A Wavelet Toolkit for Visualization and Analysis of Large Data Sets in Earthquake Research

Abstract

Wavelets have a wide range of useful functions that permit them to effectively treat problems such as data compression, scale-localization analysis, feature extraction, visualization, statistics, numerical simulation, and communication. We discuss their features and their use in an integrated manner to handle large-scale problems in earthquake physics and other nonlinear problems in the solid earth geosciences.

Feature Extraction Using Circular Statistics Applied to Volcano Monitoring

“…that can be calculated using (9) and (10). In our case, the wavelet filter used corresponds to the Daubechies with 10 taps, the sampling rate is 50 samples per second, and the detail for k = 4 corresponds to the frequency range of interest, i.e., between 1.55 and 3.11 Hz.…”

“…Some studies incorporate many frequency, amplitude and waveform features and use genetic algorithms to search a representative feature subset that improves the classifier performance [7,4]. Other methods are the wavelet transform [8,9], cross correlation methods [10] and hidden Markov models [11].…”

Variable quality compression of fluid dynamical data sets using a 3‐D DCT technique

“…In the research field of data compression several techniques exist that probably yield better compression than the approach followed in this work. Especially wavelet‐based techniques show interesting results for many applications [see, e.g., Salomon , 2000; Trott et al , 1996] and have proven to be well suited for, e.g., medical [ Ihm and Park , 1999], but also for geophysical data sets [ Erlebacher and Yuen , 2004; Kidner and Smith , 2003; Tao and Moorhead , 1994; Villasenor et al , 1996]. Our previous investigations [ Schmalzl , 2003] however indicate that wavelet‐based compression techniques provide only little improvements compared to the DCT‐based approach used in this paper when applied to CFD data sets.…”

Remote data analysis, visualization and problem solving environment (PSE) based on wavelets in the geosciences

“…These services can take many forms. They include visualization services with wavelet toolkits (Erlebacher and Yuen, 2002a) capable of handling multidimensional and multivariate data sets, registration services to allow merging of data from multiple sources into a common framework, data mining services with visualization, video creation services, and various classes of collaborative tools to allow remote access to large datasets stored in remote data-servers. We summarize these concepts in Fig.…”

“…This decomposition is achieved through a second-generation wavelet transform of the data combined with thresholding. We are currently working on the statistical analysis of non-stationary/non-homogeneous processes and robust toolkit development , Erlebacher and Yuen, 2002a, Erlebacher and Yuen, 2002b. The advantages of this new approach for the earth sciences and for on-board processing of satellite data are reduced computation time, efficient data representation at multiple scales without sacrificing spatial information and visualization on a user-specified range of scales.…”