Semiperiodic Sequences Research Articles

Forecast of Large Earthquakes Through Semi-periodicity Analysis of Labeled Point Processes

Large earthquakes have semi-periodic behavior as a result of critically self-organized processes of stress accumulation and release in seismogenic regions. Hence, large earthquakes in a given region constitute semi-periodic sequences with recurrence times varying slightly from periodicity. In previous papers, it has been shown that it is possible to identify these sequences through Fourier analysis of the occurrence time series of large earthquakes from a given region, by realizing that not all earthquakes in the region need belong to the same sequence, since there can be more than one process of stress accumulation and release in the region. Sequence identification can be used to forecast earthquake occurrence with well determined confidence bounds. This paper presents improvements on the above mentioned sequence identification and forecasting method: the influence of earthquake size on the spectral analysis, and its importance in semi-periodic events identification are considered, which means that earthquake occurrence times are treated as a labeled point process; a revised estimation of non-randomness probability is used; a better estimation of appropriate upper limit uncertainties to use in forecasts is introduced; and the use of Bayesian analysis to evaluate the posterior forecast performance is applied. This improved method was successfully tested on synthetic data and subsequently applied to real data from some specific regions. As an example of application, we show the analysis of data from the northeastern Japan Arc region, in which one semi-periodic sequence of four earthquakes with M ≥ 8.0, having high non-randomness probability was identified. We compare the results of this analysis with those of the unlabeled point process analysis.

A Bayesian Assessment of Seismic Semi-Periodicity Forecasts

Among the schemes for earthquake forecasting, the search for semi-periodicity during large earthquakes in a given seismogenic region plays an important role. When considering earthquake forecasts based on semi-periodic sequence identification, the Bayesian formalism is a useful tool for: (1) assessing how well a given earthquake satisfies a previously made forecast; (2) re-evaluating the semi-periodic sequence probability; and (3) testing other prior estimations of the sequence probability. A comparison of Bayesian estimates with updated estimates of semi-periodic sequences that incorporate new data not used in the original estimates shows extremely good agreement, indicating that: (1) the probability that a semi-periodic sequence is not due to chance is an appropriate estimate for the prior sequence probability estimate; and (2) the Bayesian formalism does a very good job of estimating corrected semi-periodicity probabilities, using slightly less data than that used for updated estimates. The Bayesian approach is exemplified explicitly by its application to the Parkfield semi-periodic forecast, and results are given for its application to other forecasts in Japan and Venezuela.

Semi-Periodic Sequences and Extraneous Events in Earthquake Forecasting. II: Application, Forecasts for Japan and Venezuela

In order to analyze observed seismicity in central Japan and Venezuela, we applied a new method to identify semi-periodic sequences in the occurrence times of large earthquakes, which allows for the presence of multiple periodic sequences and/or events not belonging to any sequence in the time series. We also explored a scheme for diminishing the effects of a sharp cutoff magnitude threshold in selecting the events to analyze. A main four-event sequence with probability P c = 0.991 of not having occurred by chance was identified for earthquakes with M ≥ 8.0 in central Japan. Venezuela is divided, from West to East, into four regions; for each of these, the magnitude ranges and identified sequences are as follows. Region 1: M ≥ 6.0, a six-event sequence with P c = 0.923, and a four-event sequence with P c = 0.706. Region 2: M ≥ 5.6, a five-event sequence with P c = 0.942. Region 3: M ≥ 5.6, a four-event sequence with P c = 0.882. Region 4: M ≥ 6.0, a five-event sequence with P c = 0.891. Forecasts are made and evaluated for all identified sequences having four or more events and probabilities ≥0.5. The last event of all these sequences was satisfactorily aftcast by previous events. Whether the identified sequences do, in fact, correspond to physical processes resulting in semi-periodic seismicity is, of course, an open question; but the forecasts, properly used, may be useful as a factor in seismic hazard estimation.

Semi-Periodic Sequences and Extraneous Events in Earthquake Forecasting: I. Theory and Method, Parkfield Application

We present a new method to identify semi-periodic sequences in the occurrence times of large earthquakes, which allows for the presence of multiple semi-periodic sequences and/or events not belonging to any identifiable sequence in the time series. The method, based on the analytic Fourier transform, yields estimates of the departure from periodicity of an observed sequence, and of the probability that the sequence is not due to chance. These estimates are used to make and to evaluate forecasts of future events belonging to each sequence. Numerous tests with synthetic catalogs show that the method is surprisingly capable of correctly identifying sequences, unidentifiable by eye, in complicated time series. Correct identification of a given sequence depends on the number of events it contains, on the sequence’s departure from periodicity, and, in some cases, on the choice of starting and ending times of the analyzed time window; as well as on the total number of events in the time series. Some particular data combinations may result in spectra where significant periods are obscured by large amplitudes artifacts of the transform, but artifacts can be usually recognized because they lack harmonics; thus, in most of these cases, true semi-periodic sequences may not be identified, but no false identifications will be made. A first example of an application of the method to real seismicity data is the analysis of the Parkfield event series. The analysis correctly aftcasts the September 2004 earthquake. Further applications to real data from Japan and Venezuela are shown in a companion paper.

Semi-periodic solutions of difference and differential equations

The spaces of semi-periodic sequences and functions are examined in the relationship to the closely related notions of almost-periodicity, quasi-periodicity and periodicity. Besides the main theorems, several illustrative examples of this type are supplied. As an application, the existence and uniqueness results are formulated for semi-periodic solutions of quasi-linear difference and differential equations.

Atomic-scale study of the adsorption of calcium fluoride on Si(100) at low-coverage regime

We investigate, experimentally and theoretically, the initial stage of the formation of Ca/Si and Si/F structures that occurs during the adsorption of CaF${}_{2}$ molecules onto a bare Si(100) surface heated to 1000 K in a low-coverage regime (0.3 monolayer). A low-temperature (5 K) scanning tunneling microscope (STM) is used to observe the topographies and the electronic properties of the exposed silicon surfaces. Our atomic-scale study reveals that several chemical reactions arise during CaF${}_{2}$ deposition, such as dissociation of the CaF${}_{2}$ molecules and etching of the surface silicon dimers. The experimental and calculated STM topographies are compared using the density functional theory, and this comparison enables us to identify two types of reacted structures on the Si(100) surface. The first type of observed complex surface structure consists of large islands formed with a semiperiodic sequence of 3 \ifmmode\times\else\texttimes\fi{} 2 unit cells. The second one is made of isolated Ca adatoms adsorbed at specific sites on the Si(100)-2 \ifmmode\times\else\texttimes\fi{} 1 surface.

Semiperiodic chirp sequences reduce autocorrelation side lobes of pulsed signals

A time-coded sequence of source pulses has been designed to allow for increased range to the target and reduced side-lobe energy with correlation. The method was designed for a new type of marine-combustion seismic source that can be fired repeatedly, but the method also can be applied to other acoustic-pulsed sources. The basic concept is that one can reduce autocorrelation side lobes by using semiperiodic sequences to concentrate much of the side-lobe noise into time intervals corresponding to the semiperiod. Signals can then be detected with better sensitivity in the time interval after the first autocorrelation peak and before the first periodic side lobe, because this interval contains only lower-level crosscorrelations between the sequence components. Compared with a source which fires pulses randomly, an 8-dB reduction of autocorrelation side lobes has been simulated for sequences of [Formula: see text] duration.

Temporal and spatial aspects of the cusp inferred from local and global ground‐ and space‐based observations in a case study

Global and local observations, from both ground and space facilities, are brought to bear to understand the origin of a stepped cusp ion dispersion observed 3 hours prenoon under an interplanetary magnetic field characterized by strongly positive By, conditions under which the cusp is believed to be shifted postnoon. Our main aim is to distinguish the temporal from the spatial cusp features. The local observations from Svalbard are from approximately the 0900–1200 MLT sector, while the in situ observations are from Polar at 0900 MLT. The global auroral observations were acquired by the Earth camera on Polar. The aurora from the ground perspective appeared as a periodic sequence of brightening events located on either side of a “midday gap aurora” centered at about 1030 MLT. At noon the aurora appeared as a semiperiodic sequence of brightening events. These were concurrent with enhancements of the overhead ionospheric Hall current. Polar observed two steps of a staircase ion energy‐latitude dispersion. These two steps were, in turn, concurrent with two consecutive auroral brightening events. We argue from this complement of observations that the stepped cusp was temporal in nature and resulted from a time‐varying reconnection process. Global UV imagery was employed to complement the ground observations for the purpose of separating the temporal from the spatial aspects. The imager captured, namely, two bands of strong UV emission in the prenoon and postnoon sectors, between which there appeared a persistent, weak UV aurora. We interpret this to be an underlying spatial substratum. Patchy and bursty UV enhancements coincided with the transients seen in the local ground and space measurements, corroborating further our distinction between space and time in the cusp. Comparing these inferences with recent work on the response of the dayside aurora to reconnection at the magnetopause, we find a close correspondence. In addition, we document the field‐aligned currents associated with the stepped cusp, which, in turn, compare favorably with recent theoretical ideas. This work is a contribution to the current debate on the nature of the stepped cusp and suggests that multiple data sets are essential to study this problem.

Multipliers on the Space of Semiperiodic Sequences

Multipliers on the Space of Semiperiodic Sequences

Multipliers on the space of semiperiodic sequences

Semiperiodic sequences are defined to be the uniform limit of periodic sequences. They form a space of continuous functions on a compact group Δ \Delta . We study the properties of the Radon measures on Δ \Delta in order to classify the multipliers for the space of semiperiodic sequences, paying special attention to those which can be realized as transference functions of physically constructible filters.

A note on matrix transformations of some generalized sequence spaces into semiperiodic sequence space

By a counter exam ple a m inör errer in the principle of the preoofs of th e inclusion theorem s on m atix transferınations of some generalized suguence spaces into semiperiodie sequence space in [12 ] is pointed and corrected w ith suitable changes in the statem ents. Our conclysion in one of the tehorem s is strengthened by anexanple dne to Prof. B. K uttner.

The conjugate space of the space of semiperiodic sequences.

The conjugate space of the space of semiperiodic sequences.

The algebra of semiperiodic sequences.

The algebra of semiperiodic sequences.

Periodic, almost-periodic, and semiperiodic sequences.

Periodic, almost-periodic, and semiperiodic sequences.

Matrix Transformations of Some Generalized Sequence spaces into semiperiodic Sequence Space

Necessary and sufficient conditions have been established on an infinite matris A = (ap]^) to transform the generalized segnence spaces 1 (p), Cp(p) and 1„ (p) into, q, the spa,ce of semipe­ riodic seguences. The special case when pjj = 1 /t gives Cp(p) and Ijo (p) es T and ,T* the spaces introdueed by V. Ganapathy lyer [2].