave propagation in lineal line-of-sight microcells

The model and implementation principles governing the computer simulation of line-of-sight (LOS) microcell wave propagation are presented. Multiray propagation above a plane earth constitutes the basic model. For rural microcells, two rays are used while, for urban microcells, 10 rays are used propagating in a dielectric canyon. The model is applied to two relevant problems. In the first, control of electric field falloff with distance, r, is studied. ln the second, the advantages of switched transversal antenna diversity are demonstrated. Power falloff rates of 1/r/sup 4/ and 1/r/sup 6/ were obtained for simple two-element array structures. This may provide an additional interference control tool in the layout and design of microcells. The interference between the various rays propagating in lineal urban microcells results in deep nulls at various locations. The deleterious effects of these nulls can be eliminated by employing simple switched transverse antenna diversity. >

Ferroelectricity in the system Pb (1− x) Ba x(Mg [formula omitted])O 3

A series of ceramics of composition Pb (1− x) Ba x (Mg 1 3 Nb 2 3 )O 3 has been prepared, with x varying in regular intervals between 0 and 1. The mixed oxide processing route to lead barium magnesium niobate (PBMN) powders involves the preparation of magnesium niobate, MgNb 2O 6, as an intermediate compound, in order to inhibit the formation of pyrochlore phase. All samples in the composition range are sintered by conventional methods, except the x = 1 composition, for which fast firing is used. The weak-field dielectric response has been measured for each composition, and the results interpreted in terms of the variation in chemical composition between the samples. The niobium-oxygen coordination polyhedra are considered to be the basic polar units, and the function of the Pb 2+ ions is to couple the individual niobium-oxygen octahedra together to form a ferroelectric network. The effect of the Ba 2+ ion is to weaken this coupling. The ferroelectric response of each composition is thought to be due to lead-rich microregions, which become progressively smaller as the relative barium content is increased. The rate of fall-off of relative permittivity with increasing barium content suggests that lead-rich ferroelectric clusters of ions persist to high values of x. An assessment is made of the contribution of this work to the development of structure-dielectric property relationships in relaxor ferroelectrics.

The propagation of axisymmetric waves on a fluid-loaded cylindrical shell

A ring drive applied to an infinite cylindrical shell immersed in a fluid will generate a bulk acoustic wave emanating from the drive and evanescent surface waves propagating along the cylinder. In this paper, the response on and near the surface of the cylinder is examined for frequencies below the ring frequency of the shell. Approximate analytic results covering almost the entire cylinder are given for the induced surface velocity field. Expressions for both the nearfield, including the drive admittance, and the farfield are given and compared with numerical results. Simple approximate formulas for the velocities and the excitation strengths of the surface waves are presented, and explicit expressions are derived for the acoustic field. Various aspects of the phenomena, the nature of the surface waves, the rate of falloff of the acoustic field, and the buildup of the evanescent fields are examined.

The coherent anomaly method and long-range one-dimensional Ising models

The authors present the results of the coherent anomaly method when applied to Ising models in one dimension with long-range interactions. This class of systems acts as an interesting and challenging test for the method because the critical exponents as well as the critical temperature values of which are given by the method, depend on the rate of fall-off of the interactions. Thus one can see how accurately the method gives results which correctly reflect this dependency. The results obtained from this method are compared with results obtained by a variety of other methods.