Takahiro Omi

Forecasting large aftershocks within one day after the main shock

Forecasting the aftershock probability has been performed by the authorities to mitigate hazards in the disaster area after a main shock. However, despite the fact that most of large aftershocks occur within a day from the main shock, the operational forecasting has been very difficult during this time-period due to incomplete recording of early aftershocks. Here we propose a real-time method for efficiently forecasting the occurrence rates of potential aftershocks using systematically incomplete observations that are available in a few hours after the main shocks. We demonstrate the methods utility by retrospective early forecasting of the aftershock activity of the 2011 Tohoku-Oki Earthquake of M9.0 in Japan. Furthermore, we compare the results by the real-time data with the compiled preliminary data to examine robustness of the present method for the aftershocks of a recent inland earthquake in Japan.

Optimizing time histograms for non-poissonian spike trains

The time histogram is a fundamental tool for representing the inhomogeneous density of event occurrences such as neuronal firings. The shape of a histogram critically depends on the size of the bins that partition the time axis. In most neurophysiological studies, however, researchers have arbitrarily selected the bin size when analyzing fluctuations in neuronal activity. A rigorous method for selecting the appropriate bin size was recently derived so that the mean integrated squared error between the time histogram and the unknown underlying rate is minimized (Shimazaki & Shinomoto, 2007). This derivation assumes that spikes are independently drawn from a given rate. However, in practice, biological neurons express non-Poissonian features in their firing patterns, such that the spike occurrence depends on the preceding spikes, which inevitably deteriorate the optimization. In this letter, we revise the method for selecting the bin size by considering the possible non-Poissonian features. Improvement in the goodness of fit of the time histogram is assessed and confirmed by numerically simulated non-Poissonian spike trains derived from the given fluctuating rate. For some experimental data, the revised algorithm transforms the shape of the time histogram from the Poissonian optimization method.

Estimating the ETAS model from an early aftershock sequence

Forecasting aftershock probabilities, as early as possible after a main shock, is required to mitigate seismic risks in the disaster area. In general, aftershock activity can be complex, including secondary aftershocks or even triggering larger earthquakes. However, this early forecasting implementation has been difficult because numerous aftershocks are unobserved immediately after the main shock due to dense overlapping of seismic waves. Here we propose a method for estimating parameters of the epidemic type aftershock sequence (ETAS) model from incompletely observed aftershocks shortly after the main shock by modeling an empirical feature of data deficiency. Such an ETAS model can effectively forecast the following aftershock occurrences. For example, the ETAS model estimated from the first 24 h data after the main shock can well forecast secondary aftershocks after strong aftershocks. This method can be useful in early and unbiased assessment of the aftershock hazard.

Intermediate‐term forecasting of aftershocks from an early aftershock sequence: Bayesian and ensemble forecasting approaches

Because aftershock occurrences can cause significant seismic risks for a considerable time after the main shock, prospective forecasting of the intermediate-term aftershock activity as soon as possible is important. The epidemic-type aftershock sequence (ETAS) model with the maximum likelihood estimate effectively reproduces general aftershock activity including secondary or higher-order aftershocks and can be employed for the forecasting. However, because we cannot always expect the accurate parameter estimation from incomplete early aftershock data where many events are missing, such forecasting using only a single estimated parameter set (plug-in forecasting) can frequently perform poorly. Therefore, we here propose Bayesian forecasting that combines the forecasts by the ETAS model with various probable parameter sets given the data. By conducting forecasting tests of 1 month period aftershocks based on the first 1 day data after the main shock as an example of the early intermediate-term forecasting, we show that the Bayesian forecasting performs better than the plug-in forecasting on average in terms of the log-likelihood score. Furthermore, to improve forecasting of large aftershocks, we apply a nonparametric (NP) model using magnitude data during the learning period and compare its forecasting performance with that of the Gutenberg-Richter (G-R) formula. We show that the NP forecast performs better than the G-R formula in some cases but worse in other cases. Therefore, robust forecasting can be obtained by employing an ensemble forecast that combines the two complementary forecasts. Our proposed method is useful for a stable unbiased intermediate-term assessment of aftershock probabilities.

Can distributed delays perfectly stabilize dynamical networks

Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integrodifferential equation that describes the collective dynamics of a neural network with distributed signal delays. With the Gamma distributed delays less dispersed than exponential distribution, the system exhibits reentrant phenomena, in which the stability is once lost but then recovered as the mean delay is increased. With delays dispersed more highly than exponential, the system never destabilizes.

Deciphering Elapsed Time and Predicting Action Timing from Neuronal Population Signals

The proper timing of actions is necessary for the survival of animals, whether in hunting prey or escaping predators. Researchers in the field of neuroscience have begun to explore neuronal signals correlated to behavioral interval timing. Here, we attempt to decode the lapse of time from neuronal population signals recorded from the frontal cortex of monkeys performing a multiple-interval timing task. We designed a Bayesian algorithm that deciphers temporal information hidden in noisy signals dispersed within the activity of individual neurons recorded from monkeys trained to determine the passage of time before initiating an action. With this decoder, we succeeded in estimating the elapsed time with a precision of approximately 1 s throughout the relevant behavioral period from firing rates of 25 neurons in the pre-supplementary motor area. Further, an extended algorithm makes it possible to determine the total length of the time-interval required to wait in each trial. This enables observers to predict the moment at which the subject will take action from the neuronal activity in the brain. A separate population analysis reveals that the neuronal ensemble represents the lapse of time in a manner scaled relative to the scheduled interval, rather than representing it as the real physical time.

Automatic Aftershock Forecasting: A Test Using Real‐Time Seismicity Data in Japan

Real‐time aftershock forecasting is important to reduce seismic risks after a damaging earthquake. The main challenge is to prepare forecasts based on the data available in real time, in which many events, including large ones, are missing and large hypocenter determination errors are present due to the automatic detection process of earthquakes before operator inspection and manual compilation. Despite its practical importance, the forecast skill of aftershocks based on such real‐time data is still in a developmental stage. Here, we conduct a forecast test of large inland aftershock sequences in Japan using real‐time data from the High Sensitivity Seismograph Network (Hi‐net) automatic hypocenter catalog (Hi‐net catalog), in which earthquakes are detected and determined automatically in real time. Employing the Omori–Utsu and Gutenberg–Richter models, we find that the proposed probability forecast estimated from the Hi‐net catalog outperforms the generic model with fixed parameter values for the standard aftershock activity in Japan. Therefore, the real‐time aftershock data from the Hi‐net catalog can be effectively used to tailor forecast models to a target aftershock sequence. We also find that the probability forecast based on the Hi‐net catalog is comparable in performance to the one based on the latest version of the manually compiled hypocenter catalog of the Japan Meteorological Agency when forecasting large aftershocks with M >3.95, despite the apparent inferiority of the automatically determined Hi‐net catalog. These results demonstrate the practical usefulness of our forecasting procedure and the Hi‐net automatic catalog for real‐time aftershock forecasting in Japan. Online Material: Figures and tables showing detailed forecast results for all considered aftershock sequences and all forecast time frames.

A non-universal aspect in the temporal occurrence of earthquakes

It has been emphasized that the temporal occurrence of earthquakes in various spatial areas and over ranges of magnitude may be described by a unique distribution of inter-earthquake intervals under suitable rescaling, implying the presence of a universal mechanism governing seismicity. Nevertheless, it is possible that some features in the fine temporal patterns of event occurrences differ between spatial regions, reflecting different conditions that cause earthquakes, such as relative motion of tectonic plates sharing a boundary. By abstracting the non-Poissonian feature from non-stationary sequences using a metric of local variation of event intervals Lv, we find a wide range of non-Poissonian burstiness present in the temporal event occurrences in different spatial areas. Firstly, the degree of bursty features in the occurrence of earthquakes depends on spatial location; earthquakes tend to be bursty in areas where they are less frequent. Secondly, systematic regional differences remain even if the overall correlation between burstiness and the rate of event occurrence is eliminated. Thirdly, the degree of burstiness is particularly high on divergent tectonic boundaries compared to convergent and transform boundaries. In this way, temporal patterns of event occurrences bear witness to the circumstances underlying event generation.

Reverberating activity in a neural network with distributed signal transmission delays

It is known that an identical delay in all transmission lines can destabilize the macroscopic stationarity of a neural network, causing oscillation. We analyze the collective dynamics of a network whose transmission delays are distributed in time. Here, a neuron is modeled as a discrete-time threshold element that responds in an all-or-nothing manner to a linear sum of signals that arrive after delays assigned to individual transmission lines. Even though transmission delays are distributed in time, a whole network exhibits a single collective oscillation with a period close to the average transmission delay. The collective oscillation cannot only be a simple alternation of the consecutive firing and resting, but also arbitrarily sequenced series of firing and resting, reverberating in a certain period of time. Moreover, the system dynamics can be made quasiperiodic or chaotic by changing the distribution of delays.

Information transmission using non-poisson regular firing

In many cortical areas, neural spike trains do not follow a Poisson process. In this study, we investigate a possible benefit of non-Poisson spiking for information transmission by studying the minimal rate fluctuation that can be detected by a Bayesian estimator. The idea is that an inhomogeneous Poisson process may make it difficult for downstream decoders to resolve subtle changes in rate fluctuation, but by using a more regular non-Poisson process, the nervous system can make rate fluctuations easier to detect. We evaluate the degree to which regular firing reduces the rate fluctuation detection threshold. We find that the threshold for detection is reduced in proportion to the coefficient of variation of interspike intervals.