Composite Source Model Research Articles

Strong ground motion from the Uttarkashi, Himalaya, India, earthquake: Comparison of observations with synthetics using the composite source model

Abstract The Uttarkashi earthquake of 19 October 1991 (MS = 7.0) occurred in the greater Himalayan region north of the main central thrust, at an estimated depth of 12 km. The fault plane solution indicates a low-angle thrust mechanism, striking northwest, consistent with the tectonic pattern of thrusting in the region. Aftershocks define a belt parallel to, and north of, the surface trace of the main central thrust, roughly 10-km wide and 30-km long. The mainshock is located at the northeast edge of this zone. The earthquake was recorded on 13 strong-motion accelerographs at distances ranging from 25 to 150 km from the epicenter. One station at Bhatwari (peak horizontal acceleration of 272 cm sec−2) is above the aftershock zone. The maximum peak horizontal acceleration was about 313 cm sec−2 at Uttarkashi, at an epicentral distance of 36 km. The amplitudes and frequency content of the strong ground motions are more or less consistent with expectations for an earthquake of this magnitude in California. Synthetics generated using the composite source model and synthetic Green's functions (Zeng et al., 1994a, b) are successful in producing acceleration, velocity, and displacement with a realistic appearance and the correct statistical properties of the two accelerograms recorded nearest the fault (Bhatwari and Uttarkashi). To produce these, we introduced trial-and-error modifications of the layered-medium velocity model within uncertainties. At more distant stations, we first used the velocity structure that worked for the two nearest stations. Differences emphasize the large potential role of unknown site and wave-propagation effects. For the station at Tehri, we explored different velocity models, and found one there that was also quite successful. We then used these two velocity models to predict strong ground motions at Bhatwari and Tehri, from a potential magnitude 8.5 earthquake filling part of the seismic gap along the Himalayan frontal faults. The synthetics show peak accelerations that are only somewhat larger than those in the Uttarkashi event, but much longer durations and increased amplitudes of response spectra at long periods.

Subevent rake and random scattering effects in realistic strong ground motion simulation

Recently Zeng et al. (1994) proposed a composite source model for convolution with synthetic Green's functions for computing strong ground motion due to a complex rupture process of a large earthquake. The composite source consists of sub‐events with a distribution of sizes, distributed randomly on the fault. In this paper, we extend our discussion of the source by allowing subevent rake to vary within the positive strain quadrant and by including the effect of the random lateral heterogeneity of the earth by adding scattered waves into the Green's function computed from a layered elastic earth model. Both of these variations contribute towards equalizing different components of the high frequency waveform train. The random scattering has the stronger effect on increasing the amplitudes of the nodal components. The early part of these scattered coda waves also tends to elongate the strong shaking of the earthquake.

A composite source model for computing realistic synthetic strong ground motions

A composite source model is presented for convolution with synthetic Green's functions, in order to synthesize strong ground motions due to a complex rupture process of a large earthquake. Subevents with a power‐law distribution of sizes are located randomly on the fault. Each subevent radiates a displacement pulse with the shape of a Brune's pulse in the far field, at a time determined by a constant rupture velocity propagating from the hypocenter. Thus, all the input parameters have a physical basis. We simulate strong ground motions for event‐station pairs that correspond to records obtained in Mexico by the Guerrero accelerograph network. The synthetic accelerations, velocities, and displacements have realistic amplitudes, durations, and Fourier spectra.

Neural network adaptive image coding

An adaptive image-coding system using neural networks is presented. The design of the system is based on the fact that system adaptability is a key to its effectiveness and efficiency. A composite source data model is suggested as a mathematical model for image data. Based on the composite source model, the coding system first classifies image data and then transforms and codes data classes with dedicated schemes. LEP, a reliable learning neural network model that uses experiences and perspectives, is proposed for image data classification using textures. A scheme for learning Karhunen-Loeve (K-L) transform basis arranged in the descent order with respect to eigenvalues in a two-layer linear-forward network is developed. These two learning mechanisms serve as essential parts of the coding system and enhance the adaptability of the system considerably. The experimental results show compressed images of good quality with bit rates as low as 0.1767 bit per pixel.

Subband image coding using jointly localized filter banks and entropy coding based on vector quantization

A method for image compression based on subband decomposition is presented. We describe a new filter bank design method for image coding applications and a new entropy coding algorithm for the compression of subband images. A set of relevant optimization criteria is defined for the filter bank design. For the compression, a composite source model is defined by combining vector quantization (VQ) and scalar quantization (SQ) with entropy coding. In the proposed scheme, VQ exploits the remaining statistical dependencies among the subband samples, while SQ allows an optimal control on local distortions. The system is based on a statistical model that uses VQ information to generate low entropy probability tables for an arithmetic coder. The bit rate can be shared between the VQ rate and the SQ rate, allowing many possible configurations in terms of performance and implementation complexity. The proposed system shows improved performance when compared with other existing methods.

Lower and upper bounds on the minimum mean-square error in composite source signal estimation

The performance of a minimum mean-square error (MMSE) estimator for the output signal from a composite source model (CSM), which has been degraded by statistically independent additive noise, is analyzed for a wide class of discrete-time and continuous-time models. In both cases, the MMSE is decomposed into the MMSE of the estimator, which is informed of the exact states of the signal and noise, and an additional error term. This term is tightly upper and lower bounded. The bounds for the discrete-time signals are developed using distribution tilting and Shannon's lower bound on the probability of a random variable exceeding a given threshold. The analysis for the continuous-time signal is performed using Duncan's theorem. The bounds in this case are developed by applying the data processing theorem to sampled versions of the state process and its estimate, and by using Fano's inequality. The bounds in both cases are explicitly calculated for CSMs with Gaussian subsources. For causal estimation, these bounds approach zero harmonically as the duration of the observed signals approaches infinity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Statistical-model-based speech enhancement systems

Since the statistics of the speech signal as well as of the noise are not explicitly available, and the most perceptually meaningful distortion measure is not known, model-based approaches have recently been extensively studied and applied to the three basic problems of speech enhancement: signal estimation from a given sample function of noisy speech, signal coding when only noisy speech is available, and recognition of noisy speech signals in man-machine communication. Research on the model-based approach is integrated and put into perspective with other more traditional approaches for speech enhancement. A unified statistical approach for the three basic problems of speech enhancement is developed, using composite source models for the signal and noise and a fairly large set of distortion measures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Itakura-Saito clustering and rate distortion functions for a composite source model of speech

Composite source (CS) models for speech signals consist of a finite number of subsources describing specific spectral characteristics and a switch process representing the variation of these characteristics. They allow the computation of rate distortion functions (RDFs) which are significantly below those for simple stochastic models. In this paper, it is discussed how to estimate a switch state sequence such that it is optimal in the computation of an RDF. Using a maximum-likelihood approach, a new relationship between Itakura-Saito clustering and rate distortion theory for composite sources is derived. The performance bounds are based on the mean squared error distortion measure. It will be shown that for a given number of subsources the resulting composite source model has the lowest possible RDF in the range of small values of distortion. In addition, a lower bound for the RDF for a composite source having an arbitrarily high number of subsources is derived. Finally, it is shown that rate distortion theory for composite sources provides explicit bit-allocation rules for a class of blockwise adaptive (switched) waveform coding schemes with time-varying transmission rate.

Classified Vector Quantization of Images

Vector quantization (VQ) provides many attractive features for image coding with high compression ratios. However, initial studies of image coding with VQ have revealed several difficulties, most notably edge degradation and high computational complexity. We address these two problems and propose a new coding method, classified vector quantization (CVQ), which is based on a composite source model. Blocks with distinct perceptual features, such as edges, are generated from different subsources, i.e., belong to different classes. In CVQ, a classifier determines the class for each block, and the block is then coded with a vector quantizer designed specifically for that class. We obtain better perceptual quality with significantly lower complexity with CVQ when compared to ordinary VQ. We demonstrate with CVQ visual quality which is comparable to that produced by existing coders of similar complexity, for rates in the range 0.6-1.0 bits/pixel.

Graph-theoretic approach to composite-source-model estimation for image coding

Random processes of considerable importance in signal processing often exhibit short-term stationary statistical attributes although in the long term they appear to behave in a nonstationary manner. Image signals belong to this category. In this work we introduce a class of composite-source models as a means of representing consistently signals of this nature. A composite likelihood function is derived, the subsequent maximisation of which yields estimates of the parameters that are associated with the composite-source model. It is a fact, that maximisation of the composite likelihood function is almost intractable by analytical means. However, by introducing optimisation techniques based on dynamic programming, maximum-likelihood estimation of composite-source models is simplified drastically. A graph-theoretic approach is adopted to demonstrate how the principle of optimality enables efficient algorithms for recursive maximum-likelihood estimation to be developed. Algorithms applied for one-dimensional as well as two-dimensional signals are presented. In both cases it is shown that the estimation problem is equivalent to the problem of identifying the maximumlikelihood path which traverses a directed graph of specific structure. Finally, it is shown that composite source models so estimated can be used in image coding systems which require the least transmission rate for prespecified levels of average distortion of the transmitted image signals.

Hierarchical modeling of EEG signals

Describes a technique for quantitative analysis of EEG signals which is based on a hierarchy of models. These models include 1) recursively estimated autoregressive model, 2) piecewise stationary autoregressive model, 3) composite source model, and 4) character string and syntactic models. This hierarchical modeling approach introduces criteria for segmentation, clustering, and identification of character substrings which reduce the need for ad hoc parameters or subjective decisions. The hierarchical representation is therefore highly operator independent, provides significant data compression of complex signals, and is compatible with a generalized classification procedure. Examples of the application of this modeling approach to clinical patient EEG data illustrate the system capabilities.

Pattern Trajectory Analysis of Nonstationary Multivariate Data

Multivariate data sets with dependency between observations are described using a feature space representation. The resulting ordered set of points in feature space is termed the pattern trajectory. A set of descriptors of the pattern trajectory has been developed. Time-dependent clusters and transition segments form the basic structural description from which both lower level properties, e.g., cluster position, cluster dispersion, transition rate, and higher level properties, e.g., rebound, periodicity, finite state model, may be derived. Two algorithms have been developed for time-dependent cluster analysis. The time-weighted minimum spanning tree (TWMST) algorithm utilizes a composite space-time distance measure and creates clusters by cutting the longest tree branches. The time-dependent Isodata (TD-ISODATA) algorithm utilizes a global clustering to initiate the segmentation into timedependent cluster cores and transition segments. Examples of the applica tion of these algorithms to nonstationary neuronal spike train data and to simulated animal migration data are described. The pattern trajectory approach appears to offer advantages in the analysis of complex nonstationary data sets where conventional time series techniques are insufficient. Time-dependent clustering provides a means to identify a composite source model.

THE RECENT OPTICAL OUTBURST OF THE SEYFERT 1 GALAXY ARAKELIAN 120.

ABSTRACT The Seyfert 1 galaxy, Arakelian 120, has undergone an optical flare from October 1977 to September 1978. The most rapid change in brightness detected was a change of 0.24 m in 25 days. This variation implies an upper limit on the size of the optical source region of 0.0202 pc based on light-travel-time arguments (assuming no relativistic effects). The optical variability and color variations are consistent with a composite galaxy-nonthermal central source model in which the nonthermal central source varies both in luminosity and color. A second possible interpretation is that the variations in color and brightness are due to variability in both the broad emission lines which are present and in the nonthermal continuum.