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Earthquake Clusters over Multi-dimensional Space, Visualization of

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Earthquakes have a direct societal relevance because of their tremendous impact on human community [59]. The genesis of earthquakes is an unsolved problem in the earth sciences, because of the still unknown underlyingphysical mechanisms. Unlike the weather, which can be predicted for several days in advance by numerically integrating non‐linear partialdifferential equations on massively parallel systems, earthquake forecasting remains an elusive goal, because of the lack of direct observations and thefact that the governing equations are still unknown. Instead one must employ statistical approaches (e. g., [61,72,82]) and data‐assimilation techniques (e. g., [6,53,81]). The nature of the spatio‐temporal evolution of earthquakes has to beassessed from the observed seismicity and geodetic measurements. Problems of this nature can be analyzed by recognizing non‐linear patterns hiddenin the vast amount of seemingly unrelated information. With the proliferation of...

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Abbreviations

Grid:

Virtual metacomputer, which uses a network of geographically distributed local networks, computers and computational resources and services. Grid Computing focuses on distributedcomputing technologies, which are not in the traditional dedicated clusters. Data Grids – represent controlled sharing and management of large amounts of distributed data.

Problem solving environment (PSE):

A specialized computer software for solving one class of problems. They use the language of the respective field and often employ modern graphical user interfaces. The goal is to make the software easy to use for specialists in fields other than computer science. PSEs are available for generic problems like data visualization or large systems of equations and for narrow fields of science or engineering.

Global seismographic network (GSN):

The goal of the GSN is to deploy permanent seismic recording stations uniformly over the earth's surface. The GSN stationscontinuously record seismic data from very broad band seismometers at 20 samples per second, and to provide for high‐frequency (40 sps)and strong‐motion (1 and 100 sps) sensors wherescientifically warranted. It is also the goal of the GSN to provide for real-time access toits data via Internet or satellite. Over 75% of the over 128 GSN stations meet this goal as of 2003.

WEB-IS:

A software tool that allows remote, interactive visualization and analysis of large-scale 3-D earthquake clusters over the Internet through the interaction between client and server.

Scientific visualization:

is branch of computer graphics and user interface design that are dealing with presenting data to users, by means of patterns and images. The goal of scientific visualization is to improve understanding of the data being presented.

Interactive visualization:

is a branch of graphic visualization that studies how humans interact with computers to create graphic illustrations of information and how this process can be made more efficient. Remote‐visualization – the tools for interactive visualization of high‐resolution images on remote client machine, rendered and preprocessed on the server.

OpenGL:

A standard specification defining a cross‐language cross‐platform API for writing applications that produce 2D and 3D computer graphics.

Sumatra‐Andaman earthquake:

An undersea earthquake that occurred at 00:58:53 UTC (07:58:53 local time) December 26, 2004, with an epicenter off the west coast of Sumatra, Indonesia. The earthquake triggered a series of devastating tsunamis along the coasts of most landmasses bordering the Indian Ocean, killing large numbers of people and inundating coastal communities across South and Southeast Asia, including parts of Indonesia, Sri Lanka, India, and Thailand.

Earthquake catalog:

Data set consisting of earthquake hypocenters, origin times, and magnitudes. Additional information may include phase and amplitude readings, as well as first‐motion mechanisms and moment tensors.

Pattern recognition:

The methods, algorithms and tools to analyze data based on either statistical information or on a priori knowledge extracted from the patterns. The patterns for classification are groups of observations, measurements, objects, defining feature vectors in an appropriate multidimensional feature space.

Data mining:

Algorithms, tools, methods and systems used in extraction of knowledge hidden in a large amount of data.

Features:

denoted f i or F j (\( { i,j } \) – feature indices) – a set of variables which carry discriminating and characterizing information about the objects under consideration. The features can represent raw measurements (data) f i or can be generated in a non‐linear way from the data F j (features).

Feature space:

The multidimensional space in which the F k vectors are defined. Data and feature vectors represent vectors in respective spaces.

Feature vector:

A collection of features ordered in some meaningful way into multi‐dimensional feature vectors F l (F l where l – feature vector index) that represents the signature of the object to be identified represented by the generated features F l .

Feature extraction:

The procedure of mapping source feature space into output feature space of lower dimensionality, retaining the minimal value of error cost function.

Multidimensional scaling:

The nonlinear procedure of feature extraction, which minimizes the value of the “stress” being the function of differences of all the distances between feature vectors in the source space and corresponding distances in the resulting space of lower dimensionality.

Data space:

The multi‐dimensional space in which the data vectors f k exist.

Data vector:

A collection of features ordered in some meaningful way into multi‐dimensional vectors f k (\( { \boldsymbol{f}_{k}, k } \) – data vector index) and \( { \boldsymbol{f}_{k} = [m_{k}, z_{k}, \boldsymbol{x}_{k}, t_{k}] } \) where m k is the magnitude and x k , z k , t k  – its epicentral coordinates, depth and the time of occurrence, respectively.

Cluster:

Isolated set of feature (or data) vectors in data and feature spaces.

Clustering:

The computational procedure extracting clusters in multidimensional feature spaces.

Agglomerative (hierarchical) clustering algorithm:

The clustering algorithm in which at the start the feature vectors represent separate clusters and the larger clusters are built-up in a hierarchical way. The procedure repeats the process of gluing-up the closest clusters up to the stage when a desired number of clusters is achieved.

k-Means clustering:

Non‐hierarchical clustering algorithm in which the randomly generated centers of clusters are improved iteratively.

Multi‐resolutional clustering analysis:

Due to clustering a hierarchy of clusters can be obtained. The analysis of the results of clustering in various resolution levels allows for extraction of knowledge hidden in both local (small clusters) and global (large clusters) similarity of multidimensional feature vectors.

N-body solver:

The algorithm exploiting the concept of time evolution of an ensemble of mutually interacting particles.

Non‐hierarchical clustering algorithm:

The clustering algorithm in which the clusters are searched for by using global optimization algorithms. The most representative algorithms of this type is k-means procedure.

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Acknowledgments

This research was supported by NSF ITR and Math-Geo grants. WD acknowledges support from the Polish Committee for ScientificResearch (KBN) Grant No. 3T11C05926. YBZ acknowledges support from the NSF, USGS and SCEC.

Author information

Authors and Affiliations

  1. Dept. of Geology and Geophysics, University of Minnesota, Minneapolis, USA

    David A. Yuen

  2. Dept. of Computer Science, AGH University of Sci. and Technol., Kraków, Poland

    Witold Dzwinel

  3. Department of Earth Sciences, University of Southern California, Los Angeles, USA

    Yehuda Ben-Zion

  4. Department of Computer Science, University of Colorado, Boulder, USA

    Ben Kadlec

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    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Yuen, D.A., Dzwinel, W., Ben-Zion, Y., Kadlec, B. (2009). Earthquake Clusters over Multi-dimensional Space, Visualization of. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_145

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