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Multidimensional Signal Processing
Published in Richard C. Dorf, Circuits, Signals, and Speech and Image Processing, 2018
Yun Q. Shi, Wei Su, Chih-Ming Chen, Sarah A. Rajala, N.K. Bose, L.H. Sibul
Multidimensional signal processing techniques have found wide application in seismology—where a group of identical seismometers, called seismic arrays, are used for event location, studies of the Earth’s sedimentation structure, and separation of coherent signals from noise, which sometimes may also propagate coherently across the array but with different horizontal velocities—by employing velocity filtering (Claerbout, 1976). Velocity filtering is performed by multidimensional filters and allows also for the enhancement of signals that may occupy the same wavenumber range as noise or undesired signals do. In a broader context, beamforming can be used to separate signals received by sensor arrays based on frequency, wavenumber, and velocity (speed as well as direction) of propagation. Both the transfer and unit impulse–response functions of a velocity filter are two-dimensional functions in the case of one-dimensional arrays. The transfer function involves frequency and wavenumber (due to spatial sampling by equally spaced sensors) as independent variables, whereas the unit impulse response depends upon time and location within the array. Two-dimensional filtering is not limited to velocity filtering by means of seismic array. Two-dimensional spatial filters are frequently used, for example, in the interpretation of gravity and magnetic maps to differentiate between regional and local features. Input data for these filters may be observations in the survey of an area conducted over a planar grid over the Earth’s surface. Two-dimensional wavenumber digital filtering principles are useful for this purpose. Velocity filtering by means of two-dimensional arrays may be accomplished by properly shaping a three-dimensional response function H(k1, k2,ω). Velocity filtering by three-dimensional arrays may be accomplished through a four-dimensional function H(k1, k2, k3, ω) as explained in the following subsection.
Seismology and site effects
Published in Mark Aschheim, Enrique Hernández-Montes, Dimitrios Vamvatsikos, Design of Reinforced Concrete Buildings for Seismic Performance, 2019
Mark Aschheim, Enrique Hernández, Dimitrios Vamvatsikos
A ground motion measured at a seismic station is just one point of a spatial wavefield. A set of stations—sometimes configured in what is called a seismic array—needs to be deployed in an area to properly characterize the spatial distribution of earthquake ground motion. Examples include the arrays in Parkfield, California, and Lotung, Taiwan.
Characterising microseismicity in a low seismicity region: applications of short-term broadband seismic arrays in Dunedin, New Zealand
Published in New Zealand Journal of Geology and Geophysics, 2020
Erin K. Todd, Mark W. Stirling, Bill Fry, Jerome Salichon, Pilar Villamor
Dense seismic arrays are effective at detecting low amplitude seismic signals, such as microseismicity originating from the same source area (e.g. Wech and Creager 2008). Another method used to detect small earthquakes originating from the same source area is template matched-filter analysis, which creates a waveform template from a master event and scans the dataset to search for repeating events with waveforms matching the master event above a specified cross-correlation threshold. Some of these methods have been applied to New Zealand faults to detect tectonic tremor, which are effectively low frequency earthquakes that are thought to be seismic manifestations of creep on a fault at depth (e.g. Kim et al. 2011; Wech et al. 2012; Chamberlain et al. 2014; Todd and Schwartz 2016), and microseismicity (e.g. Boese et al. 2012, 2013; Warren-Smith et al. 2017; Baratin et al. 2018; Michailos et al. 2019). In the following sections we describe our use of these methods and the small-aperture Dunedin seismic array deployment to detect active microseismicity beneath Dunedin.
Seismic data denoising using curvelet transforms and fast non-local means
Published in Petroleum Science and Technology, 2022
Siwei Zhao, Ibrar Iqbal, Xiaokang Yin, Tianyu Zhang, Mingkun Jia, Meng Chen
Since the 1960s, seismic arrays have produced critical data used for researching structures found on Earth and earthquake dynamics. Using data from closely spaced uniform seismometers, various array approaches can greatly improve SNRs and lower detection thresholds. In addition to equipment technology, data processing methods also have an impact on the seismic event detection resolution. The traditional earthquake detection workflow comprises phase selection (the spotting of impulsive arrivals of seismic phases) and phase association (combining various phases into a single event). A seismic similarity map of these data is shown in Figure 4.