scholarly journals Spatial Weights: Constructing Weight-Compatible Exchange Matrices from Proximity Matrices

2014 ◽  
pp. 81-96 ◽  
Author(s):  
François Bavaud
Keyword(s):  
Spatial Weights ◽  
Proximity Matrices

An Optimum 2D Seismic-Wavefield Reconstruction in Densely and Nonuniformly Distributed Stations: The Metropolitan Seismic Observation Network in Japan

2021 ◽  
Author(s):  
Takahiro Shiina ◽  
Takuto Maeda ◽  
Masayuki Kano ◽  
Aitaro Kato ◽  
Naoshi Hirata
Keyword(s):  
Metropolitan Area ◽  
Seismic Waves ◽  
Seismic Station ◽  
Weighting Functions ◽  
Seismic Observation ◽  
Tokyo Metropolitan ◽  
Tokyo Metropolitan Area ◽  
Spatial Weights ◽  
Observation Network ◽  
Seismic Wavefield

Abstract We propose an optimization method for applying the seismic-wave gradiometry (SWG) method to a dense seismic station network consisting of nonuniformly distributed seismographs. As a nonuniformly distributed station array, we consider the station layout of the Metropolitan Seismic Observation Network (MeSO-net) operated in and around the Tokyo metropolitan area, Japan. In this study, thereby, we numerically investigate optimum shapes of weighting functions, which control the spatial weights of individual stations when estimating waveforms at any grid points in the SWG method, to reconstruct seismic wavefields propagating in the MeSO-net. The functions with isotropic spatial weights are found to be appropriate for wavefield reconstructions with seismic waves incoming from practically all directions, even for nonuniformly distributed stations. The reproducibility of the wavefields is greatly improved by changing the shapes of the spatial weights reflecting density of the stations. Further plausible wavefield reconstructions are made by considering the propagation directions of the seismic waves. In these cases, if the weight of a contribution for a wavefield reconstruction is larger at far stations with a direction perpendicular to the wave propagation direction, then the reproducibility of the waveforms is significantly increased. In addition, the spatial gradients of the amplitudes are well reproduced by the optimized SWG method even though the optimization only focused on the amplitudes. Therefore, our proposed optimization scheme can be used to accurately estimate seismic wavefields in a nonuniformly distributed station array. Actually, the weighting functions optimized in this study succeeded to reconstruct the seismic wavefield of a shallow crustal earthquake that occurred around the Tokyo metropolitan area, based on the observed seismograms obtained by the MeSO-net.

Spatial Weights Matrix

2008 ◽  
pp. 1113-1113 ◽  
Author(s):  
Xiaobo Zhou ◽  
Henry Lin
Keyword(s):  
Spatial Weights ◽  
Spatial Weights Matrix

scholarly journals Constructing the Spatial Weights Matrix Using a Local Statistic

2004 ◽  
Vol 36 (2) ◽  
pp. 90-104 ◽  
Author(s):  
Arthur Getis ◽  
Jared Aldstadt
Keyword(s):  
Spatial Weights ◽  
Spatial Weights Matrix

scholarly journals Building W Matrices Using Selected Geostatistical Tools: Empirical Examination and Application

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 112-133 ◽  
Author(s):  
Elżbieta Antczak
Keyword(s):  
Spatial Data ◽  
Spatial Dependence ◽  
Regression Models ◽  
Seemingly Unrelated Regression ◽  
Spatial Data Analysis ◽  
Spatial Dependency ◽  
Empirical Examination ◽  
Spatial Panel ◽  
Spatial Weights ◽  
Unrelated Regression

This paper investigates how to determine the values (elements) of spatial weights in a spatial matrix (W) endogenously from the data. To achieve this goal, geostatistical tools (standard deviation ellipsis, semivariograms, semivariogram clouds, and surface trend models) were used. Then, in the econometric part of the analysis, the effect of applying different variants of matrices was examined. The study was conducted on a sample of 279 Polish towns from 2005–2015. Variables were related to the quantity of produced waste and economic development. Both exploratory spatial data analysis and estimations of spatial panel and seemingly unrelated regression models were performed by including particular W matrices in the study (exogenous-random as well as distance and directional matrices constructed based on data). The results indicated that (1) geostatistical tools can be effectively used to build Ws; (2) outcomes of applying different matrices did not exclude but supplemented one another, although the differences were significant; (3) the most precise picture of spatial dependence was achieved by including distance matrices; and (4) the values of the assessed parameter at the regressors did not significantly change, although there was a change in the strength of the spatial dependency.

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