![An example of one step in the IIM (schematically) for a two-dimensional MS (SMP in the figure) and three-dimensional DS. Vectors p1,p2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{{p}}_1, \mathbf{{p}}_2$$\end{document} and p3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{{p}}_3$$\end{document} form the simplex which is used in Eqs.(1)–(2) to calculate pN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{{p}}_N$$\end{document}. The final pair [pO,dO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{{p}}_O, \mathbf{{d}}_O$$\end{document}] is shown in gray](https://www.researchgate.net/publication/369413301/figure/fig4/AS:11431281174084232@1689126550438/An-example-of-one-step-in-the-IIM-schematically-for-a-two-dimensional-MSSMP-in-the_Q320.jpg)
![An illustration of the ’swing through’ method: a Two-point ray tracing in the starting model used in this study. The rays are traced with the aim to hit the receiver dM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_M$$\end{document} (black triangle). Both MPS and DS are one-dimensional. The ray parameters are the initial angles at the source, data are the distances along the surface. Angles ϕN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _N$$\end{document} and ϕN′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _{N'}$$\end{document} are calculated from Eqs. (1)–(2), ϕN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _N$$\end{document} with dM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_M$$\end{document} while ϕN′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _{N'}$$\end{document} with the mirrored receiver dM′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{M'}$$\end{document} as the target. The ray with the initial angle ϕN′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _{N'}$$\end{document} terminates at the surface 28 m to the left from the receiver. b The same situation as viewed in the joint parameter-data space. The angle-distance curve (bold black line) intersects the target line in a very close vicinity of the point (ϕN′,xN′)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi _{N'}, x_{N'})$$\end{document}. Note that in this special case (m=n=1) the IIM reduces to the secant method](https://www.researchgate.net/publication/369413301/figure/fig5/AS:11431281174056825@1689126550613/An-illustration-of-the-swing-through-method-a-Two-point-ray-tracing-in-the-starting_Q320.jpg)
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New Velocity Structure of the Novy
´Kostel Earthquake-Swarm Region, West Bohemia,
Determined by the Isometric Inversion
JIR
ˇI
´MA
´LEK,
1
JOHANA BROKES
ˇOVA
´,
2
and OLDR
ˇICH NOVOTNY
´
2
Abstract—The intraplate West Bohemia region is characterized
by relatively frequent earthquake swarms mostly concentrated in
the vicinity of the Novy
´Kostel village. Records of selected
microearthquakes of the 2008 seismic swarm from a small circular
area around Novy
´Kostel with a radius of 11 km are processed with
focus on availability of precise onset readings from all the selected
events at all the selected stations. These data were used in the joint
hypocenter-velocity inversion, employing the so-called isometric
method which is especially efficient for this task. The results are
two new one-dimensional velocity models, the constrained
(smoother) and the unconstrained one, of the upper crust down to
the depth of 11 km, and absolute locations of the selected earth-
quakes in the new constrained model. The foci delineate two
segments of a steeply dipping fault zone. Time residuals at each of
the stations display a remarkable azimuthal dependence, for both P
and S waves, caused by anisotropy. No systematic dependence on
epicentral distance was found even for stations outside the target
area, which means that the new 1D models seem to be reasonable
approximations of the real structure in the whole, much larger,
West Bohemia region. No time dependence indicating possible
changes of vP,vSand their ratio during the swarm was observed. A
set of P- and S-wave station corrections that should be used to
correct onset times in order to reach precise absolute locations was
derived as an integral part of the new models.
Keywords: Isometric inversion, West Bohemia/Vogtland,
earthquake swarm, station corrections, upper crust.
1. Introduction
Novy
´Kostel is an important locality in the geo-
dynamically active region of West Bohemia (Czech
Republic), adjacent to the Vogtland region in Ger-
many, situated in the northwestern part of the
Bohemian Massif, the largest Variscan unit in Central
Europe. Novy
´Kostel can be found at the northern
edge of the Cheb Basin (Fig. 1), a small shallow
Neogene basin that has formed at the junction of the
ENE-WSW trending Eger Rift and N-S trending
Poc
ˇa
´tky-Plesna
´zone. The Cheb basin occupies a
transition zone among three autonomous units of the
Bohemian Massif, namely the Moldanubian, Sax-
othuringian and Tepla
´-Barrandian units, see Fig. 1.
The sedimentary deposits in the basin are up to 300 m
thick (S
ˇpic
ˇa
´kova
´et al., 2000). The basin is bounded
on its eastern side by the escarpment of the NW-SE
oriented Maria
´nske
´La
´zne
ˇfault.
Despite of its intraplate character, the West
Bohemia/Vogtland region is known for pronounced
geodynamic activity manifested by Tertiary and
Quartenary volcanism, mineral springs, mantle-
derived CO2emanation, and recurrent earthquake
swarms (Jakoubkova
´et al., 2017). Many authors
propose a possible role of fluids ascending from
deeper magmatic sources suggested in earthquake-
swarm trigger mechanism models (e.g. S
ˇpic
ˇa
´k and
Hora
´lek (2001), Hora
´lek and Fischer (2008), Hainzl
et al. (2012) and Mousavi et al. (2015)). Paleoseimic
earthquakes with Mw [6.5 were discovered in the
region by S
ˇtepanc
ˇı
´kova
´et al. (2019). The region
represents the main source of seismic hazard to towns
in North and Central Bohemia including the city of
Prague (Ma
´lek et al., 2019)
The occurrence of earthquake swarms has been
relatively frequent in the past few decades (major
ones in the years 1985/1986, 1997, 2000, 2008, 2011,
2014 and 2018; micro-swarms are much more fre-
quent). The region has become the subject of many
Supplementary Information The online version contains sup-
plementary material available at https://doi.org/10.1007/s00024-
023-03250-w.
1
Department of Seismotectonics, Institute of Rock Structure
and Mechanics, Czech Academy of Sciences, Prague, Czech
Republic. E-mail: malek@irsm.cas.cz
2
Department of Geophysics, Faculty of Mathematics and
Physics, Charles University, Prague, Czech Republic.
Pure Appl. Geophys. 180 (2023), 2111–2134
Ó2023 The Author(s), under exclusive licence to Springer Nature Switzerland AG
https://doi.org/10.1007/s00024-023-03250-w Pure and Applied Geophysics
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
