The global range of subduction zone thermal models

A non-Gaussian state—space approach to the modeling of nonstationary time series is shown. The model is expressed in state—space form, where the system noise and the observational noise are not necessarily Gaussian. Recursive formulas of prediction, filtering, and smoothing for the state estimation and identification of the non-Gaussian state—space model are given. Also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas. Significant merits of non-Gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples. A typical application of this non-Gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes. Simple Gaussian state—space modeling is not adequate for this situation. Here the model with small system noise variance cannot detect jump, whereas the one with large system noise variance yields unfavorable wiggle. To work...

Non-Gaussian State—Space Modeling of Nonstationary Time Series

A self-organizing filter and smoother for the general nonlinear non-Gaussian state-space model is proposed. An expanded state-space model is defined by augmenting the state vector with the unknown parameters of the original state-space model. The state of the augmented state-space model, and hence the state and the parameters of the original state-space model, are estimated simultaneously by either a non-Gaussian filter/smoother or a Monte Carlo filter/smoother. In contrast to maximum likelihood estimation of model parameters in ordinary state-space modeling, for which the recursive filter computation has to be done many times, model parameter estimation in the proposed self-organizing filter/smoother is achieved with only two passes of the recursive filter and smoother operations. Examples such as automatic tuning of dispersion and the shape parameters, adaptation to changes of the amplitude of a signal in seismic data, state estimation for a nonlinear state space model with unknown parameters. and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method.

A self-organizing state-space model

The Norwegian Margin formed in response to early Cenozoic continental breakup and subsequent opening of the Norwegian-Greenland Sea. There is a welldefined margin segmentation and the various segments are characterized by distinct crustal properties, structural and magmatic styles, and post-opening history of vertical motions. The sedimentary basins at the conjugate continental margins off Norway and Greenland and in the western Barents Sea developed as a result of a series of post-Caledonian rift episodes until early Cenozoic time, when complete continental separation took place.

Structure and evolution of the continental margin off Norway and the Barents Sea

A computationally efficient procedure was developed for the fitting of a locally stationary autoregressive model. The amount of computations is bounded by a function of the data length and the model order only and does not depend on the number of possible arrival times. This facilitates automatic determination of arrival time by an on-line system. The on-line system FUNIMAR (fast univariate case of minimum AIC method of AR model fitting) was developed to implement the procedure. The method was checked by applying it to weak seismic signals from earthquakes which were superimposed with background noises such as traffic noise, electronic hum noise, and heavy microtremor. Experimental results confirm the effectiveness of the method for determining the onset time of P-wave and suggest that an AR model of the fifth order is sufficient to determine the onset time of the wave even if it is buried in considerably heavy noises. It is also shown that the onset time of S-wave can also be successfully determined by the method.

https://www.jstage.jst.go.jp/article/jpe1952/36/6/36_6_267/_pdf

A new efficient procedure for the estimation of onset times of seismic waves

A new efficient procedure for the estimation of onset times of seismic waves.

A computationally efficient procedure was developed for the fitting of many multivariate locally stationary autoregressive models. The details of the Householder method for fitting multivariate autoregressive model and multivariate locally stationary autoregressive model (MLSAR model) are shown. The proposed procedure is quite efficient in both accuracy and computation. The amount of computation is bounded by a multiple of Nm
2 with N being the data length and m the highest model order, and does not depend on the number of models checked. This facilitates the precise estimation of the change point of the AR model. Based on the AICs' of the fitted MLSAR models and Akaike's definition of the likelihood of the models, a method of evaluating the posterior distribution of the change point of the AR model is also presented. The proposed procedure is, in particular, useful for the estimation of the arrival time of the S wave of a microearthquake. To illustrate the usefulness of the proposed procedure, the seismograms of the foreshocks of the 1982 Urakawa-Oki Earthquake were analyzed. These data sets have been registered to AISM Data Library and the readers of this Journal can access to them by the method described in this issue.

/pdf/estimation-of-the-arrival-times-of-seismic-waves-by-s63e59b7p3.pdf

Estimation of the arrival times of seismic waves by multivariate time series model

[1] A 180 km long seismic wide-angle profile was acquired across the Voring Plateau, NE Atlantic, using a tuned air gun array and three-component ocean bottom seismometers deployed with ∼5 km spacing. The seismic P wave data have been modeled by ray tracing/inversion, and the model has been constrained by S wave and gravity modeling. The data and modeling have allowed us to depict the crustal structure and nature of the continent-ocean transition (COT) in a classical volcanic margin case. The P wave velocity near the top of the main crustal layer is estimated to ∼6.0 km/s landward of the ∼25 km wide COT. The seaward increase to ∼6.5 km/s in the COT is conformable with heavily intruded continental crust within this zone. Farther seaward, the velocity increase to ∼6.9 km/s in the same layer suggests the presence of oceanic crust. The abundant magmatism landward of, and within, the COT is primarily observed as extrusives forming wedges of seaward dipping reflectors and mafic lower crustal intrusions/underplating. The maximum thickness of the oceanic crust is measured to ∼23.5 km at the seaward termination of the COT.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004JB003026

Tetsuo Takanami

Papers

A new efficient procedure for the estimation of onset times of seismic waves

A new efficient procedure for the estimation of onset times of seismic waves.

Estimation of the arrival times of seismic waves by multivariate time series model

Continent‐ocean transition on the Vøring Plateau, NE Atlantic, derived from densely sampled ocean bottom seismometer data

Continent–ocean-transitions: Review, and a new tectono-magmatic model of the Vøring Plateau, NE Atlantic