Geodesic
Determination of spatial distribution of oscillation sources by remote measurements on a~finite set of points
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 3, pp. 203-211

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The paper deals with determination of spatial distribution of oscillation sources by remote measurements on a finite set of points. This problem is assumed to be a problem of reconstruction of the original tsunami waveform from the measurement of the arrived wave on a finite set of coastal receivers. The propagation of the wave is described by linearized shallow-water equations when the depth depends on two variables. The direct problem is approximated by the explicit-implicit finite difference scheme. The ill-posed inverse problem of reconstruction is regularized by means of singular value decomposition, so $r$-solution is a result of the numerical process. Numerical experiments for the model bottom relief, having some basic morphological features typical of the island arc regions are presented. The quality of the solution obtained is assessed as relative errors (in $L_2$-norm) in restoration of the source function. 
@article{SJVM_2004_7_3_a2,
     author = {T. A. Voronina},
     title = {Determination of spatial distribution of oscillation sources by remote measurements on a~finite set of points},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {203--211},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2004_7_3_a2/}
}
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T. A. Voronina. Determination of spatial distribution of oscillation sources by remote measurements on a~finite set of points. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 3, pp. 203-211. http://geodesic.mathdoc.fr/item/SJVM_2004_7_3_a2/